Model Predictive Control in simulation or on line of a

continuous (time) process : use of the MPC@CB1

control software

1© Université Claude Bernard Lyon 1 – EZUS, january 2007

To use MPC@CB, please contact his author: dufour@lagep.univ-lyon1.fr

http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008http://www.lagep.univ-lyon1.fr/signatures/dufour.pascal

Reference

k+Nc k+Np

Process

Model prediction

FuturPast

Control

MPC: the idea (born in the ‘70)

Present : k

Morari, M.; Lee, J. L. Model predictive control: past, present and future. Computers and Chemical Engineering 1999, 23, 667–682

MPC@CB: what for ?

• It consists in sources files that may be used with Matlab to realize the predictive control under constraints of a (time) continuous process.

• Theses codes may be easily adapted for any SISO (Single Input Single Output) process, through user defined files synchronized by few standards main files. The model has to be given as:

that is: the SISO model features any number of states variables, may be linear or not linear, time variant or time invariant, based on PDE and/or ODE. The simulated process equations and the model equations may be different.

)(

),(

xgy

uxfx

MPC@CB: for which control problem?

It is simple for the user to specify one of the MPC problem:

• Regulation problem, trajectory tracking, operating time minimization, with or without output.

• In order to study the MPC robustness, modeling uncertainties (in equations and/or parameters) may be introduced between the simulated process and the model used in the MPC.

• A cascaded process may be specified in process output.

• Any ending condition may be specified to finish the run.

• Open loop control, PID may be used for performances comparison.

MPC@CB: develop your own next versions

The programming approach used for these codes allows to easily develop your next versions of the source codes:

• MPC for any used defined constrained optimization problem

• Handle SIMO, MISO or MIMO model

• Handle observor (model based software sensor).

• Switch from simulation to real time application on the real process

• Develop your GUI

MPC@CB: references(*) for the control law used

P. Dufour, Thèse "Contribution à la commande prédictive des systèmes à paramètres répartis non linéaires", avec Y. Touré, directeur de thèse au LAGEP Université Claude Bernard Lyon 1, 2000 OAI:TEL-00337724

P. Dufour, Y. Touré, D. Blanc, P. Laurent "On Nonlinear Distributed Parameter Model Predictive Control Strategy: On-line Calculation Time Reduction and Application to an Experimental Drying Process", Computers and Chemical Engineering, 27(11), pp. 1533-1542, 2003. OAI : HAL-00352371

(*) References may be uploaded as open archives from:http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008

MPC@CB: references(*) with previous applications

• J. De Temmerman, P. Dufour, B. Nicolaï, H. Ramon, "MPC as control strategy for pasta drying processes", soumis le 12 septembre 2007, Computers and Chemical Engineering, 33(1), 50-57, 2009. OAI : hal-00350086

• B. Da Silva, P. Dufour, N. Othman, S. Othman, « Model Predictive Control of Free Surfactant Concentration in Emulsion Polymerization », submitted 6/21 September 2007 to the 17th IFAC World Congress 2008, Paper 823/1693, Seoul, South Korea, July 6-11, 2008. OAI : hal-00352737

• N. Daraoui, P. Dufour, H. Hammouri, « Model Predictive Control of the Primary Drying Stage of the Drying of Solutions in Vials: an Application of the MPC@CB Software (Part 1) », Proceedings of the 5th Asia-Pacific Drying Conference (ADC) 2007, vol. 2, pp. 883-888, Hong Kong, China, August ,13-15 2007. hal-00352431

• K. Abid, P. Dufour, I. Bombard, P. Laurent, « Model Predictive Control of a Powder Coating Curing Process: an Application of the MPC@CB© Software », Proceedings of the 26th IEEE Chinese Control Conference (CCC) 2007, Zhangjiajie, China, vol. 2, pp. 630-634, July 27-29 2007. OAI: hal-00338891

(*) References may be uploaded as open archives from:http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008

PID (regulation) MPC@CB (dynamic optimization + constraint)

Output constraint, with a parameter error

MPC@CB: application 1: powder coating curing (Abid et al., 2007)

PID (régulation)

Output constraint, with a parameter error

MPC@CB (dynamic optimization + constraint)

Conclusion : MPC@CB>PID  : • Operating time MPC Operating time  PID: - 10%• Energy consumption with MPC Energy consumption with PID: -6.72%• Accuracy : MPC allows a better regulation than PID

Since the output constraint is saturated, the control move

decreases

MPC@CB: application 1: powder coating curing (Abid et al., 2007)

Sublimation time minimization

Maximize the sublimation front

move H(t)

(Contraints on the input)

(Contraint on the output)

Ending condition: stop when H(t)=L

MPC@CB: application 2: vial lyophilisation (Daraoui et al., 2007)

0 200 400 600 800 1000 1200 14000

1

2

3x 10

-7

Tim e (m in)Su

blim

ati

on

In

terf

ac

e v

elo

cit

y (

m/s

)V eloc ity optim iz ation

S ignal optim is ed by the c ontroller (top) and the related proc es s output (bottom )

0 200 400 600 800 1000 1200 14000

0.005

0.01

0.015

Tim e (m in)

Su

blim

ati

on

In

terf

ac

e (

m)

End : H(t)=L

MPC@CB: application 2: vial lyophilisation (Daraoui et al., 2007)

0 200 400 600 800 1000 1200 1400230

235

240

245

250

255

Tim e (m in)

Bu

tto

m te

mp

era

tu

re

(°K

)

Output c ons traint

P roc ess

M ax im um allowed

Since the output constraint is saturated, the control move decreases

MPC@CB: application 2: vial lyophilisation (Daraoui et al., 2007)

In order to use the MPC@CB1 control software

for your problem, contact:

dufour@lagep.univ-lyon1.fr

http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008

http://www.lagep.univ-lyon1.fr/signatures/dufour.pascal

1© Université Claude Bernard Lyon 1 – EZUS, january 2007

MPC@CB: for you ?