H and Optimal Controller Design for the Shell Control Problem

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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

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Outline

• Shell control problem description
• Key objectives
• Design criteria and methodology
• H? and ? optimal controller results
• Prototype test case results
• Conclusions

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Shell Control Problem
Prett and Morari. Shell Process Control
Workshop, 1987.
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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

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Generalized Plant Structure
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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
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Exogenous Inputs Revisited
Prett and Morari. Shell Process Control
Workshop, 1987.
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Open Loop Characteristics
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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

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H? Controller Response
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Robust Stability of H? Controller
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? Optimal Response
iteration 1
iteration 2
iteration 3
iteration 4
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Prototype Test Cases
Worst case uncertainty set calculated by Matlab?
?1 1 ?2 -1, ?3 -0.7585, ?4 -0.5549, ?5
0.2497
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? Optimal Time Response
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Worst Case Input Frequency
?w ? 0.2754 rad/s
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Input and Rate Responses
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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

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Acknowledgements

• Dr. E.S. Meadows
• Dr. S.L. Shah
• CPC group at U of A
• NSERC
• iCore

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Questions?