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Week 15 state space rep may 25 2016 final

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Information about Week 15 state space rep may 25 2016 final

Published on May 30, 2016

Author: CharltonInao

Source: slideshare.net

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1. State Space Analysis Week 15 1 Professor Charlton S. Inao Control System Engineering,PE -3032 Defence Engineering College Bishoftu, Ethiopia

2. Instructional Objectives 2

3. State Space Analysis Approach 3

4. State Space Equation 4

5. General State Space Representation 5

6. 6

7. 7

8. State Space Model for Dynamic System DuCxy BuAxx   Matrices: A is state matrix; B is input matrix; C is output matrix; and D is direct transmission matrix Vectors: x is state vector; u is input vector; and y is output vector Note: Only apply to system that is linear and time invariant 8

9. Terminology/Nomenclature 9

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12. 12

13. State Space Block Diagram 13

14. Sample Illustration: Mass Damper Spring/Translational Mechanical System(Review) 14

15. 15

16. Vector Matrix Form/State Space Model Standard Form 16

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19. Block Diagram 19

20. 20

21. Standard Vector Matrix Form 21

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26. Correlation Between Transfer Function and State Space 26

27. Converting Transfer Function to State Space 27

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34. 34(b)

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37. Practice problem 37

38. Matlab Functions 38

39. Using Matlab Function: Use ss function creates state space models. For example:    010 3 0 25 10 2 1                     DCBAx x x >>A = [0 1;-5 -2]; >>B = [0;3]; >>C = [0 1]; >>D = [0]; >>sys=ss(A,B,C,D) a = x1 x2 x1 0 1 x2 -5 -2 Matlab Output b = u1 x1 0 x2 3 c = x1 x2 y1 0 1 d = u1 y1 0 39

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