1. Model-Based Control for Automotive Cold Start Applications J. Karl Hedrick Carlos Zavala Pannag Sanketi Mechanical Engineering Dept., University of California, Berkeley 2007 CHESS Winter Meeting

2. Coldstart Challenges Low emission - Suppressing emissions, especially HC High quality - Driveability : noise & vibration - Robustness against environmental condition and disturbance Less cost - Calibration effort - Design process, especially verification - Computational load - Sensors 0255075100 0 Speed[km/h] Cumulative HC amount Time[sec] HC Speed Regulation limit

3. Coldstart in IC Engines- The problem The catalyst is not active below temperatures of around 300C- 400C Cold Combustion Chambers and poor vaporization in intake manifold Oxygen Sensor not active at cold temperatures …more than 90% of Hydrocarbon (HC) emissions is produced during the Coldstart Cycle

4. Model Based Approach to Emissions Reduction during Coldstart Utilizes formal description of the engine to derive efficient ways of control. –Physical Models. Intuitive representation. –Black box models. Non-physical parameters. –Gray models. Combination of the two above Motivation - improved control - efficient generation of software - software reusability

5. Model Based Strategy Implementation And Testing Engine Model Catalyst Model Model Validation Controller Design Next design iteration

6. Control Oriented Modeling Simplicity in models is important dx/dt= f(x,u) Lumped Parameter Model (preferably low order ODE) Complex nonlinear system

7. Engine Subsystems Manifold Dynamics Fuel Dynamics Catalytic Converter Torque Gen Raw HC Exh Temp

8. Engine Subsystems Modeling For control of air-fuel ratio, idle speed, models developed ~1980 Combustion torque generation Rotational dynamics and time delays Actuator and sensor dynamics Air and fuel dynamics Catalytic converter dynamics Engine thermal dynamics General Purpose Engine Modeling Cold Start Engine Modeling

9. Fuel Dynamics Model Poor vaporization when air intake is cold Puddle

10. AFR Estimation using Fuel Dynamics Use of fuel- dynamics model to predict AFR. “Fuel Dynamics Model For Engine Coldstart”, Zavala, et.al, IMECE2006-15203, Nov. 2006

11. Catalytic Converter Model * conversion efficiency map cat. substrate thermal dynamics O 2 storage dynamics internal convection : * [Brandt, Wang, Grizzle, 1997] external convection : Q in =h in A in (T exh - T cat ) Q out =h out A out (T cat - T amb )

12. Important Elements in a Catalyst Model Heat transfer coefficients of the catalyst

13. Important Elements in a Catalyst Model 0102030405060708090100 0 50 100 150 200 250 300 350 T cat (C) Time (s) Typical Experimental Catalyst Temperature Profile Plateau in the Tcat profile –Due to evaporation of moisture –Starting point can be detected (~47 0 C) –For finding the end of plateau, various methods – adaptation, offline calculation of evaporation heat* *[Sanketi, Zavala, Hedrick et al., AVEC ’06]

14. Experimental plots of Catalyst

15. Raw HC and T exh Modeling Simple, intuitive models –Suitable for controller design Inputs chosen based on physics and experimental data –AFR, Spark directly affect combustion –Changes in RPM affect the combustion quality Sum of first order linear systems –such behavior observed in exp Saturations, offsets on inputs exist Use of Least Squares to find parameters

16. T exh Modeling

17. Raw HC Modeling

18. Control Design –Performance requirements –Uncertainty –Nonlinearities –Actuator bandwidth –Sensor noise –Disturbances Plant ? y u Once the plant is defined, the synthesis of a controller should considered :

19. Throttle angle Lab Engine Interface T exh sensor AFR sensor HC Analyzer Tcat sensor Catalyst model Engine out HC estimation Catalyst temperature estimation Tailpipe HC estimation Amount of Fuel Spark Timing AIR Variable Valve Timing In cylinder pressure measurement HC formation model Air induction dynamics Fuel induction dynamics Thermal model

20. Two control approaches: mean value-hybrid Plant model Control Objectives Controller Design Controller Plant model Control Objectives Hybrid Controller Design Controller 1 … Controller n Controller i Controller kController j … Mean Value Hybrid Controller Operation Design

21. Mean Value MIMO Controller

22. Trying out different profiles Different HC desired and Tcat profiles Desired Profiles

23. Model-Based Integration of Embedded Systems analysis of complex embedded systems software assurance through modeling in all phases of software development process Handling hybrid system analysis Software timing analysis The complexity of automotive systems demands the use of more sophisticated tools for control software verification:

24. Why hybrid models? Advantages –It accounts for continuous dynamics and discrete events. –It offers a more detailed description compared to mean-value models. Disadvantages –No analytic solutions for stability analysis –More complicated than mean-value models. –Analysis tools still in development

25. Engine Model Mean Value models of Intake air flow and manifold air mass. (continuous dynamics). Air and fuel flowing into cylinder calculated for each combustion cycle.(Discrete quantities). Strokes of engine considered as discrete events using finite state machines (FSM:hybrid). Torque and pollutants modeled for each combustion cycle. (continuous functions based on events: hybrid).

26. Controller Verification of Hybrid Systems Question of stability and evolution of the states Model simulations cannot cover all possible trajectories inside a set Reachability analysis –Tells you how your state space will behave with time starting given a set of initial conditions and bounds on inputs –Very useful in verifying the controller performance

27. Example Hybrid Controller Cumulative tailpipe HC function of both raw HC and catalyst efficiency Trade off exists between the two objectives A high level hybrid controller to exploit the trade-off

28. Control Hierarchy The low level T exh and AFR controllers use spark timing and fuel injection rate as the inputs respectively The T cat and HC dynamic surface controllers use T exh and AFR respectively The hybrid controller switches between the T cat and HC dynamic surface controllers

29. Hybrid Controller Modes Helps fast catalyst light-off Helps keep the raw emissions low

30. Reachable sets Test: starting from a safe set, remain in the set. Set of Initial states Forward Reachable Set Target Set Backwards Reachable Set Test: starting from an unsafe set, never touch the set of initial conditions

31. Backwards reachable set calculation is the set of states for which, for all control actions, there exists a disturbance action which can drive the system to in at most Say, the control u wants to keep the system away from target set of states whereas the disturbance d tries to drive the system to the target set G(0). Now how to compute this set? Turns out that it can be computed by solving a HJI PDE Ref. Tomlin et.al Target Set G(0) Backwards Reachable Set G(t)

32. Reachability Analysis of Coldstart Controller* Backwards Reachability *[Sanketi, Zavala, Hedrick]- IJC, 2006

33. Conclusions Hybrid modeling helped to achieve a more detailed description of engine operation Hybrid control gave the chance to explore the tradeoff of hydrocarbon emissions level and catalyst light-off. Hybrid modeling is a useful tool for coldstart analysis.

34. Future of coldstart control Fewer experiments for model validation. Closed-Loop control design Easy adaptation to new engines. Automated code generation. Automated software validation and verification. Use of AFR and HC production sensors and/or model based observers.