Minimum Variance Control Law Research Articles

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.

Control of titanium dioxide kilns

This paper reports an application of LQG theory to the control of three TiO 2 kilns. Previously derived results on steady-state modeling are used to obtain a set of linear partial differential equations to describe the process. A low-order model is derived by matching the input-output frequency responses. LQG theory is used to determine the sampling period and to justify the selection of actuating and measured variables. A minimum-variance control law is finally obtained and applied to three kilns. This control proves to be more effective than existing control, while requiring much less memory.

Optimal experiment design for linear systems with input-output constraints

The problem of optimal experiment design for parameter estimation in linear dynamic systems is studied. Results relating to both constrained input and output variances are established. For the case of constrained input variance, it is shown that a D-optimal experiment exists in which the system input is generated externally provided the system and noise transfer functions have no common parameters. For the case of constrained output variance, it is shown that an experiment in which the system input is generated by a combination of a minimum variance control law together with an external set point perturbation is D-optimal for certain classes of systems. Other related results are also presented which illustrate the role of feedback in optimal experiment design.

On self tuning regulators

The problem of controlling a system with constant but unknown parameters is considered. The analysis is restricted to discrete time single-input single-output systems. An algorithm obtained by combining a least squares estimator with a minimum variance regulator computed from the estimated model is analysed. The main results are two theorems which characterize the closed loop system obtained under the assumption that the parameter estimates converge. The first theorem states that certain covariances of the output and certain cross-covariances of the control variable and the output will vanish under weak assumptions on the system to be controlled. In the second theorem it is assumed that the system to be controlled is a general linear stochastic nth order system. It is shown that if the parameter estimates converge the control law obtained is in fact the minimum variance control law that could be computed if the parameters of the system were known. This is somewhat surprising since the least squares estimate is biased. Some practical implications of the results are discussed. In particular it is shown that the algorithm can be feasibly implemented on a small process computer.

Amplitude-constrained minimum-variance controller

Saturation of the input transducer is a frequently occurring difficulty with minimum-variance controllers. This saturation can lead to serious deterioration in the performance. In the letter, a minimum-variance control law is derived for the case when the input amplitude is constrained.

Relationship between Box-Jenkins-Åström control and Kalman linear regulator

The Box-Jenkins-Astrom minimum-variance control law for univariate linear stochastic systems is summarised. A minimum-expected-quadratic-loss feedback control law for the same system is derived using state-space theory. Subject to conditions sufficient for the control laws to exist, both theories are shown to give the same result in the 1-step-ahead (unit-delay) case. The more general case is discussed.