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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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?