Detection and diagnosis of model-plant mismatch in multivariable model-based control schemes

The extent of approximation in modelling a given process, characterized by the model-plant mismatch (MPM), amongst other factors, critically determines the performance of a model-based control scheme. It is necessary therefore to carry out model maintenance and correction on a regular basis. However, a complete re-identification is usually a costly exercise. Therefore, it is highly desirable to precisely determine the specific elements that are in mismatch and re-identify only those parameters. In the recent times, the plant-model ratio (PMR) was proposed as an effective metric for diagnosing MPM in single-input single-output (SISO) systems from closed loop data. The PMR facilitates unique detection of mismatch in gain, dynamics and delay. A straightforward application of PMR to multivariable closed-loop systems is challenging primarily due to the confounding effects of other inputs and loop-to-loop interactions under closed-loop conditions. Furthermore, the metric requires high-frequency excitation for identification of delay mismatch. In this work, we first present a method to overcome the latter requirement using Hilbert transform relation and partial cross-spectral densities. Subsequently, we present the key contribution of this work, that of generalizing the PMR approach to multivariable control systems. Two threshold-based hypothesis tests are presented for diagnosing mismatch in gain and dynamics. Three simulation case studies are presented to demonstrate the efficacy of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.