Non‐linear generalised minimum variance control using unstable state‐dependent multivariable models

Abstract

A non-linear generalised minimum variance (NGMV) control law is derived for systems represented by an input-output state dependent non-linear (NL) subsystem that may be open-loop unstable. The solution is obtained using a model for the multivariable discrete-time process that includes a state-dependent (NL and possibly unstable) model that links the output and any `unstructured' NL input subsystem. The input subsystem can involve an operator of a very general NL form, but this has to be assumed to be stable. This is the first NGMV control solution that is suitable for systems containing an unstable NL sub-system which is contained in the state-dependent model. The process is also assumed to include explicit common delays in input or output channels. The generalised minimum variance cost index to be minimised involves both dynamically weighted error and control signal costing terms. It may also include weighted values of the system states for greater generality. The controller derived is simple to implement considering the complexity of the system represented. If the plant is stable the controller structure can be manipulated into an internal model control form. This form of the controller is like an NL version of the Smith Predictor which is valuable for providing confidence in the solution.