Analysis of Multivariable Controllers Using Degree of Freedom Data

Most approaches for monitoring, diagnosis and performance analysis of multivariable control loops employ time series methods and use non-parametric statistics to analyze the process inputs and outputs. In this paper, we explore the use of a discrete variable that summarizes the status of the constraint set of the controller to analyze the long run behavior of control systems. We introduce a number of waiting and holding time statistics that describe the status of this data, which we call the degree of freedom data. We demonstrate how Markov Chains might be used to model the status of the degree of freedom data. This model-based approach has the potential to provide considerable insight into the behavior of a model based control scheme with relative ease. We demonstrate the methodologies on simulated and industrial data.