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Modeling, Identification and Control, Vol. 39, No. 2, 2018, pp. 73–89, ISSN 1890–1328
Energy Saving Potential in Knuckle Boom Cranesusing a Novel Pump Controlled Cylinder Drive
S. Ketelsen L. Schmidt V. H. Donkov T. O. Andersen
Department of Energy Technology, Aalborg University, 9220 Aalborg, Denmark. E-mail: [email protected]
Abstract
This paper is considering the application of a novel pump controlled cylinder drive, the so-called Speed-variable Switched Differential Pump (SvSDP), for knuckle boom crane actuation. Especially the controlsystem for the SvSDP drive is considered, and aiming on improving energy efficiency a refinement ofthe existing control structure is proposed. An energy efficient sizing algorithm for the SvSDP driveis developed, and fundamental differences between the achievable operating range for the SvSDP drivecompared to a conventional valve-cylinder drive are discussed. A case study is conducted with knuckleboom crane actuation, and compared to a conventional valve actuation. Simulation results show thatthe motion tracking performance is on a similar level compared to the valve actuation approach, whilethe energy consumption is drastically decreased. For the given test trajectory the valve actuation systemconsumes 0.79 kWh of electrical energy, while the SvSDP drive consume 0.06 kWh, if ideal energy recoveryand storage is assumed.
Keywords: Energy efficient hydraulic actuation, pump controlled cylinder, cylinder direct drive, offshorecranes, multivariable control
1 Introduction
The usage of hydraulics for low-speed high-force linearactuation is a well established standard in many in-dustries. Hydraulic actuation are traditionally selecteddue to the high power and force density they can of-fer. Conventionally, hydraulic cylinders are controlledusing proportional valves, which achieve the desiredmotion control performance by throttling the flows inand out of the cylinder chambers, which in turn is amajor source of losses in hydraulic systems. To re-duce the throttling losses, a load sensing pump maybe installed. This is often the case in knuckle boomcrane actuation systems, but a drawback of this strat-egy is that the supply pressure is determined by thedemand of the consumer requiring the largest pressure.This may lead to situations where a fast moving un-loaded cylinder, requires a large flow, while anothersmall flow-high pressure consumer determines the sup-
ply pressure, leading to large throttling losses for thefast moving cylinder. With increasing demands for en-ergy efficieny in most industries, research communitiesas well as industry are trying to identify other meth-ods for improving the overall efficiency of linear actua-tion in machinery, such as replacing hydraulic cylinderswith self-contained electromechanical cylinders Hagenet al. (2017). Other researchers are looking into so-called digital hydraulics. Examples of this approachinclude multi-chamber and/or multi-pressure cylindersHedegaard Hansen et al. (2018), Linjama et al. (2009)and Huova et al. (2017), hydraulic buck convertersKogler and Scheidl (2016), hydraulic power manage-ment concepts Vukovic et al. (2016), Linjama and Huh-tala (2010) etc. Most of these technologies are stillin the development phase, with the predominant chal-lenges being low reliability under high load operatingconditions for self-contained electromechanical cylin-ders Hagen et al. (2017), or the demand for faster
doi:10.4173/mic.2018.2.3 c© 2018 Norwegian Society of Automatic Control
Modeling, Identification and Control
xP
M A C B
Meq Geq
CxP2
ωm,ref
ωm
QA QC
QBQAC
QvA QvB
xvBxvAuvA uvB
PA PB
AAAB
Figure 1: Asymmetric cylinder controlled by SvSDP-system.
on/off valves for hydraulic buck converters Kogler andScheidl (2016). Another approach for reducing throt-tling losses is direct hydraulic cylinder drives/pumpcontrolled cylinders. The main idea is here to controlthe flow to the cylinder chamber directly by the pumpwithout any valves in the main transmission lines. Afundamental challenge for this concept is that an asym-metric hydraulic cylinder requires different chambervolume flows. One way of compensating the unequalflow rates is by throttling only the differential volumeflow using pilot operated check valves Rahmfeld (2002)or via an inverse shuttle valve Caliskan et al. (2016)and Michel and Weber (2012). Another approach isto use an asymmetric pump unit Quan et al. (2014),which effectively also can be obtained by using twofixed displacement pumps such as investigated in Ped-ersen et al. (2014) and Jarf et al. (2016). Here the twopumps are connected to a common shaft, but rotatein opposite directions. Furthermore, they are sized tomatch the area ratio of the cylinder.
The drive concept presented in Pedersen et al. (2014)demonstrated good hydraulic efficiency, but it wasfound that the effective pump displacement- and thecylinder area ratios, cannot be matched in the entireoperating range due to pump leakage, resulting in ir-regular performance. These issues led to the develop-ment of the Speed-variable Switched Differential Pump(SvSDP) drive, which was introduced and investigatedin Schmidt et al. (2015). The concept adds a thirdpump, only delivering flow in certain situations. InSchmidt et al. (2017) the control structure of this con-cept was further developed with the aim to decouple
Figure 2: Knuckle Boom Crane example provided byNational Oilwell Varco. c©
the motion control and chamber pressure control.The SvSDP drive topology is depicted in Fig. 1. At
positive shaft speeds, pumps A and C provide flow tochamber A of the cylinder, while pump B withdrawsfluid from cylinder chamber B. At negative shaft speedspump C idles, effectively providing no flow to the cylin-der A chamber. Hence a surplus flow into the cylinderis present in both directions of operation, and a pres-sure increase will appear for shaft speeds where pumpflow exceeds internal leakage Schmidt et al. (2015). Inorder to maintain chamber pressures at reasonable lev-els this flow mismatch may be bled off via the 2/2 pro-portional valves. Hence the system has three inputsωm,ref, uvA and uvB. As it is not possible to controlthe motion of the cylinder and both chamber pressuresindependently, only two sensible outputs may be de-fined, leaving the system over-actuated. In the currentinvestigation, the SvSDP concept from Schmidt et al.(2017) will be investigated for actuation of a knuckleboom crane similar to the one seen in Fig. 2. A modelbased approach to the sizing of the SvSDP drives ispresented, and a control strategy targeting at a highenergy efficiency is established. The resulting perfor-mance is compared to that of a conventional valve op-eration approach and simulation results demonstratesimilar motion performance, while the SvSDP drive ap-proach shows a highly improved energy efficiency com-pared to the valve actuation system.
2 Mechanical Knuckle Boom CraneModel
A knuckle boom crane may be illustrated as depictedin Fig. 3. Due to the often large cylinders, the massesof cylinder tubes and rods may be significant comparedto the crane booms and payload, and may therefore betaken into account. Hence the mechanical system maybe depicted as having seven centers of mass (CMs),all moving relative to each other. As illustrated, the
74
Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
cylinder tube and piston CMs are equivalated into acombined CM for each cylinder, resulting in five CMsto be included in the model. Defining the joint anglesϕ1, ϕ2 and ϕ3 (generalised coordinates), the CMs maybe described by:
PCM1 = A1S1, PCM2 = A1S2 + A2S3 (1)
PCM3 = A1S2 + A2S4 + A3S4, (2)
PCMcyl1 = A4S6, PCMcyl2 = A1S2 + A5S7 (3)
Here, matrices and vectors are given by:
A1 =
[cos(ϕ1) − sin(ϕ1)sin(ϕ1) cos(ϕ1)
]A2 =
[cos(ϕ1 + ϕ2) − sin(ϕ1 + ϕ2)sin(ϕ1 + ϕ2) cos(ϕ1 + ϕ2)
]A3 =
[cos(ϕ1 + ϕ2 + ϕ3) − sin(ϕ1 + ϕ2 + ϕ3)sin(ϕ1 + ϕ2 + ϕ3) cos(ϕ1 + ϕ2 + ϕ3)
]A4 =
[cos(ϕ1 − α8 − α1) − sin(ϕ1 − α8 − α1)sin(ϕ1 − α8 − α1) cos(ϕ1 − α8 − α1)
]A5 =
[cos(ϕ1 + ϕ2 − α10 + α2)sin(ϕ1 + ϕ2 − α10 + α2)
− sin(ϕ1 + ϕ2 − α10 + α2)cos(ϕ1 + ϕ2 − α10 + α2)
]S1 =
[LCCM1x
LCCM1y
], S2 =
[LCF
0
], S3 =
[LFCM2x
LFCM2y
]
S4 =
[LFJ
0
], S5 =
[LJCM3
0
]S6 =
[LCcyl1
0
], S7 =
[LFcyl2
0
]The total kinetic energy K may be expressed as:
K =m1
2PT
CM1PCM1 +m2
2PT
CM2PCM2 (4)
+m3
2PT
CM3PCM3 +mcyl1
2PT
CMcyl1PCMcyl1
+mcyl2
2PT
CMcyl2PCMcyl2 +J1
2ϕ2
1 +J2
2(ϕ1 + ϕ2)2
+J3
2(ϕ1 + ϕ2 + ϕ2)2 +
Jcyl1
2
(ϕ1 −
∂α8
∂ϕ1ϕ1
)+Jcyl2
2
(ϕ1 + ϕ2 −
∂α10
∂ϕ2ϕ2
)The total potential energy P may be expressed as:
P = gT (PCM1 + PCM2 + PCM3 + PCMcyl1 (5)
+ PCMcyl2), g = [0 g]T
Hence, the Lagrangian L = K−P may by formed, fromwhich the joint torques may be established as:
τ1 =d
dt
∂L∂ϕ1
− ∂L∂ϕ1
(6)
τ2 =d
dt
∂L∂ϕ2
− ∂L∂ϕ2
(7)
τ3 =d
dt
∂L∂ϕ3
− ∂L∂ϕ3
(8)
Lcyl
xmax = 2xmin
xmin/2
xmin
C
D
CM2
CM3
G
F
H
Jα1
B
φ1
-φ2
α2
A
α4
α5α6
α7
α9
α8
α10LFcyl2
-φ3
CM1
CMcyl1
CMcyl2
Payload
xP
xmin/2
Equivalent center of mass for cylinders
CMtube CMpiston CMcyl
α3
Figure 3: Illustration of a knuckle boom crane with two hydraulic cylinders.
75
Modeling, Identification and Control
Defining q = [ϕ1 ϕ2 ϕ3]T where ϕ1 = α1 + α3(xP1) +α4−π/2, ϕ2 = α5(xP2) +α6−α2−π, the joint torqueτ = [τ1 τ2 τ3]T may be expressed as:
τ = D(q)q + C(q, q) + G(q) (9)
Noting q = Jx, x = [xP1 xP2 0]T the dynamic modelmay be described in cylinder space as:
F = JTD(x)Jx + JT (D(x)Jx + C(x, x)) (10)
+ JTG(x)
Here, F is the linear mechanical output force given by:
F = Fhyd −Bx, B =
[Bv1 0
0 Bv2
](11)
3 SvSDP Cylinder Drive
The two structurally identical SvSDP drives neededfor knuckle boom crane actuation are subscripted withi = 1, 2 (SvSDP1 and SvSDP2).
3.1 Nonlinear Model
Considering Fig. 1, the SvSDP drive is described byEq. (12)-(20), assuming ideal check valves, no cylin-der cross port leakage, nonlinear friction phenomenaabsent, and defining VAi = VA0i + AAixPi , VBi =VB0i
−ABixPi
, αi = ABi/AAi
. i = 1, 2
xPi =AAi (PAi − αiPBi)− xPiBvi − f(x, x)
Meqi
(12)
PAi=βAi
VAi
(QACi−QvAi
− xPiAAi
) (13)
PBi=βBi
VBi
(xPiαiAAi
−QBi−QvBi
) (14)
QACi =
QAi
(ωmi)ηvAi
+ QCi(ωmi
)ηvCi, ωmi
≥ 0QAi(ωmi)/ηvAi , ωmi < 0
(15)
QBi =
QBi
(ωmi)/ηvBi
, ωmi≥ 0
QBi(ωmi)ηvB , ωmi < 0(16)
QvAi= KvAi
xvAi, QvBi
= KvBixvBi
(17)
xvAi= ω2
vAiuvAi
− 2ζvAiωvAi
xvAi− ω2
vAxvAi(18)
xvBi = ω2vBi
uvBi − 2ζvBiωvBi xvBi − ω2vBxvBi (19)
ωmi= ω2
viωm,refi − 2ζvi
ωviωmi− ω2
vωmi(20)
f(x, x) contains the gravitational load and the Coriolisforce. QAi
, QBiand QCi
are leakage free pump flows,ηvAi , ηvBi and ηvCi are pressure dependent volumet-ric pump efficiencies, PAi and PBi chamber pressures,xvAi
, xvBithe valve spool positions, ωmi
the motorshaft speed and xPi
the cylinder piston position. The
valve inputs uvAi , uvBi and the motor shaft referencespeed ωm,refi are the three system inputs. Addition-ally, Bv,i is a viscous friction coefficient, ζvAi
, ζvBi, ζvi
damping ratios, ωvAi, ωvBi
, ωvibandwidths, βAi
, βBi
the effective bulk moduli and KvA,KvB are the flowgains of the 2/2 pressure compensated proportionalvalves.
Furthermore, the hydraulic forces are given by:
Fhyd =
[AA1
(PA1− α1PB1
)AA2
(PA2− α2PB2
)
](21)
3.2 Linear Model
The inverse flow characteristics of the 2/2 proportionalvalves are used to compensate the input (uvAi
anduvBi), meaning that ideally QvAi = QvA,refi , QvBi =QvB,refi , if neglecting valve dynamics. Considering thegravitational load as a disturbance and assuming thevelocity dependent Coriolis forces negligible and equaleffective bulk moduli (i.e. βAi
= βBi= βi), the linear
model is given by Eq. (22), when defining relationsρi = VBi/VAi , ρ0i = V0Bi/V0Ai where V0Ai = VAi |x0i
,V0Bi
= VBi|x0i
and x0iis the state vector at the lin-
earisation point.
xc = Acixci + Bciurefi , ypi= Ccixci
xci =
[xpi
xui
], Aci =
[Api
BpiCui
0 Aui
]Bci =
[0
Bui
], Cci =
[Cpi
0]
(22)
xpi= [xPi xPi pAi pBi ]
T
xui = [ωmi ωmi qvAi qvAi qvBi qvBi ]T
urefi = [ωm,refi qvA,refi qvB,refi ]T
ypi= [xPi
pAipBi
]T, Cpi
=
1 0 0 00 0 1 00 0 0 1
Api=
0 1 0 0
0 − Bvi
Meqi
AAi
Meqi−αiAAi
Meqi
0 −βiAAi
V0Ai−βiKAqpi
V0Ai0
0βiαiAAi
ρ0iV0Ai
0βiKBqpi
ρ0iV0Ai
Bpi=
0 0 00 0 0
βiKAqi
V0Ai− βi
V0Ai0
− βiKBqi
ρ0iV0Ai
0 − βi
ρ0iV0Ai
KAqpi
=∂QACi
∂PAi
∣∣∣∣x0
KBqpi=∂QBi
∂PBi
∣∣∣∣x0
KAqi=∂QACi
∂ωmi
∣∣∣∣x0
KBqi=∂QBi
∂ωmi
∣∣∣∣x0
76
Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
Aui=
Au1i0 0
0 Au2i 00 0 Au3i
Au1i =
[0 1−ω2
vi−2ζvi
ωvi
]Au2i
=
[0 1
−ω2vAi
−2ζvAiωvAi
]
Cui=
1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 0
Bui=
0 0 0ω2
vi0 0
0 0 00 ω2
vAi0
0 0 00 0 ω2
vBi
The combined linear model Eq. (22) may be ex-
pressed by the transfer function matrix Eq. (24)
yp(s) = Gc(s)uref(s) (23)
Gc(s) = Cc(sI−Ac)−1Bc (24)
The transfer functions for the plant and actuator dy-namics may respectively be obtained as:
ypi(s) = Gpi
(s)upi(s)
Gpi(s) = Cpi
(sI−Api)−1Bpi
(25)
yui(s) = Gui(s)urefi(s)
Gui(s) = Cui
(sI−Aui)−1Bui
(26)
upi= [ωmi
qvAiqvBi
]T
urefi = [ωm,refi qvA,refi qvB,refi ]T
In Schmidt et al. (2017) the significance of the dy-namic couplings was studied using a relative gain array(RGA)-analysis. For the considered input-output com-binations it was found that severe dynamic couplingsare present, especially close to the system eigenfre-quency. Due to these couplings a decentralised controlstrategy may not be utilised directly on the system.
3.3 Control Strategy
In Schmidt et al. (2017) a drive control strategy hasbeen developed to handle the dynamic couplings, withthe overall structure depicted in Fig. 4. The funda-mental idea is to transform the input- and output vari-ables using y = W2yp, u = W−1
1 uref. By choosingthe transformation matrices W1 and W2 properly it
is shown possible to decouple the transformed systemstates, as shown in Eq. (27) and Eq. (28).
up = Guuref, uref = W1u ⇒ up = GuW1u (27)
y = W2yp, yp = Gpup ⇒ y = W2Gpup (28)
Substituting Eq. (27) into Eq. (28), gives the trans-formed system as:
y = W2GpGuW1u = Gcu, (29)
Note that the index i is omitted in this section, as thedeveloped control strategy is identical for both cylinderdrives.
3.3.1 Output Transformation
As mentioned, it is only sensible to control two of thenon-transformed outputs. As three inputs are avail-able the system is said to be over-actuated. In Schmidtet al. (2017) it is found desirable to formulate an out-put transformation (W2) such that more appropriatestates than the actual chamber pressures may be con-sidered. These appropriate states are selected to be thepiston position, the virtual load pressure PL, and thelevel pressure Pδ. The level pressure can be considereda weighted sum of the chamber pressures:
PL = PA − αPB, Pδ = PA + δPB, δ > 0 (30)
Using PL, Pδ then PA, PB may be written as:
PA =αPδα+ δ
+δPL
α+ δ, PB =
Pδα+ δ
− PL
α+ δ(31)
The nonlinear dynamics of the load and level pressureare described in Eq. (32) and Eq. (33).
PL = PA − αPB (32)
=β
ρVA(ρ(QAC −QvA) + α(QB +QvB)
−AA(α2 + ρ)xP)
Pδ = PA + δPB + δPB (33)
=β
ρVA(ρ(QAC −QvA)− δ(QB +QvB)
−AA(ρ− αδ)xP) +δ
δ + α(Pδ − PL)
In Eq. (33) δ is chosen as ρ/α in order to decouplevolume flow from the level pressure dynamics. Doingso, Eq. (32) and Eq. (33) become:
PL =β
ρVA(ρ(QAC −QvA) + α(QB +QvB) (34)
−AA(α2 + ρ)xP
)Pδ =
β
ρVA(ρ(QAC −QvA)− δ(QB +QvB) (35)
−xPAAρ
β
δ + 1
δ + α(Pδ − PL)
)
77
Modeling, Identification and Control
Level Pressure Ref. Generator
Inverse Flow Compensator
Valve B flow ref.
Motor speed reference
Pδ
δ-update
xP
pB
pA
Motion Reference
xP
xP
Pδ
PL
Gain Gain
+- ++ ++
-+
xref
.
Drive Controller
xP,ref
Pressure controller
Position controller
Pδ,ref
Output trans.(W2)
Input trans.(W1)
PL
Valve A flow ref. Valve signal A
Valve signal B
Transformed / virtual states Physical states
M A C B
xP
pB
pA
SvSDP Drive
QL
Qδ
Figure 4: Schematic of the complete drive control system. Schmidt et al. (2017).
The linear pressure dynamics may be obtained as:
pδ0 =β
V0A(α+ δ0)
((α+ δ0)
(K∆ωωm − qvA −
qvB
α
)− (Kδpδ +Kδp)pδ − (KδpL −Kδp)pL) (36)
−KδxdxP −KδxpxP
pL =β(α+ δ0)
V0Aδ0
(δ0
α+ δ0
(KΛωωm − qvA +
qvB
δ0
)−AAxP −
δ0KLpδ
(α+ δ0)2pδ −
δ0KLpL
(α+ δ0)2pL
)(37)
K∆ω = KAq −KBq
α, Kδpδ = αKAqp −
KBqp
α
KδpL = δ0KAqp +KBqp
α, KΛω = KAq +
KBq
δ0
KLpδ = αKAqp +KBqp
δ0, KLpL = δ0KAqp −
KBqp
δ0
Kδp =xP0AA(δ0 + 1)
β, Kδxd =
∂Pδ∂xP
∣∣∣∣∣x0
Kδxp =∂Pδ∂xP
∣∣∣∣∣x0
From the above, the output transformation may be es-tablished as:
y = W2y, y =
xP
pL
pδ
, W2 =
1 0 00 1 −α0 1 δ0
(38)
Virtual inputs in terms of level flow qδ and load flowqL are defined based on the level and load pressuredynamics in Eq. (36) and Eq. (37), as defined in Eq.
(39) and Eq. (40):
qδ = (α+ δ0)(K∆ωωm − qvA −
qvB
α
)(39)
qL =δ0
α+ δ0
(KΛωωm − qvA +
qvB
δ0
)(40)
pδ0 =β
V0A(α+ δ0)(qδ − (Kδpδ +Kδp)pδ−
(KδpL −Kδp)pL)−KδxdxP −KδxpxP (41)
pL =β(α+ δ0)
V0Aδ0
(qL −AAxP −
δ0KLpδ
(α+ δ0)2pδ (42)
− δ0KLpL
(α+ δ0)2pL
)The choice of qδ and qL is such that the non-
transformed inputs in terms of shaft velocity and pro-portional valve flows does not directly influence thepressure level and load pressure gradients, but are con-tained in qδ and qL. Control structures using these newinputs can thereby be designed independently of thevalue and sign of the shaft velocity and of the valvesignal allocation.
The input transformation matrix W1 is used totransform qδ and qL to the original input signals.
u = W1u (43)
From Eq. (39) and Eq. (40) the inverse input trans-formation matrix can be obtained as Eq. (44):
u = W−11 u
u = [qL qδ q0]T , u = [ωm qvA qvB]T
W−11 =
δ0KΛω
α+δ0− δ0α+δ0
1α+δ0
(α+ δ0)K∆ω −(α+ δ0) −α+δ0α
v31 v32 v33
(44)
78
Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
The entries v31, v32, v33 may be chosen arbitrarily. Theflow q0 is a flow constraint which is chosen based on thedesired distribution of the valve signals. The simplestflow constraint is q0 = 0, which is chosen here.
In Schmidt et al. (2017) main focus is on motion per-formance, i.e. de-emphasising energy efficiency. Theinput transformation matrix was constructed such thatthe valve flows did not influence the load flow in Eq.(40) i.e. ideally the piston motion is only driven by ωm.This can be obtained by choosing parameters v31 = 0,v32 = 1, v33 = −1/δ0, and q0 according to:
q0 = qvA −qvB
δ0= 0 (45)
The resulting input u is then given by:
uxP = WxP1 u =
α+δ0δ0KΛω
qLK∆ωαδ0KΛω
qL − α(α+δ0)2 qδ
K∆ωαKΛω
qL − αδ0(α+δ0)2 qδ
(46)
The superscript xP is added to emphasise that the in-put transformation is derived to improve motion per-formance, and is referred to as the original input trans-formation in the remainder.
In Schmidt et al. (2017) an RGA-analysis of thetransformed system, Gc in Eq. (29) using the transfor-mation matrices WxP
1 and W2 showed that an almostperfect decoupling in the frequency range below theactuator bandwidths was achieved. A decentralisedcontrol strategy of the transformed system is there-fore reasonable, where the transformed inputs qL andqδ are used to control the transformed inputs xP andpδ respectively. These decentralised controllers are de-signed based on a generic analytical linear controllerdesign approach, presented in Schmidt et al. (2017),capable of calculating appropriate controller parame-ters regardless of SvSDP drive size. This is done byincluding physical parameters such as cylinder areasand pump displacements combined with desired rel-ative stability margins in the controller design algo-rithm. The level pressure ref. generator seen in Fig. 4,is used to generate a Pδ reference. The reference is gen-erated based on which chamber pressure to keep at areasonable value pset = 20 bar and the piston position.In Schmidt et al. (2017) experimental results prove thatthe SvSDP drive and presented control strategy are ca-pable of maintaining a minimum chamber pressure at≈ pset while achieving a motion performance at least onthe same level as a conventional servo-valve controlledsystem.
3.3.2 Energy Efficient Valve Utilisation
For the presented input transformation matrix, oil is si-multaneously throttled through both 2/2 valves, which
obviously is not the optimal valve utilisation in termsof energy efficiency. For an energy efficient valve util-isation only oil from the low pressure side should bethrottled, which may be achieved by changing the in-put transformation. It is notable that only the inputtransformation needs to be changed while the outputtransformation, controller parameters etc. remain un-changed, as these are used for controlling transformedvariables. As such the input transformation is onlyused to allocate physical inputs from transformed in-puts. The input transformation, which only allows oilthrough the B-side valve can be obtained by definingv31 = 0, v32 = 1, v33 = 0 in Eq. (44) and q0 as:
q0 = qvA = 0 (47)
The resulting input uqvB is then given by:
uqvB = WqvB1 u =
α+δ0αK∆ω+δ0KΛω
qL + α(α+δ0)(αK∆ω+δ0KΛω)qδ0
(α+δ0)K∆ωααK∆ω+δ0KΛω
qL − δ0KΛωα(α+δ0)(αK∆ω+δ0KΛω)qδ
(48)
When only allowing oil through the A-side valve theinput transformation can be obtained by defining v31 =0, v32 = 0, v33 = 1 and q0 as:
q0 = qvB = 0 (49)
resulting in the following input transformation:
uqvA = WqvA1 u = −
α+δ0(K∆ω−KΛω)δ0
qL + 1(α+δ0)(K∆ω−KΛω)qδ
− (α+δ0)K∆ω
(K∆ω−KΛω)δ0qL + KΛω
(α+δ0)(K∆ω−KΛω)qδ0
(50)
Which input transformation Eq. (48) or Eq. (50) tobe used depends on which chamber pressure to be con-trolled to the minimum chamber pressure, pset . Thisswitching condition is defined from the measured loadpressure PL using Eq. (51) setting PA = PB = Pset
pLsw = Pset − αPset = (1− α)Pset (51)
As illustrated in Fig. 5(a), ideally PA = Pset for pL <pLsw
using the input transformation in Eq. (50) andPB = Pset for pL > pLsw using the input transformationin Eq. (48). To avoid abrupt jumps in the utilisedinput transformation method a switching variable Z isdefined as:
Z =
0 , pL < (pLsw
− Zband)PL−pLsw+Zband
2Zband, (pLsw
+ Zband) > pL >
(pLsw − Zband)1 , pL > (pLsw + Zband)
(52)
Z = 1− Z; (53)
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Modeling, Identification and Control
In Fig. 5(b) the switching variables are seen as a func-tion of the load pressure. The non-transformed inputsu are then defined as a weighted sum between uqvA
and uqvB according to:
u = ZuqvB + ZuqvA (54)
Eq. (54) is referred to as the energy efficient inputtransformation in the remainder.
-50 0 50
(a) Load Pressure [Bar]
0
50
100
150
Cha
mbe
r P
ress
ures
[Bar
]
-50 0 50
(b) Load Pressure [Bar]
0
0.5
1
Sw
itchi
ng
Con
ditio
n [-
]
Figure 5: (a) Ideally controlled chamber pressures as afunction of load pressure for pset = 20 barand α = 0.5. (b) Input transformationswitching variables as a function of load pres-sure for Zband = 5 bar
3.4 Energy Efficient Pump Sizing
Assuming that the considered knuckle boom craneshould be retrofitted with SvSDP-actuated cylinderdrives, it is likely that the hydraulic cylinders remainunchanged thus only replacing the conventional HPUincluding valves with SvSDP drives. This necessitatesthat the SvSDP sizing should aim at delivering ap-proximately the same flow amount in the same pres-sure range as achievable with the conventional ValveCylinder Drives (VCDs). In Schmidt et al. (2017), ex-ternal gear pumps have been used as flow suppliers inthe SvSDP drive. As these generally operate in a lim-ited pressure range, internal gear pumps are suggestedfor larger power applications as considered here. Thepump sizes selected for the system are of crucial im-portance in terms of energy efficiency, as these heavilyaffect both electrical and hydraulic losses. Ten differentpump sizes ranging from 16 cm3/rev to 125.2 cm3/rev(Rexroth, 2010) and (Rexroth, 2013) have been consid-ered for each pump, yielding a total of 1000 differentpump size combinations. In this section a selectionalgorithm aiming on selecting an energy efficient and
feasible pump combination is proposed. For doing so,the dominant system losses must be described.
3.4.1 Dominating Losses
In Fig. 6 the main losses during operation are shown.
Ehyd,pumpEel Emech,shaftEhyd,out
Electrical losses
Eβ
Mechanical losses
Volumetric losses
Throttling losses
Figure 6: Main losses during operating of the SvSDP-
actuated cylinder. Eβ is power due to thecompressibility of the oil.
The electrical losses in the frequency converter andiron losses in the electrical motor are assumed ne-glectable and thus the only electrical loss included arethe Ohmic losses in the electrical motor described by(Willkomm et al., 2014):
El,Ω = 3RcuI2 = 3Rcu
(τshaft
τnomInom
)2
(55)
Rcu is the winding resistance, and Inom is the nomi-nal current at the nominal motor torque, τnom. Theseparameters are available from datasheets. τshaft is cal-culated by:
τshaft =
(KAQ +KCQ)PA −KBQPB , ωm ≥ 0KAQPA −KBQPB , ωm < 0
(56)
where KAQ, KBQ and KCQ are the theoretical pumpdisplacements [m3/rad].
The mechanical losses due to pump friction havebeen neglected as no information for the considered in-ternal gear pumps are available. The volumetric lossesin the pump are described by:
El,v = (Kl,v1∆P +Kl,v2∆P 2)∆P (57)
where ∆P is the pressure difference across the pump,and Kl,v1 and Kl,v2 are leakage parameters. Frompump datasheet (Rexroth, 2013), a flow curve for a16 cm3/rev pump at 1450 RPM is available. This hasbeen used to fit the leakage related parameters in Eq.(57), assuming leakage-free flow at ∆P=0. The co-herence between the flow curve and the model is seen
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Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
in Fig. 7(a). In Fig. 7(b) corresponding volumetricefficiencies for different speed levels are shown. Identi-cal volumetric efficiencies have been used for all pumpsizes considered. This may be a conservative estima-tion as volumetric efficiencies are assessed to improvefor larger pump sizes.
0 50 100 150 200 250 300
(a) P [Bar]
22
23
24
Q [L/min
] Datasheet@1450RPM
Model@1450RPM
0 50 100 150 200 250 300
(b) P [Bar]
0.6
0.8
1
vol [-
]
200 RPM500 RPM1000 RPM2500 RPM
Figure 7: (a) Pump flow model compared to datasheet.(b) Pump volumetric efficiency.
Throttling losses in pipes and hoses as well as overthe ideally modelled check valves are neglected. There-fore the throttling losses only involve the oil throughthe 2/2 proportional valves, described by:
El,th = QvA · PA +QvB · PB (58)
3.4.2 Pump Selection Algorithm
The Valve Cylinder Drives (VCD) used as a benchmark(see Section 4) for the proposed SvSDP, produces max-imum flows of 160 L/min to each cylinder. Due to loadsensing it is assumed that this can be done indepen-dently of the cylinder load pressure. This translates topiston velocities ranging from -88 mm/s to 43 mm/s forcylinder 1 and from -113mm/s to 54 mm/s for cylinder2.
A fundamental difference between a (symmetrical)-valve controlled asymmetric cylinder system and theproposed SvSDP system, is that for the SvSDP thepump flows are matched to the cylinder area ratio caus-ing the achievable velocities to be somewhat symmet-rically distributed around 0 mm/s, if utilising the 2/2valve on the A-side only.
However for energy-efficient valve utilisation it is de-sired to throttle from the low pressure chamber, whichmay be any chamber, affecting the achievable pistonvelocities. E.g. if always throttling from the B-side,the steady state forward velocity is determined by the
combined flow of pump C and A, whereas the retract-ing velocity is determined by the flow of pump A onlyas the C-pump is idling. This causes the maximumvelocities to be asymmetrical around 0 mm/s. For thegiven example the forward velocity is larger than theretracting velocity, exactly opposite of a VCD.
These considerations show that a SvSDP drive sizedto achieve VCD comparable retracting velocities, maybe heavily oversized in the forward direction, due toidling of the C pump. The flow requirements (FR)are therefore relaxed in the retracting direction andformulated as:
FRωm≥0 =
1 ,((QA +QC) ≥ 160 L
min
)and
(QB/α ≥ 160 L
min
)0 , otherwise
(59)
FRωm<0 =
1 ,(−QA ≥ 0.9 · 160 L
min
)and
(−QB/α ≥ 160 L
min
)0 , otherwise
(60)
where QA, QB, QC are pump flows evaluated at maxi-mum allowed pressure and maximum positive/negativepump speed for FRωm≥0 and FRωm<0 respectively. Fora combination of pumps to be feasible FRωm≥0 =1 and FRωm<0 = 1 is required along with a match-ratio (χ) larger than 1 evaluated at ±500 RPM and225 bar. For χ > 1 a surplus of flow into the cylinderis present. χ is defined as:
χ =
QA+QC
QBα , ωm ≥ 0
QB
QAα, ωm < 0
(61)
Evaluating Eq. (59), (60) and Eq. (61) gives a num-ber of feasible designs. Assuming oil always to bethrottled from the low pressure side and by neglect-ing pump leakage the static mismatch flow for eachfeasible combination can be calculated and throttlinglosses evaluated using Eq. (58), as a function of shaftspeed and pset. Assuming a constant minimum cham-ber pressure, the shaft torque may be calculated andthe Ohmic losses may be evaluated using Eq. (55) asa function of load pressure. By sweeping over the en-tire pump velocity and load pressure range, the pumpcombination with the smallest average loss is chosen.The pump selection algorithm is summarised in Fig. 8.
ConstructDesign Vector
1000 designs
Evaluate χ @ 500 RPM / 225 Bar
Evaluate flow requirements @ 3000 RPM / 315 Bar
Reject design
>1
< 1
( 177 / 170 )
Evaluate mean losses
Satisfied
( 45 / 41 )
UnsatisfiedSelect design
with smallest mean loss
Figure 8: Pump selection algorithm. In parenthesisare shown the number of feasible designs forSvSDP1 and SvSDP2 respectively.
81
Modeling, Identification and Control
As the two cylinders have almost equivalent area ra-tios and the same flow requirement is imposed the se-lected pump combination is the same for SvSDP1 andSvSDP2. Pump A is selected as having a displacementof 50.7 cm3/rev and Pump B and C are both havinga displacement of 32.7 cm3/rev. The resulting matchratio χ for SvSDP1 is seen in Fig 9(a).
-3000 -2000 -1000 0 1000 2000 3000
(a) m1 [RPM]
0.8
1
1.2
1 [-
]
10 Bar100 Bar300 Bar
-100 -50 0 50 100
(b) dxP1 [mm/s]
0
200
pL
1 [bar
]
VCD Operating Range
-100 -50 0 50 100
(c) dxP2 [mm/s]
-200
0
200
pL
2 [bar
]
SvSDP w/ Low Pressure Throttling SvSDP w/ High Pressure Throttling
Figure 9: (a) Match ratio for the selected pump com-bination. (b) Operating range for SvSDP1
compared to VCD. (c) Operating range forSvSDP2 compared to VCD.
The obtained operating ranges, assuming that a suit-able electrical motor which does not saturate at cornerpower requirements, is seen in Fig. 9(b) and (c). Theoperating ranges are evaluated by assuming that thecontrol structure can maintain a minimum chamberpressure of 20 bar during motion, and using a max-imum operating pressure of 315 bar for the internalgear pumps.
Noting that due to the crane structure chamber Awill always be load carrying for SvSDP1 while theSvSDP2 should carry the load in both directions, thistranslates to load forces ranging from 10 to 305 bar (62kN to 1.88 MN) for SvSDP1 and -132 to 305 bar (-0.65MN to 1.5 MN) for SvSDP2 respectively.
Note, that in Fig. 9 operating ranges obtainable ifthrottling from the high pressure chamber are also de-picted. Doing so, alters the achievable operating range,at the cost of larger throttling losses.
4 Benchmark System
As mentioned, the benchmarks for the two SvSDPdrives are Valve Cylinder Drives (VCDs), convention-ally used for actuation of a knuckle boom crane. Thehydraulic system structure is shown in Fig. 10, and hasalso been used in Donkov et al. (2018). The motionof the cylinders is controlled by the directional pro-portional valves. The two directional valves are pres-sure compensated and produce maximum flows of 160L/min. Furthermore, the supply pump has load sens-ing capabilities. The larger pressure in an inlet cham-ber selects the outlet pressure setting for the pump(Ps = Pmax + 35 bar). The counterbalance valves(CBV) are used to prevent the load from overrunning.
For details on the modeling of the benchmark sys-tem, component sizes etc., see Donkov et al. (2018).
M
Meq
xP
PA1
1
Meq
Cylinder 1
Load Sensing Pump
CBV
PB1
AA1 AB1
xP
PA2
2 Cylinder 2
PB2
AA2 AB2
Figure 10: Knuckle Boom Crane hydraulic circuit fromDonkov et al. (2018).
5 Simulation Results
To compare the performance of the SvSDP conceptwith the conventional system a simulation study hasbeen conducted. A test case trajectory has been se-lected where a 5000 kg payload begins and ends in thesame place. In tool center space this can be seen inFig. 11 taken from Donkov et al. (2018). The trajec-tory consists of starting the load at point 1, moving itto point 2 and returning it to point 1.
In actuator space the trajectory is shown in Fig. 12.Key parameters, such as component sizes, crane di-mensions and masses used for the simulation study arefound in the Key Parameter List on page 88.
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Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
0 5 10 15 20-10
-5
-5
0
5
10
x [m]
y [m]
Point 1
Point 2
Figure 11: The load is moved from 1 to 2 and back to1. Donkov et al. (2018).
0 20 40 60 80 100
(a) Time [s]
0100020003000
XP
,ref
i
[mm
]
0 20 40 60 80 100
(b) Time [s]
-50
0
50
dXP
,ref
i
[mm
/s]
Cylinder 1 Cylinder 2
Point 2
Figure 12: Test case trajectory in actuator space. Thestart and end point correspond to point 1 inFig. 11. Point 2 is marked.
5.1 Motion- and Control StucturePerformance
In Fig. 13 the performance results for the VCDs areshown. It is found that satisfactory motion tracking isachieved, as the maximum position error for cylinder 1is 9 mm (0.4 % of full stroke) and 18 mm (0.6% of fullstroke) for cylinder 2. Note, in Fig. 13(e) the valvesare almost fully open in the forward direction, mean-ing that the trajectory is defined close to the forwardvelocity limits. In Fig. 13(f) the supply pressure (ps)of the common pump is adjusted accordingly to thevalve positions. This explains why during standstill psoscillates, as the valve positions oscillate around the
0-position.In Fig. 14 the performance results for the SvSDP drivesare shown, using the energy efficient input transforma-tion, Eq. (54). It is seen that motion tracking is onthe same level as for the VCDs. The SvSDP performsslightly better for cylinder 1 compared to the VCD sys-tem, with a maximum position error of 3 mm (0.1 % offull stroke). For cylinder 2 the maximum position erroris comparable to the VCD, but during forward motiona slightly larger tracking error is present for the SvSDP.In total it is assessed that the motion performance areon the same level.From Fig. 14(b) and (d) it is seen that the controlstructure manages to keep the minimum chamber pres-
0 20 40 60 80 100
(a) Time [s]
0100020003000
x Pi[m
m]
0 20 40 60 80 100
(c) Time [s]
-20
0
20
eX
Pi[m
m]
0 20 40 60 80 100
(b) Time [s]
0
50
100
pA
i [Bar
]
Cylinder 1 Cylinder 2
0 20 40 60 80 100
(d) Time [s]
050
100150
pB
i [Bar
]
0 20 40 60 80 100
(g) Time [s]
0
50
Dis
plac
emen
tA
ngle
[%]
0 20 40 60 80 100
(e) Time [s]
-100
0
100
uv [%
]
0 20 40 60 80 100
(h) Time [s]
0
200
400
[N
m]
0 20 40 60 80 100
(f) Time [s]
0
100
200
Ps [b
ar]
Common Pump
Figure 13: Performance results for the Valve Cylinder Drives (VCDs).
83
Modeling, Identification and Control
0 20 40 60 80 100
(a) Time [s]
0100020003000
x Pi[m
m]
0 20 40 60 80 100
(c) Time [s]
-20
0
20
eX
Pi[m
m]
0 20 40 60 80 100
(b) Time [s]
0
50
100
pA
i
[Bar
]
SvSDP1
SvSDP2
0 20 40 60 80 100
(d) Time [s]
0
50
100
pB
i
[Bar
]
0 20 40 60 80 100
(e) Time [s]
-100
0
100
mi
[%]
0 20 40 60 80 100
(h) Time [s]
0
10
20
QvB
i
[L/m
in]
0 20 40 60 80 100
(f) Time [s]
0
50
QvA
i
[L/m
in]
0 20 40 60 80 100
(g) Time [s]
-500
50100150
i[N
m]
Figure 14: Performance results for SvSDP drives using the energy efficient input transformation in Eq 54. In(b) and (d) the dotted black line indicates the pressure setting, pset.
sure in each cylinder close to the pressure setting atpset=20 bar. Due to the short duration of standstill atpoint 1 and 2 in the trajectory and the small leakageflows in the internal gear pumps, even at standstill theminimum chamber pressure is remaining close to theset pressure. In Fig. 14(e) it should be noted, thatthe SvSDP drives are close to the motor speed satu-ration limits in the retracting direction as opposed tothe VCD. This is due to different obtainable operatingranges, visualised in Fig. 9.As desired with the energy efficient input transforma-tion, oil is only throttled from the low pressure cham-ber, see Fig. 14(f) and (h). For SvSDP1 this meansthat only valve B is active, as chamber A is alwaysthe load carrying chamber. For SvSDP2 it is seenthat chamber B is mainly the load carrying cham-ber, why oil is throttled from chamber A. Howeverbetween 40 to 60 seconds the load carrying chamberis interchanged. In this switching process, oil is throt-tled through both valve A and B as desired. Simula-tions have also been performed using the original inputtransformation (Eq.(46)) for the SvSDP drive. Motiontracking and pressure control performance are almostidentical to what have been achieved using the energyefficient input transformation (Fig. 14(a)-(d)). Thevalve flows are however, fundamentally different. Thevalve flows using the original input transformation areseen in Fig. 15. As desired with the original inputtransformation oil is throttled using both valves, why a
0 20 40 60 80 100
(a) Time [s]
0100020003000
x Pi[m
m]
0 20 40 60 80 100
(c) Time [s]
-20
0
20
eX
Pi[m
m]
0 20 40 60 80 100
(b) Time [s]
0
50
100
pA
i [Bar
]
SvSDP1 SvSDP2
0 20 40 60 80 100
(e) Time [s]
-100
0
100
mi [%
]
0 20 40 60 80 100
(a) Time [s]
01020
QvB
i
[L/m
in]
0 20 40 60 80 100
(g) Time [s]
-500
50100150
i [Nm
]
0 20 40 60 80 100
(b) Time [s]
0
10
20
QvA
i
[L/m
in]
Figure 15: Valve flows for SvSDP drives using originalinput transformation (Eq (46)). Compareto Fig. 14(f) and (h).
degraded energy efficiency for the original input trans-formation is to be expected.
Interestingly, the simulation study does not showthat the motion tracking performance for the proposedenergy efficient input transformation is degraded com-pared to the original input transformation.
5.2 Energy Comparison
Having established that the motion tracking perfor-mance is on the same level for the SvSDP and the VCD,it is interesting to compare the energy consumption ofthe two. Included is also a comparison of the SvSDPdrives using the original input and the energy efficient
84
Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
0 20 40 60 80 100
(a) Time [s]
-200
20
0 20 40 60 80 100
(b) Time [s]
-10
0
10
0 20 40 60 80 100
(c) Time [s]
-200
20
0 20 40 60 80 100
(d) Time [s]
-100
10
0 20 40 60 80 100
(e) Time [s]
0
50
0 20 40 60 80 100
(f) Time [s]
0102030
SvSDP w/ energy efficient input transformation SvSDP w/ original input transformation VCD
hyd,
out2
hyd,
out1
el1
el
el2
l,th1
Figure 16: (a) Hydraulic output power cylinder 1. (b) Hydraulic output power cylinder 1. (c) Electrical inputpower SvSDP1. (d) Electrical input power SvSDP2. (e) Electrical input power VCD, common motor.(f) Throttling losses for cylinder 1.
input transformation.From Fig. 16(a) and (b) it may be seen that the hy-draulic output power (Fhyd · xP) is close to identical forthe SvSDP drives and the VCD, which is a necessityfor a fair evaluation of energy consumption.For the VCD the electrical input power cannot be sep-arated between the two cylinders due to the commonpump, as opposed to the SvSDP.Fig. 16(c) and (d) show that the electrical input powerfor the SvSDP using the original input transformationis slightly higher than using the energy efficient trans-formation. Note, that from 10 to 40 seconds, the elec-trical input power is negative meaning the electricalmotor effectively functions as a generator, and that apotential for energy recovery is present. As seen in Fig.16(e), the electrical input power is always positive forthe VCD, meaning that even though hydraulic poweris available for recovery, the electrical motor still needsto supply power for the system to operate.Generally, it is seen that electrical input power to theVCD is larger than for the SvSDP even though Fig.16(c) and (d) should be added to obtain the combinedinput power for operation of the knuckle boom crane.This difference is primarily due to much larger valvethrottling losses, as shown in Fig. 16(f).Note, that from 10 to 40 seconds the throttling lossesfor the VCD exceed the input power, because the hy-draulic power is negative.
5.2.1 Energy Efficiency
For the SvSDP drives it is possible to define the ef-ficiency based on transferred power individually on a
drive level as:
ηi =Eouti
Eini
Eouti =
Ehyd,outi , Eeli ≥ 0
Eeli , Eeli < 0
(62)
Eini=
Eeli , Eeli ≥ 0
Ehyd,outi , Eeli < 0
Utilising Eq. (62) it is possible to calculate the effi-ciency both when electrical energy is supplied or regen-erated during the trajectory for SvSDP1 and SvSDP2
individually.For the VCD system the energy efficiency is only
evaluated when both hydraulic power outputs are pos-itive:
ηVCD
=Eout,VCD
Ein,VCD
(63)
Eout,VCD =
Ehyd,out1
+ Ehyd,out2, ZηVCD
= 10 , otherwise
Ein,VCD =
Eel,VCD , ZηVCD = 1
0 , otherwise
ZηVCD=
1 , Ehyd,out1
> 0 and Ehyd,out2> 0
0 , otherwise
The evaluated energy efficiencies during the trajec-tory are visualised in Fig. 17.
It is found that generally the energy efficiency ishigher for the SvSDP drives using the energy efficientinput transformation compared to the original. Also,both input transformation strategies outperform theVCD. The overall efficiency during the trajectory is
85
Modeling, Identification and Control
0 20 40 60 80 100
(a) Time [s]
0
50
100
1 [%
]
SvSDP w/ energy efficient input transformationSvSDP w/ original input transformation
0 20 40 60 80 100
(b) Time [s]
0
50
100
2 [%
]
0 20 40 60 80 100
(c) Time [s]
0
50
100
VC
D [%
]
VCD
Figure 17: Evaluated energy efficiencies during the tra-jectory evaluated using Eq. (62) and Eq.(63).
calculated by a time integration of the power expres-sions from Eq. (62) and Eq. (63), and calculated usingEout/Ein: The result of this is summarised in Tab. 1.
Energy Efficiency (η)
SvSDP Input TransformationEnergy Efficient Original
SvSDP1 93.7 % 88.6 %SvSDP2 76.8 % 65.0 %VCD 44.9 %
Table 1: Evaluated energy efficiencies for the testtrajectory.
The efficiency of the VCD is significantly smallercompared to the SvSDP drives. As indicated in Fig.16(f) increased throttling losses are the main reason.
The efficiency of the SvSDP drives using the energyefficient input transformation is larger compared to theoriginal transformation. Also, SvSDP1 is seen to besignificantly more efficient than the SvSDP2, for bothinput transformations. The input energy distributionsare visualised in the Sankey diagrams in Fig. 18.
From Fig. 18 it is evident that the degraded en-ergy efficiency for SvSDP2 compared to SvSDP1, isdue to increased relative throttling losses. This com-bined with a smaller amount of converted energy forSvSDP2 explains the smaller efficiency.
Increased throttling losses, due to flow being throt-tled from both the high and low pressure chamber usingthe original input transformation, explains the smaller
Ehyd,outEel Emech,shaft Ehyd,pump
Electrical losses
Eβ
Volumetric losses
Throttling losses
93.7% (88.6%)
96.0% (96.3%)
97.6% (97.8%)
100% (100%)
2.4% (2.2%)
1.6% (1.5%)
2.3% (7.7%)
SvSDP1 X % : w/ energy efficient input transformaion (X%) : w/ original input transformation
Ehyd,outEel Emech,shaft Ehyd,pump
Electrical losses
Eβ
Volumetric losses
Throttling losses
76.8% (65.0%)
97.4% (97.7%)
99.4% (99.5%)
100% (100%)
0.6 % (0.5 %)
2.0% (1.8%)
20.6% (32.7%)
SvSDP2 X % : w/ energy efficient input transformaion (X%) : w/ original input transformation
Figure 18: Sankey diagram showing the energy distri-bution from electrical input to hydraulicoutput for the SvSDP drives. In parenthe-sis are the results using the original inputtransformation.
efficiency compared to the proposed energy efficient in-put transformation.
5.2.2 Supplied Electrical Energy
As seen from Fig. 16 the SvSDP drives are capableof recovering energy as opposed to the VCDs. It istherefore interesting to investigate how much electricalinput energy is needed in order for the knuckle boomcrane to perform the defined test case trajectory, whenassuming ideal energy recovery and storing in the grid.Also, as the efficiencies for the VCD and the SvSDPdrives are not defined equivalently, it may be more in-formative to evaluate and compare the needed inputenergy instead of efficiency. For the SvSDP system theneeded input energy is the sum of the input energy toboth SvSDP1 and SvSDP2.The required input energy during a trajectory is shownin Fig. 19 for the VCD and the SvSDP drives usingthe energy efficient input transformation.
Tab. 2 summarises the findings from Fig. 19.Clearly a large reduction in required input energy hasbeen achieved for the SvSDP drives compared to theVCD. Even without the possibility of recovering andstoring energy, the needed input energy is reduced by62 %, from 0.79 kWh to 0.30 kWh. Assuming ideal
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Ketelsen et.al., “Energy Saving Potential ... using a Novel Pump Controlled Cylinder Drive”
0 20 40 60 80 100
Time [s]
-0.20
0.20.40.60.8
Sup
plie
d E
nerg
y [k
Wh]
SvSDP SvSDP w/ ideal energy recovery VCD
Figure 19: Supplied input energy during a trajec-tory. The shown SvSDP curves areevaluated using the energy efficient inputtransformation.
energy recovery the required energy is further reducedto 0.06 kWh. This is a reduction of 92 % compared tothe VCD.
Supplied Electrical Energy
SvSDP Input TransformationEnergy Efficient Original
No recovery 0.30 kWh 0.35 kWhw/ ideal recovery 0.06 kWh 0.10 kWhVCD 0.79 kWh
Table 2: Supplied input energy for the investigatedknuckle boom crane to perform the testtrajectory.
Also, the SvSDP drives using the proposed energyefficient input transformation is consuming less inputenergy compared to the original input transformation.Here a reduction of 14 % is seen if energy cannot berecovered and 40 % if ideal energy recovery is assumed.
This emphasises the importance of proper controlconsiderations. With exactly the same SvSDP sys-tem from a hardware point of view, that performs thesame motion trajectory with equivalent tracking per-formance, the energy consumption can be drasticallydecreased, by proper control efforts.
6 Discussion
For the SvSDP drives to be valid alternatives to con-ventional valve controlled drives, the safety functionof the counterbalance valves must be imitated. Forthe SvSDP drives the risk of over-running loads are re-duced, as the pump leakage path is significantly morerestrictive than the return path of a proportional valve.However, in emergency situations where input power islost, a load may drop rapidly as the electrical motor ispassively accelerated. For safety critical applicationsthis cannot be tolerated. It is not feasible to utilise
counterbalance valves, as these prevent the opportu-nity of energy recovery. Instead the safety functional-ity may be achieved by inserting normally closed on/offvalves in the main transmission lines.
When evaluating energy efficiencies for the SvSDPdrive only three sources of losses have been included.It is therefore unlikely that the stated efficiencies canbe achieved in a real world application. However, asonly two sources of losses have been included for theValve Cylinder Drives (VCD) it is expected that therelative difference between the SvSDP and the VCD isrepresentative.
7 Conclusion
An application study, investigating the energy savingpotential for knucke boom crane actuation has beenconducted. Based on the Speed-variable Switched Dif-ferential Pump (SvSDP)-concept, which previously hasbeen experimentally verified for low power applica-tions, a system has been designed based on availablepump sizes. The control system for the over-actuatedSvSDP drive has been modified compared to previousstudies, aiming on improving the energy efficiency ofthe SvSDP drive.
A test case knuckle boom crane trajectory has beendefined to evaluate the performance of the SvSDPdrives. Simulation results show that motion trackingperformance is on a similar level compared to a ValveCylinder Drive (VCD), while the energy consumptionhas drastically decreased. This is mainly due to de-creased throttling losses, and the opportunity to re-cover energy in motoring quadrants for the SvSDP. Forthe given trajectory the VCD consumes 0.79 kWh ofelectrical energy, while the SvSDP drives consume 62% less energy (0.30 kWh) if energy cannot be recov-ered and 0.06 kWh (92.4 % decrease) if ideal energyrecovery and storage are assumed.
This result suggests that a potential for significantenergy savings exists if using the proposed novel pumpcontrolled cylinder drive for knuckle boom crane actu-ation.
Acknowledgments
The research in this paper has received funding fromThe Research Council of Norway, SFI Offshore Mecha-tronics, project number 237896/O30.
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Modeling, Identification and Control
Key Parameter List
Description Value
LCF Length, Figure 3 13.750 mLFJ Length, Figure 3 9.421 mxmin1 Cylinder Length, Fig. 3 2.333 mxmin2 Cylinder Length, Fig. 3 2.846 mm1 Mass, Fig. 3 6000 kgm2 Mass, Fig. 3 3300 kgm3 Payload, Fig. 3 5000 kgmcyl1 Cylinder Mass, Fig. 3 2000 kgmcyl2 Cylinder Mass, Fig. 3 2000 kgDA2 Piston Diameter 0.28 mDB2
Rod Diameter 0.2 mDA2
Piston Diameter 0.25 mDB2
Rod Diameter 0.18 m
KAQ Pump Displacement 50.7 cm3
rev
KBQ Pump Displacement 32.7 cm3
rev
KCQ Pump Displacement 32.7 cm3
revRcu Winding Resistance 0.06 Ωτnom Standstill torque 342 NmInom Standstill current 135.5 Aωvi Bandwidth 60 HzωvAi Bandwidth 20 HzωvBi
Bandwidth 20 Hzζvi
Damping ratio 0.5ζvAi
Damping ratio 1ζvBi Damping ratio 1Bvi
Viscous friction coefficient 40000 Nsm
ωm,maxiMax. electric motor speed 3000 RPM
ωm,miniMin. electric motor speed -3000 RPM
VA0i Initial volume 80 LVB0i Initial volume 80 LZband Switching range 1 bar
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