1. Team Green John Barker John Beverly Keith Skiles UTC ENGR329-001 2-15-06 Steady State and Step Response Performance Speed Control System

2. Outline  System Background –Description, SSOC, Step Response  FOPDT Model  Model Theory  Results  Conclusions

3. Aerator Mixer Speed Control System

4. Block Diagram of System

8. Time Response (Gain)

9. Time Response (Dead Time)

10. Time Response (Time Constant)

11. Step Response Values and Errors K (RPM/%)t0 (s) τ (s) Average17.40.110.25 Std. Dev0.050.0060.017

12. Laplace Domain FOPDT Model  System Transfer Function  G(s) = Ke / τ s+1 –Parameters t 0 =Dead Time t 0 =Dead Time K = System Gain K = System Gain τ = Time Constant τ = Time Constant -t0s-t0s

13. FOPDT Model  Model Equation in Time Domain – C(t) = A*u(t-t d -t 0 )*K*(1-e ) -( t-td-t0 )

14. Results

16. Time Response (Gain)

17. Time Response (Dead Time)

18. Time Response (Time Constant)

19. Overall Results Experimental Results: Steady State Gain : K= 17.1RPM/% ± 0.10 Dead Time : t 0 = 0.06s ± 0.012 Time Constant : τ = 0.19s ± 0.034 Model Results: Steady State Gain : K= 17.4RPM/% Dead Time : t 0 = 0.1s Time Constant : τ = 0.23s

20. Conclusions  Operating Range 150-1700RPM  K = 17.4 RPM/%  t 0 = 0.1s  τ = 0.23s

21. Red Team -Pressure- Steady State Operating And Step Response Dennis To Cory Richardson Jamison Linden 6/28/2015, UTC, ENGR-329

22. Contents  Background Description, SSOC, Step Response  FOPDT Model  Model Theory  Results  Conclusions

23. Background  System  Input  Output  SSOC  Operating Range

24. System Figure 1. Schematic diagram of the Dunlap Plant Spray-Paint Booths

25. Block Diagram Figure 2. Block diagram of paint Booth System

26. SSOC Operating Range for Output Operating Range for Input

27. Operating Range  Input operating range (45%-90%)  Output operating range (0.5-10 cm-H2O)

28. Theory  Transfer Function  Parameters

29. Transfer Function Transfer Function m(s) Input c(s) Output 1 0   s Ke st  K=Gain=∆c/∆m=(cm-H2O)/% to=Dead Time τ=Time Constant (use 0.632∆c) Uncertainties (max-min)*(t/n)

30. Parameters LowerUpper Middle

31. Results  Experimental (Step-up, Step-down)  Time Response (Gain)  Time Response (Dead Time)  Time Response (Time Constant)

32. Experimental (Step-up)

33. Experimental (Step-down)

34. Time Response (Gain)

35. Time Response (Dead Time)

36. Time Response (Time Constant)

37. FOPDT Model  Model Equation  C(t) = A*u(t-t d -t 0 )*K*(1-e -((t-t d -t 0 )/tau) ) Parameters  t d =15 sec.  A = 15 %  K =.21 cm-H 2 O /%  t 0 = 0.52 sec.  tau = 1.8 sec.  inbl= 60%  outbl=2 cm-H 2 O

40. Model Time Response (Gain)

41. Model Time Response (Dead Time)

42. Model Time Response (Time Constant)

43. Results  EXPERIMENTAL PARAMETERS INCREASING STEADY STATE GAINK0.1-0.35 cm-H2O/% DEAD TIMEto0.5 s TIME CONSTANTt1.7 s  EXPERIMENTAL PARAMETERS DECREASING STEADY STATE GAINK0.1-0.35 cm-H2O /% DEAD TIMEto0.5 s TIME CONSTANTt1.7 s

44. Conclusions  Input operating range  Output operating range  (K) goes up as the input % is increased (0.1-0.35cm-H2O/%)  (t o) stays constant (0.5sec)  ( ) stays constant (1.7sec)

45. Flow Rate Control System “Step Response Modeling” February 15, 2006 U.T.C. Engineering 329

46. Yellow Team  Jimy George  Jeff Lawrence  Taylor Murphy  Jennifer Potter

47. Outline  System Background Description, SSOC, Step Response  FOPDT Theory  Model Theory  Results  Conclusions

48. Flow System Setup

49. Block Diagram

50. Steady State Operation

51. SSOC

52. Step Response: 70%-85%

53. FOPDT Model  Transfer Function

54. FOPDT Model  Model Equation Excel Parameters  t d = Time step occurs  A = Height of Step  inbl = Initial Input  outbl= Initial Steady Value

55. Experimental and Model Results K (lb/min/%) =0.26 Tau (sec) =0.46 t0 (sec) =0.42

56. Experimental and Model Results…cont K (lb/min/%) = 0.27 Tau (sec) = 0.47 t0 (sec) = 0.47

57. Results

58. Results … cont

60. MODEL PARAMETERS DECREASING STEADY STATE GAINK2.5 V/% DEAD TIMEt o 0 s TIME CONSTANT  0.6 s / 1.2 s / 2.4 s EXPERIMENTAL PARAMETERS DECREASING STEADY STATE GAINK2.5 V/% DEAD TIMEt o 0 s TIME CONSTANT  0.2 s OVERALL RESULTS MODEL PARAMETERS STEADY STATE GAIN,K =0.25 lb/min/% DEAD TIME,t o = 0.45 s TIME CONSTANT,  0.48 s EXPERIMENTAL PARAMETERS STEADY STATE GAIN,K =0.25 lb/min/% DEAD TIME,t o = 0.39 s TIME CONSTANT,  0.51 s OVERALL RESULTS

61. b Experimental Error Standard Deviations STEADY STATE GAIN,K = ± 0.01(lb/min/%) DEAD TIME,t o = ± 0.08 (sec) TIME CONSTANT,  ± 0.03 (sec) MODEL Error Standard Deviation STEADY STATE GAIN,K = ± 0.01 (lb/min/%) DEAD TIME,t o = ± 0.02 (sec) TIME CONSTANT,  ± 0.04 (sec)