Evaluation of modelbased predictive control Student Daniel Czarkowski
Evaluation of model-based predictive control Student: Daniel Czarkowski Supervisor: Tom O’Mahony date 25/03/2003
Overview • Background Model Based – Predictive Control • Generalised Predictive control • Models • Benchmarks: GPC versus PI 2
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) 3
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 4
Model - based control 5
GPC • CARIMA model • Cost function 6
GPC • Implementation of a Genetic Algorithm for minimization IAE: – Servo response – Regulatory disturbance – Combined 7
Models • The models of benchmarked plant were taken from Astrom 8
PI controller IAE ZN: 6. 25 Lambda: 13. 79 Non-Convex: 5. 07 9
PI vs. GPC • GPC n 1=1 n 2=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 10
Sampling Period n 1=2 n 2=3 nu=1 λ=1*10 -6 T-polynomial=1+0. 9*z-1 • Ts=0. 7 sec. • Ts=0. 1 sec. IAE=0. 81 IAE=0. 3 11
Searching area 12
Benchmark of GPC • Fourth Order System: GPC n 1=2 n 2=3 nu=1 λ=1*10 -6 Tpoly=1+0. 293*z-1 IAE=0. 23 PI controller k=2. 74 IAE=0. 82 ki=4. 08 13
Benchmark of GPC Nonminimum-phase model GPC n 1=4 n 2=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 14
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 15
Questions?
- Slides: 16