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Geometric I/O Decoupling Controller Design for Multivariable Control Systems

Learn about designing a diagonal controller to achieve Geometric I/O Decoupling for multivariable systems while focusing on performance criteria and Relative Gain Array (RGA) analysis. Explore decentralized control strategies for enhanced system response.

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Geometric I/O Decoupling Controller Design for Multivariable Control Systems

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  1. Multivariable Control SystemsECSE 6460 Fall 2009 Lecture 15: 23 October 2009

  2. State Space Plant Model • Given a 2 input - 2 output plant:

  3. Coupled Plant

  4. Control Problem • We want the outputs y1 and y2 to track two reference signals r1 and r2 simultaneously. • Performance criteria for step reference response: • Overshoot less than 5% • Three scenarios for minimum rise time = [30, 3, 0.03] sec

  5. Geometric Input-Output Decoupling

  6. Geometric I/O Decoupling

  7. Geometric I/O Decoupling

  8. Geometric I/O Decoupling

  9. Controller Design + K(s) G + C - + F

  10. Performance (wc = 0.1)

  11. Performance (wc = 1 )

  12. Performance (wc = 100)

  13. Relative Gain Array (RGA) Analysis

  14. RGA computation

  15. Diagonal vs off-diagonal pairing

  16. RGA Number

  17. Decentralized Control (Diagonal Pairing)

  18. Independent Design • Idea: Design a diagonal controller while disregarding the coupling between the two I/O pairs. + C K(s) -

  19. Independent Design

  20. Performance (wc = 0.1)

  21. Performance (wc = 0.1)

  22. Performance (wc = 0.1)

  23. Increase wc to 0.2

  24. Performance (wc = 1)

  25. Performance (wc = 1)

  26. Performance (wc = 1)

  27. Increase wc to 2.5

  28. Performance (wc = 100)

  29. Performance (wc = 100)

  30. Performance (wc = 100)

  31. Decentralized Control (Off-Diagonal Pairing)

  32. Independent Design Not proper!

  33. Performance (wc = 0.2)

  34. Sinusoidal tracking (wr = 1000)

  35. Sinusoidal tracking (wr = 1000)

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