PI Control for Second Order Delay System with Tuning Parameter Optimization

In this paper, we consider the control of time delay system 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 of its stability region and the computation of the PI optimum parameters. We have used the genetic algorithms to lead the complexity of the optimization problem.

Authors:

• R. Farkh
• K. Laabidi
• M. Ksouri

Keywords:

• Genetic algorithm
• Hermit-Biehler theorem
• optimization
• PI controller
• second order delay system
• stability region.

References:

[1] S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, Robust Control:The
Parametric Approach, Upper Saddle River, NJ: Prentice-Hall, 1995.
[2] L. Cedric, Pontryagin revisit: implication sur la stabilit des PID retards,
Confrence Internationale Francophone d-Automatique CIFA-02
[3] M. Dambrine, Contribution l-tude de la stabilit des systmes retards,
Thse de doctorat, Universit de Lille, 1994.
[4] D.E. Godelberg, Genetic Algorithms in search, optimization and machine
learning, Addison-Wesley, Massachusetts, 1991.
[5] O.Lequin, M. Gevers, M. Mossberg, E. Bosmans, L. Triest, Iterative
feedback tuning of PID parameters: comparison with classical tuning
rules, Control Engineering Practice, N11, pp. 1023-1033, 2003.
[6] G.P. Liu, S.Daley, Optimal-tuning PID control for industrial systems,
Control Engineering Practice, N 9, pp. 1185-1194, 2001.
[7] S.-I. Niculescu, Delay effects on stability, Springer, London, 2001.
[8] R.Padma Sree, M.N. Sirinivas, M. Chidambaram, A simple method of
tuning PID controllers for stable and unstable FOPTD systems, Comp.
Chem. Eng, pp. 2201-2218, 2004.
[9] Z. Shafiei, A.T Shenton, tuning of PID-type controllers for stable and
unstable delay systems with time delay Automatica, pp. 1609-1615, 1994.
[10] G. J. Silva, A. Datta and S. P. Bhattacharyya, Stabilization of Time
Delay Systems, Proceedings of the American Control Conference, pp.
963-970, 2000.
[11] G. J. Silva, A. Datta and S. P. Bhattacharyya, Stabilization of First-order
Systems with Time Delay using the PID controller, Proceedings of the
American Control Conference, pp. 4650-4655, 2001.
[12] G. J. Silva, A. Datta and S. P. Bhattacharyya, New synthesis of PID
controller, IEEE transactions on automatic control, vol.47,No.2, 2002.
[13] G.J. Silva, A. Datta, S.P. Bhattacharyya, PID controllers for time delay
systems, Springer, London, 2005.
[14] M. Villain, Systmes asservis linaires, ellipses/ dition marketing S.A.,
1996.
[15] Q.C. Zhong, Robust control of time delay system, Springer, London,
2006.
[16] A. Roy, K. Iqbal, PID controller tuning for the first-order-plus-deadtime
process model via Hermite-Biehler theorem, ISA Transaction, pp.
362-378, 2005.
[17] G. J. Silva, A. Datta and S. P. Bhattacharyya, Determination of Stabilizing
gains for Second-order Systems with Time Delay, Proceedings of
the American Control Conference, pp. 25-27, 2001.
[18] C. S. Jung, H. K. Song, J. C. Hyun, A direct synthesis tuning method of
unstable first-order-plus-time-delay processes, Journal of process control,
pp. 265-269, 1999.
[19] C. Xiang, Q.G. Wang; X. Lu, L.A. Nguyen, T.H. Lee, Stabilization of
second-order unstable delay system, Journal of process control, pp. 675-
682, 2007.
[20] R. Toscano, A simple robust PI/PID controller design via numerical
optimization approach, Journal of process control, pp. 81-88, 2005.