1. Time Response System & Control Engineering Lab.
School of Mechanical Engineering

2. CHAPTER OBJECTIVES
How to find the time response from the transfer function
How to use poles and zeros to determine the response of a control system
How to describe quantitatively the transient response of first- and second-order systems
How to approximate higher-order systems as first or second order

3. POLES, ZEROS, AND SYSTEM RESPONSE
POLES OF A TRANSFER FUNCTION
ZEROS OF A TRANSFER FUNCTION
FIRST-ORDER SYSTEMS
SECOND-ORDER SYSTEMS: INTRODUCTION
THE GENERAL SECOND-ORDER SYSTEM
SYSTEM RESPONSE WITH ADDITIONAL POLES
SYSTEM RESPONSE WITH ZEROS

4. The Performance of Control Systems
Test input signals
Transient response and Steady-state response
Absolute stability, relative stability
Steady-state error

5. Typical Test Signal Step functions Ramp functions
Acceleration functions
Impulse functions
Sinusoidal functions
White noise signals

6. Typical Test Signal
Step functions
Ramp functions

7. Typical Test Signal
Sinusoidal functions
Impulse functions

8. POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

9. POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

10. POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

11. POLES AND ZEROS OF A FIRST-ORDER SYSTEM: AN EXAMPLE

12. FIRST-ORDER SYSTEMS

13. FIRST-ORDER SYSTEMS

14. FIRST-ORDER SYSTEMS

15. FIRST-ORDER SYSTEMS
TIME CONSTANT
RISE TIME, Tr
SETTLING TIME, Ts

16. Unit-Step Response of First-Order Systems
Transfer function of the first-order system
For unit-step function

17. Unit-Step Response of First-Order Systems
Inverse Laplace transform
C (t) = Force response + Free response
and t=T

18. Unit-Step Response of First-Order Systems

19. Second-Order Systems
In transfer function (Laplace Transform)

20. Second-Order Systems

21. Second-Order Systems

22. Second-Order Systems

23. Second-Order Systems

24. Second-Order Systems

25. Second-Order Systems

26. Second-Order Systems

27. Second-Order Systems

28. Second-Order Systems

29. Second-Order Systems

30. Undamped Second-Order Systems Response

31. Undamped Second-Order Systems Response

32. Undamped Second-Order Systems Response

33. Undamped Second-Order Systems Response

34. Undamped Second-Order Systems Response

35. Undamped Second-Order Systems Response

36. Undamped Second-Order Systems Response

37. Undamped Second-Order Systems Response

38. Undamped Second-Order Systems Response

39. Undamped Second-Order Systems Response

40. Undamped Second-Order Systems Response

41. Undamped Second-Order Systems Response

42. fig_04_18
SYSTEM RESPONSE WITH ADDITIONAL POLES

43. fig_04_18
SYSTEM RESPONSE WITH ADDITIONAL ZEROS