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Optimization-based PI/PID control for SOPDT process

Optimization-based PI/PID control for SOPDT process. Summary on optimization-based PI/PID control. Best achievable IAE performance by PI/PID control of FOPDT process. Optimal rise-time vs, IAE in PI/PID control of SOPDT process.

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Optimization-based PI/PID control for SOPDT process

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  1. Optimization-based PI/PID control for SOPDT process

  2. Summary on optimization-based PI/PID control

  3. Best achievable IAE performance by PI/PID control of FOPDT process

  4. Optimal rise-time vs, IAE in PI/PID control of SOPDT process

  5. Optimal rise-time vs, IAE in PI/PID control of SOPDT process

  6. FOPDT

  7. SOPDT

  8. Loop transfer functions of IMC-PID Controllers According to the IMC theory, nominal loop transfer function of a control system that has an inverse-based controller will be of the following:

  9. IMC-PID for FOPDT process

  10. Loop transfer functions of IMC-PID Controllers FOPDT processes: SOPDT processes: the resulting loop transfer function becomes:

  11. Inverse-based Controller Design • We should learn what happens to the Z-N tuned controllers? • How inverse-based controllers are synthesized?

  12. Loop transfer functions of Inverse-based Controllers • Inverse-based synthesis approach is used • Target loop transfer function (LTF) • This LTF has satisfactory control performance as well as reasonable stability robustness • ko and a are selected to meet desired control specification Defaulted value: ko=0.65 a=0.4 GM = 2.7 PM = 60 o

  13. PI/PID Controllers Based on FOPDT Model • PID controller ko=0.65 , a=0.4 • A direct synthesis approach is used • PI controller ko=0.5 • Controller parameters (actual PID)

  14. PID Controller Based on SOPDT Model • Controller parameters (ideal PID) ko=0.5

  15. Gain margin vs. phase margin at a=0.4 Phase margin Gain margin

  16. Auto-tune • Autotuning via relay feedback: Astrom and Hagglund (1984) Referred as autotune variation (ATV): Luyben (1987) Main advantage: under closed-loop

  17. Apply Z-N or T-L tuning

  18. - Underdamped SOPDT Oscillatory step response MODEL-BASED CONTROLLERS DESIGN • Reduced order models • FOPDT Monotonic step response • For zero offset, PI or PID controller is considered • Usage of PI or PID controller depend on: • The application occasions • The dynamic characteristics of given process • Processes are classified into two groups for controller tuning

  19. Criterion for Classifying model order • In general, processes with overdamped or slightly underdamped SOPDT dynamics can be identified with FOPDT models for controller tuning Q: When an SOPDT process could be reduced to an FOPDT parameterization? A: Ku > 1

  20. PI/PID Controllers Based on FOPDT Model • PID controller ko=0.65 , a=0.4 • A direct synthesis approach is used • PI controller ko=0.5 • Controller parameters (actual PID) In terms of ultimate data (Ku = kp kcu)

  21. PI controller Defaulted value: ko=0.55 a=0.4 In terms of ultimate data

  22. PID Controller Based on SOPDT Model • Only PID controller is used for significant underdamped SOPDT dynamics, i.e. • Controller parameters (ideal PID) • The values of kpand need to be estimated in advance ko=0.5 In terms of ultimate data

  23. Dynamic Process FOPDT Model SOPDT Model Group I Group II PID Controller PID Controller PI Controller

  24. Estimation of process gain kp • Start the ATV test with a temporal disturbance to setpoint or process input • Define • and have cycling responses

  25. Estimation from is subject to error, sometimes as high as 20% • From Fourier series expansion • Ultimate gain is computed exactly as:

  26. Estimation of Apparent Deadtime • In an ATV test, two measured quantities are used to characterize the effect of the apparent deadtime • For SOPDT process, this two quantities are functions of and

  27. Underdamped SOPDT processes

  28. Algorithm for estimation of apparent deadtime • Starting from a guessed value of • Calculate and , and feed them into networks to compute and • Check if the eq. holds • If not, increase the value of until the above eq. holds. At that time, is the estimated apparent deadtime

  29. In ATV test, it provides and which are functions of and • Locate • on this figure • Zone I: • FOPDT parameterization • Zone II: • SOPDT parameterization

  30. Initiate ATV test by a short period of manual disturbance and record y(t) and u(t) until constant cycling is attained • Compute kp and kcu • Estimate the apparent deadtime • Classify the process by the location of • If the process belongs to Group I, tune PI or PID controller based on FOPDT model parameterization • If the process belongs to Group II, tune PID controller based on SOPDT model parameterization

  31. Examples

  32. Ex. 3 Ex. 2 Ex. 1

  33. Ideal PID controller with an extra filter • The value of kp and need to be known in advance

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