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H  and  Optimal Controller Design for the Shell Control Problem

H  and  Optimal Controller Design for the Shell Control Problem. D. Chang, E.S. Meadows, and S.L. Shah Department of Chemical and Materials Engineering University of Alberta CSChE Annual Meeting 2002. Outline. Shell control problem description Key objectives

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H  and  Optimal Controller Design for the Shell Control Problem

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  1. H and  Optimal Controller Design for the Shell Control Problem D. Chang, E.S. Meadows, and S.L. Shah Department of Chemical and Materials Engineering University of Alberta CSChE Annual Meeting 2002

  2. Outline • Shell control problem description • Key objectives • Design criteria and methodology • H and  optimal controller results • Prototype test case results • Conclusions CSChE Annual Meeting 2002: Vancouver, BC

  3. Shell Control Problem Prett and Morari. Shell Process Control Workshop, 1987. CSChE Annual Meeting 2002: Vancouver, BC

  4. Key Objectives • Design a robustly stable controller satisfying the following constraints: • top end point and bottom reflux temperature is constrained between 0.5 and –0.5 • top draw, side draw and bottoms reflux duty is constrained between 0.5 and –0.5 • Manipulated variables have maximum move sizes between 0.05 and –0.05 CSChE Annual Meeting 2002: Vancouver, BC

  5. Generalized Plant Structure CSChE Annual Meeting 2002: Vancouver, BC

  6. Block Singularity spy(D) spy(D’) Avoid singular control problems and Meaning D12 must be full column and D21 must be full row rank. (Zhou, Doyle, and Glover, 1996) D before addition of setpoints D’ after addition of setpoints CSChE Annual Meeting 2002: Vancouver, BC

  7. Exogenous Inputs Revisited Prett and Morari. Shell Process Control Workshop, 1987. CSChE Annual Meeting 2002: Vancouver, BC

  8. Open Loop Characteristics CSChE Annual Meeting 2002: Vancouver, BC

  9. Exogenous Output Weights Performance weight • Crossover = 0.006 rad/sec  167 sec • 10% S.S. offset Controller output weight • Crossover = 0.9 rad/sec  1.1 sec CSChE Annual Meeting 2002: Vancouver, BC

  10. H Controller Response CSChE Annual Meeting 2002: Vancouver, BC

  11. Robust Stability of H Controller CSChE Annual Meeting 2002: Vancouver, BC

  12.  Optimal Response iteration 1 iteration 2 iteration 3 iteration 4 CSChE Annual Meeting 2002: Vancouver, BC

  13. Prototype Test Cases Worst case uncertainty set calculated by Matlab: 1= 1 2= -1, 3= -0.7585, 4= -0.5549, 5= 0.2497 CSChE Annual Meeting 2002: Vancouver, BC

  14.  Optimal Time Response CSChE Annual Meeting 2002: Vancouver, BC

  15. Worst Case Input Frequency w 0.2754 rad/s CSChE Annual Meeting 2002: Vancouver, BC

  16. Input and Rate Responses CSChE Annual Meeting 2002: Vancouver, BC

  17. Conclusions • A robustly stable multivariate controller can be designed with relative ease • All of the input, output and rate constraints were met for the Shell control problem •  analysis provides a consistent framework for evaluating robust performance for all controllers CSChE Annual Meeting 2002: Vancouver, BC

  18. Acknowledgements • Dr. E.S. Meadows • Dr. S.L. Shah • CPC group at U of A • NSERC • iCore CSChE Annual Meeting 2002: Vancouver, BC

  19. Questions? CSChE Annual Meeting 2002: Vancouver, BC

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