First Order Controller for Time Delay System

Lecture Notes in Control and Information Sciences, 1998

British Library Cataloguing in Publication Data Stability and control of time-delay systems.-(Lecture notes in control and information sciences ; 228) 1.Delaylines 2.Delaylines-Stability LDugard, L. II.Verriest, Eriklsidoor 003.8 ISBN 3540761934 Library of Congress Cataloging-in-Publication Data Stability and control of time-delay systems / L. Dugard and E.I. Verriest (eds.). p. cm.-(Lecture notes in control and information sciences : 228) Includes bibliographical references. ISBN3-540-76193-4 (pbk. : alk. paper) 1. Control theory. 2. Delay differential equations.

Electronic Journal of Qualitative Theory of Differential Equations

Stability and stabilization of time delay systems (even of the linear ones) is again in the mainstream of the research. A most recent example is the stability analysis of feedback control loops containing a first order controlled object with pure delay and a standard PID controller, thus generating a system with a second degree quasi-polynomial as characteristic equation. Since the classical memoir ofČebotarev and Meiman (1949) up to the more recent monographs by Stepan (1989) and several approaches to this problem have been given, aiming to find the most complete Routh-Hurwitz type conditions for this case. In fact the main problem is here a missing case in the original memoir ofČebotarev and Meiman and its significance within the framework of the most recent analysis of Górecki et al. The present paper aims to a fairly complete analysis of the problem combined with some hints for the nonlinear case (Aizerman problem).

MATLAB for Engineers - Applications in Control, Electrical Engineering, IT and Robotics, 2011

Journal of Dynamic Systems, Measurement, and Control, 2003

This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.

IEEE Transactions on Automatic Control, 1985

For linear time-invariant systems with one or more noncommensnrate time delays, necessary and sufficient conditions are given for the existence of, a fiite-dimensional stabilizing feedback compensator. In particular, it is shown that a stabilizable time-delay system can always be stabilized using a finite-dimensional compensator. The problem of explicitly constructing finite-dimensional stabilizing compensators is also considered. I. STABILIZATION OF SYSTEMS WITH DELAYS In this note we consider the problem of stabilizing a linear timeinvariant continuous-time system with q noncommensurate time delays h,, hZ, .-., h,. The systems we shall study are given by a state representation of the form dxo= (fldh,, dh2.. ' ' 9 dhq)x)(t) + (G(dhl, dh2, '. ' 9 dhq)lo(t) dt y((t)=(ff(db,, dbp " ' I dh8)x)(r)+(J(dh,. dhz, dhq)U)(f) (1.1) where the m-vector u(t) is the input at time t, the n-vector x(t) is the instantaneous state at time t , the p-vector y(r) is the output at time t, and matrices whose entries are polynomials in the delay operators dh,,. .. , dhq with coefficients in the reds m. (Here (d&f)(t)= Atrhi) for any positive integer r.) With the system (l.l), we shall associate the quadruple (F(z), G(z), H(z), J(z)), where z = (z,, z2,. .. , z,) and F(z), G(z), H(z), J(z) are the coefficient matrices in (1.1) with dhi replaced by zi. Conversely, any quadruple (F(z), G(z), H(z), J(z)) of matrices over the ring R[z] of polynomials in the zi defines a time-delay system of the form (1.1) in the ob\rious way. We s h d always assume that J(z) = 0 for the given system (l.l), and we shall denote this system by the triple (F(z), G(z), H(z)). A fundamental problem in the control of systems with delays is determining whether or not there is an (output) feedback system (A(z), B(z), a z) , D(z)) over the polynomial ring R[z] or over the reals El (the finitedimensional case) such that the closed-loop system consisting of the given system (F(z), a z) , H(z)) and the feedback system is internally asymptotically stable. If such a feedback system exists, we say that (F(z), G(z), H(z)) is regulable. Several individuals have worked on the problem of feedback stabilization of systems with delays. Much of this past work has centered on the commensurate-delay case (q = 1) with delays in control only, delays in

Journal of Circuits, Systems, and Computers, 2011

In this paper, the Generalized Kharitonov Theorem for quasi-polynomials is exploited for the purpose of synthesizing a robust controller. The aim here is to develop a controller to simultaneously stabilize a given interval plant family with unknowing and bounded time delay. Using a constructive procedure based on HermiteÀBiehler theorem, we obtain all PI gains that stabilize an uncertain¯rst-order delay system. An application example is presented for the temperature control of a heated air stream, process trainer P T326.

Kybernetika

ISA Transactions, 2010

In this paper, stabilizing regions of a first-order controller for an all poles system with time delay are computed via parametric methods. First, the admissible ranges of one of the controller's parameters are obtained. Then, for a fixed value of this parameter, stabilizing regions in the remaining two parameters are determined using the D-decomposition method. Phase and gain margin specifications are then included in the design. Finally, robust stabilizing first-order controllers are determined for uncertain plants with an interval type uncertainty in the coefficients. Examples are given to illustrate the effectiveness of the proposed method.

Mechanical Systems and Signal Processing, 2009

We consider the problem of assigning eigenvalues of a linear vibratory system by state feedback control in the presence of time delay. It is shown that for a system with n degrees of freedom we may assign 2n eigenvalues. Assigning 2n eigenvalues in a timedelayed system does not necessarily regulate the dynamics of the system or even guarantee its stability. We therefore separate the eigenvalues into two groups, primary and secondary eigenvalues. The primary eigenvalues are the 2n finite eigenvalues of the system without time delay. The secondary eigenvalues are the other eigenvalues emerging from infinity due to the delay. A method of a posteriori analysis to identify the primary eigenvalues and to ensure that they have been properly assigned is proposed in the paper. The method is demonstrated by various examples.

2009

In this paper, we consider the control of time delay sys- tem by Proportional-Integral (PI) controller. By Using the Hermite- Biehler theorem, which is applicable to quasi-polynomials, we seek a stability region of the controller for first order delay systems. The essence of this work resides in the extension of this approach to second order delay system, in the determination