Fast parallel self-tuning controllers

Abstract

Fast self-tuning discrete-time control algorithms based on 'recursive least squares' parameter estimation and 'generalized minimum-variance' (GMV) control design are presented both in lattice and transversal forms. This derivation relies both on the linear prediction interpretation of GMV control and on the embedding of the pole-zero predictive model (for the system output) into a multichannel all-pole model for the joint system input-output process. The proposed multichannel algorithms are simplified via a modular decomposition principle which converts all matrix recursions into coupled scalar recursions. The resulting control algorithms require 0(n) computations per time instant, where n denotes the controller order. Furthermore, we present parallel implementations of such fast 'self-tuning controllers' (STCs) in O(n) processor arrays. Several structures, obtained for different implementations of the controller and of the identifier, are devised to this end but, as far as we are concerned with an 'ideal' STC (i.e. one which generates the control signal at each time instant with the best and most recent currently available parameter estimates), none of them can lead to a pipelined STC. We show that a pipelined STC can be obtained by implementing the controller in transversal form and introducing an O(n) 'lag' in the transfer of parameters from the identifier to the controller. This amounts to using delayed parameter estimates in the control computation which. for slowly time-varying systems, could be a viable solution in order to increase the sampling rate.