This document provides an overview of state space analysis for dynamic systems. It introduces state space equations and models using matrix representations. Key matrices include the A matrix for the state, B for input, C for output, and D for direct transmission. The document discusses converting transfer functions to state space models and provides a mass-damper-spring example. It also outlines related terminology and using Matlab functions to create state space models from matrices.

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

10. 10

11. 11

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

17. 17

18. 18

19. Block Diagram
19

20. 20

21. Standard Vector Matrix Form
21

22. 22

23. 23

24. 24

25. 25

26. Correlation Between Transfer
Function and State Space
26

27. Converting Transfer Function to
State Space
27

28. 28

29. 29

30. 30

31. 31

32. 32

33. 33

34. 34(b)

35. 35

36. 36

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

40. 40

41. 41

42. 42

43. 43

44. 44