Autocovariance-based MPC model mismatch estimation for SISO systems

Model predictive control (MPC) has become the de-facto standard for multivariable control in the process industries. MPC systems are able to handle complex dynamics, interactions and constraints, but are vulnerable to plant-model mismatch. The deviation of the process model from the plant is an inevitable phenomenon, caused by drifting equipment properties and process conditions. In this contribution, we introduce a novel autocovariance-based framework for estimating MPC plant-model mismatch from closed-loop operating data. Our initial results focus on SISO systems, where we begin by establishing an explicit relationship between the autocovariance of process input and output data, and the magnitude of the plant-model mismatch. We use this result to establish an optimization-based approach for solving the inverse problem, that is, computing plant-model mismatch from available data. We present a numerical study, where we demonstrate the excellent performance of the proposed framework.