Analysis and design of linearised single-input extremum control systems

Abstract

Certain single input, linearised extremum controllers of the empirical type described in the literature have been designed and their performances have been compared to that of an approximately optimal controller. The plant is subject to disturbances, lags and measurement noise. A dimensionless performance criterion and description of the plant have been used to present the results. A design procedure for a sinusoidal perturbation controller in connection with the above plant has been obtained, using a linear equivalent circuit for the system together with an experimentally obtained estimate of the equivalent circuit validity. Experimental results have shown that the resulting design is the best, and that the system is likely to remain stable, when the performance of the system is limited mainly by the measurement noise. This empirical controller has been compared with Roberts approximately optimal controller and has been shown to perform equally well if the effect of the lag is small. The performances of three different types of extremum controller have been compared when the plant lags can be neglected. The three controllers use sine wave perturbation, square wave perturbation, and square wave perturbation with a sample and hold unit in the controller. It has been shown that all three the perturbation frequency is infinite. When the perturbation frequency is limited, as in a practical system, the controllers without the sample and hold unit give better performance, at the expense of requiring the adjustment of an additional controller parameter.