Adaptive Internal Model Control: Design and Stability Analysis*

1. Adaptive Internal Model Control: Design and Stability Analysis* 報告人:鄭景元

2. outline • The YJBK parameterization • Adaptive internal model control • Robust adaptive internal model control • conclusion

3. YJBK parameterization The YJBK parametrization seeks to parametrize the set of all compensators C(s) that guarantee the stability of the closed- loop system.

4. Bezout identity Where are stable rational transfer functions X(s) and Y(s) denote a solution of the equation where Q(s) varies over the set of all stable rational transfer functions.

5. IMC structure for stable plants as a special case of theYJBK parametrization. Now suppose the plant P(s) is open-loop stable and then the Bezout identity holds with X(s) = 0 and Y(s) = 1 We can get the form:

6. Adaptive internal model control • Equation error method • Linear estimation method plays a critical role • Design and stability analysis concentrate on the ideal case

7. Mathematical Description plant parameters rewrite linear parametric model

8. System Block Diagram • Adaptive law • Control law

9. Analysis of stability and asymptotic performance For any bounded r, all signals in the closed-loop system are uniformly bounded and the internal model output converges to the actual plant output y(t) as t →infinite

10. Robust adaptive internal model control • Based on adaptive internal model control • Focus on unmodelled dynamics or bounded disturbance

11. Mathematical Description plant equation multiple function Λ

12. Robust adaptive law • Control law

14. conclusion • Adaptive is based on plant states estimation • The controller plays a role that is error correction • MIMO system should be considered

15. Thank For Your Attention!