Multivariate Controller Performance Analysis: Methods, Applications and Challenges

This paper provides a tutorial introduction to the role of the time-delay or the interactor matrix in multivariate minimum variance control. Minimum variance control gives the lowest achievable output variance and thus serves as a useful benchmark for performance assessment. One of the major drawbacks of the multivariate minimum variance benchmark is the need for apriori knowledge of the multivariate time-delay matrix. A graphical method of multivariate performance assessment known as the Normalized Multivariate Impulse Response (NMIR), that does not require knowledge of the interactor, is proposed in this paper. The use of NMIR as a performance assessment tool is illustrated by application to two multivariate controllers. Two additional performance benchmarks are introduced as alternatives to the minimum variance benchmark, and their application is illustrated by a simulated example. A detailed performance evaluation of an industrial MPC controller is presented. The diagnosis steps in identifying the cause of poor performance, e.g. as due to model-plant mismatch, are illustrated on the same industrial case study.