Optimal Design of Feedforward Regulators for Multivariable Systems

A method to design optimal multivariable feedforward regulators is presented for stochastic plants described by rational transfer matrices. The plant is assumed to have an arbitrary feedback stabilizing compensator. Standard Wiener-Hopf variational argument is employed to minimize the weighted sum of inputs and outputs variances for both cases: continuous-time and discrete-time plants. The method involves spectral factorization and the solution of a polynomial matrix diophantine equation. The plant can be of non-minimum phase with delays. The solution is simple and computationally attractive. An example of feedforward on a distillation column is given to illustrate the design procedure.