(703f) A Novel Plant-Model Mismatch Estimation Method for Model Predictive Control
Model predictive control (MPC) has become the de-facto standard for multivariable control in the process industries. The widespread adoption of MPC systems can be attributed to their ability to deal with complex process interactions as well as with constraints imposed on the process states, and input and output variables. MPC performance is strongly dependent on the accuracy with which process behavior is predicted, which, in turn, is vitally dependent on the quality of the process model that is employed in the controller. Inherent process changes (induced, e.g., by fouling, corrosion, catalyst deactivation) lead to plant-model mismatch and can compromise the operation of the MPC system. In principle, these shortcomings could be addressed by performing regular model updates. This is, however, a costly undertaking and is generally only performed when closed-loop performance has degraded beyond the point where serious economic penalties are incurred in plant operations.
Current MPC performance assessment techniques typically adopt a two-step procedure. In the first step, the control performance degradation caused by the mismatch is identified and quantified. In the second step, the plant-model mismatch is estimated based on the degradation information. The first step has spurred several research efforts, with approaches based on multivariate statistical process control (MSPC) or controller performance benchmarking concepts being proposed. MSPC uses multivariate statistical tools, such as principal component analysis (PCA) and partial least squares (PLS) to identify abnormal operation . Controller benchmarking defines a controller performance index using a theoretical or empirical metric [2, 3]. The second, mismatch estimation step, has received comparatively little attention. For instance, identifying the variable that contributes most to the degradation of controller performance using a control chart  has been proposed.
In this work, we introduce a novel plant-model estimation approach for MPC using the autocovariance matrices of process closed-loop data. We focus on estimation in the presence of moderate mismatch, in the sense that we seek early detection of plant-mode discrepancies based on operating data collected from seemingly "normal" operating conditions, where process economic performance is not sensibly degraded. We make the assumption that in this case the active set of the MPC does not change during operation. On this basis, we derive explicit expressions of the autocovariance matrices of the process inputs and outputs as functions of the magnitude of the plant-model mismatch. Subsequently, we solve an inverse problem to obtain an estimate of the plant-model mismatch from closed-loop input and output data. The proposed approach is illustrated in with several case studies.
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