Autocovariance-based MPC model mismatch estimation for systems with measurable disturbances

Abstract

In this paper, we propose a novel autocovariance-based plant-model mismatch estimation approach for linear MPC MIMO control loops with changing setpoints and measurable disturbances. Assuming a noise model is available and that there are of periods of operating data where the active set of the controller is fixed and the plant-model mismatch is invariant, we establish an explicit relation between the autocovariance matrices of the mean-centered process outputs and the plant-model mismatch. We then formulate the mismatch estimation problem as an optimization aimed at minimizing the difference between the theoretical autocovariance, computed from the established relation, and actual output autocovariances, calculated from the plant data. We elaborate our results for step-response models typically used in MPC, as well as for parametric (transfer function models) in both continuous time and discrete time. A simulation case study for an unconstrained MPC controller with measurable disturbances is used to illustrate the theoretical results.