Journal of Process Control, Vol.12, No.2, 257-276, 2002
Time series methods for dynamic analysis of multiple controlled variables
Research results in controller performance monitoring for multivariate systems have mainly focused on the problem of estimating the control invariant component of the closed-loop output covariance (Harris, T.J., Boudreau, F. and MacGregor, J.F. Performance assessment of multivariable feedback controllers. Automatica, 32:1505-1518, 1996; Huang, B., Shah, S.L. and Kwok, K.E. Good, bad or optimal? performance assessment of multivariable processes. Automatica, 33(6):1175-1183, 1997b.). The contributions of this paper lie on the dynamic analysis side of multivariate controller performance monitoring, where no a priori information is available, yet assessment of dynamic interactions between loops is of interest. Using results from the statistics, identification, and econometrics literature, graphical methods for analyzing the dynamic performance of vectors of tracking error variables are presented. The multi-output dynamic analysis problem can be simplified considerably by treating the tracking error trends as a vector process of endogenous stochastic variables and using a vector autoregressive (VAR) structure to model the dynamic relationships. Once such a model has been estimated, a host of post-estimation diagnostics, such as multivariate impulse response analysis, can be used to interpret the dynamic interactions between the tracking error variables. These methods will be discussed in detail and demonstrated on simulated and industrial control system data. Crown Copyright