Performance assessment of multivariable feedback controllers

Procedures are developed for assessing the performance of multi-input multi-output (MIMO) linear feedback control system. The predicted performance of the MIMO minimum variance controller is used as a lower bound against which current performance is assessed. To use the procedures, one needs only a set of representative data on the controlled variables collected under the current feedback control scheme, and an estimate of the process interactor matrix characterizing the dead-time structure of the process. A non-parametric correlation test allows for a quick check on the closeness of the performance of the current feedback control system to the theoretical lower bound. A quantitative analysis then provides an estimate of the theoretical lower bound on the variance-covariance matrix of the controlled variables, and on the quadratic performance objective of the minimum-variance controller. A measure of controller performance based on the ratio of the current value of the quadratic objective to this thoeretical lower limit can then be monitored on-line. The purpose of these methods is to allow engineers to assess the current performance of the existing control systems, to monitor how this performance changes over time, to see which variables are well controlled and which are not, and to help in deciding whether or not there is sufficient incentive to reidentify the process model and/or redesign the controller.