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PI Control for Nonlinear System with Application to a Converter Module

PI Control for Nonlinear System with Application to a Converter Module. Ricky Chan AAE 666 April 30, 2005. Outline. Objective PI control Converter Module implementation Result Conclusion. Objective.

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PI Control for Nonlinear System with Application to a Converter Module

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  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, 1919-1926

  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 = [ 0.4961 2.3211 0.0562] • 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 = 0.0167

  19. Study 2:

  20. Study 3:

  21. Study 4:

  22. Conclusion Comparison to other methods: • 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

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