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. CSChE Annual Meeting 2002: Vancouver, BC2 Outline  Shell control problem description  Key objectives  Design criteria and methodology  H  and  optimal controller results  Prototype test case results  Conclusions

3. CSChE Annual Meeting 2002: Vancouver, BC3 Shell Control Problem Prett and Morari. Shell Process Control Workshop, 1987.

4. CSChE Annual Meeting 2002: Vancouver, BC4 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

5. CSChE Annual Meeting 2002: Vancouver, BC5 Generalized Plant Structure

6. CSChE Annual Meeting 2002: Vancouver, BC6 Block Singularity spy(D)spy(D’) and Avoid singular control problems Meaning D 12 must be full column and D 21 must be full row rank. (Zhou, Doyle, and Glover, 1996) D before addition of setpoints D’ after addition of setpoints

7. CSChE Annual Meeting 2002: Vancouver, BC7 Exogenous Inputs Revisited Prett and Morari. Shell Process Control Workshop, 1987.

8. CSChE Annual Meeting 2002: Vancouver, BC8 Open Loop Characteristics

9. CSChE Annual Meeting 2002: Vancouver, BC9 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

10. CSChE Annual Meeting 2002: Vancouver, BC10 H  Controller Response

11. CSChE Annual Meeting 2002: Vancouver, BC11 Robust Stability of H  Controller

12. CSChE Annual Meeting 2002: Vancouver, BC12  Optimal Response iteration 1 iteration 2 iteration 3 iteration 4

13. CSChE Annual Meeting 2002: Vancouver, BC13 Prototype Test Cases Worst case uncertainty set calculated by Matlab  :  1 = 1  2 = -1,  3 = -0.7585,  4 = -0.5549,  5 = 0.2497

14. CSChE Annual Meeting 2002: Vancouver, BC14  Optimal Time Response

15. CSChE Annual Meeting 2002: Vancouver, BC15 Worst Case Input Frequency  w  0.2754 rad/s

16. CSChE Annual Meeting 2002: Vancouver, BC16 Input and Rate Responses

17. CSChE Annual Meeting 2002: Vancouver, BC17 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

18. CSChE Annual Meeting 2002: Vancouver, BC18 Acknowledgements  Dr. E.S. Meadows  Dr. S.L. Shah  CPC group at U of A  NSERC  iCore

19. CSChE Annual Meeting 2002: Vancouver, BC19 Questions?