Detection and diagnosis of model-plant mismatch in MIMO systems using plant-model ratio

The performance of any model-based controller depends on the quality of the model and hence on the model-plant mismatch (MPM). Model maintenance and correction is necessary to achieve desired performance. However, a complete re-identification of the model is usually a costly exercise. Therefore, it would be highly desirable to detect the precise location of the mismatch and update only those parts. The recently introduced plant-model ratio (PMR) was found to be effective in detecting and diagnosing MPM from closed loop operation data for SISO systems. The PMR facilitates a unique identification of the source of mismatch - namely gain, dynamics and delay mismatches. However, direct application of PMR to MIMO systems is a challenge due to the presence of interactions between the various input-output channels. In this paper, the PMR approach is extended to MIMO control systems. It is assumed that the control loop is driven through broadband excitation in the set-points. The key step in the proposed methodology involves decoupling interactions using partial cross-spectral density. The proposed methodology is able to detect the input-output channels with significant mismatch as well as identify the source of mismatch within these channels. The efficacy of this method is demonstrated through two simulation case studies.