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Controllability Analysis for Process and Control System Design

Controllability Analysis for Process and Control System Design. September 26, 2003. Thesis Overview. Introduction pH-neutralization: Integrated process and control design Buffer tank design Control design for serial processes MPC without active constraints

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Controllability Analysis for Process and Control System Design

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  1. Controllability Analysis for Process and Control System Design September 26, 2003

  2. Thesis Overview • Introduction • pH-neutralization: Integrated process and control design • Buffer tank design • Control design for serial processes • MPC without active constraints • Feedforward control under the presence of uncertainty • Offset free tracking with MPC: An experiment • Conclusions and directions for further work Appendix A and B: Published material not covered in the other chapters

  3. Outline of the Presentation • Introduction • Part 1 (Chapter 2 and 3): Buffer tank design. • Idea: Handle disturbances neither handled by the process itself nor the feedback controllers • Part 2 (Chapter 6): Feedforward control under uncertainty • Part 3 (Chapter 4, 5 and 7): Multivariable control: • Feedforward effects • Integral action • Uncertainty • Summary

  4. IntroductionKårstø gas processing plant: Steam pressure

  5. u1 d u2 u3 ym,1 ym,2 ym,3 y1 y3 y2 r3 Process Example: Neutralization in Three Tanks

  6. d y Gd + + dm u G Kff - ym + + K - Controller Process Block Scheme Model scaling: • Require for output • Expect from disturbance • Given for control inputs r

  7. Controllability With a Scaled Model Disturbance, d Output, y Require Expect

  8. y=ym d + Gd + Controller + u G K r - Process Controllability • Effect of disturbances on the output: • Low frequencies • High frequencies • Required performance for all w

  9. Outline of the Presentation • Introduction • Part 1 (Chapter 2 and 3): Buffer tank design. • Idea: Handle disturbances neither handled by the process itself nor the feedback controllers • Part 2 (Chapter 6): Feedforward control under uncertainty • Part 3 (Chapter 4, 5 and 7): Multivariable control: • Feedforward effects • Integral action • Uncertainty • Summary

  10. Two Sources for Disturbances • Quality disturbance In concentration or temperature “Averaging by mixing” • Flow rate disturbance Slow level control “Averaging level control” Figure 3.1(I) Figure 3.1(II)

  11. Use Buffer Tanks to Modify the Response Typical buffer tank transfer function: (logarithmic scales) Figure 3.4 |h| w

  12. How Buffer Tanks Modify the Response I Quality disturbance: Mixing tank Assume perfect mixing n tanks II Flow disturbance: Slow level control P controller gives 1st order filter Volume selected to keep level within limits: t t

  13. pH-neutralization (Chapter 2) • Quality disturbance: mixing tanks • Gd,0= kd (constant) and kd is large ( 103 or larger) • Consider frequency where S=1 • Obtain minimum total volume requirement where q is flow rate n is number of tanks q is time delay in control loops • May reduce total volume with more tanks

  14. pH-neutralization (continued) • Numerical computations • Local PI/PID in each tank with different tunings: • Ziegler-Nichols, IMC, SIMC • Optimal tuning: Minimizing buffer volume • Frequency response • Step response in time domain • Conclusions: • Equal tanks • Total volume

  15. More General Buffer Tank Design (Chapter 3) • All kinds of processes • Both mixing tanks and surge tanks • Feedback control system given or not • Two steps • Find the required transfer functionh(s) • Design a tank (and possibly a level controller) to realizeh(s)

  16. Outline of the Presentation • Introduction • Part 1 (Chapter 2 and 3): Buffer tank design. • Idea: Handle disturbances neither handled by the process itself nor the feedback controllers • Part 2 (Chapter 6): Feedforward control under uncertainty • Part 3 (Chapter 4, 5 and 7): Multivariable control: • Feedforward effects • Integral action • Uncertainty • Summary

  17. Kff - d + y=ym Gd + r + u G K + - Controllers Process Controllability (Revisited) • Effect of disturbances on the output: • Low frequencies • High frequencies • Feedforward control required if for any frequency • Feedforward from the reference

  18. Feedforward Sensitivity Functions • Output with feedforward and feedback control: • Introduce feedforward sensitivity functions: and obtain • Feedforward from the reference, r: • Feedforward effective: • Balchen:

  19. Ideal Feedforward Controller • No model error: • When applied to actual plant and : i.e. the relative errors inG/GdandG

  20. Some Example Feedforward Sensitivities Gain error Delay error w (logarithmic scale) w Figure 6.2(a) and (b)

  21. Some Example Feedforward Sensitivities Gain and time constant error Time constant error Figure 6.2(c) and (d)

  22. Combined Feedforward and Feedback Control • No model error Sff SGd SSffGd

  23. Combined Feedforward and Feedback Control • Delay error Sff SGd SSffGd

  24. Robust Feedforward Control • Scali and co-workers: H2 /H optimal combined feedforward and feedback control • Detune ideal feedforward controller (reduce gain, filter) • m-optimal feedforward controller Figure 6.9

  25. Outline of the Presentation • Introduction • Part 1 (Chapter 2 and 3): Buffer tank design. • Idea: Handle disturbances neither handled by the process itself nor the feedback controllers • Part 2 (Chapter 6): Feedforward control under uncertainty • Part 3 (Chapter 4, 5 and 7): Multivariable control: • Feedforward effects • Uncertainty • Integral action • Summary

  26. Serial Processes • One process unit after another in a series • Material flow and information go in one direction • Example • Here: Each unit controlled separately

  27. Serial Processes: Model Structure

  28. Possibly input resetting Local feedback control “Feedforward” control Control of Serial Processes

  29. Example: Three Tanks in Series • 10s delay in each tank • Local PID controllers Figure 4.5(a)

  30. Example: Three Tanks in Series • Feedforward control Figure 4.5(b)

  31. Example: Three Tanks in Series • MPC – Model predictive control • Input disturbance estimation • First version: Did not handle model error (Fig. 4.9) • Modified version: Correct integral action (Fig. 4.11) Figure 4.7(a)

  32. MPC With No Active Constraints • Can be expressed as state feedback: • Extended to non-zero reference, output feedback, input disturbance estimation and possibly input resetting • The full controller on state-space form • Makes it possible to • Plot the controller gain of each channel • Sensitivity function for each channel

  33. Example: Three Tanks in Series Controller gains Sensitivity functions Figure 4.10

  34. Summary • Design of pH neutralization plants • Design of buffer tanks to achieve required performance • Feedforward control under uncertainty • Feedforward sensitivity functions • When is feedforward needed? • When is it useful? • Multivariable control makes use of both feedforward and feedback control effects • Nominally good performance • Sensitive to uncertainty • Integral action • Model predictive controller without active constraints • State space form of controller and estimator

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