*Engineering and Industrial Services, TATA Consultancy Services Limited **Professor Emeritus, IIT Bombay

Transcription

1 System Identification and Model Predictive Control of SI Engine in Idling Mode using Mathworks Tools Shivaram Kamat*, KP Madhavan**, Tejashree Saraf* *Engineering and Industrial Services, TATA Consultancy Services Limited **Professor Emeritus, IIT Bombay Copyright 24, Tata Consultancy Services Limited. All Rights Reserved

2 Agenda Introduction MPC Overview Case Study MPC Work Flow and Virtual Set up System Identification of engine model for idle mode Plant Model Validation Controller Synthesis MIL results Benefits Future Scope 2

3 Introduction A stable and fuel efficient idle running of automotive engines has been crucial part of engine management system for OEMs and Tier-s Low rpm idling : Trade off between fuel consumption, stability and disturbance performance 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 3

4 MPC Overview : What, Why? MPC = Model + Prediction + Correction (Control) ast future Target error predicted input profile Predictive model Engine EMS th, spk, FPW.. feedback 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 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 4

5 MPC : How? past future desired error predicted Minimize J ( u M ) = history input profile P j = e q y k + j + Q j u k + j q S j a. 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. b. Deploy only the first element of the solution vector, i.e. the control move for k +. (RHC) 2. At time k + read the output feedback and repeat the step. Structure of Model Predictive Control Desired Output + - Controller Predicted Error Process Model - + Process Output 5

6 MPC : How? γ (t) Objective function: J= m l= l 2 ( y ( k+ ) y ( k+ ) ) + λ U( k+ ) set Error term p i= Penalty on 2 u (k-2) u (k-) u (k) u (k + ) CONTROL HORIZON Y m (t) - PREDICTION Y p (t) - FUTURE TRAJECTURY WITH NO CHANGE IN CONTROL OBSERVATION HORIZON u (k + 2) Constraints: U l u min U Prediction horizon Control horizon control moves uk ( + j) umax ; j= ( k + j ) U ; i= to l u to y y ( k + j ) y ; j = to l p u Tuning l m PAST k k + k + 2 FUTURE Penalty factors on control moves Weights on output variables Hard / soft Constraints on inputs and outputs Constraints on rate of change of inputs 6

7 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. 2, No., January x -5 Fuel mass in Kg 2 75 rpm rpm Lower the idle rpm, lesser is the fuel consumption However, the tradeoff is with stable running, disturbance rejection performance and tracking performance Fuel consumption for idle running at 75 and rpm idling of endyna* simulator * endyna is engine simulator from Tesis-Dynaware. 7

8 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 EMS Actuator Signals endyna Engine Simulator Step response and PRBS excitation IDENT tool for transfer function identification Sensors signals Linear discrete (Ts =ms) 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 8

9 Case Study : SysID Step response.5 Throttle step response Throttle deg SysID using IDENT toolbox speed in rpm ΔThrottle/Δrpm TF output comparison Δspk/Δrpm TF output comparison 9

10 Case Study : SysID PRBS response PRBS signal applied to SA in open loop with constant throttle.5 throttle deg interval for sysid Ignition angle deg Assuming throttle/rpm and spk/rpm relationships as linear, a combined MISO state space model is obtained. Comparison of the outputs by PRBS SS model and endyna Measured and simulated model output interval for sysid rpm P3DZU output, accuracy 47.9% endyna output Time

11 Case Study : Plant Model Validation Comparison of the outputs of state space Δ /Δ models (Step Response) and endyna endyna rpm step response model rpm PRBS model rpm Controller was constructed using the step response model as the predictive model for MPC

12 Case Study : Controller Synthesis Using the MPC toolbox, MPC object was created Plant Model directly imported from IDENT session 2

13 Case Study : Controller Synthesis. Tuning : Horizons Tuning : Constraints on inputs and output 3

14 Case Study : Controller Synthesis. 2 Plant Output: Out delta rpm Delta RPM Time (sec) Plant Inputs I n Delta throttle delta throttle Pre-closed loop simulation Simple and straight forward tuning iterations I n Time (sec) delta spark adv Delta Spark 4

15 Case Study : MIL closed loop validation ECU EMULATOR SI AccPedalPos [_] 2 CrankSpd [rad/s] AccPedalPos [_] CrankSpd [rad /s] IgnitionAng [rad ] IgnitionAng [rad] Manual Switch Clock Simulation Time [s] 75 / base idle speed 3 EngineAirMFlow [kg/s] EngineAirMFlow [kg /s] IdleSpd [rad/s ] InverseIntLambda [-] Default EMS InjectionTime [s ] 4 2 EngineStateCtrl [/] Injection Time Engine On or Off [s] Intended _ lambda 5 BatteryVolt [V] BatteryVolt [V] CrankAng [rad ] 3 Crank Ang [rad ] 6 FuelPres [Pa] 7 ManifoldPres [Pa ] FuelPres [Pa ] ManifoldPres [Pa ] ThrottleAng [deg ] Manual Switch 2 4 ThrottleAng [deg ] Drive EMS.54 th rpm for bumpless transfer throttle _bias -K- rad /s to rpm Manual Switch 4 feedback MPC MVs setpoint spk 75 rpm _bias Signal Signal 2 Signal Builder rpm _setpoint _bias Manual Switch 3 MPC controller 7.45 spk_bias -K- deg to rad Idle 5

16 Case Study : MIL closed loop validation scenario Engine cranked by electric motor, target idle speed 75 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 75 rpm to 85 The idle set point ramped down from 85 rpm to 75 The step load of 25Nm applied as 75 rpm (hostile) idle rpm, removed in or 2 seconds The scenario applied for predictive model that included additional integral state 6

17 Case Study : ISC with default PID controller 9 ISC with default PID controller (may not be optimally tuned) 85 Fuel cut for reaching the limit Disturbance load applied endyna rpm PID regulation response Reference ramp applied to set point set point restored Disturbance load removed 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 7

18 Case Study : Closed Loop Simulation Results 95 (e) steady state at new setpoint set point rpm (a) Fuel cut for reaching the limit (g) disturbance applied (b) PI controller's regulation action (c) Switch over to MPC (bumpless) (f) setpoint restored (h) disturbance applied throttle deg spk deg Time Scale (sec) 8

19 Case Study : Addition of Integral Element for Disturbance Rejection feedback 2 setpoint Ts (z+ 2(z-) Discrete-Time Integrator mo ref Linear _MPC mv MVs MPC Controller _int rpm _Integration _setpoint 95 (a) Fuel cut for reaching the limit set point rpm 9 (e) steady state at new setpoint 85 (d) Reference ramp applied to setpoint (g) disturbance applied 8 (b) PI controller's regulation action (f) setpoint restored 75 7 (c) Switch over to MPC (bumpless) (h) disturbance applied Time Scale (sec) 9

20 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 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 2

21 Thank You Copyright 24, Tata Consultancy Services Limited. All Rights Reserved 2