On simple algebraic control design and possible controller tuning for linear systems with delays

Abstract

This paper is aimed at possible controller tuning of infinite-dimensional controllers of a predictor (compensator) type obtained from an algebraic-based controller structure design method for linear systems with delays. The design procedure is simple enough so that it can attract practitioners. The controllers are of a generalized proportional-integral(-derivative) (PI(D)) type after a trivial limit approximation, and those obtained for stable controlled processes can be compared to the well-known Smith predictor scheme. Some well-established tuning rules for three study cases are then used and compared; namely, the Chien-Hrones-Reswick and the equalization methods are applied for first and second order plants with input and state delays, and the quasi-continuous shifting procedure with the spectral abscissa minimization versus the triple-dominant-root setting are used to the unstable first-order case. These tuning rules are directly applied to PI(D) laws in the simple feedback structure as well, which is compared to the results for the compensation controllers. The robustness of designed controllers is simply benchmarked via some selected perturbations in the static gain and both delays. Simulation outputs and performance measures are given to the reader to display and quantify the obtained results for clearer comparison. © 2018, North Atlantic University Union. All rights reserved.