Meromorphic observer-based pole assignment in time delay systems

summary:The paper deals with a novel method of control system design which applies meromorphic transfer functions as models for retarded linear time delay systems. After introducing an auxiliary state model a finite-spectrum observer is designed to close a stabilizing state feedback. The observer finite spectrum is the key to implement a state feedback stabilization scheme and to apply the affine parametrization in controller design. On the basis of the so- called RQ-meromorphic functions an algebraic solution to the problem of time- delay system stabilization and control is presented that practically provides a finite spectrum assignment of the control loop

Polynomial approximation of quasipolynomials based on digital filter design principles

This contribution is aimed at a possible procedure approximating quasipolynomials by polynomials. Quasipolynomials appear in linear time-delay systems description as a natural consequence of the use of the Laplace transform. Due to their infinite root spectra, control system analysis and synthesis based on such quasipolynomial models are usually mathematically heavy. In the light of this fact, there is a natural research endeavor to design a sufficiently accurate yet simple engineeringly acceptable method that approximates them by polynomials preserving basic spectral information. In this paper, such a procedure is presented based on some ideas of discrete-time (digital) filters designing without excessive math. Namely, the particular quasipolynomial is subjected to iterative discretization by means of the bilinear transformation first; consequently, linear and quadratic interpolations are applied to obtain integer powers of the approximating polynomial. Since dominant roots play a decisive role in the spectrum, interpolations are made in their very neighborhood. A simulation example proofs the algorithm efficiency. © Springer International Publishing Switzerland 2016

PPSA: A tool for suboptimal control of time delay systems: Revision and open tasks

Abstract During the development of algebraic controller design in a special ring for time delay systems (TDSs) a problem of a suitable free controller parameters setting appeared. The first author of this contribution recently suggested a natural idea of placing the dominant characteristic numbers (poles) and zeros of the infinite-dimensional feedback control system on the basis of the desired overshoot for a simple finite-dimensional matching model and shifting of the rest of the spectrum. However, the original procedure called the Pole-Placement Shifting based controller tuning Algorithm (PPSA) was not developed and described entirely well. The aim of this paper is to revise the idea of the PPSA and suggest a possible ways how to improve or extend the algorithm. A concise illustrative example is attached to clarify the procedure for the reader as well

Quasipolynomial Approach to Simultaneous Robust Control of Time-Delay Systems

A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law

Implementation of a New Quasi-Optimal Controller Tuning Algorithm for Time-Delay Systems

The aim of this chapter is to describe, demonstrate and implement a new quasi-optimal pole placement algorithm for SISO LTI-TDS based on the quasi-continuous pole shifting to the prescribed positions. The desired positions are obtained by overshoot analysis of the step response for a dominant pair of complex conjugate poles. A controller structure is initially obtained by algebraic controller design in RMS. Note that the maximum number of prescribed poles (including their multiplicities) equals the number of unknown parameters. If the prescribed roots locations can not be reached, the optimizing of an objective function involving the distance of shifting poles to the prescribed ones and the roots dominancy is utilized. The optimization is made via Self-Organizing Migration Algorithm (SOMA). Matlab m-file environment is utilized for the algorithm implementation and, consequently, results are tested in Simulink on an attractive example of unstable SISO LTI-TDS.P(ED2.1.00/03.0089), Z(MSM7088352102

On Finite-Dimensional Transformations of Anisochronic Controllers Designed by Algebraic Means: A User Interface

This chapter intended to propound the reader a methodology for algebraic controller design for systems with internal delays, followed by a comparison of several easy-handling techniques for rational (i.e. finite-dimensional) approximation of anisochronic (i.e. infinite-dimensional) controllers – or their transfer functions, more precisely. Matlab with Simulink was a very useful assistant here. The authors programmed a simple user interface which enables the user to enter a nominal transfer function and select approximation methods to be used and their orders. As a result, the program returns the accuracies in both text and graphical forms. Simulation experiments with the program were made. Control of a simple stable TDS, control of unstable TDS of a skater on the swaying bow and control of a laboratory circuits heating plant were benchmark examples. The results were very interesting and startling because the habitual Padé approximation proved to be very good and, moreover, the higher order approximation did not automatically mean the better result for systems with internal delays.P(ED2.1.00/03.0089