Bayesian vector autoregression methods for multivariable control loop performance assessment in cross-directional control

The minimum variance (MV) lower bound has been applied to many multivariable control systems in order to assess their performance based on routine operating data. However, such analysis often depends on the selection of a suitable dynamic model of the data and for multivariable systems, there can be many candidate models. Also, uncertainty is often not considered, because standard approximations do not exist for the sampling distribution of these multivariable performance indices. This paper addresses these two issues by using the Bayesian approach to vector autoregression (VAR) modelling with Markov Chain Monte Carlo (MCMC) numerical methods. Dynamic model selection is carried out by using the Reversible Jump (RJ) MCMC sampler and it is shown that MCMC can be used to overcome the problem of the non-standard statistical distributions that exist in multivariable MV performance indices.