1. Voltage Control System: Proportional Integral (PI) Controllers Team Purple: John Pangle Jessica Raymond Justin Whitt ENGR 329 November 30, 2005

2. Outline Voltage System Background Previous Work: SSOC, Step, Sine, Bode, P-Only PI Model Results PI Experimental Results Conclusions Luyben Method Review Recent Results Conclusions

3. Purple Team 9/14/05 Voltage System Schematic

4. Block Diagram M(t) is measured in % and C(t) is in Volts.

5. Purple Team 10/25/05 Operating Range: Output = 50V to 140V Operating Range: Input = 70% to 100% 75%-100% Input Slope = 2 V/%

6. Background: Step Input Voltage System K – Gain (Volt/%) t 0 – Dead Time (s) τ – Time Constant (s)

7. Background: FOPDT Fit

8. FOPDT Model

9. Background: Sinusoidal Input K – Gain (Volt/%) t 0 – Dead Time (s) τ – Time Constant (s)

10. Values taken from Point A  AR = 1.5  f = 4 Hz Bode Plot  K = 2 V / %   = 0.04 sec  t o = 0.08 sec

12. Background: Sinusoidal Input

13. Background: FOPDT Averages

14. Background: Feedback Loops Kc 1 0   s Ke st  R (volts) E ( ) M (%) C (volts) + - CE =

15. Background: P-Only Controllers

29. PI Controllers

33. PI Controllers (Kc = 0.8)

34. PI Controllers (Kc = 0.5)

35. PI Controllers (Kc = 0.4)

36. PI Controllers (Kc = 0.2)

37. PI Controllers (Kc = 0.1)

38. PI Controllers (Kc = 0.05)

39. PI Controllers

41. τIτI

43. Conclusions Recommend PI over P-only Recommend τ I = 0.1 Yields widest range of desirable decay ratios. Provides acceptable settling times.

44. Luyben Method Presented by William L. Luyben, Ph.D at Reno AIChE Meeting Nov. 6, 2001

45. Luyben Method 1.Insert relay into feedback loop. Relay 1 0   s Ke st  R (volts) E ( ) M (%) C (volts) + -

46. Luyben Method 2.Specify upper & lower limits of m(t)

47. Luyben Method

49. 3.Find T u from c(t) 4.Calculate K cu

50. Luyben Method

55. What about t o and τ? I still have to run another test right?

56. Luyben Method

58. F=1 for Voltage System t o /τ = 2

59. Luyben Method t o = 2τ τ = 0.01 and t o = 0.02

60. Luyben Method

62. Conclusion Only one simple test required (7 steps) Works well for any order systems Similar Results to Bode