On a controller parameterization for infinite-dimensional feedback systems based on the desired overshoot

Abstract

The aim of this paper is to introduce, in detail, a novel approach for tuning of anisochronic singleinput single-output controllers for infinite-dimensional feedback control systems. A class of Linear Time- Invariant Time Delay Systems (LTI TDSs) is taken as a typical representative of infinite-dimensional systems. Control design to obtain the eventual controller structure is made in the special ring of quasipolynomial meromorphic functions (RMS). The use of this algebraic approach with a simple feedback loop for unstable or integrating systems leads to infinite-dimensional (delayed) controllers as well as the whole feedback loop. A natural task is to set tunable controller parameters in order to form the crucial area of the infinite closed-loop spectrum. It is worth noting that not only poles yet also zeros are taken into account. The prescribed positions of the right-most reference-to-output poles and zeros are given on the basis of the desired overshoot for a simple finite-dimensional matching model the detailed analysis of which is provided. The dominant poles and zeros are shifted to the prescribed positions using the Quasi-Continuous Shifting Algorithm (QCSA) followed by the use of an advanced optimization algorithm. The whole methodology is called the Pole-Placement Shifting based controller tuning Algorithm (PPSA). The PPSA is demonstrated on the setting of parameters of delayed controller for an unstable time delay plant of a skater on the controlled swaying bow. This example, however, shows a treachery of the algorithm and a natural feature of an infinite-dimensional system - namely, that its spectrum or even its dominant part can not be placed arbitrarily. Advantages and drawback as well as possible modification of the algorithm are also discussed.