1. A Nonlinear Hybrid Model of a 4-Cylinder Engine for Idle Speed Control Andrea Balluchi (1), Marco Zoncu (1), Tiziano Villa (1), Alberto L. Sangiovanni-Vincentelli (1, 2) (1) PARADES E.E.I.G., Roma, Italy. (2) Dept. of EECS, University of California, Berkeley CA. CC Meeting in Amsterdam June 16-17, 2003.

2. The Idle Speed Control Problem specifications: Maintaining the crankshaft speed within a specified range despite load torque disturbances and transmission engagements/disengagements. constraints: Good combustion and emission quality; Acceptable NVH characteristics.

3. Nonlinear Hybrid Model of the Engine Power-train (CTS + FSM) Cylinders (FEM + DES) Intake manifold (CTS) n(t)  (t) p(t)  (t) T(t) T load (t) spark clutch control inputs disturbance inputs

4. Intake Manifold: Continuous Dynamics Pressure dynamics: Equivalent throttle area: Air flow rate:

5. Power-train: Scheme Cylinders

6. Power-train: Continuous Dynamics Driveline segments dynamics (clutch open): Connected driveline dynamics (clutch closed): Crankshaft angle:

7. Power-train: Finite State Machine off / clutch open clutch closed on /

8. Single Cylinder’s Finite State Machine dc spk spk&dc dc I H BS AS PA NA C E negative spark advance positive spark advance positive spark advance T := 0AS to H  := -  T := T E (m, -  ) NA to AS T := T E (m,  ) PA to AS  := 180 -  T := -T C (p,n) BS to PA m := G mp p + M 0 T := -T C (p,n) I to BS

9. Cylinders: Finite State Machine

10. Cylinders: Discrete Event System

12. The Clutch Closing Manoeuvre

15. Hybrid Model’s Successive Refinements single-location automaton two-location automaton with spark advance

16. Hybrid Model’s Successive Refinements two-location automaton with clutch state

17. Hybrid Model’s Successive Refinements two-location automaton with manifold dynamics

18. Hybrid Model’s Successive Refinements three-location automaton

19. Comparative Simulations Single-location Vs Two-location with spark advance TlTl TgTg dc TgTg TlTl spark  =20 o  =14 o

20. Comparative Simulations Single-location Vs Two-location with spark advance dc n spark n

21. Comparative Simulations Two-location without and with manifold TgTg TlTl  = 20 o  o  = 6.7 o  o TlTl TgTg  = 6.7 o  = 20 o

22. Comparative Simulations Two-location without and with manifold n  = 6.7 o  = 20 o n  = 6.7 o  o  = 20 o  o

23. Comparative Simulations Two-location Vs Three-location TlTl TgTg TgTg TlTl  = 5 o  = 0 o  = -3.7 o  o  = 5 o  o  o  o

24. Comparative Simulations Two-location Vs Three-location TlTl  = 5 o  o n  = 5 o  o  = 0 o  o n  = 5 o  o  = -3.7 o  o

25. Conclusions Nonlinear model of the intake manifold; Better modeling of the torque generation mechanism; Modeling of the secondary driveline.