(317b) Diagonal Interactors And Adaptive Weighting For Mimo Control Performance Monitoring And Improvement

As one of the most prosperous research areas in process control community, control performance assessment and monitoring (CPA/CPM) has become increasingly attractive in both academia and industry. So far, minimum variance control (MVC) benchmark is the most popular performance benchmark and has been successfully applied to feedback control, feedback/feedforward control, cascade control and model predictive control. Nevertheless, the accurate estimation of interactor matrix and MVC benchmark for MIMO systems is still numerically tedious and needs plenty of a priori process information, such as a full plant model or at least the first few Markov parameters. The unrealistic requirement of a priori process knowledge and the complicated procedures of numerical estimation pose the challenging issues for the industrial applications of MVC based performance monitoring techniques.

To simplify the model requirement and numerical procedures of MVC benchmark, a right diagonal interactor matrix is first used for a class of well designed MIMO processes. Then an easier solution to the MIMO MVC benchmark is developed using the right diagonal interactor. Further, both the left and right diagonal interactors are integrated to characterize the more complex time-delay structure of an extended class of multivariate processes. The factorization of the combined left/right diagonal interactors and the corresponding MVC benchmark estimation are also presented. The advantages of the new approach lie in the reduced a priori process knowledge and the simplified numerical procedures. The diagonal interactors can be constructed from the pairwised input-output time delays only, which are much easier to obtain than the entire process model or leading Markov parameters. The existence condition and uniqueness of diagonal interactors are further explored. In addition to the control performance assessment, an adaptive strategy to select the output weighting matrix underlying the linear quadratic (LQ) objective function is developed. The eigenvalue decomposition (EVD) on the output covariance matrix is implemented to find out the directions with the largest variance inflation. Based on this information, the weighting matrix is constructed so that more control efforts are assigned to those directions with the worst performance. Through the iterative update of weighting matrix, the control performance in terms of output covariance can be improved and pushed close to the MVC boundary. A number of simulated examples are provided to illustrate the validity and effectiveness of the proposed control performance monitoring and improvement approach.