A control weighted minimum-variance controller for non-minimum phase systems

Abstract

A now minimum-variance type of control law is derived for use in self-tuning control schemes where the plant is non-minimum phase. The controller has some of the features of the minimum-variance controller and is related to the generalized or λ minimum-variance controller which includes control weighting terms. The controller has the advantage that when the control-weighting scalar tends to zero the system is assured of being asymptotically stable. The generalized minimum-variance controller, employed in the self-tuning control law, results in an unstable closed-loop system in this situation. The controller may also be used to stabilize plants which are both unstable and non-minimum phase (the closed-loop system corresponding to the generalized minimum variance controller may be unstable for all values of the weighting scalar in this situation)