h and optimal controller design for the shell control problem d. chang, e.s. meadows, and s.l....

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

CSChE Annual Meeting 2002: Vancouver, BC 2

Outline

Shell control problem descriptionKey objectivesDesign criteria and methodologyH and optimal controller results

Prototype test case resultsConclusions

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

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

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

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

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 2iteration 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. MeadowsDr. S.L. ShahCPC group at U of ANSERCiCore

CSChE Annual Meeting 2002: Vancouver, BC 19

Questions?