A Suboptimal Shifting Based Zero-pole Placement Method for Systems with Delays

Abstract

An appropriate setting of eventual controller parameters for a derived controller structure represents an integral part of many control design approaches for dynamical systems. This contribution is aimed at a practically applicable and uncomplicated controller tuning method for linear time-invariant time delay systems (LTI-TDSs). It is based on placing the dominant poles as well as zeros of the given infinite-dimensional feedback control system by matching them with the desired ones given by known dynamical properties of a simple fixed finite-dimensional model. The desired placing is done successively by applying the Quasi-Continuous Shifting Algorithm (QCSA) first such that poles and zeros are forced to be as close as possible to those of the model. Concurrently, rests of both system spectra are shifted to the left as far as possible to minimize the spectral abscissa. The obtained results are then enhanced by a non-convex optimization technique applied to a selected objective function reflecting the distance of desired model roots from the eventual system ones and the spectral abscissae. Retarded LTI-TDS are primarily considered; however, systems with neutral delays are touched as well. The efficiency of the proposed method is proved via numerical examples in Matlab/Simulink environment. Some drawbacks and possible improvements or extensions of the algorithm for the future research are also concisely suggested to the reader.