Wiener-filter-based Minimum Variance Self-tuning Regulation

Abstract

This paper presents a new direct discrete-time self-tuning minimum variance control scheme for not necessarily minimum-phase SISO systems that are operating in a stochastic environment. It is assumed that the open-loop system is asymptotically stable, or can be stabilized by a fixed controller, and that the noise model satisfies the standard SPR properties. No assumptions are made regarding the zero polynomial of the controlled plant. The proposed direct self-tuning scheme consists of two-parameter adaptation algorithms (PAA) running simultaneously. The first PAA is an adaptive whitening filter. The adaptive whitening filter error residual is fed into an adaptive finite impulse response (FIR) filter, which generates the control signal. The second PAA estimates the parameters of the optimal Wiener FIR filter which minimizes the variance of the system output. A complete stability analysis and a discussion of the convergence and self-tuning properties of the proposed self-tuning scheme is included.