TIME RESPONSE PART I
by Nooradilla aziz
1. ZEROS
2. are found from the numerator
3. The values of the Laplace transform variables, s, that cause the transfer function to become zero
4. Any roots of the numerator of the transfer function that are common to roots of the denominator
5. The s-plane
6. The positions of the poles can be plotted on a graph with : → the real part of the pole value as the x-axis . → the imaginary part as the y-axis
7. The output response of a system is the sum of two responses
8. the forced response and the natural response
9. DYNAMIC RESPONSE
10. Dynamic response of a control system determines how the output of systems changes when there is a change in input
11. Example: System→mercury-in-glass thermometer Input→temperature Output→level of the mercury in the glass capillary
12. FIRST ORDER SYSTEM
13. Time constant
14. Rise Time
15. Settling Time
16. Rise time = the time taken from the 0.1 to 0.9 of amplitude (10% to 90%). Settling time = the time taken between 0.98 and 1.02. (choose the latter time). Steady state value = the value steady at 1 Peak value = The maximum amplitude. Peak time = the time taken from peak amplitude Percent overshoot
17. Two real poles ζ > 1 The output takes longer than critical damping to reach the steady-state value.
18. are found from the denominator
19. The values of the Laplace transform variables, s, that cause the transfer function to become infinite
20. Any roots of the denominator of the transfer function that are common to roots of the numerator
21. TYPES OF INPUT
22. Step
23. Ramp
24. Impulse
25. Input suddenly being switched to a constant value at some particular time
26. A unit step input which starts at a time t = 0 and rises to the constant value 1 has a Laplace transform of the input as an s function multiplied by 1/s
27. Input existing for just a very brief time before dropping back to zero
28. A unit impulse input which starts at a time t = 0 and rises to the value 1 has a Laplace transform of the input as an s function multiplied by 1
29. Input starting at some time and then increasing at a constant rate
30. A unit ramp input which starts at time t = 0 and rises by 1 each second has a Laplace transform of the input as an s function multiplied by 1/s2
31. SECOND ORDER SYSTEM
32. 4 types of damping
33. Underdamped
34. Overdamped
35. Undamped
36. Critically Damped
37. Two complex poles 0 < ζ < 1 Output oscillates but the closer the damping factor is to 1 the faster the amplitude of the oscillations diminishes
38. Two imaginary poles. ζ = 0 The system output oscillates with a constant amplitude and a frequency of ωn.
39. Two real pole (repeated poles). ζ =1 There are no oscillations and the output just gradually approaches the steady-state value.
