Evaluation of model-based predictive control

1. Evaluation of model-based predictive control Student: Daniel Czarkowski Supervisor: Tom O’Mahony date 25/03/2003

2. Overview • Background Model Based – Predictive Control • Generalised Predictive control • Models • Benchmarks: GPC versus PI

3. MBPC • Features of MBPC • All of them use a process model • The optimum control sequence is obtained through the minimization of a cost index • Only the first element of this sequence is transmitted to the plant as the current control u(t) (receding horizon)

4. MBPC • Model Based Predictive Control can be achieved according to: • The type of model used • The type of cost function used • The optimization method applied

5. Model - based control

6. GPC • CARIMA model • Cost function

7. GPC • Implementation of a Genetic Algorithm for minimization IAE: • Servo response • Regulatory disturbance • Combined

8. Models • The models of benchmarked plant were taken from Astrom

9. IAE ZN: 6.25 Lambda: 13.79 Non-Convex:5.07 PI controller

10. PI vs. GPC • GPC n1=1 n2=2 nu=1 λ=1*10-6 T-polynomial=(1-0.63*z-1) Sampling Period = 0.7 (sec.) IAE=0.91 • PI controller k=0.862 ki=0.461 IAE=5.07

11. Sampling Period • Ts=0.7sec. IAE=0.81 • Ts=0.1sec. IAE=0.3 n1=2 n2=3 nu=1 λ=1*10-6T-polynomial=1+0.9*z-1

12. Searching area

13. Benchmark of GPC • Fourth Order System: • GPC • n1=2 n2=3 nu=1 λ=1*10-6 Tpoly=1+0.293*z-1 • IAE=0.23 • PI controller • k=2.74 ki=4.08 • IAE=0.82

14. Benchmark of GPC Nonminimum-phase model GPC n1=4 n2=4 nu=1 Ts=0.83 Tpoly=(1-0.224*z-1)3 IAE=8.10 PI controller k=0.294 ki=0.184 IAE=14,4

15. Conclusions • The Åström benchmark test was developed for PI controller • A Genetic Algorithm was implemented for tuning GPC controller • Part of comparison has been done

16. Questions?