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Chapter 7 Adjusting Controller Parameters

Chapter 7 Adjusting Controller Parameters. Professor Shi-Shang Jang Chemical Engineering Department National Tsing-Hua University Hsin Chu, Taiwan. 7-1 Basic Requirement of a controller. The closed loop system must be stable

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Chapter 7 Adjusting Controller Parameters

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  1. Chapter 7 Adjusting Controller Parameters Professor Shi-Shang Jang Chemical Engineering Department National Tsing-Hua University Hsin Chu, Taiwan

  2. 7-1 Basic Requirement of a controller • The closed loop system must be stable • The effects of disturbance must be minimized, good disturbance rejection (regulation performance) • Rapid, smooth responses to set-point changes are required, good servo performance • Steady state error (offset) is eliminated • Excessive control action is avoided (control action should avoid oscillation, input stable) • The control system robust, that is, insensitive to changes in process

  3. 7-1 Quarter Decay Ratio By Ultimate Properties

  4. 7-1 Example (Example 6-1.1 Ku=10.4 Pu=4.6min

  5. 7-1 Example (Example 6-1.1- Cont.

  6. 7-2 Open Loop Characterization

  7. 7-2 Open Loop Characterization

  8. 7.2 61.5 7-2 Open Loop Characterization -Example

  9. 7-2 Tuning for Quarter Decay Ratio

  10. 7-2 Tuning for Quarter Decay Ratio - Example

  11. 7-2.2 Tuning for Integral Criteria • Integral of absolute value of the error (IAE) • Integral of the square error (ISE) • Integral of the time-weighted abolute error (ITAE)

  12. 7-2.2 Tuning for Integral Criteria - IAE

  13. 7-2.2 Tuning for Integral Criteria - IAE

  14. 7-2.2 Tuning for Integral Criteria – IAE : Example

  15. Example – Cont.

  16. Example – Cont.

  17. Example – Cont.

  18. Example – Cont.

  19. Step Response Test; FOPDT Fit 2

  20. Regression Test Response; C Time (min)

  21. Step Response Test; SOPDT, Smith’s Method Response; C time

  22. Response; C Time (min)

  23. PID Control Comparison FOPTD Temperature; C SOPTD Time, min

  24. 7-3 Summary • A control loop should be stable, fast responding and robust • Z-N QD tuning and IAE tuning are widely used in the industries • On-Line tuning is also widely used

  25. Homeworks • Text p 271 • 7-3, , 7-12, 7-15, 7-19, 7-22

  26. Supplemental Materials

  27. Synthesis of Feedback Controllers Chapter 7 • Controller synthesis • Given the transfer functions of the components of a feedback loop, synthesize the controller required to produce a specific closed-loop response • Formula derivation

  28. Chapter 7 • For perfect control • This says that in order to force the output to equal the set point at all times, the controller gain must be infinite. • In other words, perfect control cannot be achieved with feedback control. • This is because any feedback corrective action must be based on an error.

  29. Specification of the Closed-Loop Response Chapter 7 • The simplest achievable closed-loop response is a first-order lag response • τc is the time constant of the closed-loop response • The single tuning parameter for the synthesized controller • Design parameter τc provides a convenient controller tuning parameter that can be used to make the controller more aggressive (small τc) or less aggressive (large τc).

  30. ~ Chapter 7 • This controller has integral mode • No offset • i.e. unity gain

  31. Notes Chapter 7 Although second- and higher-order closed-loop responses could be specified, it is seldom necessary to do so. When the process contains dead time, the closed-loop response must also contain a dead-time term, with the dead time equal to the process dead time.

  32. If the process transfer function contains a known time delay θ, a reasonable choice for the desired closed-loop transfer function is: • The time-delay term is essential because it is physically impossible for the controlled variable to respond to a set-point change at t = 0, before t = θ. • If the time delay is unknown, θ must be replaced by an estimate. Chapter 7

  33. Although this controller is not in a standard PID form, it is physically realizable. • Using a truncated Taylor series expansion: Chapter 7 Note that this controller also contains integral control action.

  34. FOPDT Model Consider the standard FOPDT model, Chapter 7

  35. SOPDT Model Consider a SOPTD model, Chapter 7 where:

  36. Example Use the DS design method to calculate PID controller settings for the process: Consider three values of the desired closed-loop time constant: . Evaluate the controllers for unit step changes in both the set point and the disturbance, assuming that Gd = G. Repeat the evaluation for two cases: Chapter 7 • The process model is perfect ( = G). • The model gain is = 0.9, instead of the actual value, K = 2. Thus,

  37. The controller settings for this example are: Chapter 7

  38. The values of Kc decrease as increases, but the values of and do not change. Chapter 7

  39. Perfect process model Chapter 7

  40. With model mismatch Chapter 7

  41. Comparison to quarter decay ratio response Chapter 7

  42. Chapter 7 Set the parameters of the PID controller according to Table 7-1.1

  43. Chapter 7

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