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 feedback‐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.