A tuning procedure for ARX-based MPC of multivariate processes

Abstract

Abstract-We present an optimization based tuning procedure with certain robustness properties for an offset free Model Predictive Controller (MPC). The MPC is designed for multivariate processes that can be represented by an ARX model. The stochastic model of the ARX model identified from inputoutput data is modified with an ARMA model designed as part of the MPC-design procedure to ensure offset-free control. The MPC is designed and implemented based on a state space model in innovation form. Expressions for the closed-loop dynamics of the unconstrained system is used to derive the sensitivity function of this system. The closed-loop expressions are also used to numerically evaluate absolute integral performance measures. Due to the closed-loop expressions these evaluations can be done relative quickly. Consequently, the tuning may be performed by numerical minimization of the integrated absolute error subject to a constraint on the maximum of the sensitivity function. The latter constraint provides a robustness measure that is essential for the procedure. The method is demonstrated for two simulated examples: A Wood-Berry distillation column example and a cement mill example.

A Realistic Process Example for MIMO MPC based on Autoregressive Models

“…Box constraints may be formulated for the sequence ofû k+j|k and ∆û k+j|k . The unconstrained MPC can be represented as the convex quadratic optimization problem with the solution given in Jørgensen et al [4] and a tuning algorithm based on this formulation is presented in Olesen et al [11,12].…”

“…One drawback from introducing integrating modes in the controller is that it leads to a deliberate model plant mismatch which complicates the tuning procedure. Through a number of recent publications, we have advocated for a methodology for offset free ARX based linear MPC that is simple to implement [2,4,3,12,5]. This methodology is based on estimation of linear MISO models by standard convex optimization tools, a simple noise model to ensure offset-free tracking and a state space system formulation in innovation form.…”

An analytical tuning approach to multivariable model predictive controllers

“…In [16] a tuning strategy is proposed for constrained multivariable MPC of uncertain plants based on particle swarm optimization techniques. In [17], an optimization based tuning procedure with certain robustness properties for an offset free MPC is presented for multivariable processes.…”

A model-free approach for auto-tuning of model predictive control

“…Hence, in this work, the key performance indicator of the auto-tuning method is the output variance. The output variance is also considered in the tuning procedure of Huusom et al (2012) and Olesen et al (2013). In Tran et al (2013), Tran et al (2012) and Ozkan et al (2012), it is shown that in the presence of model-plant mismatch and measurement noise, there ex-ists an optimal closed-loop bandwidth which corresponds to the minimum output variance.…”