Minimum Variance Control Strategy Research Articles

Adaptive control with recursive identification for stochastic linear systems

This paper presents a stochastic adaptive control algorithm which is shown to possess the following properties when applied to a possibly unstable, inverse stable, linear stochastic system with unknown parameters, whenever that system satisfies a certain positive real condition on its (moving average) noise dynamics. 1) The adaptive control part of the algorithm stabilizes and asymptotically optimizes the behavior of the system in the sense that the (limit of the) sample mean-square variation of the-output around a given demand level equals that of a minimum variance control strategy implemented with known parameters. This optimal behavior is subject to an offset μ2where μ2is the variance of a dither signal added to the control action in order to produce a continually disturbed control. For \mu^{2} > 0 , it is shown that the input-output process satisfies a persistent excitation property, and hence, subject to a simple identifiability condition, the next property holds. 2) The observed input and output of the controlled system may be taken as inputs to an approximate maximum likelihood algorithm (AML) which generates strongly consistent estimates of the system's parameters. Results are presented for the scalar and multivariable cases.

A Self-Tuning Control Algorithm for Systems with Unknown Time Delay

A class of self-tuning regulators based on the minimum variance control strategy and recursive least square estimation is discussed in this paper. The self-tuning control algorithm is an extension of the one using successive output estimations (Bayoumi, Wong, and El-Bagoury, 1981) to control a system with unknown time delay. This extra property of the algorithm is illustrated by simulation examples.

Nonlinear control of nonminimum-phase systems

In the paper, the regulation of nonminimum systems using a nonlinear minimum-variance control strategy is considered. The relationship between output variance and control limit of a saturating actuator is investigated. Both ultimatum simulation studies and an approximate analysis based on the statistical linearisation of the nonlinearity are presented. The results of these studies demonstrate that a minimum exists on this relationship. The connection between the use of a nonlinear controller and a suboptimal linear control law is discussed.

A self-tuning automatic voltage regulator

A self-tuning automatic voltage regulator (AVR) for a synchronous generator is presented. The regulator proposed improves the system stability; it is simple and can handle stochastic load changes. The algorithm for the proposed AVR combines a least-squares estimator with a minimum variance control strategy computed from an estimated model. It is shown that if the parameter estimates converge, the control law obtained is in fact the minimum variance control law that would be computed if the parameters of the system were known. The algorithm proposed has been tested by simulation and also by implementation on a minicomputer. Results show that, in general, the system performance is improved with a self-tuning regulator.

Design of digital controllers for multivariable stochastic systems

A new approach for designing controllers for randomly disturbed interactive multivariable systems is proposed. This is based on an extension of the inverse-Nyquist-array method and the minimum variance control strategy for single-input/single-output systems.