Performance Assessment of Model Predictive Control

1. Performance Assessment of Model Predictive Control R.H. Julien & W.R. Cluett Department of Chemical Engineering & Applied Chemistry University of Toronto M.W. Foley Department of Chemical Engineering University of the West Indies April 28, 2003 U of T

2. Outline • Model Predictive Control (MPC) • Performance Assessment of Feedback Control Systems • Performance Assessment Benchmark for MPC • Simulation Example • Experimental Results • Summary • Future Work

3. at Gd(z-1) Ut rt = 0 Yt Gc(z-1) Gp(z-1) - Univariate Feedback System Plant Transfer Function Unmeasured Disturbance z-1 = backshift operator Dt

4. Minimum Variance Control (MVC) • Linear Quadratic Gaussian (LQG) • Typical Commercial MPC, e.g. DMC Model Predictive Control

5. LQG Benchmark (Huang & Shah, 1999) Performance Assessment of Feedback Control Systems • Minimum Variance Benchmark (Harris, 1989) -

6. Controller model assumed in MPC design : Actual process model : Limitations in Assessing MPC  inherent process-model mismatch due to controller structure

7. MPC vs. LQG benchmark

8. Cannot normally identify Gp and Gd from routine operating data Can identify Gp (in FIR form) if Gd is known Performance Assessment using Routine Operating Data Basis for Harris index : First b impulse response coefficients of the closed-loop transfer function are feedback invariant  first b impulse response coefficients of disturbance model are always identifiable.

9. Process identified for controller design: “ old process model ” 2.5 2 1.5 Output Variance 1 0.5 OCOP 0 0 0.05 0.1 0.15 0.2 Variance of Differenced Input Simulation Example

10. Disturbance model of true plant changes: “ new process model ” Simulation Example

11. Simulation Example…cont. First b impulse response coefficients of closed-loop transfer function  first b impulse response coefficients of disturbance model 5 4.5 4 3.5 3 Impulse Response 2.5 2 1.5 1 0.5 0 2 4 6 8 10 12 14 16 18 Sample Interval

12. Simulation Example…cont. Comparison of true and estimated disturbance model

13. Simulation Example…cont. Comparison of true and estimated plant model

14. Simulation Example…cont. New performance curves

15. Experimental Results Continuous Stirred Tank Heater (CSTH)

16. Process identified for controller design: “ old process model ” Experimental Results…cont.

17. Experimental Results…cont. True process dynamics changed

18. Experimental Results…cont. New performance curves

19. Summary New performance benchmark for univariate MPC • Tuning guide • Model diagnostic Method for evaluating MPC performance • Routine operating data • Potential economic benefit of new response test.

20. Future Work Joint confidence region for operating point

21. Future Work cont... • Extend MPC performance curve to include • Multivariate systems • Model uncertainty description • Validation of proposed MPC performance assessment method using industrial data set.