Root Locus Method

1. Root Locus Method

2. Root Locus Method

3. Root Locus Method

4. Root Locus Method

7. Roots of the characteristic equation Depends on Kc (tuning) of the loop.

8. 1- This control loop will never go unstable. 2- When Kc=0, the root loci originates from The OLTF poles:-1/3, and -1 3- The number of root loci/branches=number Of OLTF poles=2 4- As Kc increases, the root loci approaches infinity

10. 1- This control loop can go unstable. 2- When Kc=0, the root loci originates from The OLTF poles:-1/3, -1, -2 3- The number of root loci/branches=number Of OLTF poles=3 4- As Kc increases, the root loci approaches infinity

12. 1- This control loop can never go unstable. As Kc increases the root loci move away from I-axis, and D- mode adds a lead to the loop makes it more stable. Addition of lag reduces stability 2- When Kc=0, the root loci originates from the OLTF poles:-1, -1/3 3- The number of root loci/branches=number Of OLTF poles=2 4- As Kc increases, one rout locus approaches – infinity and the other -5, the zero of the OLTF

13. The rout locus must satisfy the MAGNITUDE and the ANGLE conditions

14. The rout locus must satisfy the MAGNITUDE and the ANGLE conditions

15. MAGNITUDE CONDITION ANGLE CONDITION

16. MAGNITUDE CONDITION ANGLE CONDITION

21. Example:

26. Matlab comands: rlocus Evans root locus Syntax rlocus(sys) rlocus(sys,k) rlocus(sys1,sys2,...) [r,k] = rlocus(sys) r = rlocus(sys,k)

27. Matlab comands: Find and plot the root-locus of the following system. h = tf([2 5 1],[1 2 3]); Rlocus(h, k)

28. Frequency Response Technique • Process Identification: • A- Step Test Open-Loop Response • B- Frequency Response.

29. Frequency Response Technique B- Frequency Response.

30. Frequency Response Technique Recording from sinusoidal testing

31. Frequency Response Technique • Mathematical Interpretation:

32. Frequency Response Technique • Mathematical Interpretation (Continued): Amplitude of the response degrees radian

33. Frequency Response Technique • Mathematical Interpretation (Continued): Amplitude of the response Magnitude Ratio Amplitude Ratio

34. Frequency Response Technique • Mathematical Interpretation (Continued): • All these terms (AR, MR, and Phase angle) are functions of • Frequency response is the study of how AR(MR) and phase angle of different components change as frequency changes. • Methods of Generating Frequency Response: • A- Experimental Method • B- Transforming the OLTF after a sinusoidal input

35. Frequency Response Technique • Methods of Generating Frequency Response: • B- Transforming the OLTF after a sinusoidal input

36. Frequency Response Technique • Methods of Generating Frequency Response: • B- Transforming the OLTF after a sinusoidal input

37. Frequency Response Technique • Methods of Generating Frequency Response: • B- Transforming the OLTF after a sinusoidal input

38. Frequency Response Technique • Methods of Generating Frequency Response: • B- Transforming the OLTF after a sinusoidal input Long time

39. Frequency Response Technique • Methods of Generating Frequency Response: • B- Transforming the OLTF after a sinusoidal input

40. Frequency Response Technique • Methods of Generating Frequency Response: • B- Transforming the OLTF after a sinusoidal input

41. Frequency Response Technique • Example:

42. Frequency Response Technique • Example:

43. Frequency Response Technique • Example:

44. Frequency Response Technique • Generalization

45. Frequency Response Technique • Generalization

46. Frequency Response Technique • 1- Bode Plots, 2-Nyquist Plots, and 3- Nichols Plots • 1- Bode Plots

47. Frequency Response Technique • 1- Bode Plots

48. Frequency Response Technique • 1- Bode Plots

49. Frequency Response Technique • 1- Bode Plots

50. Frequency Response Technique • 1- Bode Plots