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System Identification and Model System Identification and Model Predictive Control of SI Engine in Idling Predictive Control of SI Engine in Idling
1
Predictive Control of SI Engine in Idling Predictive Control of SI Engine in Idling Mode using Mathworks ToolsMode using Mathworks ToolsShivaram Kamat*, KP Madhavan**, Tejashree Saraf *
*Engineering and Industrial Services, TATA Consultancy Services Limited**Professor Emeritus, IIT Bombay
© Copyright 2014, Tata Consultancy Services Limited. All Rights Reserved
Agenda
� Introduction
� MPC Overview
� Case Study – MPC � Work Flow and Virtual Set up � System Identification of engine model for idle mode
2
� System Identification of engine model for idle mode� Plant Model Validation� Controller Synthesis� MIL results
� Benefits
� Future Scope
Introduction
� A stable and fuel efficient idle running of automotive engines has been crucial part of engine management system for OEMs and Tier-1s
� Low rpm idling : Trade off between fuel consumption, stability and disturbance performance
3
� Prevalent ISC scenario• EMS’ address ISC using variants of PI/PID/FF/compensators • Use of maps/LUTs for idle air requirement and idling load compensation• No / indirect use of model for idle behavior for the tuning of the controller
� Proposed scenario • Use of simplified, linear discrete state space model in idling• Receding Horizon Model Predictive Control• Inherently stable , constrained optimal control with improved tracking and
disturbance rejection performance
MPC Overview : What, Why ?
MPC = Model + Prediction + Correction (Control)
predicted
input profile
error
futurepast
predicted
input profile
error
futurepast
Target Predictive model
EMSth, spk, FPW..
Engine
4
� Established and proven beneficial in the process control domain � Potential to leverage it for automotive with the advent and abundance of high
capacity, faster processors � A constrained MPC algorithm holds promise to achieve stable and tighter idle
speed control
A Model of the Process (Plant) is used to Predict the future evolution of the process and control signal is computed to minimize the deviation of the predicted output from the target by exercising the correction at every time interval
feedback
MPC : How ?
q
Sjk
q
Q
P
j
yjk
M
j
j
ue
uJMinimize
+=
+ ∆+∑
=
1
)(
desired
predicted
input profilehistory
error
futurepast
desired
predicted
input profilehistory
error
futurepast
5
1a. At time instant k, construct and solve optimal control problem to minimize the error between the target and predicted output over finite prediction steps, m.
1b. Deploy only the first element of the solution vector, i.e. the control move for k +1…. (RHC)
2. At time k +1 read the output feedback and repeat the step 1. …
Structure of Model Predictive Control
Desired Output
Process Output
Controller Process
Model
Predicted Error
-+
-+
MPC : How ?
( ) ( )( ) ( )∑∑−
==
+++−+=1
0
2
1
2 111l
i
m
lpset kUkykyJ λObjective
function:Penalty on
control moves
Error term
( ) 10; −=≤+≤ ltoiUjkUU ul
10;)( maxmin −=≤+≤ ltojujkuu
mtojyjkyy upl 1;)( =≤+≤
Constraints:
OBSERVATION HORIZON
γ (t)
Yp (t) - FUTURE TRAJECTURY WITH NO CHANGE IN CONTROL
Ym (t) - PREDICTION
6
Tuning� Prediction horizon
� Control horizon
� Penalty factors on control moves
� Weights on output variables
� Hard / soft Constraints on inputs and outputs
�Constraints on rate of change of inputs
mtojyjkyy upl 1;)( =≤+≤
u (k-2) u (k-1)
u (k) u (k + 1)
u (k + 2)
CONTROL HORIZON
k k + 1 k + 2 PAST FUTURE
Case Study : Idle Speed Control of 2.9L V6 SI engine
� MPC based ISC
Basis of the work : ‘Model Predictive Idle Speed Control: Design, Analysis, and Experimental
Evaluation’, Stefano Di Cairano,Diana Yanakiev, Alberto Bemporad, Ilya. V. Kolmanovsky, and Davor
Hrovat, IEEE Transactions on Control Systems Technology, Vol. 20, No. 1, January2012
1.5
2
2.5x 10
-5 Fuel mass in Kg
750 rpm1000 rpm
� Lower the idle rpm, lesseris the fuel consumption
7
0 500 1000 1500 2000 25000
0.5
1
1.5� However, the tradeoff is with stable running, disturbance rejection performance and tracking performance
Fuel consumption for idle running at 750 and 1000 rpm
idling of enDYNA* simulator
* enDYNA is engine simulator from Tesis-Dynaware.
Case Study : Work Flow and Virtual Set up
• enDYNA engine simulator for system identification of model during idling
• MISO model with throttle opening and spark advance as inputs and rpm as output
• Step response and PRBS excitation
• IDENT tool for transfer function identification
EMS
enDYNAEngine
Simulator Actuator Signals
8
identification
•Linear discrete (Ts =10ms) MISO state space model from SISO TFs (throttle and spark advance as inputs and rpm as output)
• Controller synthesis using MPC Toolbox
• Closed Loop simulation with MPC controller
Simulator
Sensors’ signals
Case Study : SysID – Step response
0 100 200 300 400 500 600 7000
0.5
1
1.5
800
900
1000
Throttle deg
speed in rpm
Throttle step response SysID using IDENT toolbox
9
0 100 200 300 400 500 600 700700
800
ΔThrottle/ Δrpm TF output
comparisonΔspk/ Δrpm TF output comparison
Case Study : SysID – PRBS response
30
0 500 1000 1500 2000 2500 3000 35000
0.5
1
1.5
throttle deg
PRBS signal applied to SA in open loop with constant throttle
Assuming throttle/rpm and spk/rpm relationships as linear, a combined
5.5 5.6 5.7 5.8 5.9 6 6.10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
100 500 1000 1500 2000 2500 3000 3500
700
750
800
850
900
950
0 500 1000 1500 2000 2500 3000 35005
10
15
20
25
Ignition angle deg
rpm
interval for sysID
interval for sysID
Comparison of the outputs by PRBS SS model and enDYNA
0 5 10 15-20
0
20
40
60
80
100
Time
Measured and simulated model output
P3DZU output , accuracy 47.91%
enDYNA output
relationships as linear, a combined MISO state space model is obtained.
600
800
1000
1200
Comparison of the outputs of state space Δ / Δ models (Step Response) and enDYNA
Case Study : Plant Model Validation
11
0 500 1000 1500 2000 25000
200
400
enDYNA rpm
step response model rpm
PRBS model rpm
Controller was constructed using the step response model as the predictive model for MPC
Case Study : Controller Synthesis
� Using the MPC toolbox, MPC object was created
12
Plant Model directly imported from IDENT
session
Case Study : Controller Synthesis….
13
Tuning : Horizons
Tuning : Constraints on
inputs and output
Plant Inputs
0 0.5 1 1.5 2 2.5 3-20
0
20
40
60
80
100
120Plant Output: Out1
Time (sec)
delta rpm
Delta RPM
Case Study : Controller Synthesis ….
14
0
0.2
0.4
0.6
0.8
1
1.2
In1
0 0.5 1 1.5 2 2.5 3
-10
-5
0
5
In2
Time (sec)
delta throttle
delta spark adv
Delta Spark
Delta throttle
� Pre-closed loop simulation � Simple and straight forward tuning
iterations
ThrottleAng [deg ]
4
Crank Ang [rad ]
3
Injection Time [s]
2
IgnitionAng [rad ]
1
base idle speed
750 /9.5493
Simulation Time [s]
Manual Switch 2
Manual Switch 1
Intended _1|lambda
1
Engine On or Off
ECU EMULATOR SI
AccPedalPos [0_1]
CrankSpd [rad /s]
EngineAirMFlow [kg /s]
IdleSpd [rad/s ]
InverseIntLambda [-]
BatteryVolt [V]
FuelPres [Pa ]
ManifoldPres [Pa ]
IgnitionAng [rad ]
InjectionTime [s ]
CrankAng [rad ]
ThrottleAng [deg ]
Clock
7
FuelPres [Pa]
6
BatteryVolt [V]
5
EngineStateCtrl [0/1]
4
EngineAirMFlow [kg/s]
3
CrankSpd [rad /s]
2
AccPedalPos [0_1]
1
Case Study : MIL closed loop validation
Drive EMS
Default EMS
15
throttle _bias
0.1514 th
spk_bias
17 .45
spk
rpm _bias
750
rpm
rad /s to rpm
-K-
for bumplesstransfer
0
deg to rad
-K-
Signal Builderrpm _setpoint _bias
Signal 1
Signal 2
Manual Switch 4
Manual Switch 3
Manual Switch 2
MPC controller
feedback
setpoint
MVs
ManifoldPres [Pa ]
MPC
EMS
Idle
� Engine cranked by electric motor, target idle speed 750 rpm regulated by default PID control loop
� The MPC controller switched on after matching the initial conditions for the bump-less transfer.
� The idle set point ramped from 750 rpm to 850 rpm @100rpm/s
Case Study : MIL closed loop validation scenario
16
� The idle set point ramped down from 850 rpm to 750 rpm @100rpm/s
� The step load of 25Nm applied as disturbance @ 750 rpm (hostile) idle rpm , removed in 1 or 2 seconds
� The scenario applied for predictive model that included additional integral state
700
750
800
850
900ISC with default PID controller (may not be optimally tuned)
enDYNA rpmFuel cut for
reaching the
limit
Reference
ramp
applied to
set point
Disturbance
load
removed
PID
regulationset point
restored
Disturbance
load applied
Case Study : ISC with default PID controller
17
0 500 1000 1500 2000 2500 3000500
550
600
650
set point removed
responserestored
� The controller may not be optimally tuned for KP, KI, KD
� Under-damped behavior at set point change and disturbance � Marginal improvement after conducting Simulink response optimization
Case Study : Closed Loop Simulation Results
600
650
700
750
800
850
900
950
1000 set point
rpm
(a) Fuel cut forreachingthe limit
(b) PIcontroller'sregulation action
(c) Switchoverto MPC(bumpless)
(e) steady stateat new setpoint
(f) setpointrestored
(g) disturbance applied
(h) disturbance applied
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0 200 400 600 800 1000 1200 1400 1600500
550
0 200 400 600 800 1000 1200 1400 1600-15
-10
-5
0
5
10
15
0 200 400 600 800 1000 1200 1400 1600-10
0
10
20
30
40
throttle deg
spk deg
Time Scale (sec)
Case Study : Addition of Integral Element for Disturbance Rejection
MVs1
rpm _Integration _setpoint
0 MPC Controller _int
Linear _MPC mv
mo
ref
Discrete-TimeIntegrator
K Ts (z+1
2(z-1)
setpoint
2
feedback
1
1000
190 500 1000 1500 2000 2500 3000 3500650
700
750
800
850
900
950
1000
set point
rpm
(b) PIcontroller'sregulation action
(c) Switchoverto MPC(bumpless)
(a) Fuel cut forreachingthe limit
(d) Reference ramp applied to setpoint
(e) steady stateat new setpoint
(f) setpointrestored
(g) disturbance applied
(h) disturbance applied
Time Scale (sec)
Benefits and Future Scope
Benefits� The approach
• Stable low rpm idling saving fuel • Improved performance for idle loads such as AC, PS, lighting• Constraints imposition
� The tools• GUI based Time effective and simplified system identification using IDENT
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• GUI based Time effective and simplified system identification using IDENT• GUI based simple and time effective controller synthesis • Seamless interface between the tools
Future Scope� Real Time overheads calculations to include MPC-ISC in the EMS� HiL validation on RCP ECU and virtual tuning/calibration� Modeling disturbance for rejection performance / improving the
integral action for tracking performance � Explore fast MPC on embedded hardware for automotive applications
Thank You
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Thank You
© Copyright 2014, Tata Consultancy Services Limited. All Rights Reserved