Optimal sample policies for multirate digital control

The sample frequency at which a digital controller operates affects the performance of the controlled continuous system. For a single rate digital controller, designers often choose the sample frequency to be 10 to 40 times the closed loop bandwidth. This sample frequency gives a reasonable trade-off between performance and the computational load on the control processor. For a multirate digital controller, the selection of sample frequency and its effect on performance is not as clear.;This dissertation investigates the effect of sample frequency and sample policy on the performance of digitally controlled continuous systems. It considers both single rate and multirate digital controllers. These controllers regulate the systems driven by white noise. The controllers are designed to minimize some combination of the state errors and control effort while simultaneously requiring low controller computational load. The optimal multirate controller is the basis for the controller design. This dissertation extends previous results of multirate control theory to include analysis of sample phasing and solutions for the current state and predicted state multirate estimator. Additionally, this dissertation develops a cost functional that explicitly defines the effect of sample frequency. A two step parameter optimization and integer programming procedure uses this cost functional to calculate the optimal multirate regulator and estimator gains, sample frequency and sample policy that together minimize the cost functional.;The optimization procedure is used to design example controllers for a simple two degree of freedom system consisting of two masses connected by a damped spring. These controllers were used to examine the effect of sample frequency, sample policy, and controller quantization on the closed loop system performance. These examples revealed the important factors contributing to a reasonable sample policy. These factors are the distribution of disturbances in the system, the open loop and closed loop plant frequency characteristics, the control effort, the measurement process, and the controller implementation.;A computer program, OMDPRG, was developed to solve the optimal sample policy multirate control problem. The program was based on MTRLIB, a library of matrix routines.