Dynamic Behavior and Stability of Closed-Loop Control Systems

1. Dynamic Behavior and Stability of Closed-Loop Control Systems

3. Block diagram for process dynamics

4. Block diagram for sensor and transmitter

5. Block diagram for controller

6. Gain of I/P transmitter

7. Block diagram for control valve

9. Closed-Loop transfer functions

16. Proportional Control:

20. Simulation with Matlab L y + + + - R

21. Simulation with Matlab SIMLINK

22. Effect of P- control K=5 K=2 K=1

23. Effect of P- control K=3 K=2 K=1 K=0.5

24. Effects of P-mode on control performance • Speed up the response; • Result in offset; • Offset decreases when loop gain increases; • Oscillatory response due to existence of process dead time.

26. Responses of PI control for integration process

27. Open-loop unstable process

29. L y + + + - R

30. Effect of K under constant I mode K=2 K=1 K=0.2

31. K=2.0 K=1.0 Effect of K under constant I mode K=0.2

32. Effects of I-mode on control performance • Eliminate steady state offset; • Speed up response along with increasing proportional constant or decreasing the integral time; • Has dynamic characteristics range from over damped to under damped.

33. Effect of D mode on controller output Contributed by derivative mode CO Time

34. Effect of D-mode P+D P

35. K=1.5 K=1 Effect of K under constant D-mode

36. Effects of D-mode on control performance • Provides an initial momentum to the process at the moment when input change occurs; • Results in heavier damped dynamics; • Has no direct effect on reducing the offset, nevertheless, offset reducing is usually achieved indirectly due to this D-mode; • Derivative mode will amplify the effect of noises.

37. PI PID P

43. Uses of P, I, D, modes in process control loops • Level control loops • Flow control loops • Pressure control loops • Temperature control loops

44. Level control loops • Tight control at constant height --- constant head for steady process flow, --- protection of centrifugal pumps, --- to provide precise heat transfer rate in an evaporator, --- to guarantee product quality, (e.g. precise sizing in warp yarn coating), --- etc.

47. Level control loops • Averaging level control --- to provide storage inventory. --- to absorb disturbances from an upstream units

50. Level control • Proportional controller with a wide band is sufficient for most averaging control; • Tight control is usually accomplished with a narrow proportional band; • For constraints or safety such as override or high/low signal selection, a very narrow band of proportional control is used.