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Controllability and Observability Of State Space

2009 Lecture Side. January 2009. Lecture by. Controllability and Observability Of State Space . Chapter Eleven week3. Control Engineering. Review Exercise. Control Engineering. Controllability of State Space. Controllability.

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Controllability and Observability Of State Space

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  1. 2009 Lecture Side January 2009 Lecture by Controllability and Observability Of State Space Chapter Eleven week3 Control Engineering

  2. Review Exercise Control Engineering 2009 Subject Name Automotive Automatic Control

  3. Controllability of State Space • Controllability • A system is completely controllable if there exists an unconstrained control u(t) that can transfer any initial state x(t0) to any other desired location x(t) in a finite time t0tT. nn Controllable nm nn 제 14강 3 Control Engineering 2009 Subject Name Automotive Automatic Control

  4. Example 1 • Controllability • Example 1: Controllability of a system Controllable 제 14강 4 Control Engineering 2009 Subject Name Automotive Automatic Control

  5. Observability of State Space • Observability • A system is completely observable if and only if there exists a finite time T such that the initial state x(0) can be determined from the observation history y(t) given the control u(t). 1n Controllable n1 nn 제 14강 5 Control Engineering 2009 Subject Name Automotive Automatic Control

  6. Example 2 • Observability • Example 2: Observability of a system Observable 제 14강 6 Control Engineering 2009 Subject Name Automotive Automatic Control

  7. Example 3 • Observability • Example 3: Controllability and Observability of a two-state system Not Controllable and Not Observable Control Engineering 2009 Subject Name Automotive Automatic Control

  8. Exercise 1 Is the following system completely state controllable and completely observable? Control Engineering 2009 Subject Name Automotive Automatic Control

  9. MATLAB Exercise 1 State variables System equations Output equation Control Engineering 2009 Subject Name Automotive Automatic Control

  10. MATLAB Exercise 1 (2) Control Engineering 2009 Subject Name Automotive Automatic Control

  11. MATLAB Exercise 1 (3) Control Engineering 2009 Subject Name Automotive Automatic Control

  12. MATLAB Exercise 2 From Example 11-6 in OGATA Book Control Engineering 2009 Subject Name Automotive Automatic Control

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