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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. MBPC. Features of MBPC

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Evaluation of model based predictive control

Evaluation of model-based predictive control

Student: Daniel Czarkowski

Supervisor: Tom O’Mahony

date 25/03/2003


Overview
Overview

  • Background Model Based – Predictive Control

  • Generalised Predictive control

  • Models

  • Benchmarks: GPC versus PI


Evaluation of model based predictive control
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)


Evaluation of model based predictive control
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



Evaluation of model based predictive control
GPC

  • CARIMA model

  • Cost function


Evaluation of model based predictive control
GPC

  • Implementation of a Genetic Algorithm for minimization IAE:

    • Servo response

    • Regulatory disturbance

    • Combined


Models
Models

  • The models of benchmarked plant were taken from Astrom


Pi controller

IAE

ZN: 6.25

Lambda: 13.79

Non-Convex:5.07

PI controller


Pi vs gpc
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


Sampling period
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



Benchmark of gpc
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


Benchmark of gpc1
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


Conclusions
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