1. Modeling in the Time Domain
System & Control Engineering Lab.
School of Mechanical Engineering

2. CHAPTER OBJECTIVES
How to find a mathematical model, called a state space representation, for a linear, time-invariant system
How to convert between transfer function and state-space models
How to linearize a state-space representation

3. THE GENERAL STATE-SPACE REPRESENTATION

4. State-space equation
Linearized state equation and output equation
A(t) – State matrix; B(t) – Input matrix
C(t) – Output matrix; D(t) – Direct transmission matrix

5. State-space equation
Block diagram the linear, Continuous time control system
represented in state space

6. THE GENERAL STATE-SPACE REPRESENTATION

7. State-space equation

8. State-space equation

9. THE GENERAL STATE-SPACE REPRESENTATION

10. THE GENERAL STATE-SPACE REPRESENTATION

11. THE GENERAL STATE-SPACE REPRESENTATION

12. THE GENERAL STATE-SPACE REPRESENTATION

13. THE GENERAL STATE-SPACE REPRESENTATION

14. State-space equation Ex: Mechanical system

15. State-space equation Ex: Mechanical system

16. State-space equation Ex: Mechanical system

17. State-space equation Ex: Mechanical system
Output

18. State-space equation Ex: Mechanical system
Standard form

19. CONVERTING A TRANSFER FUNCTION TO STATE SPACE
phase variables

20. CONVERTING A TRANSFER FUNCTION TO STATE SPACE

21. CONVERTING A TRANSFER FUNCTION TO STATE SPACE

22. CONVERTING A TRANSFER FUNCTION TO STATE SPACE

23. CONVERTING A TRANSFER FUNCTION TO STATE SPACE

24. CONVERTING FROM STATE SPACE TO A TRANSFER FUNCTION
From state-space equation
Laplace Transform

25. CONVERTING FROM STATE SPACE TO A TRANSFER FUNCTION

26. CONVERTING FROM STATE SPACE TO A TRANSFER FUNCTION

27. CONVERTING FROM STATE SPACE TO A TRANSFER FUNCTION

28. CONVERTING FROM STATE SPACE TO A TRANSFER FUNCTION: EX

29. CONVERTING FROM STATE SPACE TO A TRANSFER FUNCTION: EX