Stabilization of time delay systems

We first consider the problem of stabilizing a first-order plant with dead time using a constant gain controller. Using a version of the Hermite-Biehler theorem applicable to quasipolynomials, a complete analytical characterization of all stabilizing gain values is provided as a closed form solution. A similar approach is then used to tackle the problem of stabilizing a first-order plant with time delay using a PI controller, and once again the complete stabilizing set is determined.

[1]  Nevzat Ozturk,et al.  On the Robust Stability of the Time Delay Systems , 1991, 1991 American Control Conference.

[2]  V. Kharitonov,et al.  Robust stability of time-delay systems , 1994, IEEE Trans. Autom. Control..

[3]  Shankar P. Bhattacharyya,et al.  A linear programming characterization of all stabilizing PID controllers , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[4]  Shankar P. Bhattacharyya,et al.  Generalizations of the Hermite–Biehler theorem , 1999 .

[5]  Erik I. Verriest,et al.  Stability and Control of Time-delay Systems , 1998 .

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

[7]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1994 .

[8]  A. Hatley.  Mathematics in Science and Engineering , Volume 6: Differential- Difference Equations. Richard Bellman and Kenneth L. Cooke. Academic Press, New York and London. 462 pp. 114s. 6d. , 1963, The Journal of the Royal Aeronautical Society.

[9]  Aniruddha Datta,et al.  Control system design using low order controllers: constant gain, PI and PID , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).