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Controllability and Observability Of State Space

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Presentation on theme: "Controllability and Observability Of State Space"— Presentation transcript:

1 Controllability and Observability Of State Space
2009 Lecture Side January 2009 Lecture by Suradet Tantrairatn Instructor and Researcher Controllability and Observability Of State Space Chapter Eleven week3 Control Engineering

2 Review Exercise Control Engineering
2009 Subject Name Automotive Automatic Control Month 200X

3 Controllability of State Space
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 제 14강 nn 3 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

4 Example 1 Example 1: Controllability of a system Controllable
제 14강 4 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

5 Observability of State Space
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 제 14강 nn 5 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

6 Example 2 Example 2: Observability of a system Observable
제 14강 6 Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

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 Month 200X

8 Exercise 1 Is the following system completely state controllable and completely observable? Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

9 MATLAB Exercise 1 State variables System equations Output equation
Control Engineering 2009 Subject Name Automotive Automatic Control Month 200X

10 MATLAB Exercise 1 (2) Control Engineering
2009 Subject Name Automotive Automatic Control Month 200X

11 MATLAB Exercise 1 (3) Control Engineering
2009 Subject Name Automotive Automatic Control Month 200X

12 MATLAB Exercise 2 From Example 11-6 in OGATA Book Control Engineering
2009 Subject Name Automotive Automatic Control Month 200X

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