On the extraction of dead-time controllers and estimators from delay-free parametrizations

A novel approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay-free controllers in the DT design. In particular, DT con- trollers can be extracted from such delay-free parametrizations. In this paper, the extraction procedures are developed in both and settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators.

[1]  David L. Kleinman,et al.  Optimal control of linear systems with time-delay and observation noise , 1969 .

[2]  J. Bontsema,et al.  An application driven guide through infinite-dimensional systems theory , 1997 .

[3]  H. Dym,et al.  Explicit formulas for optimally robust controllers for delay systems , 1995, IEEE Trans. Autom. Control..

[4]  Israel Gohberg,et al.  Time varying linear systems with boundary conditions and integral operators. I. The transfer operator and its properties , 1984 .

[5]  Karl Brammer,et al.  Kalman-Bucy filters , 1989 .

[6]  Leonid Mirkin,et al.  State-space parametrization of all stabilizing dead-time controllers , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[7]  Tamer Başar,et al.  H1-Optimal Control and Related Minimax Design Problems , 1995 .

[8]  J. E. Marshall,et al.  Control of Time-Delay Systems , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[10]  Ruth F. Curtain,et al.  A weighted mixed-sensitivity H∞-control design for irrational transfer matrices , 1996, IEEE Trans. Autom. Control..

[11]  Z. J. Palmor,et al.  Improved dead-time compensator controllers , 1985 .

[12]  Ruth F. Curtain,et al.  A weighted mixed-sensitivity H-infinity-control design for irrational transfer matrices , 1996 .

[13]  K. S. Smith,et al.  Time domain simulation of cycloconverter-fed variable speed AC drives with closed-loop control , 1994 .

[14]  Guoxiang Gu,et al.  Computation of /spl Lscr//sub 2/[0, h] induced norms , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[15]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[16]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[17]  Qing-Chang Zhong,et al.  A Nehari theorem for continuous-time FIR systems , 2002 .

[18]  Leonid Mirkin,et al.  H∞ control of system with I/O delay: a review of some problem‐oriented methods , 2002 .

[19]  Allen Tannenbaum,et al.  Abstract model and controller design for an unstable aircraft , 1992 .

[20]  Hitay Özbay,et al.  Robust Control of Infinite Dimensional Systems: Frequency Domain Methods , 1996 .

[21]  Onur Toker,et al.  H∞ optimal and suboptimal controllers for infinite dimensional SISO plants , 1995, IEEE Trans. Autom. Control..

[22]  I. Gohberg,et al.  Classes of Linear Operators , 1990 .

[23]  K. Nagpal,et al.  ${\cal H}_\infty$ Control and Estimation Problems with Delayed Measurements: State-Space Solutions , 1997 .

[24]  Israel Gohberg,et al.  The band method for positive and strictly contractive extension problems: An alternative version and new applications , 1989 .

[25]  O. Toker,et al.  Complexity Issues in System Theory and Solution Procedures for Certain Robust Control Problems , 1995 .

[26]  Leonid Mirkin,et al.  On the characterization of sampled-data controllers in the lifted domain , 1997 .

[27]  LEONID MIRKIN,et al.  H2 and Hinfinity Design of Sampled-Data Systems Using Lifting. Part I: General Framework and Solutions , 1999, SIAM J. Control. Optim..

[28]  Hans Zwart,et al.  On 𝒽∞ control for dead-time systems , 2000, IEEE Trans. Autom. Control..

[29]  Gilead Tadmor,et al.  The standard H∞ problem in systems with a single input delay , 2000, IEEE Trans. Autom. Control..

[30]  Akira Kojima,et al.  Robust controller design for delay systems in the gap-metric , 1995, IEEE Trans. Autom. Control..

[31]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[32]  O Smith,et al.  CLOSER CONTROL OF LOOPS WITH DEAD TIME , 1957 .

[33]  Masami Ito,et al.  A process-model control for linear systems with delay , 1981 .

[34]  Leonid Mirkin,et al.  On discrete-time H∞ problem with a strictly proper controller , 1997 .

[35]  Etsujiro Shimemura,et al.  Predictive control for systems with time delay , 1983 .