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H and Optimal Controller Design for the Shell Control
Problem
D. Chang, E.S. Meadows, and S.L. ShahDepartment of Chemical and Materials
EngineeringUniversity of Alberta
CSChE Annual Meeting 2002
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CSChE Annual Meeting 2002: Vancouver, BC 2
Outline
Shell control problem descriptionKey objectivesDesign criteria and methodologyH and optimal controller results
Prototype test case resultsConclusions
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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
0
)(
212
12111
21
DC
DDC
BBA
sPspy(D) spy(D’)
I
D0
12 ID 021 and
Avoid singular control problems
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
2
1
1
Cs
BsAsw
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 2iteration 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. MeadowsDr. S.L. ShahCPC group at U of ANSERCiCore
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Questions?