NGMV Control Using Unstable State-Dependent Multivariable Models

A Nonlinear Generalized Minimum Variance control law is derived for systems represented by an input-output state dependent nonlinear 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 (nonlinear and possibly unstable) model that links the output and any unstructured nonlinear input subsystem. The input subsystem can involve an operator of a very general nonlinear 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 nonlinear sub-system which is contained in the statedependent 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 error and control signal costing terms but to increase generality weighted states are also included in the cost index. 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 a nonlinear version of the Smith predictor which is valuable to provide confidence in the solution.