Performance assessment of cascade control loops

The minimum variance control law for a cascade control system is derived for two cases: the primary process has stable and unstable inverses. The expression for the primary output variable under the minimum variance cascade control is shown to be feed-back-invariant. An estimate of the minimum achievable variance in a cascade control loop can be obtained via multivariate time-series modeling of the primary and secondary measurements collected under normal operation. The utility of the proposed performance assessment method is demonstrated using simulated and industrial data.