Offset Free Tracking with MPC under Uncertainty: Experimental VerificationAudun Faanes* and Sigurd SkogestadDepartment of Chemical EngineeringNorwegian University of Science and TechnologyN-7491 Trondheim N, Norway*Also affiliated with Statoil ASA, TEK, Process Control, N-7005 Trondheim, Norway Author to whom all correspondence should be addressed. E-mail: skoge@chemeng.ntnu.no, Tel. : +47 73 59 41 54, Fax.: +47 73 59 40 80

AbstractA laboratorial experiment is used to investigate some aspects related to integral action in MPC. MPC is used for temperature control of a process with two tanks in series. Since this often improves performance, an extra the temperature measurements was applied. To avoid outlet temperature steady-state offset, estimates of input disturbances have been used in the calculation of the steady-state control input. Simulations may indicate that integral action is present and that disturbances are handled well, but in practice unmodelled phenomena may give a poor result in the actual plant, also at steady-state. If should be verified that integral action (feedback) is actually present and not an apparent effect of perfect feedforward control.The experiments verify that output feedback through input disturbance estimation is efficient, provided that it is correctly done. To obtain integral action, care must be taken when choosing which input disturbance estimates to include. It is not sufficient to estimate a disturbance or bias in the control input(s), even if the control input(s) are sufficient to control the process. The present work verifies that the number of independent disturbance estimates must equal the number of measurements. In our experiment the use of estimates of input disturbances to both tanks gave satisfactory performance with no steady-state error.

Experimental set-upHot and cold water are mixed in two tanks in series, and the temperature of the outlet water (y) shall be kept constant despite disturbances d1 (variation in hot water flow rate) and d2 (cold water addition in main tank). Manipulated variable, u, is cold water flow rate. In the main tank there is a loop where the water is circulated with a pump. y is measured in this loop, and therefore we get a delay. The circulation loop also gives mixing. The levels are controlled with an overflow drain (in the mixing tank) and an on-off drainage valve (in the main tank).

ConclusionsExperiment: temperature control in a process with two tanks in seriesModel predictive control, MPCNon-square case: two measurements, one manipulated variableOffset-free steady state obtained by input disturbance estimates for the determination of the manipulated variable steady-stateSimulation indicates that estimation of one disturbance is sufficientThe experiment shows that two disturbance estimates are needed, i.e., the number of disturbance estimates must equal the number of measurements (in accordance with Pannocchia and Rawlings (2003) and Faanes and Skogestad (2003))Offset free steady state in the simulation is an apparent effect of perfect feedforward control Estimates of input disturbances have been described in the literature as efficient for a quick response back to the desired steady state. The present work confirms this (provided that it is correctly done).AcknowledgementsThe experimental equipment has been set up at Norsk Hydro Research Centre, and was originally designed by Jostein Toft, Arne Henriksen and Terje Karstang. Norsk Hydro ASA has financed the experiments.ReferencesFaanes, A. (2003). Controllability Analysis for Process and Control Structure Design. PhD thesis. Department of Chemical Engineering, Norwegian University of Science and Technology.Faanes, A. and Skogestad, S. (2003). On MPC without active constraints. Submitted to Modeling, Identification and Control, MIC.Lee, J. H., M. Morari and C. E. Garcia (1994). State-space interpretation of model predictive control. Automatica 30(4), 707-717.Lundstrm, P., J. H. Lee, M. Morari and S. Skogestad (1995). Limitations of dynamic matrix control. Comp. Chem. Engng. 19(4), 409-421.Muske, K. R. and Badgewell, T. A. (2002). Disturbance modeling for offset-free linear model predictive control. Journal of Process Control. 12, 617-632Muske, K. R. and J. B. Rawlings (1993). Model predictive control with linear models. AIChE Journal. 39(2), 262-287.Pannocchia, G. and J. B. Rawlings (2003). Disturbance Models for Offset-Free Model-Predictive Control. AIChE Journal. 49(2), 426-437.

AAA

AAA1

TIH

TI1

TI2

FI1

Main tank

Mixing tank

Cold water reservoir

Hot water reservoir

Circulation

u

d1

d2

Heat loss

Cold water

y

Aim: To control this temperature

Disturbance 1

Disturbance 2