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A New Mobile Fluid Power Source based on
Hydraulic Free Piston Engine
A DISSERTATION
SUBMITTED TO THE FACULTY OF THE
UNIVERSITY OF MINNESOTA
BY
Keyan Liu
IN PARTIAL FULFILLMENT OF THE REQUIERMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Professor Zongxuan Sun, Advisor
June 2020
©Keyan Liu, 2020
i
Acknowledgements
First of all, I would like to thank my advisor, Prof. Zongxuan Sun for the
guidance and support during my PhD study. Second, I would like to express
my gratitude to my parents, to whom I’ll always be in debt. Thanks to all my
lab mates and friends for all the inspiring discussions and happy moments.
Also, a special thanks to the CSE machine shop. Ron, Bob and Peter, this
project won’t be possible without your excellent skills and insights in
machining. Last but not least, I would like to thank Ford motor company for
donating the prototype free piston engine, the CCEFP for funding this
research, and Trelleborg for helping me with the customized hydraulic seals.
Michael, your seal works like a charm!
ii
To all working people in the world.
iii
Abstract
Fluid power is widely used nowadays due to its many advantages, and many of these
applications are mobile, where the power source has to be carried on board. However, the
energy efficiency for such systems is relatively low, mainly due to the inefficient power
source architecture, whose centralized architecture and slow response introduce
significant loss. To tackle this issue, we propose to use the hydraulic free piston engine
(HFPE) as a power source to provide the actuator with demanded flow at desired pressure
in real time.
To achieve this goal, a novel operation scheme of HFPE is proposed in this study,
where the HFPE is essentially used as a digital pump. In the proposed system, within
each cycle, while the piston travels full strokes, only a part of the output flow is directed
to the load, and the rest is dumped back to low pressure by controlling the valve system.
This operation scheme is validated through simulations, while a systematical method is
proposed accordingly to find the optimal operation parameters so as to achieve maximum
overall efficiency. Simulation results show that the proposed system can provide the
desired flow rate at any load pressure with very fast response time as well as a very high
fuel-to-hydraulic energy efficiency.
To ensure robust operation of the proposed system, an in-cycle robustness
reinforcement method and a cycle-to-cycle robustness reinforcement method are
proposed. The former employs the idea of trajectory tracking to regulate the piston
motion and improve robustness, while the later improves system robustness by detecting
and recovering the system from misfires. Both methods are experimentally validated,
with results showing significant robustness improvements.
To summarize, this study is the first one that combines a digital pump with a HFPE.
The relationships among the HFPE operation parameters, HFPE efficiencies and working
conditions are clearly revealed. Key issues for robust operation are addressed.
Performance of the proposed system is demonstrated through simulations and
experiments, showing its feasibility and benefits. Together with the HFPE’s intrinsic
advantages, the proposed solution can provide highly efficient, fast responding, compact
and modular power sources for mobile hydraulic applications.
iv
Table of Contents
Contents
List of Tables .............................................................................................................. vii
List of Figures ............................................................................................................ viii
Chapter 1. Introduction ......................................................................................... 1
1.1. Motivations ................................................................................................... 1
1.2. Previous Attempts on Efficient Fluid Power Source .................................... 2
1.3. Digital Pumps................................................................................................ 3
1.4. Free Piston Engines....................................................................................... 5
1.5. Contributions of the Dissertation ................................................................ 11
1.6. Overview of the Dissertation ...................................................................... 12
Chapter 2. Working Principle of Independent Pressure and Flow Rate
Control ............................................................................................................. 13
2.1. System Description ..................................................................................... 13
2.1.1. OPOC Hydraulic Free Piston Engine ...................................................... 13
2.1.2. SP Hydraulic Free Piston Engine ............................................................ 14
2.2. Working Principle ....................................................................................... 15
Chapter 3. System Modeling and Concept Validation ...................................... 21
3.1. System Modeling ........................................................................................ 21
3.1.1. Piston Dynamics ...................................................................................... 22
3.1.2. Hydraulic Dynamics ................................................................................ 23
3.1.3. Thermodynamics ..................................................................................... 25
3.1.4. Combustion ............................................................................................. 25
3.2. Controller Design ........................................................................................ 26
v
3.2.1. Inner Loop Control .................................................................................. 27
3.2.2. Outer Loop Control ................................................................................. 30
3.3. Simulation Results ...................................................................................... 30
3.3.1. Steady State Operation ............................................................................ 31
3.3.2. Transient Performance ............................................................................ 33
3.4. Efficiency Analysis and Optimal Working Point ....................................... 35
3.4.1. Thermal Efficiency .................................................................................. 36
3.4.2. Mechanical Efficiency............................................................................. 37
3.4.3. Overall Efficiency and Optimal CR Selection ........................................ 39
3.5. Chapter Conclusion ..................................................................................... 41
Chapter 4. Testbed Characterization and Switch based IPFC ........................ 43
4.1. HFPE Testbed Characterization .................................................................. 43
4.1.1. Testing System Overview ....................................................................... 43
4.1.2. HPFE Characterization ............................................................................ 46
4.2. Working Cycle and Control Design ............................................................ 53
4.3. Testing Results ............................................................................................ 55
4.3.1. Working Condition and Switch Point Calibration .................................. 55
4.3.2. IPFC Test Results .................................................................................... 56
4.4. Performance Analysis and Discussion ........................................................ 57
4.4.1. Output Flow Estimation .......................................................................... 58
4.4.2. Energy Analysis ...................................................................................... 63
4.4.3. Low Robustness of Switch-Based Method ............................................. 69
4.5. Chapter Conclusion ..................................................................................... 71
Chapter 5. Robust Realization of IPFC .............................................................. 72
vi
5.1. Trajectory Tracking based IPFC ................................................................. 72
5.1.1. Introduction ............................................................................................. 72
5.1.2. Stable Operation, Flow Output and Trajectory Tracking ........................ 73
5.1.3. Controller Design .................................................................................... 77
5.1.4. Testing Results ........................................................................................ 83
5.2. Misfire Recovery ........................................................................................ 89
5.2.1. Introduction ............................................................................................. 89
5.2.2. Misfire Detection..................................................................................... 91
5.2.3. Control Design ........................................................................................ 97
5.2.4. Testing Results ...................................................................................... 100
5.2.5. Performance Discussion ........................................................................ 102
5.3. Chapter Conclusion ................................................................................... 104
Chapter 6. Conclusion and Future Work ......................................................... 106
Bibliography ............................................................................................................. 109
Appendix. A .............................................................................................................. 116
vii
List of Tables
Table 3.1 Key modeling parameters of the free piston engine ..................................... 22
Table 4.1. Sensors and actuators in the HFPE testbed................................................ 45
Table 4.2. Dead volume measurement data ................................................................. 48
Table 4.3. Calibrated HPFE parameters ..................................................................... 53
Table 4.4. Operation parameters for switch based IPFC ............................................ 56
Table 4.5. Energy breakdown for switch based IPFC ................................................. 67
Table A.1. Key components of the supercharger system ............................................ 116
viii
List of Figures
Figure 1.1 Crankshaft-based ICE with rotational hydraulic pump. .............................. 2
Figure 1.2. Schematic of a digital pump piston/cylinder ............................................... 4
Figure 1.3. Configuration of modern FPEs ................................................................... 6
Figure 2.1. Detailed schematics of an OPOC HFPE .................................................. 13
Figure 2.2. Detailed schematics of a Single Piston HFPE .......................................... 15
Figure 2.3. Schematic of operating OPOC HFPE using IPFC ................................... 16
Figure 2.4. Flow condition of IPFC with one valve OPOC HFPE ............................. 18
Figure 2.5. Schematic of operating SP HFPE using IPFC.......................................... 20
Figure 3.1 Model scheme of the HFPE ........................................................................ 21
Figure 3.2 Free body diagram of the FPE’s lumped piston pair................................. 22
Figure 3.3. Block diagram of the IPFC with PI control .............................................. 27
Figure 3.4. Steady state performances of the HFPE with the IPFC at various load
conditions. ......................................................................................................................... 31
Figure 3.5. Steady state performance at fixed pressure but various output flow rate,
from top to bottom: piston position, instantaneous flow, digital valves opening ............. 32
Figure 3.6. Steady state performance at fixed output flow rate but various pressure . 33
Figure 3.7. FPE performance under step flow demand ............................................... 34
Figure 3.8. Duty cycle section test ............................................................................... 35
Figure 3.9. Thermal efficiency with respect to CR at load pressure 15 MPa.............. 37
Figure 3.10. Mechanical efficiency as well as throttling loss and friction loss with
respect to CR at load pressure 15 MPa ............................................................................ 38
Figure 3.11. Upper: optimal efficiency. Bottom: CR for load pressure 15MPa ......... 40
Figure 3.12. Optimal overall efficiency of the HFPE with the IPFC at different load
conditions .......................................................................................................................... 41
Figure 4.1. Schematics of the testing system................................................................ 44
Figure 4.2. Photo of the test bed .................................................................................. 45
Figure 4.3. Scavenging pump and combustion chamber cut-out view ........................ 47
Figure 4.4. System block diagram for servo valve system ID ...................................... 49
Figure 4.5. Servo valve orifice estimation from system ID data .................................. 51
ix
Figure 4.6. Servo valve dynamics bode plot ................................................................ 52
Figure 4.7. Valve model response vs. estimated orifice ............................................... 52
Figure 4.8. Ideal working cycle of switch based IPFC ................................................ 54
Figure 4.9. Switch based IPFC with overcorrection ................................................... 57
Figure 4.10. Flow condition for switch based IPFC ................................................... 59
Figure 4.11. Flow Estimation of switch based IPFC ................................................... 60
Figure 4.12. Cumulative flow for switch based IPFC ................................................. 61
Figure 4.13. Flowmeter data for non-overcorrection switch based IPFC .................. 63
Figure 4.14. Energy breakdown structure for HFPE working under IPFC ................ 64
Figure 4.15. Energy breakdown for switch-based IPFC with overcorrection ............ 67
Figure 4.16. Cycle-wise hydraulic efficiency, engine mechanical efficiency and overall
mechanical efficiency ........................................................................................................ 69
Figure 4.17. Switch based IPFC with old hydraulic seals and corresponding switch
points ................................................................................................................................. 70
Figure 4.18. Switch based IPFC with new hydraulic seals and old switch points ...... 70
Figure 5.1. Flow distribution under different conditions ............................................ 74
Figure 5.2. Relationship between hydraulic force and output flow fraction ............... 75
Figure 5.3. IPFC with partial reference tracking ........................................................ 76
Figure 5.4. Control block diagram for reference tracking .......................................... 77
Figure 5.5. Top: Bode plot of conventional Q filters of different orders; Bottom:
Change of -3dB cut-off frequency with filter order for conventional Q filters. Sample time
Ts = 0.1ms ......................................................................................................................... 79
Figure 5.6. Bode plot of new Q filter and H(s)H(s) ..................................................... 81
Figure 5.7. Bode plot of repetitive controller .............................................................. 82
Figure 5.8. Bode plot of the closed loop system sensitivity function ........................... 82
Figure 5.9. Trajectory reference and feedforward signal for tracking based IPFC with
calibration based feedforward signal ............................................................................... 84
Figure 5.10. Operation overview of IPFC with trajectory tracking and calibrated
feedforward ....................................................................................................................... 85
x
Figure 5.11. Trajectory tracking with repetitive control and calibration based
feedforward ....................................................................................................................... 85
Figure 5.12. Efficiency of tracking with repetitive control and calibration based
feedforward ....................................................................................................................... 86
Figure 5.13. Operation overview of IPFC with trajectory tracking and inaccurate
calibrated feedforward...................................................................................................... 87
Figure 5.14. Trajectory tracking with repetitive control and inaccurate calibration
based feedforward ............................................................................................................. 88
Figure 5.15. Efficiency of tracking with repetitive control and inaccurate calibration
based feedforward ............................................................................................................. 89
Figure 5.16. Piston acceleration calculated using piston position data ..................... 92
Figure 5.17. Piston acceleration vs. piston position and separation line ................... 94
Figure 5.18. Deviation from separation line vs. steps from TDC ................................ 95
Figure 5.19. Flow chart of the misfire detection with roll back .................................. 96
Figure 5.20. Bode plot of repetitive controller used in misfire recovery ..................... 98
Figure 5.21. Transient controller and controller transitions during misfire recovery 99
Figure 5.22. Misfire recovery reference generation .................................................. 100
Figure 5.23. Tracking of misfire recovery reference ................................................. 101
Figure 5.24. Misfire recovery performance ............................................................... 102
Figure 5.25. Flow output around misfire recovery section ....................................... 103
Figure 5.26. Energy break down around misfire recovery section............................ 104
Figure A.1. Drawing of the supercharger system ...................................................... 116
Figure A.2. Photo of the supercharger system ........................................................... 117
1
Chapter 1.
Introduction
1.1. Motivations
Since Blaise Pascal published the fundamental law of hydrostatics in 1647, human
beings have been exploring and developing fluid power systems for more than 370
years[1]. Compared to other power transfer methods, fluid power has many advantages,
including high power density, self-lubricating, simplicity in overloading protection, low
space requirement and simplicity in providing longitudinal motion[1], [2]. Nowadays, it
is widely used in a spectrum of industries including manufacturing, transportation,
aerospace, agricultural, mining and construction. A study in 2012 shows that up to 3
quadrillion kJ of energy is consumed by hydraulic systems in the US each year[3].
Among all these applications, an important section is mobile hydraulic applications,
where the energy source has to be carried on board. The study in 2012 shows that up to
1.4 quadrillion kJ is used in such systems[3], whereas another study in 2017 suggests this
number to be as high as 1.9 quadrillion kJ[4]. Despite all the advantages of hydraulic
systems, they have relatively low efficiencies. Depending on the type of applications,
hydraulic systems can have efficiencies ranging from less than 9% to 60%, with the
average efficiency being 22%. Furthermore, mobile applications’ efficiency is only 14%
on average, and lays near the lower end of this efficiency range[3].
This low efficiency largely roots back to the inefficient architecture employed in such
systems. In conventional mobile hydraulic systems, the power source is usually a variable
displacement pump driven by an internal combustion engine (ICE), as shown in Figure
1.1. This configuration has three major limitations. First, the engine is sized for the
maximum power demand. However, for a significant portion of its duty cycle, the power
demand is far less than the maximum and the engine needs to work at part load
conditions with lower efficiency. Second, due to the large inertia of an ICE and the
response time of the pump, it is not possible for the power source to respond fast enough
to meet the load demand in real-time. As a result, in order to achieve precise actuator
control, the engine and pump always need to generate more power than what is actually
2
needed, and use throttling downstream to get desired power/flow. Last but not least, the
high-pressure fluid produced by the engine driven pump needs to be distributed and
throttled to various actuators to meet different pressure and flow rate requirements. This
will apparently generate significant throttling losses in the fluid power system. The
current situation suggests that a better solution for power source needs to be found for
mobile hydraulic applications, and thus motivating this research.
Figure 1.1 Crankshaft-based ICE with rotational hydraulic pump.
1.2. Previous Attempts on Efficient Fluid Power Source
Attempts have been made by numerous researchers to design a better mobile fluid
power source, and some of them are already being adapted in industry. To mitigate the
throttling losses in fluid power systems, the load sensing concept was proposed, which
connects the pump control to the load[5]. On top of that, Djurovic and Heldusesr[6] also
proposed the idea of flow matching for the general electro-hydraulic load sensing, which
requires the flow generated by pump to meet the demand from the actuator exactly.
Usually, the pump flow is adjusted either by changing the pump speed or the pump
displacement. Specifically, the former is achieved by driving a fixed displacement pump
with an electric motor and controlling the motor speed in real time. Lovrec et al followed
this idea and experimentally verified that a prototype fluid power system with a speed-
controlled motor is feasible for the metal-forming machines with lower energy losses and
improved control dynamics[7]. Chiang et al also developed such a fluid power system,
with a variable rotational speed AC servo motor and a constant displacement axial pump,
3
for a hydraulic injection molding machine[8]. By applying a signed-distance fuzzy
sliding model control, the molding machine possesses fast response and high efficiency
velocity control. However, in spite of these successful cases, such systems’ dependence
on electrical power source makes it difficult to apply them for heavy-duty mobile
applications.
The second flow changing method utilizes a variable displacement pump driven by an
ICE and adjusts the flow rate by changing the pump’s displacement. There are three main
pump architectures that commonly have variable displacement: axial piston with swash
plate, bent axis and vane. Among them, the axial piston pump is the most widely used in
mobile applications due to its compact size and robust design[9]. This kind of pump’s
displacement can be varied continuously by changing the angle of a swash plate relative
to the pump’s axis. Extensive researches have been conducted to explore the performance
of these variable displacement pumps employed in mobile applications[10], [11].
However, the response time of such a pump is still relatively slow compared to current
valve-based hydraulic systems, and its efficiency is lower at partial displacement due to
its almost constant leakage loss[12]. Due to the aforementioned drawbacks, researchers
have also proposed other variable displacement pump solutions. For instance, Wilhelm
proposed linkage based system to achieve variable pump displacement[13], which could
provide better efficiency than swashplate based piston pumps. Another set of novel
solutions are the digital pumps, which will be discussed in detail in the next section. No
matter what mechanism is applied in realizing variable displacement, when applied to
mobile applications, variable displacement pumps still have to be driven by ICEs. Even
though some pumps may possess fast response to load variation, the ICEs would need a
longer duration to vary their power output accordingly. As a result, this architecture
won’t be able to meet the need for fast response to load variations for mobile applications
by itself, and valve-based throttling is still needed downstream.
1.3. Digital Pumps
Digital pump is a relatively new solution for variable displacement pumps. Its basic
idea is to integrate a fixed displacement pump, usually a piston pump, with digital valves
4
(on/off valves) to control the effective pump displacement. The schematic of a typical
digital pump piston/cylinder is illustrated in Figure 1.2.
Figure 1.2. Schematic of a digital pump piston/cylinder
The early digital pump idea employs a cylinder enabling/disabling method, where a
whole stroke of oil is either all pumped or all dumped. By controlling the number of
enabled and disabled strokes during a certain period of time, the output flow rate and
therefore the effective pump displacement can be varied. In 1990, Rampen et.al proposed
a digital pump that uses a solenoid valve as the inlet valve of a piston pump[14]. When
the piston is near its bottom dead center (BDC) and is ready to pump out oil, a decision is
made regarding whether or not to energize the solenoid, which in turn controls whether
the piston will pump to high pressure or low pressure during the coming pumping stroke.
This system is later proved to be effective in maintaining a constant system pressure at
different flow rate [15]. Later on, this method is extended to changing the valve
connection in the middle of a stroke, thus pumping part of the in cylinder oil to the load
side and changing the displacement of a single piston continuously[16]. Also, by
changing the valve connection, the pump can also work as a motor, where high pressure
oil is used to power the piston motion[17]. Some other researchers suggest that digital
pump displacement modulation can also be achieved through a flow-limiting method[18],
[19].
5
By using a digital pump, the effective pump displacement is varied by adjusting the
opening and closing of specific valves. Since the variation of displacement is determined
by the dynamics of valves and pump rotational speed, rather than the pump dynamics,
digital pumps’ response time is expected to be much shorter. Literatures reported a
response time between 30ms and 50ms using the cylinder enabling method [15], [17]. At
the same time, commercial digital pumps claim to reduce loss by 90% through cutting
leakage and throttling loss[20].
No matter what displacement varying scheme is applied, all digital pumps’ stroke
length is independent of their current displacement. This is important to hydraulic free
piston engines (HFPEs) and will be discussed in later sections.
However, as mentioned above, despite all the advantages of digital pumps, this
solution still only looks at the response of pump side rather than the whole system. There
is still a limiting factor of ICE response time when applying them in mobile hydraulic
systems.
1.4. Free Piston Engines
Free Piston Engines (FPEs) have been around for almost a century. In 1928, a free
piston air compressor was patented by Pescara[21]. This is usually believed to be the first
free piston engine invention, although there were many other researchers working on
similar concepts around the same time[22]. In early years, FPEs are usually used as air
compressors [23]or gas generators for turbines[24].
Modern FPEs usually transform combustion energy directly into hydraulic energy
through a linear piston pump (Hydraulic FPEs, HFPEs)[25]–[28], or into electricity
through a linear generator (Free Piston Engine Generators ,FPEGs)[29]–[31]. Depending
on the arrangement of load elements (hydraulic pistons or linear generators) and
combustion cylinder/pistons, modern FPE schematics can be classified into four
categories, namely the Single-Piston (SP) configuration, Opposed-Cylinder (OC)
configuration, Opposed Piston (OP) configuration and Opposed-Piston Opposed-Cylinder
(OPOC) configuration, as illustrated in Figure 1.3.
6
Figure 1.3. Configuration of modern FPEs. From top to bottom: SP, OP, OC and
OPOC
Free piston engines are usually two stroke engines, since there are no fly wheels and a
power stroke is needed in each cycle[32]. Together with less moving parts and simpler
motion transmission, FPEs have the advantage of high power density and high
compactness. For OP and OPOC FPEs, since motion of the pistons are symmetric, the
engine is also self-balancing, thus producing less vibration and noise[28], [33]. In
addition, due to the absence of the mechanical crankshaft, FPEs have the ultimate
freedom on its piston motion and therefore is able to produce variable output works with
higher thermal efficiency[34]–[36]. Other than that, FPEs have much lower inertia
compared to conventional ICEs, which enables much faster response to load changes.
7
All these advantages of FPE give the HFPE a good potential as a throttle-less mobile
fluid power source that produces various output flow rate at different working pressures
in real time. However, there are several obstacles to overcome before realizing such a
system.
The first issue is the difficulty in flow rate modulation. Conventionally, for a piston
pump, the flow rate is changed by either changing the operation frequency, or changing
the displacement through varying stroke length. In a HFPE, however, the operation
frequency is determined solely by the dynamics of the engine, and is only affected by
operation parameters including the load pressure and the compression ratio. This means
that the operation frequency is dependent on the load condition and cannot be adjusted
freely to vary the output flow rate. On the other hand, to operate efficiently, the HFPE
requires a certain compression ratio range, which in turn requires the piston stroke length
to be in a certain range. Since the combustion pistons and hydraulic pistons are direct
coupled, this means changing stroke length to modulate output flow rate is also not
feasible.
Previously, attempts have been made by researchers to address this issue. Peter Achten,
et al proposed a Pulse Pause Modulation (PPM) method for a single piston HFPE in [26].
Its main idea is to hold the piston at its BDC after each combustion, and use a flow
control valve to adjust the waiting period between consecutive cycles. In this way, the
effective operation frequency of HFPE can be changed and thus the average flow rate is
modulated. Similar ideas were also proposed by Hibi, et al in [25]. This idea is somewhat
similar to the original digital pump idea proposed in [14], [15], in the sense that both tries
to modulate the flow output through digitally changing the number of strokes per second,
while keeping the same displacement per stroke. However, since this method requires the
piston to reset at BDC after a single cycle, it is only feasible to those FPE configurations
with a single combustion chamber, i.e. the SP configuration and the OP configuration.
Secondly, FPEs’ operation is not inherently robust. Due to the absence of the
mechanical crankshaft and fly wheel, the FPEs’ piston motion solely depends on the
forces exerted on the pistons and the pistons’ inertia. When the external forces are not
well balanced, the piston motion will go out of control. This issue could be mitigated to
8
some extent when the FPE works in a discrete fashion, as suggested in [25], [26], since
the condition is reset after each cycle and disturbances won’t propagate to the next
combustion cycle. However, when OC or OPOC configuration is applied, the FPE has to
operate continuously, and the disturbance will be propagated from cycle to cycle, making
the FPE’s control more challenging[37], [38]. One extreme case is when misfire happens,
the gas force will not be strong enough to overcome the resistance force from the load, so
the piston motion won’t be able to provide a high enough compression ratio, and the
following combustion will not occur.
To address this problem, Li et al proposed to use the idea of motion tracking, and put
forward the virtual crankshaft mechanism to regulate the piston motion of an OPOC
HFPE during motoring[28], [39]. Later, a transient control scheme was also proposed to
handle the transition from motoring to combustions[40]. Tikkanen et al used calibration
based open-loop control on a OC HFPE and reported the first cycles of operation in [32].
After that, those researchers proposed to use feedforward plus PID control, with an
adaptive proportional gain, to control the fuel injection amount of an OC HFPE[27].
Operation under constant load pressures were achieved in simulation using this method.
Despite all their effort and progress, their solutions didn’t take the output flow regulation
into consideration. Also, these control methods didn’t address how to handle misfires.
At the same time, efforts are also put into the investigation of FPEGs by numerous
researchers. Since many challenges, technologies, and philosophies are the same for
HFPEs and FPEGs, it is necessary to also look into development in this area. Researchers
in the German Aerospace Center (DLR) did a thorough study of the FPEGs as range-
extenders for hybrid passenger vehicles. They published their preliminary simulation
work based on Modelica in 2005[41], where the basic dynamics of a FPEG was studied.
Then, a comparison study was conducted where the FPEGs were compared with fuel
cells, micro gas turbines and conventional ICEs for the suitability as a range extender
[42], [43]. According to the study, although a FPEG may be slightly heavier and larger
than a conventional ICE based solution, it was still concluded to be the best overall
option due to high efficiency, fuel flexibility, fast response and ease of integration. After
that, in depth investigations were conducted following a three-phase development plan
9
including the sub-system validation phase, the development system phase and the
autarkic function demonstrator phase[44]. Topics including solid lubrication system[45],
in-chamber gas exchange process[46], spark ignition (SI) and homogeneous charge
compression ignition (HCCI) combustion strategies[47] and linear generators[48], [49]
are studied respectively as subsystems with either simulations or hydraulic actuated
subsystem components. At the development system phase, a MPC style controller was
proposed to regulate the linear generator forces and thus controlling piston BDC and
TDC(Top Dead Center) positions [50]. This method was then successfully validated on a
double bounce chamber system with ‘virtual combustions’ emulated by the linear
generator force[44]. Meanwhile, the possibility of switching between SI and HCCI
combustions was demonstrated on a hydraulic assisted FPEG[51]. The idea was to
implement a hybrid strategy that uses SI combustions during full load and HCCI
combustions during partial loads to improve efficiency. Ultimately, a single piston
autarkic function demonstrator was built and the overall system functions and
performances were tested[29], [52].
Performance wise, the subsystem testing of SI combustion shows an indicated engine
efficiency of 27.3% at a compression ratio of 10 for the opposed-piston lay out[47]. SI
and HCCI combustion tests at a compression ratio of 9 on a hydraulic assisted FPEG
during phase 2 show efficiencies of 33.3% and 34.4%, respectively[51]. Since the SI case
was on full load and HCCI case was on partial load, this work demonstrated the
efficiency advantage of HCCI over SI on FPEGs. Finally, tests on the autarkic function
demonstrator shows an overall efficiency from fuel to electricity is reported to be 17.9%
with an indicated engine efficiency of 31.8% realized through SI[29]. In a more recent
work, they reported higher indicated engine efficiency ranging from 35.6% to 38.1% for
different working conditions acquired through HCCI combustions[52].
Another important institute in the study of FPEGs is the Sandia national labs. Their
goal is to use hydrogen as fuel and transform its chemical energy into electricity
efficiently using the FPEGs. Their early simulation works were conducted based on an
opposed cylinder architecture, and drew the conclusion that the indicated engine thermal
efficiency can be as high as 65% while complying the NOx emission standards proposed
10
at the time[53]. Also, fuel to electricity efficiency of as high as 50% could be reached
with very low NOx emission[54], [55]. Acknowledging the importance of scavenging
process in the FPE[53], their work shifted towards uniflow scavenging[56], [57] and
ultimately adopted an opposed piston architecture with bounce chambers. On the
generator side, a detailed generator model was presented and experimentally validated in
2009[58]. Later on, with an 30kW prototype built, tests were conducted[59], [60]. In their
system, the bounce chambers were used to control the motion of pistons, while the linear
generators are not actively controlled. During each cycle, compressed air flows in and
vents out the bounce chamber at BDC and TDC, respectively. Control of the compression
ratio and BDC position is therefore realized by regulating the input pressure and vent
back pressure. The parallelly connected two linear generators shows some passive piston
synchronization capability from the electromagnetic coupling, but eventually can’t hold
this synchronization due to unbalanced pressure and friction forces on the two sides[59].
Compared to the efficiencies reported by DLR[29], the Sandia FPEG reports a lower
linear generator efficiency(from expansion work to electricity) that reduces with power
output and lays between 60% and 35%[59]. This is mostly because of the inefficient
active bounce chamber utilized in the Sandia FPEG. Thanks to the high indicated engine
efficiency of 60% brought by a very high compression ratio of 20 to 70 and HCCI
combustions, the overall efficiency from fuel to electricity can still peak at 33.6% with a
typical value of 20% to 25%[59], [60].
Other researchers also contributed to the study of FPEGs. At Toyota, Goto etc.
realized stable operation of a single piston free piston engine with linear generator using a
PD controller with velocity compensation term[30]. Two years later, a more sophisticated
control method using velocity control with adaptive velocity reference was realized by
the same group[31]. An observer was also proposed by them to estimate the damping
coefficient and bounce chamber pressure, as well as to improve the position sensor
resolution[61]. Researchers at West Virginia University explored the possibility of using
mechanical springs instead of air springs in FPEGs and its impact on system
dynamics[62].
11
1.5. Contributions of the Dissertation
This dissertation documents the investigation of a novel mobile fluid power source
that combines the digital pump and the HFPE. On one side, the digital pump has a high
efficiency and very fast response time compared to other variable displacement pump
solutions. On the other side, the HFPE is modular, fast responding and inherently more
efficient as well as greener compared to conventional ICEs. More importantly, the digital
pump idea can provide continuous displacement modulation without changing the overall
stroke length, making it an ideal pumping mechanism for a HFPE, where the stroke
length is coupled with compression ratio and cannot be adjusted freely. As will be shown
later in the dissertation, combining the two concepts will join the advantages of them and
provide a highly efficient fluid power solution for mobile applications. Nevertheless, the
proposed operation method works for all four FPE configurations illustrated in Figure 1.3.
To the best of the author’s knowledge, this is the first time such attempts are made.
The contributions of this dissertation include:
1. The idea of independent pressure and flow rate control (IPFC) is proposed and
validated. With IPFC, HFPEs and digital pumps are combined for the first time to
realize a fast responding, highly efficient fluid power source for mobile hydraulic
applications. The working principle of IFPC is clearly articulated for different
HFPE configurations. The feasibility of the proposed method is validated through
simulation, with the corresponding dynamics and performance analyzed. Energy
loss analysis unveiled the underlying trade off in the selection of operation
parameters, and a systematical method is proposed accordingly to find the
optimum for different working conditions. Simulation results show that the
proposed system can respond to load change in a matter of tens of milliseconds,
and provides an overall fuel to hydraulic energy efficiency between 28% and
58%[63].
2. A comprehensive HFPE model is established. A physics-based model is built for
an OPOC HFPE and calibrated with the apparatus in the test cell. The piston
dynamics, gas dynamics, combustion process, hydraulic dynamics and valve
dynamics are all captured in the model. This model is used to validate/evaluate the
12
IPFC idea, as well as to guide the robust controllers’ design. Good model fidelity
is shown through simulation and tests.
3. Robust operation methods are proposed for IPFC and experimentally validated.
Based on the feature of the IPFC and dynamics of HPFE, two control methods are
proposed to achieve the robust realization of IPFC. The first one is in-cycle
robustness reinforcement, which ensures robust operation of the HFPE by
regulating the piston motion to track a prescribed trajectory in each cycle.
Particularly, with the correlation among hydraulic force, piston trajectory and flow
output analyzed in detail, a hybrid control scheme is proposed to enhance
robustness while ensuring efficient flow output. The second robust realization
method is cycle-to-cycle robustness reinforcement, which employs a misfire
recovery mechanism. The controller detects misfires and brings the HPFE back to
operation with the least amount of energy and time after a misfire. Experimental
results show that both methods work well even with large variance in combustion
performance, and robust operation of HFPE under IPFC can be realized.
1.6. Overview of the Dissertation
The rest of this dissertation is organized as follows:
Chapter 2 discusses the system schematics considered in this research, and shows the
basic working principle of IPFC under different FPE configurations. Then, in Chapter 3,
a comprehensive physics-based model of HPFE is established, and the IPFC is validated
through simulations with results analyzed. The testbed set up and characterization, as
well as the switch based IPFC realization are presented in Chapter 4. Chapter 5 describes
two robust realization methods for the IPFC, with performance for each case analyzed.
Finally, conclusions and future works are shown in Chapter 6.
13
Chapter 2.
Working Principle of Independent Pressure and Flow Rate Control
As mentioned in previous sections, the goal of this research is to design a universal
method of operating a HFPE as mobile fluid power source that is independent of HFPE
configurations. From a control’s perspective, if we neglect the synchronization issue of
pistons, the OP configuration is essentially the same as the SP configuration, since the OP
configuration can be considered as two SP HFPEs arranged back to back. Similarly, the
OC configuration has the same requirements for controllers as the OPOC configuration.
Therefore, without losing generality, the IPFC idea is described in detail for OPOC
HFPEs and SP HFPEs here.
2.1. System Description
2.1.1. OPOC Hydraulic Free Piston Engine
Figure 2.1. Detailed schematics of an OPOC HFPE
The detailed set up for an OPOC HFPE is shown in Figure 2.1. There are two piston
pairs in the HFPE, namely the outer piston pair and inner piston pair, in the HFPE. The
outer piston pair connects two outer pistons through two shafts and the inner piston pair
connects two inner pistons through one shaft. At each end of the HFPE, one outer piston
and one corresponding inner piston as well as the cylinder around them form a
combustion chamber. Due to the symmetric structure, the TDC of the left combustion
14
chamber is the BDC of the right combustion chamber and vice versa. Therefore,
combustions will take place inside each combustion chamber alternatively.
Between the combustion chambers, there is a hydraulic block in the middle. Three
hydraulic pistons, mounted on three shafts respectively, divide the hydraulic cylinders
into six hydraulic chambers, as shown in Figure 2.1. Chamber 1 and 3 are connected to
each other, forming a unit hydraulic chamber named as the outer hydraulic chamber.
Chamber 2 itself forms another unit hydraulic chamber, named the inner hydraulic
chamber. As can be seen, the outer hydraulic chamber and inner hydraulic chamber are
connected to two ports of a servo valve respectively. Therefore, depending on the
opening of the servo valve, two unit hydraulic chambers can be connected to either the
high pressure (HP) or low pressure (LP) respectively. Chamber 4, 5 and 6 are
interconnected to each other to synchronize the motion of the piston pairs. During
operation, the two combustion chambers fire alternatively and push the corresponding
hydraulic pistons to move and therefore providing output flow from each stroke.
It is worth noting that the servo valve depicted in Figure 2.1 could be divided into two
three-position-three-way valves, as will be shown later in Figure 2.3. Although this will
add in one more valve, it brings the benefit of decoupling the connection of the inner
hydraulic chambers from that of the outer hydraulic chamber. Later analysis shows this
decoupling could benefit system efficiency when operating under IPFC.
2.1.2. SP Hydraulic Free Piston Engine
Figure 2.2 shows the schematics of a SP HFPE. For SP FPEs, since there is no
crankshaft or fly wheel, special arrangements have to be made in order to push the piston
to compress the combustion chamber after BDC. Similar to [26], [44], a bounce chamber
is added opposite to the combustion chamber for this purpose.
As shown in the figure, the combustion piston, hydraulic piston and bounce chamber
piston are connected with a push rod and always move simultaneously. Hydraulic
chambers 1 and 2 are the pumping chambers, which are connected to two ports of a servo
valve respectively. Depending on the connection of the servo valve, the hydraulic
chambers can be connected to either the high pressure or the low pressure. Both
15
chambers are also connected to high pressure and low pressure through check valves.
When a combustion happens at TDC, all three pistons are pushed to the right. In this
process, oil is pumped out of chamber 1 while drawn into chamber 2. At the same time,
the bonce chamber is compressed, converting piston kinetic energy into air spring
potential energy. After that, when the pistons reach BDC, this stored potential energy is
extracted through the expansion of the bounce chamber and the pistons are pushed back
toward TDC, thus completing a cycle. During the compression stroke of the combustion
chamber, hydraulic chamber 1 will draw in oil and chamber 2 will pump out oil. Note
that similar to the OPOC HFPE, the servo valve in the system can be divided into two
digital valves to decouple connections of hydraulic chambers.
It is also worth noting that if the OPOC HFPE only enables combustions in one
chamber, and use the other combustion chamber as a bounce chamber, it will decay into
an OC HFPE, which effectively has the same working cycle as the SP HFPE described
above.
Figure 2.2. Detailed schematics of a Single Piston HFPE
2.2. Working Principle
16
Figure 2.3. Schematic of operating OPOC HFPE using IPFC: (a) TDC of the left
combustion cylinder. (b) Expansion stroke of the left cylinder before the switch point. (c)
Expansion stroke of the left cylinder after the switch point. (d) BDC of the left
combustion cylinder.
The basic idea of independent pressure and flow rate control, or IPFC, is to use the
HFPE as a digital pump by controlling the digital or servo valves in the system. Figure
2.3 illustrates the IPFC for an OPOC HFPE. Note that in this case, the inner and outer
hydraulic chambers are connected to high pressure (load circuit) and low pressure
through two separate 3-position-2-way digital valves.
The working principle of the IPFC is proposed as follows:
1. The left combustion cylinder fires at its TDC point, and the combustion force
pushes the two piston pairs away from each other (Figure 2.3 (a)).
2. At this time, digital valve 1 is at its top position or neutral position, while digital
valve 2 is at its bottom position. The movements of the two piston pairs force
the outer hydraulic chamber to pump hydraulic oil to the high pressure and the
inner hydraulic chamber to draw oil from the low pressure (Figure 2.3 (b)).
These valve positions sustain until the pistons reach a desired point, marked as
17
the switch point. The flow from outer hydraulic chamber to the HP up to this
point is the effective output flow produced in the stroke. This part of the stroke
is referred to as the pumping phase.
3. At the switch point, digital valve 2 switches to its top position, while digital
valve 1 sustains its position (Figure 2.3 (c)). As a result, both the outer and
inner hydraulic chambers are connected to the low pressure. As the piston
motions continue, hydraulic oil in the outer hydraulic chamber will flow into
the low pressure rather than the high pressure.
4. The pistons move until the BDC of the left combustion cylinder is reached,
which is also the TDC point of the right combustion cylinder (Figure 2.3 (d)).
At this time, digital valve 1 moves to the neutral position. The part of the stroke
from switch point to till here is called the dumping phase, for oil is dumped to
low pressure from the discharging outer hydraulic chamber. Now the right
cylinder fires and another stroke starts. Process similar to step 1 through 3 will
occur again and digital valve 1 will switch in the middle of the stroke. The two
cylinders fire in an alternative fashion and the hydraulic chambers pump out
hydraulic oil continuously in each stroke.
Apparently, the effective output flow produced in each stroke is determined by the
switch point: if digital valve 2 doesn’t switch until the end of the stroke, then all the
hydraulic oil in the outer hydraulic chamber is pumped into the HP, which produces 100%
displacement output flow; if the digital valve 2 switches its position at the middle of the
stroke, then 50% pump displacement is produced. Therefore, by changing the switch
point, the effective output flow, or the pump displacement, can be varied continuously
from 0 to 100% for each stroke. This is essentially the same flow modulation mechanism
used in digital pumps.
The same idea can also be realized using the one valve architecture shown in Figure
2.1. With such an architecture, the first phase, i.e. the pumping phase, is the same as that
in the two-valve architecture, while differences lay in the dumping phase. With only one
valve in the system, the intake chamber has to be connected to high pressure when the
discharge chamber is connected to low pressure. As a result, flow into the intake chamber
18
will be supplied by the high pressure. From the high pressure side, such a connection
would pose a negative output flow. Therefore, the net flow from a stroke in this case is
the output flow in the pumping phase (Q1) minus the negative flow in the dumping phase
(Q2), as illustrated in Figure 2.4. Consequentially, when the switch point is in the middle
of a stroke, the flow rate would be zero. It is necessary to note that this architecture
would cause more throttling loss during the dumping phase, since more flow will pass
through the servo valve orifice. Also, when the intake chamber is connected to the high
pressure, a net hydraulic force helping the piston motion will be produced, so the
dumping phase in this case can also be referred to as the helping phase.
Figure 2.4. Flow condition of IPFC with one valve OPOC HFPE
For a SP HFPE, there is only one combustion in each cycle and the two strokes are
asymmetric. For such cases, IPFC can work in the same fashion as the OPOC HFPE by
switching the valve once during each stroke. However, the existence of bounce chamber
makes it unwise to do so for the following two reasons. Firstly, switching during the
power stroke could cause significant throttling. In the SP configuration, piston speed
during the expansion stroke will be higher since part of the kinetic energy has to be
converted into bounce chamber potential energy to power the compression stroke. This
will cause an increase in throttling loss across the servo valve, especially during the valve
transient. Secondly, bounce chamber loss is not minimized under such an operation
manner. Energy has to go through a double conversion through the bounce chamber at a
less-than-one efficiency before it can be output as hydraulic energy during the
19
compression stroke. The two switches per cycle method cannot minimize the
compression stroke energy output so it does not minimize the bounce chamber loss.
To improve the efficiency, the one switch method is proposed. The method is
illustrated using a one valve SP HFPE in Figure 2.5. The working cycle is explained as
follows.
1. Combustion starts at the TDC of the combustion chamber, pushing the piston to
the right. The servo valve is connecting chamber 2 to high pressure at this time,
so oil will be drawn into chamber 1 from low pressure and pumped out of
chamber 2 to high pressure through the servo valve and check valves. During the
expansion stroke, control signal is sent to move the servo valve to its middle
position. At the same time, the bounce chamber potential energy increases as it is
compressed. (Figure 2.5(a) and (b))
2. At the BDC, the servo valve is parked to neutral. Under the bounce chamber
force, the piston starts to move to the left. Note that at BDC, the discharge and
intake chambers switch, so oil is pumped to high pressure from chamber 1 and
drawn from low pressure to chamber 2 through check valves. (Figure 2.5(c) and
(d))
3. The piston continues to move to the left until the switch point in the middle of
compression stroke is reached. Then, the servo valve switches to connect
chamber 1 to low pressure and chamber 2 to high pressure. As the piston
continues to move, oil is pumped to low pressure from chamber 1 and drawn
from high pressure to chamber 2 through the servo valve, causing a negative net
output flow. Simultaneously, the hydraulic force will help the motion of
hydraulic pistons. (Figure 2.5(d) and (e))
4. When the piston arrives at TDC, servo valve is at the same position as in step 1,
and a new cycle is ready to start with a combustion. The net flow output is the
sum of positive flow from (a) to (d) minus the negative flow from (e) to (f).
(Figure 2.5(f) and (a))
Apparently, the output flow rate can be modulated by changing the switch point. It is
worth mentioning that depending on the sizing of SP HFPEs, when the displacement
20
fraction is very low, the combustion could be too weak to push the piston to a proper
BDC under this method, and the one-switch-per-stroke method has to be used. Also, this
method is compatible with the two-valve architecture, where chambers 1 and 2
connections are decoupled, just like in the OPOC HFPE case. The only difference is that
in such a case, when the output displacement is lower than 50%, the valve switch will
happen during the expansion stroke and the whole compression stroke will have both
chambers connected to low pressure.
Figure 2.5. Schematic of operating SP HFPE using IPFC: (a) TDC of the combustion
cylinder. (b) BDC at the end of expansion stroke (c) BDC at the beginning of the
compression stroke. (d) Compression stroke before switch point. (e) Compression stroke
after switch point (f) TDC at the end of the compression stroke
21
Chapter 3.
System Modeling and Concept Validation
To validate the IPFC idea proposed in Chapter 2, simulation studies are conducted
based on a two valve OPOC HFPE. First, a comprehensive physics-based model is
established for the engine. Then, a two-layer controller is proposed to ensure the HPFE’s
stable operation under IPFC. After that, simulation results are shown for both steady state
and transient working conditions, demonstrating the feasibility of IPFC. Finally,
efficiency analysis is conducted based on the simulation results, and method for optimal
operation parameter determination is proposed.
3.1. System Modeling
A model is herein developed to describe the dynamic behavior of the HFPE and
validate the control strategies proposed in this paper. The basic model scheme is shown
in Figure 3.1. The entire dynamic system can be divided into four parts, namely the
piston dynamics, hydraulic dynamics, thermodynamics, and combustion.
Figure 3.1 Model scheme of the HFPE
Key parameters used in the modeling process are listed in Table 3.1.
Parameter Description Value
Ag combustion piston area 0.002 m2
Ah
Aori_max
Cd
Dp
Dck
Fhigh
Flow
hydraulic piston area
digital valve maximum orifice
digital valve discharge coefficient
hydraulic chamber diameter
check valve disc diameter
output check valve preload
intake check valve preload
1.41×10-4 m2
1.90×10-5 m2
0.7
20 mm
10 mm
16.5 N
6 N
22
h
hck
kv
kck
Khigh
Klow
Lp
M
Mck
Δh
R
Τr
β
βck
𝛾
ρfluid
cylinder/chamber clearance
maximum check valve disc lift
friction coefficient
check valve disc damping coefficient
output check valve spring stiffness
intake check valve spring stiffness
piston length
piston pair mass
check valve disc mass
digital valve overshot
gas constant
digital valve 0% to 100% rise time
hydraulic oil bulk modulus
check valve discharge flow angle
specific heat ratio
hydraulic oil density
35 μm
2.14 mm
2.33
3 (N∙s)/m
7000 N/m
2600 N/m
66 mm
4.5 kg
1.1×10-3 kg
10%
296.25 J/kg-K
3.25 ms
1.0×109 Pa
54.6 °
1.31
870 kg/m3
xin position of intake port 48 mm
A pre-exponential factor 2502
Ea activation energy 1831930 J
n power of pressure 1.367
QLHV low heating value of the fuel 47 MJ/kg
Cv constant volume heat capacity 719 J/kg.
e burn duration averaging parameter 0.5
k burn duration parameter 9e-5
Ec activation energy for combustion 185 KJ
Ru
µd
universal gas constant
hydraulic oil dynamic viscosity
8.314 J/mol/K
20×10-2 Pa·S
Table 3.1 Key modeling parameters of the free piston engine
3.1.1. Piston Dynamics
Piston dynamics of the HFPE is governed by the in-cylinder gas force, the hydraulic
force and the friction forces. For simplicity, the two piston pairs are considered to be
perfectly synchronized and lumped into one rigid body. The free body diagram of the
lumped piston pair is shown in Figure 3.2.
Figure 3.2 Free body diagram of the FPE’s lumped piston pair
The piston motion is governed by the Newton second law, as shown in (3.1).
23
�̈� =1
𝑀(𝐹𝑙𝑒𝑓𝑡(𝑥, �̇�) − 𝐹𝑟𝑖𝑔ℎ𝑡(𝑥, �̇�) − 𝐹𝑓(�̇�) + 𝐹𝑖𝑛𝑛𝑒𝑟(�̇�)
− 𝐹𝑜𝑢𝑡𝑒𝑟(�̇�))
=1
𝑀(𝐹𝑛𝑒𝑡(𝑥, �̇�) + 𝐹𝑓(�̇�) − 𝐹ℎ𝑦𝑑(�̇�))
(3.1)
where 𝑥, �̇� and �̈� are the displacement, velocity and acceleration of the piston. M is the
piston mass. Fleft, Fright and Fnet are the left, right and net in-cylinder gas force,
respectively, which can be calculated through the combustion chamber pressure P and
combustion piston area Ag. Finner, Fouter and Fhyd are the hydraulic forces from the inner
chamber, outer chamber and the net hydraulic force, which are determined by the
hydraulic pressure in each hydraulic chamber. The detailed derivations of those forces are
presented in the subsequent subsections. Ff is the friction force, whose calculation is
shown below:
𝐹𝑓(�̇�) = 𝑘𝑣 ∙ �̇� = π𝑑𝑝𝑙𝑝
𝜇𝑑ℎ�̇� (3.2)
In the equation, kv is the friction coefficient, which is determined by the clearance
between the piston and the cylinder h, piston’s length 𝑙𝑝 and diameter 𝑑𝑝 , as well as the
oil dynamic viscosity 𝜇𝑑.
3.1.2. Hydraulic Dynamics
As shown in Figure 2.3, hydraulic chambers 1, 2 and 3 on the left side are connected
to either the HP or LP through the check valve and the digital valves, whereas the three
right hydraulic chambers 4, 5 and 6 are interconnected and serve as the synchronization
mechanism. As perfect synchronization is assumed, chamber 4, 5 and 6 are neglected in
modeling. Hydraulic pressure in the other chambers can be modeled as follows:
�̇�𝑐ℎ𝑎𝑚𝑏𝑒𝑟 =
𝛽
𝑉𝑐ℎ𝑎𝑚𝑏𝑒𝑟(𝑄𝑝𝑖𝑠𝑡𝑜𝑛 + 𝑄𝑑𝑖𝑔𝑖𝑡𝑎𝑙+𝑄𝑐ℎ𝑒𝑐𝑘) (3.3)
where �̇�𝑐ℎ𝑎𝑚𝑏𝑒𝑟 is the hydraulic pressure rate of left chamber, β is the bulk modulus of
the fluid, and Vchamber is the chamber volume. Qpiston is the flow caused by the piston
24
motion, Qdigital represents the flow through the digital valve and Qcheck is the flow through
the check valve.
Based on the velocity of the piston, Qpiston can be easily derived:
𝑄𝑝𝑖𝑠𝑡𝑜𝑛 = 𝐴ℎ�̇� (3.4)
where Ah is the hydraulic piston area.
Flow through digital valves and check valves are calculated through orifice equation
shown in (3.5), where Qvalve is the flow rate, Cd is the discharge coefficient, Aor is the
valve orifice area and ρfluid is the oil density. Pchamebr and Pout stand for hydraulic
pressures in the chamber and on the other side of valves.
𝑄𝑣𝑎𝑙𝑣𝑒 = 𝑠𝑖𝑔𝑛(𝑃𝑜𝑢𝑡 − 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟)𝐶𝑑𝐴𝑜𝑟 ∙ √2 ∙ |𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 − 𝑃𝑜𝑢𝑡|
𝜌𝑓𝑙𝑢𝑖𝑑 (3.5)
Dynamic behavior of digital valves is modeled as a second order system with a 0 to
100% rise time of Tr and a percentage overshot of Δh, as shown in (3.6). Vsignal and Vmax
are the input and maximum signal amplitude. K and Kmax denotes the effective and
maximum orifice area, respectively.
𝐾(𝑠)
𝑉𝑠𝑖𝑔𝑛𝑎𝑙(𝑠)=𝐾𝑚𝑎𝑥𝑉𝑚𝑎𝑥
∙𝜔𝑛
2
𝑠2 + 2𝜉𝜔𝑛s + 𝜔𝑛2 (3.6)
where 𝐾𝑚𝑎𝑥 = 𝐶𝑑 ∙ 𝐴𝑜𝑟𝑖_𝑚𝑎𝑥, 𝜉 = √(𝑙𝑛Δℎ)2
𝜋2+(𝑙𝑛Δℎ)2 and 𝜔𝑛 =
𝜋+2∙asin𝜉
2𝑇𝑟√1−𝜉2.
Each check valve in Figure 2.3 consists four unit check valves, with parameters shown
in Table 3.1 and dynamics shown in (3.7) [64]. Valve orifice used in (3.5) is the total
orifice area.
𝑀𝑐𝑘
𝑑2𝑥𝑐𝑘𝑑𝑡2
+ 𝑘𝑐𝑘𝑑𝑥𝑐𝑘𝑑𝑡
+ 𝐹𝑓𝑙 + 𝐹𝑠𝑝𝑟 + ∆𝑃 ∙ 𝑆𝑐𝑘 = 0 (3.7)
where, Mck, kck, xck are the mass, damping coefficient and lift of the check valve disc,
respectively. Fspr is the spring force with preload. ∆𝑃 and Sck are the pressure difference
across the valve along flow direction and check disc cross sectional area. Flow force Ffl
can be calculated through (3.8), where Ack is the check orifice calculated from (3.9) and
βck is the output flow angle.
25
𝐹𝑓𝑙 = 2𝐶𝑑2𝐴𝑐𝑘∆𝑃 cos𝛽𝑐𝑘 (3.8)
𝐴𝑐𝑘 = 𝜋𝑥𝑐𝑘 sin 𝛽𝑐𝑘 (𝐷𝑐𝑘 − 𝑥𝑐𝑘 sin 𝛽𝑐𝑘 cos 𝛽𝑐𝑘) (3.9)
In the equation, Dck is the diameter of check valve disc.
3.1.3. Thermodynamics
During the scavenging process, the in-cylinder gases temperature T and pressure P are
kept as a constant T0 = 450 K and P0 = 1.5 bar, respectively.
After the exhaust/intake ports are closed, the thermodynamics of the in-cylinder gases
is governed by the first law of thermodynamics for a closed system and the ideal gas law,
as shown in (3.10) through (3.12).
�̇� = �̇� − �̇� (3.10)
�̇� =
𝛾 − 1
𝑉(�̇� −
𝛾
𝛾 − 1𝑃�̇�) (3.11)
𝑃𝑉 = 𝑚𝑅𝑇 (3.12)
where U stands for the internal energy, Q stands for the heat transfer, and W is the
expansion work. γ is the specific heat rate, m is the mass of the in-cylinder gases,
respectively. R stands for the gas constant of air. On top of that, the combustion cylinder
volume V is determined by the piston dynamics, while the pressure P affects the in-
cylinder gases force acting on the pistons.
The heat transfer between gas mixture and engine wall is defined as:
�̇� = ℎ ∙ 𝐴𝑤𝑎𝑙𝑙(𝑇 − 𝑇𝑤𝑎𝑙𝑙) (3.13)
where Awall is the variable engine wall surface area, Twall is the wall temperature, and h is
the heat transfer coefficient, which is derived from a modified Woschni correlation [65].
3.1.4. Combustion
Due to the flexibility of the FPE, HCCI combustion is considered here. Unlike
conventional combustion, the ignition of the HCCI combustion is determined by the
chemical kinetics inside the combustion cylinder. In order to predict the start of
combustion (SOC) in each stoke, an Arrhenius integral is employed[66]:
26
∫ 𝐴 ∙ 𝑃𝑛 ∙ 𝑒𝑥𝑝(−𝐸𝑎𝑅𝑇)
𝑡𝑠𝑜𝑐
𝑡𝑖𝑝𝑐
= 1 (3.14)
In this Arrhenius integral, A is the pre-exponential factor, P and T are the pressure and
temperature of the in-cylinder gases respectively, Ea is the activation energy and R is the
gas constant. The integration should start when the intake port closes tipc and end when
the value of the integral becomes to 1, which represents the SOC timing tsoc.
Afterwards, the combustion duration t as well as the temperature rise T due to the
combustion occurrence are shown in (3.15) to (3.17)[66].
𝑇𝑚 = 𝑇𝑠𝑜𝑐 + 𝑒 ∙ Δ𝑇 (3.15)
Δ𝑇 =
𝑄𝐿𝐻𝑉 ∙ 𝑚𝑓𝑢𝑒𝑙
𝐶𝑣 ∙ (𝑚𝑔𝑎𝑠 +𝑚𝑓𝑢𝑒𝑙) (3.16)
∆𝑡 = 𝑘 ∙ (𝑇𝑠𝑜𝑐)−23(𝑇𝑚)
13 𝑒𝑥𝑝(
𝐸𝑐3𝑅𝑢𝑇𝑚
) (3.17)
where Tm is the mean temperature during the combustion process, Tsoc is the
instantaneous temperature at the SOC timing, e is the burn duration averaging parameter,
QLHV is the lower heating value of the fuel, mfuel is the mass of the fuel, Cv is the constant
volume heat capacity of the in-cylinder gases, mgas is the mass of the intake charge, k is
the burn duration parameter, Ec is the activation energy for combustion reaction and Ru is
the universal gas constant.
3.2. Controller Design
The goal of the HFPE controller is to control the fuel injection amount and digital
valves switch timing so as to achieve stable operation of the HFPE and realize
independent pressure and flow rate control (IPFC). To achieve this goal, a two-layer
architecture consisting an inner loop and an outer loop is employed, as shown in Figure
3.3.
27
Figure 3.3. Block diagram of the IPFC with PI control
3.2.1. Inner Loop Control
The inner loop control includes a feed-forward controller and a feedback controller. As
can be seen, the input to the inner loop control is the measured load pressure the flow rate
demand and the FPE piston trajectory. The output of the inner loop control is the fuel
injection amount and digital valve command signal to the HFPE.
The feed-forward controller is a look-up table, which provides the optimal valve
switch timing xswitch, fuel injection amount mfuel and the operational compression ratio
(CR) of the HFPE at any given load condition, in terms of load pressure and flow rate
demand. It should be noted here that the operational CR is a unique control parameter
enabled by the HFPE only. This additional control means enables the HFPE to operate in
a more efficient and cleaner way compared to the conventional ICE-driven pump. More
detailed discussion related to this point will be presented later in this chapter.
Specifically, the feed-forward controller is obtained as follows. Given any specific
load condition, an operational CR within the range of 12 to 30, is selected first. The range
of CR is determined by considering the structural and material limitations of the engine
wall as well as the feasibility of HCCI combustion. The other two control parameters,
xswitch and mfuel can then be calibrated using the HFPE model developed in Section III. As
a result, a control parameter set U1 for this specific load condition is obtained:
𝑈1 = {𝑥𝑠𝑤𝑖𝑡𝑐ℎ, 𝑚𝑓𝑢𝑒𝑙, 𝐶𝑅} (3.18)
28
By sweeping through different CRs and repeating the calibration process above, other
control parameter sets U can be achieved. Afterward, the optimal set Uopt can be
determined by comparing the total efficiency ηoverall of the HFPE operation under all
possible sets, which is defined in equation (3.19).
𝜂𝑜𝑣𝑒𝑟𝑎𝑙𝑙 = (
𝑉𝑜𝑢𝑡𝑝𝑢𝑡 ∙ 𝑃𝑙𝑜𝑎𝑑
𝑄𝐿𝐻𝑉 ∙ 𝑚𝑓𝑢𝑒𝑙) (3.19)
where Voutput stands for the output flow within a stroke, and Pload is the load pressure.
Such an optimal control parameter set Uopt is then recorded for this specific load
condition. By repeating this procedure for a certain number of other load conditions, a
look-up table of optimal parameter sets can be established. For any other load conditions
not defined in the table/controller, its corresponding optimal control parameter set can be
acquired through interpolation from this table.
Based on the switch point from this table and the FPE piston trajectory, the digital
valve command signal can be generated. Notice that if the digital valve connects the
pumping chamber to HP right after the TDC, there could be a negative flow from HP to
the chamber, as the chamber pressure is lower than that of the HP at this point. To
eliminate this negative flow, the valve is hold at neutral for a while after the TDC to
allow the in-chamber fluid to be compressed by the piston and build up pressure.
Due to the uncertainty in model, interpolation error and possible disturbances, the
feedforward controller alone cannot guarantee stable running of the HFPE and a feedback
controller is needed. The main idea of the IPFC feedback controller is to compare the
actual operational CR, calculated from the piston trajectory, to the target operational CR
and adjust the fuel injection amount accordingly. In this way, the target CR can be
tracked, enabling the HFPE to work robustly with disturbances and load condition
transients.
The feedback controller includes two parts. The first is a PI controller, which removes
any difference between the target CR and the actual operational CR. The second part is a
transient compensator, which is aimed to reduce the transient behavior of the HFPE
facing a large load variation. Although the feedforward controller provides the CR
reference, fuel amount and valve command, it is only for steady states. During large
29
transient between load conditions, especially when the CR changes, a compensation term
in fuel amount will be needed. The reason is explained as follows.
At the two ends of each stroke, there is some energy stored in the compressed in-
cylinder gas. Apparently, this energy is determined by the compression ratio. For steady
state cases, the CRs are the same at the beginning and the end, so the net expansion work
will provide just enough energy to push the pistons and provide demanded output flow.
In such cases, we can consider that the energy of compressed air transfers from one
chamber to the other and the combustion provides energy only for the pumping process.
However, when the load condition changes, the compression ratio could also change,
causing the initial compressed air energy to be different than the final energy, with the
difference shown in equation (19). For simplicity, adiabatic process is assumed in such
energy calculation. In the equation, P0 stands for the intake pressure. Ecomp stands for the
difference in compression energy, i.e. the additional energy needed to compress in-
cynlinder gas to the new reference CR. CRnow and CRpre is the current and previous CR
reference, respectively. Description of other symbols can be found in Table I. Apparently,
when CRnow>CRpre, Ecomp>0, meaning that the combustion needs to provide extra energy
to compress the in-cylinder gas during this transient stroke.
𝐸𝑐𝑜𝑚𝑝 = −𝑃0 ∙ (𝐴𝑔 ∙ 𝑥𝑖𝑛)
𝛾
1 − 𝛾∙ [(
𝐴𝑔𝑋𝑖𝑛
𝐶𝑅𝑛𝑜𝑤)1−𝛾
−(𝐴𝑔𝑋𝑖𝑛
𝐶𝑅𝑝𝑟𝑒)
1−𝛾
] (3.20)
Moreover, when the CR changes, the stroke length will also vary, causing a change in
oil output as well as energy demand during this stroke. The energy demand change can be
calculated using (3.21), where Efluid is the difference between the pumping energy needed.
Note that for simplicity, the mechanical efficiency here is assumed to be 1 so the
difference in hydraulic energy output is equal to the difference in combustion energy
needed. Also, when the CRnew>CRpre, the stroke length in the transient stroke will be
shorter than that of a steady state stroke, so Efulid will be negative.
𝐸𝑓𝑙𝑢𝑖𝑑 = 𝑃𝐻𝑃 ∙ (𝑥𝑖𝑛
𝐶𝑅𝑛𝑜𝑤−
𝑥𝑖𝑛𝐶𝑅𝑝𝑟𝑒
) ∙ 𝐴ℎ (3.21)
To ensure that the desired compression ratio is achieved during the transient stroke,
the aforementioned energy differences have to be compensated by changing the fuel
30
injection amount for this stroke. The calculation of fuel amount change can be expressed
as equation (3.22).
𝑚𝑓𝑢𝑒𝑙_𝑎𝑑𝑗 =𝐸𝑖𝑛𝑡 + 𝐸𝑓𝑙𝑢𝑖𝑑
𝜂𝑡ℎ𝑒𝑟𝑚𝑎𝑙 ∙ 𝑄𝐿𝐻𝑉 (3.22)
In the equation, mfuel_adj represents the fuel adjustment amount. ηthermal is the thermal
efficiency, which is approximated as a constant number.
The transient compensator in the inner loop is added to detect the change in CR
reference and perform corresponding compensations. It should be noted that in the IPFC
of the HFPE, the transient compensator only functions for the subsequent fuel injection
event, when the variation of the target CR is large enough (
|∆CR| > 2).
3.2.2. Outer Loop Control
The inner loop control ensures the stable operation of the FPE and provide an output
flow rate at the given load pressure based on the feedforward information. However, due
to interpolation error and possible disturbances, the actual flow rate can be different than
the demand value. Therefore, an PI controller is employed in the outer loop to make up
for the flow rate error. The input of the outer loop controller is the flowrate indicator
error. This can be either a direct flow rate measured at the actuator side, or an indirect
indicator like the linear or rotational speed of the actuator. Note that the outer loop
controller should be integrated into the hydraulic circuit controller in actual applications
with better control designed for specific applications.
3.3. Simulation Results
The performance of the HPFE with the IPFC and cycle-to-cycle control is evaluated in
this section. Both steady state performance and transient performance are presented,
which demonstrates the effectiveness of the IPFC. Furthermore, a detailed analysis on the
efficiencies of the HFPE with the IPFC under various working conditions is documented.
Such an efficiency analysis includes the thermal efficiency from the engine side and the
mechanical efficiency from the pump side. Both efficiencies as well as the overall
31
efficiency are benchmarked with similar applications to further demonstrate the HFPE’s
advantages at a system level.
3.3.1. Steady State Operation
Steady state simulations are first conducted at different load conditions, in terms of
various load pressure and flow rate demand. Simulation results show that under the IPFC
controller, the FPE can work in a stable fashion and provide demanded flow rate. As
shown in Figure 3.4, the steady state performance of the HFPE with the IPFC is quite
accurate and the relatively error of the produced output flow rate is less than 2% at the
load pressure ranging from 5 MPa to 35 MPa.
Figure 3.4. Steady state performances of the HFPE with the IPFC at various load
conditions.
Figure 3.5 shows the comparison of piston trajectories, instantaneous flow rates, and
digital valves opening between two cases, which have the same load pressure of 15 MPa,
but different output flow rate of 2×10-4 m3/s and 5×10-4 m3/s, respectively. Note that for
32
the valve control signal, positive value means connecting the chamber to HP. It can be
seen that for each load condition, by varying the digital valves opening/closing duration,
different portion of the in chamber oil goes to the load side and different stroke average
flow rate can be achieved. In addition, the TDCs points in these two cases are slightly
misaligned since the HFPE is actually running at different optimal CRs for different load
conditions.
Figure 3.5. Steady state performance at fixed pressure but various output flow rate,
from top to bottom: piston position, instantaneous flow, digital valves opening
33
Figure 3.6. Steady state performance at fixed output flow rate but various pressure,
from top to bottom: piston position, instantaneous flow, digital valves opening
Figure 3.6 shows another set of comparison, where the flow rate demands are the
same (5×10-4 m3/s) but the load pressures are different (15MPa and 35MPa, respectively).
Clearly, the valve control signals and trajectories are different for the two cases.
3.3.2. Transient Performance
Due to its compact structure and substantially less inertia, the HFPE with the IPFC
enables significantly shorter response for any load transition by adjusting both the digital
valve opening strategy and the fuel injection amount in each stroke. Such a fast transient
performance is a key feature of the proposed system in minimizing the difference
between the desired output flow and the produced output flow at any given load pressure
and reducing the throttling losses.
To verify the fast response of the HFPE with the IPFC, a simulation is conducted to
evaluate the HFPE performance at a fixed load pressure of 35 MPa, and a step flow rate
34
demand from 2×10-4 m3/s to 7×10-4 m3/s, as shown in Figure 3.7, where the dashed line
shows the instant when the step variation of the flow rate demand applies. Clearly, the
transient takes only one stroke to cover most of the flow demand variation with the
assistance of the transient compensator. Then, the PI controllers in both the inner and
outer loop work together to bring the produced output flow rate to the desired level
within 100ms.
Figure 3.7. FPE performance under step flow demand
It is widely known that in hydraulic mobile applications, the load pressure change is
usually coupled with the flow rate change. To address this issue and further evaluate the
performance of the HPFE with the IPFC as a fluid power source for mobile applications,
another set of simulation is conducted to evaluate the system’s performance on an actual
loader duty cycle. The corresponding simulation results are shown in Figure 3.8. It can
be seen that even with continuously changing load pressure and flow rate demand, the
system can still track the flow rate demand properly. Further analysis shows that the
output flow rate error is within -5.74 510− m3/s and 6.81 510− m3/s of the desired output
35
flow rate. The CR reference can also be tracked properly, meaning that the HFPE is
always running in a stable fashion during the entire duty cycle.
Figure 3.8. Duty cycle section test, from top to bottom: flow rate tracking, CR tracking,
load pressure.
3.4. Efficiency Analysis and Optimal Working Point
The efficiency analyses of the proposed system are conducted in this section. To
facilitate the analyses, the overall efficiency in (3.19) is expanded to the product of
thermal efficiency and mechanical efficiency, as shown in (3.23).
𝜂𝑜𝑣𝑒𝑟𝑎𝑙𝑙 = 𝜂𝑡ℎ𝑒𝑟𝑚𝑎𝑙 ∙ 𝜂𝑚𝑒𝑐ℎ. =𝑊𝑔𝑎𝑠
𝑄𝐿𝐻𝑉 ∙ 𝑚𝑓𝑢𝑒𝑙∙𝑉ℎ𝑦𝑑 ∙ 𝑃𝑙𝑜𝑎𝑑
𝑊𝑔𝑎𝑠 (3.23)
where Wgas is the expansion work of the in-cylinder gas within a stroke and Vhyd stands
for the volume of the produced high pressure hydraulic oil.
It should be noted that unlike conventional ICE-driven hydraulic pump, the HFPE has
an additional control means, i.e. variable CR, to optimize the system efficiency. As
mentioned before, variable CR provides a degree of freedom at choosing the control
36
parameter sets. Therefore, choosing the optimal parameter sets is essentially choosing
optimal CR for each load condition. As CR affects both the thermal efficiency and the
mechanical efficiency, they will be discussed separately before the optimal CR as well as
overall efficiency can be found.
3.4.1. Thermal Efficiency
As shown in (3.23), thermal efficiency represents the ratio of the in-cylinder gas
expansion work over the total chemical energy of the injected fuel. The corresponding
losses mainly come from two aspects. One is the exhaust loss, which is stored in high-
temperature exhaust gas. The other one is the heat transfer loss, which dissipates the
combustion heat to the engine wall and the surrounding environment.
According to [65], the exhaust loss is directly related to the operational CR of the
engine. Usually, a higher CR indicates longer expansion stroke and therefore more
chemical energy is converted to the useful expansion work and less exhaust loss is
generated in turn.
In addition, the heat transfer loss is related to the temperature difference between the
chamber wall and the in-cylinder gas, the velocity of the piston, the surface area of the
combustion chamber and the duration of the stroke, as indicated by (3.13). By increasing
the CR, the in-cylinder temperature before the combustion event will increase. However,
higher CR reduce the temperature profile after the combustion event, since less fuel is
needed due to higher combustion efficiency and less exhaust loss[65]. As the majority of
heat transfer loss is generated after the combustion event, higher CR can actually reduce
the heat transfer loss. In addition, since the operation frequency rises with the CR in the
HFPE, the stroke duration will be shorter at high CR, which further reduces the heat
transfer loss.
Figure 3.9 shows the derived thermal efficiency of the HFPE with respect to the
operational CR at a fixed load pressure of 15 MPa and various flow rate demand. Noted
that by changing the CR, the frequency and the total stroke length will vary, causing the
available maximal flow rates at each CR to be different as well. The flow rate can be
37
normalized into equivalent displacement fraction by the maximum flow possible, which
is full displacement under CR=30.
Figure 3.9. Thermal efficiency with respect to CR at load pressure 15 MPa
Obviously, the thermal efficiency of the HFPE increases with both the CR and flow
rate. In addition, the thermal efficiency is substantially higher (peak efficiency is close to
62% and efficiency at 20% equivalent displacement is higher than 46%) compared to the
conventional ICE, whose peak efficiency is only about 45%[65]. This higher thermal
efficiency comes from the FPE’s unique character of completely free piston motion.
Attributed to this ultimate freedom, the FPE can employ the advanced combustion mode,
i.e. HCCI combustion, and significantly reduce the heat loss by increasing the CR and
reduce the time duration while in-cylinder gas is at high-temperature conditions[34]–[36].
3.4.2. Mechanical Efficiency
The mechanical losses mainly come from two sources, the friction loss and the
throttling loss mainly caused by the switching of the digital valves.
38
Figure 3.10 shows the mechanical efficiency with respect to CR and flow rate at a
load pressure of 15MPa. Clearly, the mechanical efficiency is higher at lower CR and
increase rapidly with the flow rate. The mechanical efficiency of the HFPE at the 20%
equivalent displacement fraction condition is still over 55%. In addition, the mechanical
efficiency of the HFPE at maximum flow rate is over 95%.
Figure 3.10. Mechanical efficiency as well as throttling loss and friction loss with
respect to CR at load pressure 15 MPa
Throttling loss herein refers to energy loss when oil is pumped through orifices of the
digital valves in the HFPE. Throttling loss increases rapidly as the flow rate decreases,
mainly due to the higher piston speed near switch point and smaller power output.
Apparently, most throttling will happen when the digital valves are switching and the
orifice is small. The faster the piston moves around the switch point, the more hydraulic
oil is pumped through the reduced orifice and the more throttling loss occurs. Also,
higher CR increases the overall piston velocity, causing the throttling loss to rise.
It is also obvious from Figure 3.10 that the friction losses are relatively small
compared to the throttling loss. This advantage is attributed to the unique design of the
39
HFPE. Compared to the conventional ICE-driven hydraulic pump, the HFPE possess
much less components, which significantly reduces the friction. On top of that, the main
friction loss comes from the piston motion. However, since the piston is moving linearly,
the side force around the piston is much smaller compared to its counterpart in the
conventional engine and therefore further mitigate the friction losses.
3.4.3. Overall Efficiency and Optimal CR Selection
The overall efficiency is the product of the thermal efficiency and the mechanical
efficiency. As shown in the previous subsection, the CR value has opposite effects on the
thermal and mechanical efficiency. Therefore, it is necessary to balance the tradeoff and
find an optimal CR with the highest overall efficiency.
Figure 3.11 shows the optimal efficiency and CR for load pressure 15MPa. Obviously,
at lower flow rate, the HFPE prefers to operate at lower CR. This is because the reduction
of the mechanical efficiency caused by high CR is too aggressive at low flow rate and
thus the IPFC has to sacrifice some thermal efficiency by reducing the CR to improve the
mechanical efficiency and therefore the overall efficiency. On the other hand, when the
flow rate is high, since the thermal efficiency can be improved significantly at higher CR
[65] and the mechanical efficiency curves are flatter, the IPFC increases CR to achieve
optimal overall efficiency.
40
Figure 3.11. Upper: optimal efficiency. Bottom: CR for load pressure 15MPa
41
Figure 3.12. Optimal overall efficiency of the HFPE with the IPFC at different load
conditions
With the optimal CR determined, the optimal overall efficiency for each load
condition can be calculated. The result is shown in Figure 3.12. For each pressure, the
overall efficiency is higher with high flow rates. The overall efficiency lies between 28%
and 58% for the HFPE with IPFC. Note that due to the fast response of the system, the
actuator demand can be met in real time so the throttling loss downstream will be
significantly reduced. In practice, the hydraulic mobile applications powered by
conventional ICE-driven hydraulic pump generally has the overall efficiency of 10-
12%[67]. Compared to this value, the HFEP with the IPFC possesses great potential to
significantly enhance the overall efficiency at a system level.
3.5. Chapter Conclusion
This chapter documented the modeling of an OPOC HFPE. Performance of the HFPE
with the IPFC is evaluated through extensive simulations using this model. The results
42
show that the IPFC not only stabilizes the system operation, but also enables the HFPE to
realize millisecond-scale response time to any load variations. By matching the produced
fluid power with the desired load in real-time, the proposed system can significantly
reduce throttling losses and thus enhancing system efficiency. In addition, the freedom of
the piston motion in the HFPE offers another control means, i.e. variable CR, to raise the
thermal efficiency from the engine side. Combining the two improvements, the overall
efficiency of the HFPE with IPFC is significantly higher than the conventional ICE
driven pump system.
43
Chapter 4.
Testbed Characterization and Switch based IPFC
The first attempt to implement IPFC on the hardware is to use the most straight-
forward switch-based method, which is similar to that shown in Chapter 3. Although this
method lacks robustness and requires tedious calibration process, it provides direct
insight into IPFC’s feasibility on the hardware and lays a baseline for further
investigations. Yet prior to the implementation, the hardware system has to be upgraded
and characterized, while the simulation model has to be calibrated accordingly such as to
guide testing. In this chapter, the testbed hardware and its characterization are first
presented. After that, the basic idea and control design of switch based IPFC is put
forward and the parameter calibration method is presented. Then, system performance is
analyzed to unveil the baseline performance of IPFC. Finally, the lack of robustness of
the switch based IPFC is discussed.
4.1. HFPE Testbed Characterization
4.1.1. Testing System Overview
The test bed used in this study is built around a protype OPOC HFPE donated by Ford
motor company. The HFPE has a rated power of 55kw and maximum operation pressure
of 41.4MPa. Figure 4.1 below shows the schematics of the testing system. A hydraulic
stand is connected to the HFPE to provide high pressure and low pressure through two
bladder type accumulators. A compressed air driven hydraulic pump pre-charges both
accumulators prior to testing to provide appropriate back pressures as well as piston
motoring energy. To help with the scavenging process, an AC motor driven twin-screw
supercharger system is connected to the intake manifold of the HFPE. More details of the
supercharger system can be found in Appendix A. The measurement and control system
consists of a dSPACE real-time controller, a PC, AD/DA converters, as well as signal
conditioners/drivers. Measurement signals from the testbed are conditioned and
transmitted to dSPACE through A/D converters, while control signals are sent to the test
bed through D/A converters and drivers. A PC is connected to the dSPACE as a user
interface for programming and controls.
44
Figure 4.1. Schematics of the testing system1
A photo of the test bed is shown in Figure 4.2. Important measurements and control
signals are summarized in Table 4.1 below. Index in the table corresponds to the
sensor/actuator locations marked in Figure 4.2.
Variable
Symbol Index Description Unit
Pinner 1 Outer hydraulic chamber pressure Pa
Pouter 2 Inner hydraulic chamber pressure Pa
Pcouple 3 Coupling hydraulic chamber pressure Pa
Paccu 4 High pressure accumulator pressure Pa
Phigh 5 High pressure rail pressure Pa
Plow 6 Low pressure rail pressure Pa
Psc 7 Supercharger output air pressure Pa
Pport 8 Left intake port air pressure Pa
Pexhaust 9 Exhaust air pressure Pa
Pleft 10 Left combustion chamber pressure Pa
Pright 11 Right combustion chamber pressure Pa
Tintake 12 Intake manifold air temperature ˚C
TExhaust 13 Exhaust manifold air temperature ˚C
Qair 14 Intake air mass flow kg/s
Qfw 15 Hydraulic flow meter – forward channel m3/s
Qbw 16 Hydraulic flow meter – backward channel m3/s
1 “dSPACE” is a trademark of dSPACE GmbH. Logo of dSPACE adopted from https://www.dspace.com.
Photo of signal conditioners adopted from https://www.omega.com
45
xinner 17 Inner piston position m
xouter 18 Outer piston position m
λ 19 Exhaust oxygen level %
uservo I Servo valve control signal V
usync-high II High pressure sync. valve signal on/off
usync-low III Low pressure sync. valve signal on/off
Spk IV Spark signal on/off
Inj V Fuel injection signal on/off
Table 4.1. Sensors and actuators in the HFPE testbed
Figure 4.2. Photo of the test bed
46
4.1.2. HPFE Characterization
The HFPE hardware has to be characterized so as to help understanding its key
dynamics. Meanwhile, although the ideal model established in Chapter 3 captured most
important dynamics of a typical HFPE, it doesn’t accurately reflect all dynamics of the
testing apparatus. To better support testing, the model has to be updated, where
previously unmodeled elements will be added and model parameters will be recalibrated
according to the HFPE characterization. Specifically, in this section, the modeling of
friction/scavenging force, the measurement of dead volumes and oil bulk modulus, as
well as the characterization of servo valve dynamics are be presented. Other parameters
of the modified HFPE are also summarized in a table.
4.1.2.1. Scavenging force and Friction Force
The scavenging pumps are neglected in the ideal model. In the actual test bed, there
are two scavenging pumps located at the two ends of the HFPE, as shown in Figure 4.2.
Figure 4.3 shows the detailed scavenging pump structure for one side of the HFPE.
Chambers 1 and 2 mark the two scavenging pump chambers while chamber 3 is the
combustion chamber. Note that the outer combustion piston and the scavenging pump
piston are rigidly connected into one piece. Chamber 1 includes the cavity of the
combustion/scavenging piston, and chamber 2 is connected to the annular gas chamber
around the intake ports. During compression stroke of the combustion chamber, chamber
1 expands, sucking air into it from the intake manifold on the top through reed valves.
Then, during the combustion chamber’s expansion stroke, air is pumped from chamber 1
to chamber 2 through another set of reed valves on the bottom. Near the end of the
expansion stroke, intake ports are uncovered by the combustion piston, and fresh air
flows from chamber 2 into combustion chamber through them. Clearly, force generated
from pressurized air in scavenging chambers 1 and 2 will directly act on the pistons and
affect their motion. Modeling of the scavenging chamber pressure dynamics requires a
detailed model of the reed valves as well as dead volume measurement of scavenging
chambers, which is not only complex and tedious by itself, but also not the focus of this
study. Meanwhile, the scavenging force cannot be directly measured due to hardware
47
limitations, meaning that even if a reed valve and scavenging chamber air dynamics are
established, they cannot be properly calibrated. Similarly, the friction force cannot be
directly measured, and the model cannot be calibrated for it.
Figure 4.3. Scavenging pump and combustion chamber cut-out view
To model scavenging force and friction indirectly, a data driven model is proposed. As
shown in (4.1), the sum of friction and scavenging force can be inferred from piston
motion through the Newton second law. In the equation, Fsca is the scavenging force.
Theoretically, the scavenging force mostly depends on the piston position, while the
friction force depends on factors including piston velocity, hydraulic chamber pressures
and possible side forces. In this study, a 1-D lookup table with piston position as index is
used to describe scavenging and friction force. Considering friction’s dependence on
velocity and different air condition in scavenging pumps for different strokes, tables are
established for expansion and compression strokes separately. Data in the tables are
acquired from preliminary tests using (4.1).
48
𝐹𝑓/𝑠𝑐𝑎 = 𝐹𝑓 + 𝐹𝑠𝑐𝑎 = 𝐹𝑔𝑎𝑠 − 𝐹ℎ𝑦𝑑 −𝑀�̈� (4.1)
4.1.2.2. Dead volume of pumping chambers and oil bulk modulus measurement
Dead volume of the pumping chambers is not readily available in this case and has to
be measured. Since the geometry of the hydraulic channels cannot be directly measured,
the method used here is to fill the dead volume with oil and measure the oil volume.
Measured dead volume data is shown in Table 4.2.
Parameter Description Measure. 1 Measure. 2 Measure. 3 Mean Value
Vd_inner Inner Chamber
Dead Volume 22.6ml 23.6ml 21ml 22.4ml
Vd_outer Outer Chamber
Dead Volume 26ml 27.5ml 26.5ml 26.6ml
Table 4.2. Dead volume measurement data
Although the ideal hydraulic oil bulk modulus is given by the data sheet for the oil
used in the testing, in reality, oil bulk modulus can be affected by entrained air and oil
contaminations, and deviate from the ideal value. Therefore, it is necessary to calibrated
it on the HFPE. Assuming the response time of check valves is fast enough, the oil bulk
modulus can be calibrated using the following method. First, start the HFPE and go into
normal operation with combustions using the method proposed in [40]. Once combustion
starts, send zero servo valve signal. Once the servo valve parks at neutral, flow can only
be pumped out through check valves. At the BDCs and TDCs when piston change motion
direction, the discharge chamber and intake chamber will switch, causing pre-
compression and decompression in hydraulic chambers. Since the check valves are
assumed to be fast enough and the servo valve is closed, all pressure changes during pre-
compression and decompression must be caused by piston motions, as indicated in (4.2).
In (4.2), Vchamber is the hydraulic chamber volume, which is determined by the dead
volume, piston position and hydraulic cylinder geometry. Plugging in expressions of
Qpiston and Vchamber and integrating (4.2) yield (4.3) below. In the equation, Ah is the
hydraulic piston area, x1 and x2 are the piston positions at the beginning and end of the
pre-compression or decompression, respectively, while Vd_inner and Vd_outer are the dead
volumes for inner and outer chambers, respectively. Pchamber is the hydraulic pressure for
either the inner or outer chamber. Lc stands for the hydraulic cylinder length. Plugging in
49
the pre-compression/decompression testing data, oil bulk modulus can be solved to be
1.2GPa.
�̇�𝑐ℎ𝑎𝑚𝑏𝑒𝑟 =𝛽
𝑉𝑐ℎ𝑎𝑚𝑏𝑒𝑟𝑄𝑝𝑖𝑠𝑡𝑜𝑛 (4.2)
∆𝑃𝑐ℎ𝑎𝑚𝑒𝑏𝑟 =
{
𝛽 ln
𝐴ℎ𝑥1 + 𝑉𝑑_𝑖𝑛𝑛𝑒𝑟𝐴ℎ𝑥2 + 𝑉𝑑_𝑖𝑛𝑛𝑒𝑟
𝐼𝑛𝑛𝑒𝑟 𝑐ℎ𝑎𝑚𝑏𝑒𝑟
𝛽 ln𝐴ℎ(𝐿𝑐 − 𝑥1) + 𝑉𝑑_𝑜𝑢𝑡𝑒𝑟𝐴ℎ(𝐿𝑐 − 𝑥2) + 𝑉𝑑_𝑜𝑢𝑡𝑒𝑟
𝑂𝑢𝑡𝑒𝑟 𝑐ℎ𝑎𝑚𝑏𝑒𝑟
(4.3)
4.1.2.3. Servo Valve Dynamics
Servo valve dynamics describes the dynamics between the servo valve orifice and the
servo valve command, and is a key element of the HFPE dynamics. The valve used in the
HPFE is a two-stage servo valve from Moog. Previous researches have indicated that
although a servo valve is a nonlinear system, the dynamics from voltage input to valve
orifice size can be approximated using a linear system with acceptable accuracy[68].
Therefore, a system identification is conducted to fit the servo valve dynamics with a
linear transfer function.
Figure 4.4. System block diagram for servo valve system ID
The system diagram used in servo valve dynamics ID is shown in Figure 4.4. Since
the HPFE is a boundary stable system, a proportional control is implemented to stabilize
it. Sinusoid signals with different frequencies are sent as the reference (ref) and
50
corresponding piston motions are recorded as system response (x). At the same time,
servo valve command signal (u), pressures at both the high pressure and low pressure
ports of the servo valve (Plow and Phigh), as well as the outer and inner hydraulic chamber
pressures (Pouter and Pinner) are recorded. Using recorded data, flow rate from each
hydraulic chamber can be calculated from piston motion, chamber dead volume and
chamber pressure measurements, as shown in (4.4) and (4.5). In the equations, Qouter and
Qinner are flow rates into the outer and inner chamber, respectively, while Pouter and Pinner
are the chamber pressures.
𝑄𝑜𝑢𝑡𝑒𝑟 = −𝐴ℎ ∙ �̇� +
(𝑉𝑑_𝑜𝑢𝑡𝑒𝑟 + 𝐴ℎ𝑦𝑑 ∙ (𝐿𝑐 − 𝑥))�̇�𝑜𝑢𝑡𝑒𝑟
𝛽 (4.4)
𝑄𝑖𝑛𝑛𝑒𝑟 = 𝐴ℎ ∙ �̇� +
(𝑉𝑑_𝑖𝑛𝑛𝑒𝑟 + 𝐴ℎ𝑦𝑑 ∙ 𝑥)�̇�𝑖𝑛𝑛𝑒𝑟
𝛽 (4.5)
Furthermore, according to the orifice equation, the orifice size can be calculated using
flow rate, discharge coefficient, and hydraulic pressures. Since the chamber pressures are
always between Plow and Phigh, the flow direction can only be either from the chambers to
low pressure or from high pressure to the chamber. Meanwhile, the check valves are
always closed due to the chamber pressures, therefore all flow has to go the servo valve,
i.e. the servo valve flow equals to the chamber flow. As a result, the orifice can be
expressed as follows:
𝐴𝑜𝑟 =
{
𝑄𝑐ℎ𝑎𝑚𝑏𝑒𝑟
𝐶𝑑√2(𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟 − 𝑃𝑙𝑜𝑤)/𝜌𝑄𝑐ℎ𝑎𝑚𝑒𝑟 ≤ 0
𝑄𝑐ℎ𝑎𝑚𝑏𝑒𝑟
𝐶𝑑√2(𝑃ℎ𝑖𝑔ℎ − 𝑃𝑐ℎ𝑎𝑚𝑏𝑒𝑟)/𝜌𝑄𝑐ℎ𝑎𝑚𝑏𝑒𝑟 > 0
(4.6)
In the equation, Aor is the orifice size, with positive value defined as connecting
chamber to high pressure. Qchamber and Pchamber are the flow rate and pressure of either the
outer or inner hydraulic chamber. Cd is the orifice discharge coefficient, while ρ is the oil
density. The orifice can also be normalized into percentage of maximum opening for
more straight forward understanding, as shown in (4.7). Value of 𝐴𝑜𝑟_𝑚𝑎𝑥, Cd and ρ can
be found later in the section in Table 4.3. Plugging data measured from system ID into
equation (4.4) through (4.7) yields the valve orifice estimation shown in Figure 4.5.
51
𝐴𝑜𝑟_𝑛 =
𝐴𝑜𝑟𝐴𝑜𝑟_𝑚𝑎𝑥
(4.7)
Figure 4.5. Servo valve orifice estimation from system ID data
Sending the command signal u and estimated normalized orifice Aor_n to Matlab
system ID toolbox, and a transfer function can be acquired to represents the servo valve
dynamics. Equation (4.8) below shows the resulting transfer function. Figure 4.6 and
Figure 4.7 illustrate the Bode plot of the estimated servo valve dynamics, and the
comparison between the estimated servo valve orifice and linear servo valve model
response, respectively. Clearly, the linear model can represent the servo valve dynamics
with decent accuracy.
𝑇𝐹𝑠𝑒𝑟𝑣𝑜 =
−90.96𝑠 + 7.82 × 104
𝑠2 + 732.4𝑠 + 5.83 × 104 (4.8)
52
Figure 4.6. Servo valve dynamics bode plot
Figure 4.7. Valve model response vs. estimated orifice
53
4.1.2.4. Calibrated HFPE parameters
Key parameters calibrated for the HFPE testbed and corresponding model is
summarized below in Table 4.3.
Parameter Description Value
Aor_max Maximum servo valve orifice 1.81×10-5m2
Cd Servo valve discharge coefficient 0.7
ρ Hydraulic oil density 860kg/m3
β Hydraulic oil bulk modulus 1.2GPa
Ah Hydraulic piston area 1.51×10-4m2
Ag Combustion chamber area 4.96×10-3m2
Lc Length of hydraulic cylinder 64mm
xin Intake port location 51mm
xout Exhaust port location 50mm
Min Inner piston pair mass 4.50kg
Mout Outer piston pair mass 4.62kg
Table 4.3. Calibrated HPFE parameters
4.2. Working Cycle and Control Design
The switch based method changes the valve connection at certain switch timing to
sustain continuous HFPE operation under IPFC. Here switch timing is defined using
piston position. Once the piston passes a pre-calibrated position, i.e. the switch point, the
valve command signal will change. Since this step-shape switching signal provides the
fastest valve switching, this method will minimize the amount of fluid squeezed through
small servo valve orifice during valve transient and thus minimizing throttling loss.
In this study, combustions are only enabled in the left combustion chamber, while the
compression and expansion of the right chamber facilitating conversion between piston
kinetic energy and compressed air potential energy, so as to enable reciprocating piston
motion. In this way, the OPOC HFPE essentially works as an OP HFPE with a bounce
chamber. Correspondingly, the IPFC implemented here consists of a full stroke of output
from the outer hydraulic chamber during the expansion stroke right after each combustion,
followed by a compression stroke where the output flow from the inner hydraulic
chamber is digitally modulated to match the combustion energy.
The ideal working cycle of a switch based IPFC is illustrated in Figure 4.8. In the
figure, positive servo valve signal indicates connecting the inner chamber to low pressure
and outer chamber to high pressure. As shown in the figure, right after each BDC, for the
54
first half of the compression stroke, the servo valve stays at neutral and let the inner
chamber pump out oil to high pressure through check valves. Then, at the switch point,
servo valve command is sent to connect the outer chamber to high pressure and the inner
chamber to low pressure. For the rest of the stroke, oil will be drawn in from high
pressure into the outer chamber and the inner chamber will pump oil to low pressure. The
hydraulic force will be helping piston motion during this time. When the TDC is reached
and combustion happens, the pistons are pushed away from each other in the left chamber,
and the servo valve command moves the valve to neutral to let the outer chamber pump
out oil to high pressure through check valves throughout the expansion stroke. The switch
point here is calibrated so as to match the fuel injection amount and load pressure,
delivering a desirable compression ratio.
Figure 4.8. Ideal working cycle of switch based IPFC. From top to bottom: Piston
trajectory, Servo signal, Hydraulic pressure and net hydraulic force; Net flow output.
55
As shown in Figure 4.8, due to the system dynamics, there is a delay between the
switch signal and hydraulic force. Also, right after the TDC, the servo valve will still be
connecting the outer chamber to high pressure and inner chamber to low pressure. This is
not an issue during the expansion stroke, since the outer chamber will be pumping to high
pressure anyway. However, the servo valve has to be back to neutral before the BDC to
prevent throttling and flow loss during the compression stroke. It’s also worth mentioning
that if the servo valve isn’t at the neutral position at the switch point, the following valve
orifice profile will start at a non-zero position, which will affect the switch point
calibration.
To ensure the neutral valve position at BDC, an overcorrection signal can be sent to
pull back orifice right after TDC, as shown in Figure 4.8. Clearly, this overcorrection
depends on the switch timing, and should be calibrated accordingly. Overcorrection is
particularly needed when the switch point is early in the compression stroke and valve
orifice at TDC is large.
4.3. Testing Results
4.3.1. Working Condition and Switch Point Calibration
Experiments are conducted to evaluate the feasibility of switch based IPFC. The
switch point and over correction are calibrated using the following method:
1. Set the switch timing to 0, i.e. the valve stays at neutral all the time. In this way,
oil is always pumped to high pressure and displacement fraction is 100%. Due to
the imbalance of combustion force and hydraulic force, the bounce chamber is not
able to push pistons back to the preceding TDC, causing the TDC position to rise
and ultimately misfire will happen.
2. Gradually increase the switch timing, such that the TDC will be steady and
consecutive combustions can be sustained. Note that without overcorrection, the
valve is connecting the discharge chamber (the inner chamber) to low pressure at
switch point.
3. Use the servo valve model and piston motion after TDC to estimate the
overcorrection timing, such that the valve orifice can be pulled to neutral.
56
4. Implement the overcorrection timing from 3. with switch timing acquired in 2.
Now that the servo valve will be at neutral instead of connecting the discharge
chamber to low pressure at the switch point, the orifice opening profile will be
delayed compared to that in 2, causing the TDC to rise again and misfire to happen.
5. Repeat 2 through 4 until the TDC stops increasing and a stable operation is
achieved. The final switch timing and over correction timing are the valve timings
for the current operation condition.
It is worth noting that the switch point is calibrated using the measured piston position,
which shows a delay compared to actual piston position due to sensor dynamics.
The resulting switch point and other operation parameters are shown below in Table
4.4.
Parameter Value
Load pressure (MPa) 20.7
Tank Pressure (MPa) 2.1
Fuel Injection Amount (mg) 57.1
Switch timing (mm) 45
Overcorrection timing (mm) 32
Table 4.4. Operation parameters for switch based IPFC
4.3.2. IPFC Test Results
An overview of a typical set of switch based IPFC test result is given in Figure 4.9.
From top to bottom, there are piston position, servo signals, hydraulic chamber pressures,
and gas chamber pressures. The estimation of normalized servo valve orifice is also
shown alongside the servo valve command. Overall, as expected, consecutive
combustions can be achieved with a steady TDC position. Servo valve orifice estimation
shows that the servo valve connects the inner chamber to low pressure after the switch
point, as designed. After TDC, the orifice is pulled back rapidly with the overcorrection
signal, converges near zero before the following BDC, and stays there until the next
switch point. From the hydraulic pressures, we see that aside from some pressure
transient, the pumping chamber pressure is just above the load pressure (high pressure)
for the whole expansion stroke and the first part of the compression stroke, indicating that
57
oil is being pumped to the load through check valves. Meanwhile, the pressure changes
soon after the servo valve switch signal is sent, inverting the resisting hydraulic force into
helping piston motion at the end of the compression stroke. Gas chamber pressures show
that there are still variations in combustion timing and magnitude, but the controller is
able to keep the system running stably. The peak bounce chamber pressure is higher than
that of the combustion chamber since the kinetic energy has to be stored using an
aggressive compression around BDC. This will inevitably increase the gas pressure in the
bounce chamber and introduce loss due to heat transfer and leakage, which will be
discussed in the next section.
Figure 4.9. Switch based IPFC with overcorrection
4.4. Performance Analysis and Discussion
58
Performance is analyzed for the switch based IPFC and a performance baseline is
established in the section. Also, the lack of robustness of switch-based method is
demonstrated through testing with changed system parameter.
4.4.1. Output Flow Estimation
To evaluate the performance, the first step is to estimate the flow output. Ideally, a
flow rate meter should be able to directly measure the flow output from the HFPE.
However, as indicated in Figure 2.4 and Figure 4.8, the flow direction changes within
one cycle when the HFPE is operating under IPFC. The turbine based flow meter used in
the apparatus could be inaccurate when working with such fast changing flow. As a
workaround, in this section, the output flow rate is first estimated using the HFPE model.
Then, this estimated output flow is compared with the flow meter measurement to check
for consistency.
4.4.1.1. Valve model based flow estimation
As in indicated in (3.3), for each hydraulic chamber, flow can be divided into servo
valve flow(Qdigital or Qservo), check valve flow(Qcheck) and motion induced flow(Qpiston).
Qdigital in (3.3) is essentially the same as Qservo hereafter. Note that the sign convention
used here is to consider flow into the chamber as positive. With the hydraulic chamber
pressures measured and the servo valve orifice estimated using the valve model and valve
command, Qservo can be calculated using the orifice equation (3.5). Note that due to the
symmetric design of the servo valve, when one chamber is connected high pressure, the
other one has to be connected to low pressure. Qpiston can be calculated through the piston
velocity and area using (3.4). Theoretically, Qcheck can also be calculated using the check
valve model and orifice equation. However, when the check valves open, the pressure
difference across the valve is in the order of 100kPa, which is within the error band of
hydraulic pressure sensors, making the pressure difference measurement not reliable and
flow calculation not viable. On the other hand, if we define pressure induced flow Qpres
using (4.9), equation (3.3) can be rewritten into (4.10). Since Qpiston, Qservo and Qpres can
be calculated by (3.4), (3.5) and (4.9), respectively, Qcheck can be calculated indirectly
59
through (4.10). Note that although Qcheck here represents the sum of low pressure check
valve flow and high pressure check valve flow, they can be easily separated considering
the single direction flow feature of check valves.
𝑄𝑝𝑟𝑒𝑠 = −�̇�𝑐ℎ𝑎𝑚𝑏𝑒𝑟𝑉𝑐ℎ𝑎𝑚𝑏𝑒𝑟
𝛽 (4.9)
𝑄𝑐ℎ𝑒𝑐𝑘 = −(𝑄𝑝𝑖𝑠𝑡𝑜𝑛 + 𝑄𝑠𝑒𝑟𝑣𝑜 + 𝑄𝑝𝑟𝑒𝑠) (4.10)
Looking from the load side, the output flow Qoutput is the sum of additive inverses of
high pressure side servo valve flow (Qservo_high) and high-pressure check valve
flow(Qcheck_high) for both chambers, as shown in (4.11).
𝑄𝑜𝑢𝑡𝑝𝑢𝑡 = ∑ −(𝑄𝑐ℎ𝑒𝑐𝑘_ℎ𝑖𝑔ℎ + 𝑄𝑠𝑒𝑟𝑣𝑜_ℎ𝑖𝑔ℎ)
𝐵𝑜𝑡ℎ𝐶ℎ𝑎𝑚𝑏𝑒𝑟𝑠
(4.11)
Figure 4.10. Flow condition for switch based IPFC: (a) expansion stroke; (b)
compression stroke
Specifically, for the switch based IPFC, since the valve is either connecting the inner
chamber to low pressure or parked at neutral, depending on the stroke, the flow
distribution can be illustrated using Figure 4.10. In the figure, subscripts inner and outer
stand for inner and outer chamber, respectively. To avoid confusions, flow symbols stand
only for the magnitude of flow and flow directions are indicated by arrows. Figure 4.10
(a) and (b) represents the flow condition during expansion strokes and compression
strokes, respectively. Clearly, during the expansion stroke, flow out of the outer chamber
60
all goes to the load through either the high pressure check valve (Qcheck_outer), or the servo
valve (Qservo_outer). Net flow output is the sum of these two components. On the other
hand, during the expansion stroke, flow into the outer chamber could either come from
the low pressure through the low pressure check valves (Qcheck_outer), or come from the
load through the servo valve (Qservo_outer). Meanwhile, flow out of the inner chamber
either goes to the load through the high pressure check valve (Qcheck_inner), or to the low
pressure through the servo valve (Qservo_inner). The net output flow therefore is the
difference between Qcheck_inner and Qservo_outer.
Figure 4.11. Flow Estimation of switch based IPFC. From top to bottom: Piston
trajectory, Inner chamber flow, Outer chamber flow, Output flow, Servo valve command
and normalized estimated orifice
61
Applying the aforementioned flow analysis method to the testing result yields a
detailed flow break down shown in Figure 4.11. In the figure, chamber flows sign
conservation is the same as that in (4.10), where negative flow indicates flow out of the
chamber. Servo valve flow for each chamber is divided into Qservo_high and Qservo_low,
which stands for servo valve flow with load and tank, respectively. As expected, positive
output flow is generated during the expansion stroke as flow goes from the outer chamber
to load through check valves and the servo valve. Due to a practically zero servo valve
orifice at the BDC, good output flow during the first half of the compression stroke is
also achieved, as reflected by the virtually zero Qservo_high and negative Qcheck for the inner
chamber, as well as the positive Qoutput. After valve switch signal is sent, Qservo_high rises
for the outer chamber while Qcheck goes to zero gradually for the inner chamber, bringing
Qoutput to a negative value. Simultaneously, flow from the inner chamber starts to be
pumped to low pressure, as indicated by the negative Qservo_low. Since the positive portion
Figure 4.12. Cumulative flow for switch based IPFC. From top to bottom: Piston
trajectory, Cumulative flow, Servo valve command and normalized estimated orifice
62
of Qoutput is larger than the negative portion, the net output flow for the compression
stroke will still be positive. As for the pressure induced flow, it is only prominent around
BDCs and valve switch points, where pressure changes are rapid.
The cumulative flow rate for each stroke and cycle is shown in Figure 4.12.
Cumulative flow is 7.8ml for the expansion stroke and 3.2ml for the compression stroke.
The cycle flow output is 11.0ml, which corresponds to 71% displacement fraction.
4.4.1.2. Flow meter reading
As mentioned before, the output flow rate can be measured by a turbine based flow
meter in the system. Two hall effect sensors are installed 120˚ apart on the meter, whose
pules frequency can be used to determine flow rate and phase difference can show the
flow direction. Because of the inertia of turbine and the fact that the meter is calibrated
under steady state, this kind of sensor has difficulty measuring fast changing flow like the
one encountered here. Also, oil dynamics in the hose between HFPE and flow meter will
introduce extra difficulty in matching instantaneous flow. However, in spite of potential
large measurement error, the flow meter should still be able to capture the general trend
of the output flow to provide insights, and is therefore analyzed below.
Figure 4.13 shows the flow meter reading under switch based IPFC. Positive and
negative reading portions are marked with red and blue shades, respectively, for the first
two cycles. As can be observed from the figure, the flow meter data shows a positive-
negative cycle behavior as expected, and the flow profile generated from flow meter
measurements matches that from the model as well.
The flow rate calculated from flow meter reading is ~12.9ml/cycle, which is 17%
higher than what the model shows.
63
Figure 4.13. Flowmeter data for non-overcorrection switch based IPFC. From top to
bottom: Piston trajectory, Flowmeter output, Instantaneous flow.
4.4.2. Energy Analysis
With the flow rate known, energy analysis can be conducted. The cycle-wise energy
breakdown in the HFPE is illustrated in Figure 4.14. For all the chemical energy stored in
the fuel, most is released as heat through combustion, while some is lost in the form of
unburnt fuel. Out of the combustion energy, some is lost through heat transfer between
the in-cylinder charge and the chamber wall, i.e. heat loss, while some is taken away in
the form of exhaust enthalpy, also known as blowdown loss. The rest is the usable energy
converted into mechanical work through the expansion of in-cylinder gas, and is then
distributed in three ways. Part of the mechanical work is used to drive the scavenging
pumps and overcome frictions in the system. Another part of mechanical work is
dissipated in the form of air spring loss, which accounts for the heat loss and air leakage
in the bounce chamber during its expansions and compressions. The rest of the
mechanical energy goes into overcoming the hydraulic forces and moving hydraulic
64
pistons, and is defined as hydraulic input. Finally, some of the hydraulic input energy is
dissipated into heat through throttling, while the rest becomes the useful hydraulic energy
output.
Figure 4.14. Energy breakdown structure for HFPE working under IPFC
In this research, the heat loss and incomplete combustion loss are not measured due to
the instrument limitations. From the motion of the piston and combustion chamber
pressure, the net heat release of a cycle, which is the combustion heat minus heat loss,
can be expressed by rearranging (3.11) and integrating it between two scavenging events,
as shown in (4.12).
𝑄ℎ𝑒𝑎𝑡_𝑐𝑦𝑐𝑙𝑒 = ∫ �̇�ℎ𝑒𝑎𝑡𝑑𝑡𝑡𝑠𝑠_𝑛+1
𝑡𝑠𝑒_𝑛
= ∫ (𝛾𝑃𝑐𝑜𝑚𝑏𝛾 − 1
�̇� +𝑉
𝛾 − 1�̇�𝑐𝑜𝑚𝑏)𝑑𝑡
𝑡𝑠𝑠_𝑛+1
𝑡𝑠𝑒_𝑛
(4.12)
In the equation, Qheat_cycle is the net heat release of a cycle, and �̇�ℎ𝑒𝑎𝑡 is the net heat
release rate. γ represents the specific heat ratio of in-cylinder gas. Pcomb stands for the
measured combustion chamber pressure, and V is the volume of the combustion chamber,
which can be calculated from piston positions and piston area. tse_n and tss_n+1 are end
time of the n-th scavenging event and start time of the n+1-th scavenging event,
respectively.
Mechanical work can be calculated by integrating the product of piston velocity and
gas force, as shown in (4.13). In the equation, Wgas is the mechanical work for a cycle, Ag
65
is the piston area, �̇�𝑜𝑢𝑡𝑒𝑟 and �̇�𝑖𝑛𝑛𝑒𝑟 are the velocities of outer and inner piston pair,
respectively. Note that in the system the positive directions of outer piston and inner
piston are defined oppositely, so �̇�𝑜𝑢𝑡𝑒𝑟 + �̇�𝑖𝑛𝑛𝑒𝑟 is essentially the relative velocity of the
two pistons.
𝑊𝑔𝑎𝑠 = ∫ 𝑃𝑐𝑜𝑚𝑏𝐴𝑔(�̇�𝑜𝑢𝑡𝑒𝑟 + �̇�𝑖𝑛𝑛𝑒𝑟)𝑑𝑡𝑡𝐵𝐷𝐶𝑛+1
𝑡𝐵𝐷𝐶𝑛
(4.13)
With Qheat_cycle and Wgas available, blowdown loss can be expressed as the difference
between them, as shown in (4.14).
𝐸𝑏𝑙𝑜𝑤𝑑𝑜𝑤𝑛 = 𝑄ℎ𝑒𝑎𝑡_𝑐𝑦𝑐𝑙𝑒 −𝑊𝑔𝑎𝑠 (4.14)
Similar to gas work calculation, the air spring loss can be calculated, as shown in
(4.15). Psping in the equation is the air spring pressure. Wsping is the work done by the air
spring, which should be a negative value. Minus signs before piston velocities indicate
that positive piston velocity corresponds to compression of the air spring.
𝐸𝑠𝑝𝑟𝑖𝑛𝑔𝑙𝑜𝑠𝑠 = −𝑊𝑠𝑝𝑟𝑖𝑛𝑔 = −∫ 𝑃𝑠𝑝𝑖𝑛𝑔𝐴𝑔(−�̇�𝑜𝑢𝑡𝑒𝑟 − �̇�𝑖𝑛𝑛𝑒𝑟)𝑑𝑡𝑡𝐵𝐷𝐶𝑛+1
𝑡𝐵𝐷𝐶𝑛
(4.15)
The hydraulic input energy can be computed by integrating the product of hydraulic
pressure and volume changing rate, as shown in (4.16). WhydIn is the hydraulic input
energy for a cycle. Pouter and Pinner are the hydraulic chamber pressure for outer and inner
chamber, respectively. Ah_outer and Ah_inner are the hydraulic piston areas. Signs in the
equation are assigned based on the positive direction of velocities.
𝑊ℎ𝑦𝑑𝐼𝑛 = ∫ (𝑃𝑜𝑢𝑡𝑒𝑟𝐴ℎ_𝑜𝑢𝑡𝑒𝑟�̇�𝑜𝑢𝑡𝑒𝑟 − 𝑃𝑖𝑛𝑛𝑒𝑟𝐴ℎ_𝑖𝑛𝑛𝑒𝑟�̇�𝑖𝑛𝑛𝑒𝑟)𝑑𝑡𝑡𝐵𝐷𝐶𝑛+1
𝑡𝐵𝐷𝐶𝑛
(4.16)
As discussed in previous chapters, the friction and scavenging force cannot be
separated in this study, hence friction loss and scavenging loss are lumped together here.
Given that Wgas, Whydin and Espringloss are all known, loss from friction and scavenging can
be expressed using (4.17).
𝐸𝑓𝑟𝑖/𝑠𝑐𝑎 = 𝑊𝑔𝑎𝑠 −𝑊ℎ𝑦𝑑𝑖𝑛 − 𝐸𝑠𝑝𝑟𝑖𝑛𝑔𝑙𝑜𝑠𝑠 (4.17)
Next, the hydraulic energy output can be represented by the integral of the difference
of output hydraulic power and input hydraulic power, as shown in (4.18). WhydOut is the
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output hydraulic energy in a cycle. Phigh and Plow are the hydraulic pressure at the high
pressure and low pressure rail, respectively, as illustrated in Figure 4.2. Note that for both
QOutput and QIntake, positive sign means flow out of the HFPE and negative sign means
flow into the HFPE.
𝑊ℎ𝑦𝑑𝑂𝑢𝑡 = ∫ (𝑄𝑂𝑢𝑡𝑝𝑢𝑡𝑃ℎ𝑖𝑔ℎ + 𝑄𝐼𝑛𝑡𝑎𝑘𝑒𝑃𝑙𝑜𝑤)𝑑𝑡𝑡𝐵𝐷𝐶𝑛+1
𝑡𝐵𝐷𝐶𝑛
(4.18)
Lastly, the throttling loss can be represented by the difference of hydraulic input
energy and hydraulic energy output, as shown in (4.19), where Wthrottling indicates the
throttling energy in a cycle. Since throttling across check valves are negligible compared
to that across the servo valve, Wthrottling can also be approximated using the servo valve
throttling energy 𝑊𝑡ℎ𝑟𝑜𝑡𝑡𝑙𝑖𝑛𝑔′ , as detailed in (4.20). In the equation, Qservo_outer and
Qservo_inner are the servo valve flow corresponding to outer and inner chamber,
respectively, and ΔPouter and ΔPinner are the corresponding pressure difference across the
servo valve. Testing data shows that the difference between Wthrottling and 𝑊𝑡ℎ𝑟𝑜𝑡𝑡𝑙𝑖𝑛𝑔′ is
less than 2%.
𝑊𝑡ℎ𝑟𝑜𝑡𝑡𝑙𝑖𝑛𝑔 = 𝑊ℎ𝑦𝑑𝐼𝑛 −𝑊ℎ𝑦𝑑𝑂𝑢𝑡 (4.19)
𝑊𝑡ℎ𝑟𝑜𝑡𝑡𝑙𝑖𝑛𝑔′ = ∫ (|(𝑄𝑠𝑒𝑟𝑣𝑜_𝑜𝑢𝑡𝑒𝑟Δ𝑃𝑜𝑢𝑡𝑒𝑟| + |𝑄𝑠𝑒𝑟𝑣𝑜_𝑖𝑛𝑛𝑒𝑟Δ𝑃𝑖𝑛𝑛𝑒𝑟|)𝑑𝑡
𝑡𝐵𝐷𝐶𝑛+1
𝑡𝐵𝐷𝐶𝑛
(4.20)
Figure 4.15 shows the energy breakdown under IPFC. As shown in the figure, each
combustion produces about 627J of heat with heat loss excluded. The largest portion of
loss is the blow down loss, followed by air spring loss, scavenging/friction loss and
throttling loss. Detailed average absolute and percentage energy breakdown are listed in
Table 4.5 below. Loss from the air spring here is relatively high compared to some other
systems with bounce chambers. For instance, DLR’s FPEG only reported an air spring
loss of 1.9%[29]. This is mainly due to the high compression ratio in the bounce chamber.
As shown in Figure 4.9, the pressure in the right combustion chamber, i.e. the bounce
chamber, is up to 4 MPa around BDC. According to the ideal gas law, gas temperature
around this time would be very high, hence introducing significant loss through heat
transfer to the chamber wall. Higher bounce chamber pressure would also cause more
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leakage. This loss could be mitigated if the bounce chamber piston is redesigned to have
a larger area, hence smaller compression ratio and lower temperature is needed to store
the same amount of energy. Incidentally, the high loss from friction and scavenging also
suggests improvements can be made in the corresponding subsystems.
Energy Attribute Symbol Energy Percentage
Blowdown loss Eblowdown 305J 48.6%
Air spring loss Esrpingloss 41J 6.5%
Friction/scavenging loss Efri/sca 41J 6.5%
Throttling loss Wthrottling 49J 7.8%
Hydraulic energy output Whydout 192J 30.6%
Total N/A 627J 100%
Table 4.5. Energy breakdown for switch based IPFC
Figure 4.15. Energy breakdown for switch-based IPFC with overcorrection
Consequently, net power output can be calculated using per cycle hydraulic energy
output and operation frequency, as shown in (4.21). In the equation, 𝑓𝑜𝑝 is the operation
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frequency. In this set of data, the net output hydraulic power under IPFC is 8.87KW,
which is about 16.1% of the rated power of 55KW.
𝑃𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑊ℎ𝑦𝑑𝑂𝑢𝑡 × 𝑓𝑜𝑝 (4.21)
To better quantify HPFE’s performance under IPFC, the following efficiency criteria
are defined. To quantify the efficiency of HPFE in converting gas expansion work to
overcome hydraulic forces, the engine mechanical efficiency is defined as the ratio
between hydraulic input energy WhydIn and gas work Wgas, as shown in (4.22).
𝜂𝑚𝑒𝑐ℎ_𝑒𝑛𝑔𝑖𝑛𝑒 =𝑊ℎ𝑦𝑑𝐼𝑛
𝑊𝑔𝑎𝑠× 100% (4.22)
Hydraulic efficiency is defined in (4.23) to show how much energy consumed by the
hydraulic system turns into usable hydraulic energy output.
𝜂ℎ𝑦𝑑 =𝑊ℎ𝑦𝑑𝑂𝑢𝑡
𝑊ℎ𝑦𝑑𝐼𝑛× 100% (4.23)
Mechanical efficiency here is define as the product of engine mechanical efficiency
and hydraulic efficiency to indicate how much mechanical work done by the gas
ultimately becomes hydraulic energy output.
𝜂𝑚𝑒𝑐ℎ = 𝜂𝑚𝑒𝑐ℎ_𝑒𝑛𝑔𝑒𝑖𝑛 × 𝜂ℎ𝑦𝑑 =𝑊ℎ𝑦𝑑𝐼𝑛
𝑊𝑔𝑎𝑠× 100% (4.24)
Figure 4.16 shows the efficiencies for each IPFC cycle. The average engine
mechanical efficiency is 74.7% while the average hydraulic efficiency is 79.5%. The
overall mechanical efficiency is 59.4%, which is lower than that acquired in the
simulation in Chapter 3, mainly due to the one-valve architecture, a much slower valve,
the use of an inefficient air spring and much higher friction/scavenging loss in the
hardware.
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Figure 4.16. Cycle-wise hydraulic efficiency, engine mechanical efficiency and overall
mechanical efficiency
4.4.3. Low Robustness of Switch-Based Method
As mentioned earlier, although the switch-based method can achieve IPFC in a
straightforward manner, this method relies heavily on calibration of switch points and
lacks robustness to parameter changes. In reality, even during normal operation, the
parameters of the HFPE can drift gradually. For instance, the hydraulic seal can wear out
over time, causing the friction to change; the oil temperature can change overtime and
causes different viscosity, which will affect both leakage and friction. All these will
affect the system dynamics and requires a tedious re-calibration of switch timings.
Otherwise, the system would not operate reliably.
An example of such robustness related failures is shown below. Figure 4.17 shows a
switch based IPFC test performed with an old set of hydraulic seals. The switch point was
calibrated accordingly so that stable operation could be achieved. However, when a new
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Figure 4.17. Switch based IPFC with old hydraulic seals and corresponding switch
points
Figure 4.18. Switch based IPFC with new hydraulic seals and old switch points
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set of hydraulic seals was installed, the friction changes and the system dynamics was
affected. When the old switch points calibrated with the old seals were used with the new
seals, energy balance was broken and the system lacked the energy to compress the
combustion chamber enough, leading to a rising TDC and ultimately misfire, as shown in
Figure 4.18.
4.5. Chapter Conclusion
The HFPE testbed was presented and characterized in this chapter. Then, the switch-
based IPFC realization is proposed and validated. Test results show that with proper
switch timing and over correction carefully calibrated, the IPFC can be successfully
implemented on the hardware. For the tested working condition of 71% displacement
fraction, an overall mechanical efficiency of 59.4% is achieved. Analysis shows that
some mechanical energy is consumed on the air spring, friction/scavenging, and over
throttling, indicating areas for improvements. Specifically, for the hydraulic part, an
efficiency of 79.9% is obtained with the major loss being throttling loss through the servo
valve. At the same time, experiments also show that due to the lack of sophisticated
feedback control, the switch based IPFC method is not robust to changes and
disturbances, hence a more robust control scheme is needed to make IPFC practical.
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Chapter 5.
Robust Realization of IPFC
Since the switch-based method lacks robustness, more robust controllers are needed to
realize the IPFC. In this chapter, two robustness reinforcement methods are proposed to
address the robustness issues from both the in-cycle robustness perspective and cycle-to-
cycle robustness perspective. Both methods are tested experimentally with performance
analyzed.
5.1. Trajectory Tracking based IPFC
5.1.1. Introduction
The hydraulic part of the HFPE is essentially an electrohydraulic actuation (EHA)
system. The control of such a system has wide applications and has been studied by many
researchers. Due to the nonlinear feature of the servo valve orifice equation(3.5), the
electrohydraulic actuators are essentially nonlinear systems. This nonlinearity is
investigated in depth using generalized frequency response functions by Yoon and
Sun[69], [70]. From their analysis, EHAs’ nonlinearity is stronger when there is a smaller
pressure drop across the servo valve. When the pressure drop across the valve is large,
the EHA behaves more similar to a linear system. Some researchers proposed to directly
control the EHA as a nonlinear system. Yao et al. proposed to use nonlinear adaptive
robust control on a double rod EHA[71] and later expanded the method to single rod
EHAs[72]. Guan and Pan applied adaptive sliding mode control on an EHA and
compensated for linear and nonlinear uncertainties[73]. Yao et al. put forward an
adaptive controller for EHA motion control that can handle nonlinearity, model
uncertainty and severe measurement noise[74]. On the other hand, many researchers
proposed to control EHA motion using linear controllers and consider the nonlinearity as
system uncertainties. Kim and Tsao showed that a two stage servo valve can be modeled
as a linear system around the equilibrium and high control performance can be achieved
with this linear model [68]. Among the linear methods, robust repetitive control [75] is
particularly powerful for systems with reciprocal motion. Although it is a linear
controller, the high order harmonics generated from system nonlinearity can still be
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properly handled as high gains are placed on all harmonics of the reference trajectory.
Kim and Tsao proposed a linear motion control system for EHA consisting of robust
performance control, repetitive control and feedforward control, and demonstrated its
performance in [76]. Sun, et al incorporated adaptive control with robust repetitive
control and achieved asymptotic convergence under system parametric uncertainties[77].
Sun and Kuo used robust repetitive controllers to regulate the motion of an EHA for the
moving sections of a reference trajectory, while a PID controller is used for the dwelling
sections of the reference [78].
Previously, attempts are made in our group to precisely control the piston motion of
the HFPE during motoring. Li first used a robust repetitive controller to regulate the
piston motion[28]. Later, linear and nonlinear feedforward controls were added to the
system for improved system performance[39]. Some preliminary work were also done to
address the motion control during the transition between motoring and combustions[40].
However, the motion control issue during combustion was not fully addressed, especially
with flow output considered.
5.1.2. Stable Operation, Flow Output and Trajectory Tracking
A key feature defining a FPE is that its motion is regulated solely by the forces exerted
on the pistons rather than a mechanical mechanism, as demonstrated by the free body
diagram in Figure 3.2. In order to achieve stable operation of the FPE, all forces have to
be balanced to produce a stable piston motion. Moreover, the piston trajectory has to
ensure high enough BDC for efficient scavenging and low enough TDC for combustion.
As the only continuously controllable force in the HFPE, the hydraulic force is
selected to be the control means in this study, and is actively adjusted to maintain desired
piston motion. From the HFPE schematic shown in Figure 2.1, it is clear that the
maximum hydraulic resisting force will be reached when the servo valve is parked at
neutral and all intake/output flow goes through check valves. Meanwhile, for any given
piston motion, the maximum hydraulic helping force will be reached when the servo
valve is connecting the discharge chamber to low pressure and intake chamber to high
pressure with the maximum orifice. Between the maximum helping and resisting forces,
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the hydraulic force changes continuously with the servo valve orifice. In other words, all
possible hydraulic forces can be reached by connecting the discharge chamber to low
pressure with different valve orifices. Similar to that shown in Figure 4.10, flow
condition corresponding to different valve orifices can be illustrated using Figure 5.1.
Without losing generality, the inner chamber is considered as the discharge chamber here.
Subscript discharge and intake mark flow corresponding to the intake and discharge
chambers, respectively. When the orifice is relatively large and the pressure drops across
the servo valve are low, all flow will go through the servo valve and a negative net flow
is generated, as shown in Figure 5.1(a). When the orifice gets smaller, the pressure drops
are high enough and check valves are open, therefore changing the flow distribution, as
shown in Figure 5.1(b). The net output flow under this condition becomes the difference
between the intake chamber servo valve flow (Qservo_intake) and the discharge chamber
check valve flow (Qcheck_discharge). One extreme case is when the servo valve orifice is zero,
then all flow goes through check valves and the output flow is maximized.
Figure 5.1. Flow distribution under different conditions: (a) check valves are closed; (b)
check valves are open
A more detailed force-pressure-flow-orifice correlation is generated through
simulation and illustrated in Figure 5.2, with a working condition of 5m/s piston speed
and 20.7MPa load pressure. In the figure, negative servo valve connection stands for
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connecting the discharge chamber to low pressure. Positive direction of hydraulic force is
defined as the direction resisting piston motion and the force magnitude is normalized by
dividing the maximum hydraulic force when the piston is stationary. Chamber pressures
are normalized by dividing the load pressure and flow rates are normalized by dividing
the product of piston velocity and piston area. As expected, output flow stays the same
until check valves are open, and reaches maximum when the servo valve is at neutral.
Note that once the check valves are open, the net hydraulic force practically stays the
same.
Figure 5.2. Relationship between hydraulic force and output flow fraction. From top
to bottom: hydraulic force, chamber pressures, output flow rate
It is clear from the aforementioned analysis that while the hydraulic force is
controllable, the control of force cannot be achieved simultaneously with efficient flow
output. Considering the digital flow modulation nature of IPFC, a hybrid control scheme
can be proposed, as illustrated in Figure 5.3. Basically, the servo valve is parked at
neutral using feedforward control during the pumping section of the IPFC cycle to ensure
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high output efficiency, while trajectory tracking is implemented during the helping
section. The switch of controllers is triggered by the piston position. In this way, all
disturbances and uncertainties during the pumping section shows up in the helping
section as initial velocity error that is to be compensated by the following trajectory
tracking. During the helping section, since the servo valve is connecting the discharge
chamber to low pressure, full control over hydraulic force can be achieved, thus enabling
trajectory tracking. It is worth noting that due to the existence of check valves, servo
valve dynamics and the small pumping portion at the beginning of trajectory tracking,
some flow can be output during the tracking control. However, this output is very
sensitive to trajectory since the output flow changes quickly under a small hydraulic force
change after the open of check valves. To help increasing net output flow and therefore
the overall efficiency, a feedforward control is used together with the feedback trajectory
tracking control so that the system operations are efficient and robust.
Figure 5.3. IPFC with partial reference tracking
All aforementioned discussions are based on the one valve HPFE architecture shown
in Figure 2.1. For two valve systems, the flow into the intake chamber always comes
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from the low pressure, so there won’t be any negative output flow. However, the basic
ideas of output flow control, hydraulic force control, as well as the method of hybrid
control scheme stay the same.
5.1.3. Controller Design
A feedforward + feedback control scheme is proposed to realize trajectory tracking
under IPFC. The control block diagram is shown in Figure 5.4. In this study, the HFPE is
approximated as a linear system, with nonlinearities considered as model uncertainties
and unmodeled dynamics.
Figure 5.4. Control block diagram for reference tracking
5.1.3.1. Feedback control
The feedback portion of the controller consists of a proportional controller, and a
repetitive controller[75]. From the model in Chapter 3, it is clear that a constant servo
valve signal will result in a constant piston speed for the HFPE, hence making it a
boundary stable system. Therefore, the proportional controller is implemented to stabilize
the HFPE. Then, the stabilized plant is modeled using a discrete transfer function in the
form of (5.1). The stabilized plant is controlled by a repetitive controller, whose control
law is given below in(5.2) and (5.3). In the equations, k is the discrete time index and
G(q-1) is the plant transfer function. N is the length of reference cycle. Q(q-1) is a low pass
filter added for system robustness, and will be discussed in detail later. Kr is the repetitive
control gain within (0, 2). B+(q-1) is the stable part of B(q-1), while B-rev(q
-1) is the
approximation of B(q-1)’s unstable part calculated according to [79].
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𝑦(𝑘) = 𝐺(𝑞−1)𝑢(𝑘) =𝐵(𝑞−1)
𝐴(𝑞−1)𝑢(𝑘) (5.1)
𝑢(𝑘) = 𝑀(𝑞−1)𝑄(𝑞−1)𝑞−𝑁
1 − 𝑄(𝑞−1)𝑞−𝑁𝑒(𝑘) (5.2)
𝑀(𝑞−1) = 𝐾𝑟𝐴(𝑞−1)𝐵𝑟𝑒𝑣
− (𝑞−1)
𝑏𝐵+(𝑞−1)𝑒(𝑘)
𝑏 ≤ max|𝐵𝑟𝑒𝑣− (𝑒−𝑗𝜔)|
2
(5.3)
The plant model G(q-1) was acquired through system identification in previous work
of our group[80], and shown in (5.4).
𝐺(𝑞−1)
=𝑞−4(−0.006709 + 0.02038𝑞−1 − 0.02099𝑞−2 + 0.007379𝑞−3)
1 − 3.788𝑞−1 + 5.417𝑞−2 − 3.468𝑞−3 + 0.8385𝑞−4
(5.4)
The repetitive controller imposes high gains on all harmonics of the reference signal to
ensure tracking of periodical signal. However, since the system uncertainty is usually
high at high frequencies, the high gain there could cause instability and therefore has to
be attenuated with a Q filter. According to [81], the Q filter has to satisfy the conditions
given by (5.5) through (5.7) for the system to be robustly stable. In the equations, Ts is
the sample time, ω is the radian frequency and −𝜋 ≤ 𝜔𝑇𝑠 < 𝜋. G0 and G stand for the
nominal plant and actual plant, respectively. Specifically, equation (5.5) and (5.6)
requires the Q filter to apply a strong enough attenuation on the system uncertainties,
while (5.7) indicates the Q filter to be zero phase.
1
|∆(𝑒−𝑗𝜔𝑇𝑠)|≥ |𝑄(𝑒−𝑗𝜔𝑇𝑠)| (5.5)
∆(𝑒−𝑗𝜔𝑇𝑠) =𝐺0(𝑒
−𝑗𝜔𝑇𝑠) − 𝐺(𝑒−𝑗𝜔𝑇𝑠)
𝐺0(𝑒−𝑗𝜔𝑇𝑠) (5.6)
𝑄(𝑞−1) =𝐻(𝑞−1)𝐻(𝑞)
ℎ2
ℎ = max|𝐻(𝑒−𝑗𝜔𝑇𝑠)|
(5.7)
From a time domain perspective, the Q filter works as a forgetting factor on the
previous control signal and a mitigation factor of last cycle’s error. Control signal of the
current cycle is the sum of attenuated previous cycle signal plus the effect from the
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previous cycle error. As a result, there always has to be an error to sustain the control
signal and perfect tracking cannot be achieved where Q<1. This agrees with the
frequency domain interpretation where the Q filter leads to a finite gain at harmonics.
Figure 5.5. Top: Bode plot of conventional Q filters of different orders; Bottom: Change
of -3dB cut-off frequency with filter order for conventional Q filters. Sample time Ts =
0.1ms
Conventionally, Q filter is constructed using the form shown in (5.8). In the equation,
n is the order of the filter. With the order n increasing, the roll off rate of the filter will
increase and the cut-off frequency will decrease. However, the changing rate bandwidth
frequency drops drastically as n gets higher, as shown in Figure 5.5. This issue is
particularly prominent when the sample rate is high but a low cut-off frequency is needed.
𝑄(𝑞−1) = (𝑞 + 2 + 𝑞−1
4)
𝑛
(5.8)
To address this issue, the following Q filter design method is proposed. First,
determine the roll-off rate and cut-off frequency based on the plant uncertainty. Without
losing generality, a sample frequency of 2kHz, roll off rate greater than -60dB/dec and a
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cut-off frequency of 110Hz is assumed for the following discussion. Then, design H(s)
such that bandwidth and roll off rate of H(s)∙H(s) meets the demand for Q filter. Clearly,
H(s) can be a second order low pass filter shown in (5.9). Discretizing H(s) yields (5.10),
which has overlapping poles at 0.449+0i.
𝐻(𝑠) =2.56 × 106
𝑠2 + 3200𝑠 + 2.56 × 106 (5.9)
𝐻(𝑞−1) =0.191𝑞−1 + 0.112𝑞−2
1 − 0.899𝑞−1 + 0.202𝑞−2 (5.10)
Plugging (5.10) into (5.7) should give the required Q filter. However, when
substituting q-1 with q, the pole locations will move out of the unite cycle, making the
resulting Q filter unstable. To handle this, a series expansion based method similar to that
used in [79] can be applied to approximate the unstable poles with zeros, as shown in
(5.11). In the equation, a represents a pole of the transfer function. Since q is evaluated at
|q| = 1, and the unstable pole a has |a| > 1, the condition |q|<|a| is always satisfied. In
implementation, if the series expansion is truncated after the m1-th term, the additive
truncation error ET(m1) would be bounded by the circle defined in (5.12). Note this error
affects both phase and gain.
1
𝑞 − 𝑎= ∑ −(−𝑎)−𝑚𝑞𝑚−1,
∞
𝑚=1
|𝑞| < |𝑎| (5.11)
𝐸𝑇(𝑚1) ≤ −(−𝑎)−𝑚1𝑒𝑗𝜔𝑇𝑠(𝑚1−1) (5.12)
Using the aforementioned method and keeping the first 4 terms of series expansion,
H(q) and the Q filter can be expressed using (5.13) and (5.14), respectively. Compared to
(5.7), in (5.14), h2 is replaced by sup𝐻(𝑞−1)𝐻(𝑞) to account for the truncation error’s
effect on the DC gain.
𝐻(𝑞) = 0.000922𝑞8 + 0.005677𝑞7 + 0.0207 𝑞6 + 0.06403𝑞5
+ 0.1372 𝑞4 + 0.2165𝑞^3 + 0.2839𝑞2 + 0.1912𝑞 (5.13)
𝑄(𝑞−1) =𝐻(𝑞−1)𝐻(𝑞)
sup𝐻(𝑞−1)𝐻(𝑞)=
𝐵𝑄(𝑞−1)
1 − 0.899𝑞−1 + 0.202𝑞−2
𝐵𝑄(𝑞−1) = (1.916𝑞7 + 12.92𝑞6 + 49.94𝑞5 + 158.3𝑞4 + 363.2𝑞3
+ 617.0𝑞2 + 853.5𝑞 + 743.0 + 232.8𝑞−1) × 10−4
(5.14)
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Figure 5.6 shows the bode plot of the resulting Q filter and H(s)∙H(s). As can be seen,
the new Q filter closely reproduces the gain profile of H(s)∙H(s) while providing a phase
shift close to 0. The bandwidth of the new Q filter is 122Hz and maximum phase shift is
4.67˚.
Figure 5.6. Bode plot of new Q filter and H(s)H(s)
As proved in [81], a zero phase Q filter is sufficient to guarantee the stability of a
repetitive controller, but it is not a necessary condition. The closed loop transfer function
of the whole system is shown down in (5.15). Plugging in (5.3) (5.4) and (5.14), it can be
shown that for any 𝑁 ∈ [20,200], the closed loop system is stable.
𝑃𝑐𝑙 =𝐺𝑀𝑄𝑞−𝑁
1 + (𝐺𝑀 − 1)𝑄𝑞−𝑁 (5.15)
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Figure 5.7. Bode plot of repetitive controller
Figure 5.8. Bode plot of the closed loop system sensitivity function
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With the Q filter designed, the whole repetitive controller can be built for a 11ms long
reference. Figure 5.7 and Figure 5.8 below shows the bode plot of the repetitive
controller and the closed loop system sensitivity function, respectively. Due to the
bandwidth limitation of the controller, error is mainly being penalized at the DC and first
two harmonics.
5.1.3.2. Feedforward control
The feedforward control during the trajectory tracking part serves two purposes. First,
as mentioned previously, it can improve the flow output during the trajectory tracking
section. Second, it helps robust operation by providing a good initial control signal. the
HFPE’s combustion relies heavily on the piston trajectory. If the trajectory is off from
nominal by too much, misfire or abnormal combustions could happen before the piston
trajectory converges to the reference under feedback control. Therefore, a feedforward
control is needed to bring the initial trajectory near the nominal and sustain combustions.
The feedforward signal used here is based on the switch based IPFC.
Under switch based IPFC, the valve control signal is acquired through calibrating the
switch timing. Since the feedforward signal is injected as the input of the stabilized plant,
it can be calculated using the valve signal, corresponding piston trajectory, and
proportional control gain, as shown in (5.16). In the equation, uff is the feedforward signal,
uswitch and yswitch represents the valve signal and piston trajectory during switch based
IPFC, respectively. Kp is the proportional control gain.
𝑢𝑓𝑓 =𝑢𝑠𝑤𝑖𝑡𝑐ℎ𝐾𝑝
+ 𝑦𝑠𝑤𝑖𝑡𝑐ℎ (5.16)
As for the feedforward signal used during the pumping section, it is directly taken
from the switch based case since it is also directly given as the servo valve signal.
5.1.4. Testing Results
The proposed control methods are put into test on the testbed. For fair comparison, the
working condition is kept the same as the switch based case, i.e. same fuel injection
amount of 57.1mg/cycle and load pressure of 20.7MPa.
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5.1.4.1. Tracking based IPFC under normal operation conditions
The reference and feedforward signal both come from the set of switch based IPFC
test shown in Figure 5.9. Such switch based IPFC cases meet the references’ requirement
of pumping at neutral. As shown in Chapter 4, switch signal alone can provide stable
operation but doesn’t have enough robustness to disturbances.
Figure 5.9. Trajectory reference and feedforward signal for tracking based IPFC with
calibration based feedforward signal. From top to bottom: piston trajectory and
reference, hydraulic pressure in reference case, feedforward signal.
With the feedforward + feedback controller implemented, tests are carried out under
exactly the same HFPE working condition settings, with results shown in Figure 5.10.
Clearly, the system works stably as expected, with resisting hydraulic force for the
expansion stroke and the first half of the compression stroke. The tracking error lays in
the band of ±2mm with a discretization induced initial error of ±1.5mm, as shown in
Figure 5.11. Since the feedforward signal is well calibrated and matches the reference
signal well, the feedback controller’s contribution to the overall servo valve signal is
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Figure 5.10. Operation overview of IPFC with trajectory tracking and calibrated
feedforward. From top to bottom: piston position, hydraulic pressures and servo signals.
Figure 5.11. Trajectory tracking with repetitive control and calibration based
feedforward
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small and the estimated servo valve opening is very similar to that solely from the
feedforward signal.
Energy and efficiency wise, since the feedback signal has very limited impact on the
servo valve orifice, the flow output and system efficiency are very similar to that in the
switch based case. The output flow rate in the test is 11.2ml/cycle, while the engine
mechanical and hydraulic efficiencies are 75.9% and 84.0%, respectively, as shown in
Figure 5.12. Compared to the switch based case, neither efficiencies nor flow output was
compromised.
Figure 5.12. Efficiency of tracking with repetitive control and calibration based
feedforward
To better demonstrate the improved robustness of tracking based IPFC, a set of tests
with inaccurate feedforward signal is performed. As mentioned in Chapter 4, the switch
point changed once a new set of seal was installed. With the switch based control
calibrated for the old seal, the forces are imbalanced, causing the TDC to rise and
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ultimately the misfire to happen. When the feedback control is added, the deviation from
reference trajectory will be captured by the repetitive controller, who in turn tries to
regulate the piston motion and reinstall desired trajectory by changing the servo valve
opening. The testing result is shown below in Figure 5.13 and Figure 5.14. Clearly, the
system can operate stably now. From the tracking performance, it is clear that with the
repetitive control, the tracking error decreases gradually. Meanwhile, due to the large
tracking error, the feedback signal takes up a much larger portion of the overall servo
valve signal, compared to previous cases where the feedforward signal is accurate. From
a physical perspective, the repetitive control signal is essentially making the servo valve
open earlier, therefore decreases the hydraulic resisting force and increases the helping
force.
Figure 5.13. Operation overview of IPFC with trajectory tracking and inaccurate
calibrated feedforward. From top to bottom: piston position, hydraulic pressures and
servo signals.
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Figure 5.14. Trajectory tracking with repetitive control and inaccurate calibration
based feedforward
However, this increased stability comes at a price of lower hydraulic efficiency. Since
the valve switch is advanced, the flow output will decrease. At the same time, due to the
slower valve switching compared to the switch based case, the pressure change is slower
and the throttling loss is higher. Even with the feedback control, the TDC achieved is still
higher than the reference, making the stroke length shorter and further reduced the flow
output. The final hydraulic and engine mechanical efficiency is shown in Figure 5.15.
The hydraulic efficiency settles around 61.7%, which is a 17.8% drop compared to the
case with accurate feedforward signal. The final net flow output is 7.1ml/cycle,
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Figure 5.15. Efficiency of tracking with repetitive control and inaccurate calibration
based feedforward
5.2. Misfire Recovery
5.2.1. Introduction
Misfire is the phenomenon where no combustion or only partial combustion happens
around the TDC. It can happen in an engine due to many reasons including lack of spark
energy, insufficient fuel, poor air fuel mixing and low compression pressure. Particularly,
the advanced combustion modes supported by a HFPE such as lean combustions,
advanced engine timing[82], and HCCI combustion[83] are susceptible to misfire.
Meanwhile, the flexibility of HFPE enabled by the ultimate piston motion freedom[35]
poses a unique challenge for combustion control, where the risk of misfire stands out.
When discrete misfires happen to an conventional ICE, despite causing some highly
dynamic oscillations in the powertrain[82], increasing the fuel consumption and
degrading the emission performance[84], [85], the piston motion can be sustained by
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inertia and the crankshaft mechanism, such that normal combustion can resume in the
next cycle. However, for FPEs, whose piston motion solely depends on the balance of
forces, the conditions cannot be setup naturally for consequential combustions after a
single misfire. As a result, misfire recovery has to be designed as a cycle-to-cycle
robustness reinforcement for the FPEs to operate robustly.
Misfire recovery has been attempted by researchers before for mostly FPEGs. In the
work of DLR, misfire recovery was integrated under the same MPC framework used for
combustion control[44], [50]. The linear generator force changes according to the
estimated combustion chamber pressure and bounce chamber pressure so as to bring the
piston to a desirable BDC. However, this method uses fixed plant model calibrated
during combustion and does not account for changes such as friction forces under misfire,
therefore cannot achieve proper BDC control[44]. Moreover, this method was only
reported to be tested under a ‘virtual combustion/misfire’, so its performance under real
misfires, including the corresponding misfire detection capability, remains unclear[44].
Researchers at Toyota also proposed to use the combustion controller to handle abnormal
combustions including knocking and misfiring[30]. In their work, a PD style controller
was used to regulate linear generator force and let the piston roughly follow a prescribed
trajectory. However, the tracking performance was not quite good even under normal
combustions and the performance under misfire was not demonstrated. As for HPFEs,
since the response time of hydraulic systems is much longer than linear generators,
misfire recovery becomes a more challenging problem. Peter Achten proposed to solve
this issue by re-proposing a creeping control valve to reset combustion piston position
after a misfire[26]. But this method only works when the PPM control is used, which
requires holding the piston stationary between cycles and therefore doesn’t work for any
architectures requiring continuous operation, such as OC or OPOC architectures, or
SP/OP HFPEs with only bounce chambers. To put it in a nutshell, a systematical and
universally applicable misfire recovery method is still in need, especially for HFPEs.
In order to recover from misfire in a systematical fashion, three tasks are proposed.
First, the misfire has to be detected properly. Second, controller has to be designed to
regulate hydraulic force such as to produce a trajectory that enables the next combustion.
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Lastly, when combustions resume, control has to be shifted back to IPFC control to
ensure output flow. Correspondingly, the reminder of this section is arranged as follows.
Subsection 5.2.2 proposed a misfire detection mechanism. Then, a reference tracking
based controller is proposed in 5.2.3 to regulate the piston motion during misfire recovery
as well as the transient periods. After that, the proposed method is put into test and the
results are shown in 5.2.4. Finally, the performance of the proposed misfire recovery
method is discussed in 5.2.5.
5.2.2. Misfire Detection
5.2.2.1. Misfire Detection Methods
Given its essential importance, misfire detection algorithms are proposed by varies
researchers previously. The most straightforward way is to detect combustion/misfire
using chamber pressure, since a misfired cycle will show different pressure profile than
that of the normal ones due to lower or no heat release[86]. However, due to the extreme
thermal and mechanical environment the pressure sensors are exposed to, their durability
and reliability can be an issue[87], so they are usually used only for research purpose.
Alternatively, the chamber pressure can be estimated indirectly using other parameters.
For instance, Molinar-Monterrubio, et al proposed a sliding mode based observer to
observe the chamber pressure using crank angle measurement and achieved misfire
detection. Other direct measurements form the combustion chamber such as the ion
current in the spark plug can also be used as means of misfire detection[88]. Some other
researchers also use torque estimation[82], [89], vibration signal analysis[90], and
exhaust temperature fluctuation[91] to detect misfire.
In the HFPE, previous work has been done to detect combustion based on chamber
pressure measurement and piston position[40]. Although this provides a feasible way of
detecting misfire, the use of chamber pressure sensor makes it not suitable for real world
applications. To address this issue, a piston acceleration based misfire detection is
proposed in this study. When misfire happens, the chamber pressure after TDC is lower
than the nominal case and consequentially the piston acceleration will be lower. Due to
the small inertia of the HFPE, its acceleration change after a misfire will be much
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prominent than that of a conventional ICE. Also, due to the OPOC architecture, the
determination of misfiring chamber is evident once misfire is detected, avoiding a major
complication in conventional ICE misfire detection.
5.2.2.2. Piston Acceleration Estimation
The piston position measurement is readily available from the LVDT sensor, and the
acceleration can be acquired by operating double derivative on the position. However,
due to the measurement noise, the double derivative of piston position is very noisy and
unusable, as shown by the blue curve in Figure 5.16. To facilitate online detection of
misfires, a Kalman filter/estimator[92] is implemented.
Figure 5.16. Piston acceleration calculated using piston position data. Top: Piston
Trajectory; Bottom: Piston Acceleration
Suppose that the 4th order derivative of piston position, i.e. the jounce, is a normal
distribution around zero, the discrete time state space model of the piston dynamics can
be established as in (5.17) and (5.18). In the equation, x, v, a, j and s are the piston
position, velocity, acceleration, jerk (derivative of acceleration) and jounce, respectively.
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k is the step index and Ts is the time step size. y is the system output, which is the system
output.
[
𝑥(𝑘 + 1)𝑣(𝑘 + 1)𝑎(𝑘 + 1)𝑗(𝑘 + 1)
] = 𝐴 [
𝑥(𝑘)𝑣(𝑘)𝑎(𝑘)𝑗(𝑘)
] + 𝐵𝑠(𝑘)
=
[ 1 𝑇𝑠
1
2𝑇𝑠2
1
6𝑇𝑠3
0 1 𝑇𝑠1
2𝑇𝑠2
0 0 1 𝑇𝑠0 0 0 1 ]
[
𝑥(𝑘)𝑣(𝑘)𝑎(𝑘)𝑗(𝑘)
] +
[ 1
24𝑇𝑠4
1
6𝑇𝑠3
1
2𝑇𝑠2
𝑇𝑠 ]
𝑠(𝑘)
(5.17)
𝑦(𝑘) = 𝐶
[ 𝑥(𝑘)
𝑣(𝑘)
𝑎(𝑘)
𝑗(𝑘)] + 𝐷𝑠(𝑘) = [1 0 0 0] [
𝑥(𝑘)𝑣(𝑘)𝑎(𝑘)𝑗(𝑘)
] + 0 × 𝑠(𝑘) (5.18)
Since we consider jounce s to have normal distribution around zero, it can be
considered as the process noise with covariance Q and the system input can be considered
to be zero. Additionally, the measurement noise can also be regarded as a normally
distributed noise around zero with covariance R, and affects measurement y in an additive
fashion. Under these assumptions, if we mark [x(k), v(k), a(k), j(k)]T as X(k), then the
Kalman filter/estimator can be put into (5.19) and (5.20). In the equations, L is the
filter/estimator gain, and P solves the corresponding discrete time algebraic Riccati
equation, which involves covariance Q.
𝑋(𝑘 + 1) = 𝐴𝑋(𝑘) + 𝐿(𝑦(𝑘) − 𝐶𝑋(𝑘)) (5.19)
𝐿 = 𝐴𝑃𝐶𝑇(𝐶𝑃𝐶𝑇 + 𝑅)−1 (5.20)
The filter’s performance depends on the ratio of Q/R. In this case, a Q/R ratio in the
order of 1025 is used. The red curve in Figure 5.16 shows the result of the Kalman filter
proposed. Clearly, the acceleration data is now much less noisy and usable. Later analysis
shows this level of smoothness is sufficient for combustion/misfire detection.
5.2.2.3. Rule based Misfire Detection
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With the Kalman filter/estimator, the acceleration of piston can be acquired for both
combustion and non-combustion cases, as shown in Figure 5.17. Since the acceleration is
closely related to the gas chamber pressure, which in turn depends on the piston position,
the acceleration is plotted against piston position. Also, since the misfire detection is
performed after TDC, only the acceleration right after TDC is shown. Clearly, the curves
fall into three clusters, namely the normal combustion cluster, the late combustion cluster
and the non-combustion/misfire cluster. In most cases, when a combustion happens, the
piston acceleration rises rapidly after TDC and goes above 2000m/s2. These combustions
are considered normal combustions. However, sometimes, due to issues like poor air fuel
mixing existing on the prototype HFPE, the combustion can happen well after the TDC,
thus producing a late combustion. Although combustion heat release is late in such cases,
usually they can still provide enough power to sustain piston motion. If combustions
don’t occur, i.e. the HPFE is motoring or misfire happened, the acceleration curve will
stay low all the time. The non-combustion/misfire cluster can be separated from the other
two with a separation line shown in red dashed line in the figure.
Figure 5.17. Piston acceleration vs. piston position and separation line
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The goal of misfire detection is to distinguish non-combustion/misfire cases from the
rest as quickly as possible after the TDC, so it is also necessary to observe the
acceleration profile in the time domain. If we define deviation from separation line as
piston acceleration minus the separation line value at the same piston position, Figure
5.18 can be plotted. From the figure, it’s clear that for normal combustion cases, the
acceleration rises above the separation line and becomes clearly differentiable with non-
combustion cases within 2 steps, or 1ms, after the TDC. However, due to the existing of
late combustions, the possibility of combustion happening cannot be ruled out until a few
more steps later, therefore deterministic misfire detection will not be possible until then.
Figure 5.18. Deviation from separation line vs. steps from TDC
Considering the late combustion issue, to deliver quick misfire detection, a rule based
misfire detection method is proposed, as illustrated in the flow chart in Figure 5.19.
Three basic rules are made for the detection procedure. First, if the compression ratio is
too low (< 2.3), misfire must have happened, for the in-cylinder mixture cannot be
ignited at such low compression ratios. Second, if the compression ratio is high enough,
and the piston acceleration is above the separation line 1ms after the TDC, it is decided
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that a normal combustion have happened. Third, if the compression ratio is high enough,
but the piston acceleration is below the separation line 1ms after the TDC, it is tentatively
decided that a misfire happened and misfire recovery control will be enabled. Yet the
piston acceleration continues to be monitored until 4ms after the TDC or the compression
ratio drops below 1.7 so that late combustions can be detected. Once the piston
acceleration passes the separation line during the monitoring, it is considered that a late
combustion happened. If combustion happened in the last cycle and it is either decided or
tentatively decided that misfire happened, the misfire recovery control will be enabled. If
a late combustion is detected after a tentative misfire decision, the misfire recovery
control will be terminated and normal IPFC control will resume. In this way, the misfire
detection can be done quickly while reducing the risk of faulty detection.
Figure 5.19. Flow chart of the misfire detection algorithm
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5.2.3. Control Design
The basic idea of misfire recovery control is to design a proper reference that supports
scavenging and the combustion for the recovery process, and use trajectory tracking to
enforce it. Transient controls also have to be designed to help transit between IPFC and
the misfire recovery control.
5.2.3.1. Reference Design
For misfire recovery to work properly, the trajectory needs to meet the following
conditions. First, the BDC has to be high enough to support good scavenging process.
The intake ports are at 51mm of piston motion. The misfire recovery trajectory has to
present a BDC higher than this to provide enough fresh air. The higher the BDC is, the
more efficient the scavenging process will be, and the sooner combustion can be
recovered. Second, the TDC has to be low enough to provide good compression for
combustions. Typically, during normal IPFC operation, the TDC position is between
8mm and 12mm.
In other words, a reference with a long stroke is desired. To achieve a trajectory with
maximum stroke length, it is desired that the hydraulic force always helps the piston
motion in both strokes with the largest magnitude, which in turn requires the servo valve
orifice to switch at TDCs and BDCs. Using the physics based model of the HFPE, a
square wave signal can be calibrated to achieve the aforementioned requirements. Then
the calibrated signal is tested on the hardware for validation. The corresponding piston
trajectory from the test is recorded and used as misfire recovery reference.
5.2.3.2. Controller Design
Although the misfire recovery trajectory can be achieved using the square wave signal,
a reference tracking controller is still needed to handle disturbances, such as change in
load pressure and friction force, and increase misfire recovery robustness. A feedforward
+ feedback controller similar to that described in section 5.1.3 is applied. The
feedforward signal is generated by plugging the square wave signal calibrated in the
previous subsection into (5.16). The feedback controller is a repetitive controller with a
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bandwidth of 110Hz and period of 35ms, which is 70 steps with a sample frequency of
2kHz. The bode plot of the designed repetitive controller is shown in Figure 5.20.
Figure 5.20. Bode plot of repetitive controller used in misfire recovery
5.2.3.3. Transient Control Design
When misfire happens, at the corresponding TDC, the servo valve is connecting the
outer chamber, which will be the pumping chamber during the following expansion
stroke, to high pressure, and will produce a net hydraulic force resisting piston motion.
This is opposite to the desired hydraulic force in the misfire recovery and could lead to a
very poor tracking performance, especially a very low BDC position, in the first cycle of
misfire recovery. Although with the trajectory tracking controller, the piston trajectory
can eventually converge to the desired reference, adding a transient control right after a
misfire is detected will help the trajectory to converge faster and therefore recover
combustions in fewer cycles.
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Since the basic idea is to connect the inner chamber to high pressure as soon as
possible, and bring the servo valve orifice to neutral at the BDC so that it can connect the
inner chamber to high pressure during the following compression stroke, a
straightforward switch based feedforward controller is used. As shown in Figure 5.21,
upon detection of misfire, a servo valve command is sent to connect the outer chamber to
high pressure, before a switch in servo signal happens to pull the orifice the other way so
that it goes to neutral at the BDC. The switch timing is acquired through calibration on
the HFPE model. Once the BDC is reached, the transient controller stops and the
trajectory tracking control takes over to deliver the misfire recovery trajectory. This
transient control is called the post misfire transient control.
Figure 5.21. Transient controller and controller transitions during misfire recovery
Similarly, when combustion resumes, under the misfire recovery control, the outer
chamber will be connected to low pressure at the corresponding TDC, and needs to be
brought to neutral so that the hydraulic force can be generated to resist piston motion and
oil can be pumped out during the expansion stroke. Similar to the post misfire transient
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control, a feedforward signal is calibrated using the HFPE model to do this. The control
is handed over to IPFC control at the first BDC after combustion recovery. This part of
transient control can be referred to as the post resumption transient. The whole process of
misfire recovery and controller scheduling can be found in Figure 5.21.
5.2.4. Testing Results
Tests are conducted to verify the feasibility of the proposed misfire recovery
mechanism. First, a square wave signal is calibrated to generate misfire recovery
reference, as discussed in 5.2.3.1. Then, the calibrated square wave signal is implemented
on the HFPE testbed, with results shown in Figure 5.22. Clearly, the hydraulic force
helps the piston motion in both strokes. A BDC of 53.7mm and TDC of 6.4mm is
achieved under this signal. The section marked in red is recorded as the reference for
misfire recovery.
Figure 5.22. Misfire recovery reference generation
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Figure 5.23. Tracking of misfire recovery reference
Next, the tracking of misfire recovery reference trajectory is tested to validate the
reference tracking controller. The result is shown below in Figure 5.23. As expected, the
reference is tracked properly with an error within +1 to -3mm.
Finally, the misfire recovery mechanism is put into test to recover a man-made misfire.
In order to do this, a switch signal similar to that described in Chapter 4 is calibrated to
deliver the IPFC. Once the switch point is reached during the compression stroke, a
feedforward is sent to switch the valve and conduct the overcorrection afterwards. As
shown below in Figure 5.24, the fuel injection is skipped after the 9th combustion at
around 4.29s to create a misfire at the next TDC, and the misfire recovery control takes
over once the misfire is detected. Upon triggering, the post misfire transient control is
enabled and connects the inner chamber to high pressure so as to push the piston to a
BDC of 53.2mm to facilitate a good scavenging process. After that, tracking control
signal is enabled to track the misfire recovery reference. Due to an efficient scavenging
process and proper piston trajectory, combustion is resumed at the following TDC.
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During the following expansion stroke, the post resumption transient control ensures a
zero servo valve orifice at the BDC before normal IPFC control resumes in the
compression stroke. Repeating such tests shows that the misfire is usually recovered after
the first cycle, with few exceptions where combustions resume after two cycles.
Figure 5.24. Misfire recovery performance. From top to bottom: piston trajectory,
hydraulic chamber pressures, servo valve signal
5.2.5. Performance Discussion
As mentioned in the last section, misfire can be recovered within one cycle. Since the
misfire recovery process doesn’t produce output flow but takes energy from the high
pressure instead, it is necessary to see what its impact on flow output and power output
are.
The flow condition around the misfire recovery section is shown below in Figure 5.25.
During normal IPFC operation, the flow output is 10.1ml/cycle. Then, during the misfire
recovery cycle, the flow direction changes and a net output flow of -13.7ml is produced
in the cycle. After that, flow for the first cycle after misfire recovery is also lower than
nominal mainly due to the post resumption transient and corresponding flow through the
servo valve. Data shows that about 7.0ml of flow is lost due to this transient, resulting in
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a cycle flow of 3.1ml for the first cycle after combustion resumption. From the second
cycle after combustion resumption, flow output comes back to normal.
Figure 5.25. Flow output around misfire recovery section
Energy wise, since flow is lost during the misfire recovery, hydraulic energy loss is
expected, as illustrated in Figure 5.26. In the figure, positive energy means net energy
input or propelling energy, and negative energy stands for energy dissipation. During the
misfire recovery cycle, the propelling energy is hydraulic energy while in normal IPFC
cycles it would be the expansion work from the left chamber. A total amount of 221J of
energy is taken form the high pressure side during the misfire recovery cycle. Out of that,
most energy, 122J, was consumed on throttling across the servo valve. 52.4J was
dissipated in overcoming friction and scavenging force, while 38.3J and 8.4J goes into
overcoming loss in the left and right chambers, i.e. compression work and air spring loss,
respectively. The air spring loss during this cycle is much lower than that from normal
operation cycles due to a lower compression ratio and therefore lower heat loss and
leakage in the air spring. After the misfire cycle, throttling loss increased significantly for
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the first cycle after combustion resumption, accounting for the 7ml extra flow loss
through servo valve during expansion stroke. The friction/scavenging loss and air spring
loss are also slightly higher than normal due to a faster piston motion and higher BDC
position. Just like flow output, the energy output returns to normal condition from the
second combustion after misfire.
Figure 5.26. Energy break down around misfire recovery section
5.3. Chapter Conclusion
In this chapter, robust realization of IPFC was attempted from two aspects, i.e. the in-
cycle robustness reinforcement based on trajectory tracking and the cycle-to-cycle
robustness reinforcement based on misfire recovery. Experimental results show that both
methods can provide a more robust realization of IPFC compared to the switch based
control.
Specifically, for the in-cycle robustness reinforcement method, even with the presence
of model uncertainty/disturbance, the system could still operate continuously with the
tracking based control. As for the misfire recovery method, it solved the problem of
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complex dynamics after misfire and is able to reliably resume combustion as well as
energy output in a short time with relatively small energy loss. The proposition and
validation of robust realization methods in this chapter pushed the IPFC technology one
step further and paved the road for practical application of the HPFE with IPFC.
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Chapter 6.
Conclusion and Future Work
Enlighted by the idea of free piston engine and digital pump, a novel method of using
HFPE as a mobile fluid power source, namely independent pressure and flow rate control,
or IPFC, is proposed and studied in this dissertation. The IPFC works for all current
HFPE architectures and is elaborated on both an OPOC HFPE and a single piston HFPE.
The system performance is investigated through simulation, where the system response
time and efficiency were investigated through a comprehensive physics based model of
OPOC HFPE. With both the engine side control and the pump side control addressed
under this unified framework, the simulation results show a response time in the order of
10ms and an overall efficiency ranging between 28% and 58%, which is significantly
superior compared to conventional ICE based fluid power sources. Optimal operation
conditions that balance thermal efficiency and mechanical efficiency are also studied,
where conclusions can be drawn that a higher compression ratio provides higher overall
efficiency at high flow demand.
Next, a HFPE testbed based on a prototype OPOC HFPE is presented, and the IPFC is
implemented with corresponding control schemes. With a limited robustness, the switch
based IPFC can achieve basic stable operation of HFPE under IPFC, thus validating the
feasibility of the IPFC. With detailed energy analyses, the bounce chamber and
scavenging/friction design are identified as key areas for improvement. Moreover, two
robustness reinforcement methods are proposed and experimentally validated, where
significant improvement of robustness is achieved with minimum performance sacrifice.
To the best knowledge of the author, this study is the first that combines the concept of
digital pump and HPFE and pushes forward the study in application of HFPE, laying the
foundation of efficient application of HFPE in mobile machineries. Through this study, it
is clear that a highly efficient, fast responding, multi-fuel capable and modular mobile
fluid power source can be achieved by HFPE using IPFC, showing great potential in
energy saving as well as greater impact on the environment protection.
Along the general idea of this study, some further work could be done.
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1. Combined optimization with more sophisticated combustion model. In this study,
although both the thermal efficiency and mechanical efficiency are considered, the
combustion model is only a simple Arrhenius integration based model, which
doesn’t reflect the detailed combustion process. As pointed out by Zhang, et al[36],
the combustion process can be affected by the piston trajectory, and therefore
produce different efficiency and emission performance. Implementing a more
detailed combustion model into the HPFE model can help establish better
understanding of the overall system performance, and provide possibility for
combined optimization regarding both emission and system efficiency, so as to
achieve a better balanced working condition.
2. Evaluating other working mode of digital pump with IPFC. The essence of IPFC is
the combination of digital pump and HFPE. Although only one mode of digital
pump operation, the flow diverting mode, is applied in this study, the general idea
of IPFC is compatible with all digital pump modes, including cylinder
enabling/disabling mode[14], [93], flow limiting mode[18], [19], and their hybrids
using the sequential pumping idea[18], [19]. Since these operation modes direct
relate to the hydraulic force and therefore piston motion, exploring these possible
combinations could lead to better piston trajectory and improved system efficiency.
3. Exploring asymmetric operation of OPOC HFPE. In this study, operation
conditions of both strokes in an OPOC HFPE are controlled to be the same. In
reality, they can be different, in compression ratio, valve timing and valve strategy
and therefore producing different combustion force and consequentially different
piston trajectory. Moreover, implementing this idea will support the use of
sequential pumping, providing a wider operation space and possibility for
optimization.
4. Further testing of IPFC method including transient performance. Due to the
hardware limitation, the experimental validation of the IPFC is only conducted
under constant working conditions. To better evaluate the IPFC, the hardware
could be improved to enable validation of IPFC under different working conditions
as well as under transient working conditions.
108
109
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Appendix. A
Details of the supercharger system
A twin screw based supercharger system is built to improve the scavenging process of
the HFPE. The drawing of the supercharger system is shown in Figure A.1. The key
components are listed in Table A.1.
Figure A.1. Drawing of the supercharger system
Index Name Description
1 Motor starter
2 Electric motor 254T Frame, 3 phase, 3600rpm, 15HP
3 Tension rod 1
4 MAF sensor Bosch HFM5
5 Tension rod 2
6 Tension rod 3
7 Supercharger head 1.6L/rev displacement
8 V belt system AX section belt ×2, 1:1 ratio
9 Discharge manifold
10 Relief valve Set at 18psi
11 Intake filter
12 Intake manifold
Table A.1. Key components of the supercharger system
The supercharger head is driven by a 3600rpm electric motor through a 1 to 1 V belt
transmission. Three thread rods work as tension rods and connects the mounting plate of
117
the supercharger head to the frame. Together with the mounting plate surface, all 6
degrees of freedoms are eliminated, and the supercharger head position can be
determined. Adjusting the tension rods can align the pulleys and apply tension on the belt.
The relief valve on the discharge manifold ensures an output pressure of 18psig. At such
a working condition the system can deliver approximately 48L/s compressed air and
meets the system input air demand. The actual output mass air flow to the HFPE can be
measured by the MAF sensor on the discharge manifold. Actual supercharger output
pressure is measured by a pressure sensor, which is sensor 7 in Figure 4.2.
A photo of the supercharger system hardware is shown below in Figure A.2.
Figure A.2. Photo of the supercharger system
