Huusom, Jakob Kjøbsted1; Poulsen, Niels Kjølstad7; Jørgensen, Sten Bay8; Jørgensen, John Bagterp9
1 Department of Chemical and Biochemical Engineering, Technical University of Denmark2 Computer Aided Process Engineering Center, Department of Chemical and Biochemical Engineering, Technical University of Denmark3 Department of Informatics and Mathematical Modeling, Technical University of Denmark4 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark5 Center for Energy Resources Engineering, Center, Technical University of Denmark6 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark7 Department of Applied Mathematics and Computer Science, Technical University of Denmark8 Centre for oil and gas – DTU, Center, Technical University of Denmark9 Copenhagen Center for Health Technology, Center, Technical University of Denmark
In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.
Journal of Process Control, 2012, Vol 22, Issue 10, p. 1997-2007
Model Predictive Control; Autoregressive models; Disturbance modeling; Controller tuning