1. PI Control for Nonlinear System with Application to a Converter Module
Ricky Chan
AAE 666
April 30, 2005

2. Outline Objective PI control Converter Module implementation Result
Conclusion

3. Objective
To design a controller, which guarantees that, for any initial conditions, any constant reference output r and any constant disturbance input w, we have

4. Proposed PI Control Reference:
Açikmeşe, A. B., & Corless, M. (2002). Robust output tracking for uncertain/nonlinear systems subject to almost constant disturbances. Automatica, 38,

5. Consider a dynamical system:
Proposed PI Control
Where Kp and Ki are constant matrices of appropriate dimensions

6. Additional state
Leads to the augmented state vector

7. And the augmented system
Where,

8. One may arrive at the matrices defining the derivative augmented system as follows.

9. The derivative augmented system is quadratically stable via linear state feedback if there exists matrices
such that for all x,u,w

10. System Description
dc-dc Converter Module

11. States:
Constant Disturbance Input:
Controller Input
Output

12. Load: Constant Power Load Therefore
The load may be changed as necessary (Shown on the result slides)

13. LMI

14. LMI

15. Result
K = [ ]
Slight modification to the input controller to guarantee that

16. Implement the control along with the converter module model in ACSL (Advanced Continuous Simulation Language)
Error Model:

17. Study 1:

18. Study 1:
Error =

19. Study 2:

20. Study 3:

21. Study 4:

22. Conclusion Comparison to other methods: Possible improvement:
Pole Placement
Genetic Algorithm (GA)
Possible improvement:
Faster transient
Investigate the behavior on Study 4 and figure out why it behaves that way
Implement the controller for a switch level model

23. Questions