Optimal Choice of thesampling Interval for Discrete Process Control

This paper is concerned with the choice of the sampling interval for use in discrete regulatory control of processes subject to stochastic disturbances where the purpose is to maintain the process output as close as possible to some fixed target value. The analysis is restricted to single input-single output systems sampled at discrete equispaced intervals of time. Assuming that a discrete linear dynamic-stochastic model of the system has been identified from data collected at one sampling interval the question which often arises and to which this paper is addressed is: “How much worse off would one be (in the sense of one's ability to control the process output) if the processwere sampled less frequently?” By showing how the form and parameters of the dynamic-stochastic models for the system will change as the sampling interval is increased to integer multiples of the basic interval, one is able to predict the performance of the optimal stochastic controller at these larger intervals and thereby make a reasonable choice of the best interval. The method is applied to several real and hypothetical processes involving both stationary and nonstationary disturbances and various amounts of process dead time.