PD Controller Design with H¥ Performance for Linear Systems with Input Delay

Document Type : Research Article

Authors

Corresponding Author, The authors are with the Advanced Robotic and Automates Systems (ARAS), Faculty of Electrical and Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran, (e-mail: Shariati@eetd.kntu.ac.ir).

Abstract

This paper presents H∞ control problem for input-delayed systems. A neutral system approach is considered to the design of PD controller for input delay systems in presence of uncertain time-invariant delay. Using this approach, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed coefficient terms depend on the controller parameters. This condition provides challenging issues in theoretical research and provides new horizons in applications. In the present paper, new delay-dependent sufficient condition is derived for the existence of H∞ controller in terms of matrix inequalities. The resulting H∞ controller stabilizes the closed-loop neutral system and assures that the H∞ performance norm to be less than a prescribed level. An application example is presented to illustrate the effectiveness of the proposed method.

Keywords

References

[1]     M. Deng, A. Inoue, "Networked non-linear control for an aluminum plate thermal process with time-delays," International Journal of Systems Science, vol. 39, pp. 1075-1080, 2008.
[2]     A. V. Rezounenko, J. Wu, "A Non-Local PDE Model for Population Dynamics with State-Selective Delay: Local Theory and Global Attractors," Journal of Computational and Applied Mathematics, vol. 190, pp. 99-113, 2006.
[3]     L. E. Zárate,, F. R. Bittencout, "Representation and Control of the Cold Rolling Process Through Artificial Neural Networks via Sensitivity Factors," Journal of Material Processing Technology, vol. 197, pp. 344-362, 2008.
[4]     R. Ortega, A. de Rinaldis, M. W. Spong, S. Lee and K. Nan, "On Compensation of Wave Reflections in Transmission Lines and Applications to the Overvoltage Problem AC Motor Drives," IEEE Transaction on Automatic Control, vol. 49, pp. 1757-1762, 2004.
[5]     J.D. Chen, "LMI-based robust H∞ control of neutral systems with state and input delays," Journal of Optimization Theory and Applications, vol. 126, pp. 553-570, 2005.
[6]     C.H. Lien, "H∞ observer-based control for a class of uncertain neutral time-delay systems via LMI optimization approach," Journal of Optimization Theory and Applications, vol. 127, pp. 129-144, 2005.
[7]     U. Baser, "The H∞ control problem for neutral systems with multiple delays,” presented at the 15th IFAC World Congress, Barcelona, Spain, 2002.
[8]     U. Baser, "Output feedback H∞ control problem for linear neutral systems: delay independent case," Journal of Dynamic Systems, Measurement, and Control, vol. 125, pp. 177-185, 2003.
[9]     V. Suplin, E. Fridman, U. Shaked, "H∞ control of linear uncertain time-delay systems-a projection approach, " IEEE Transactions on Automatic Control, vol. 51, pp. 680-685, 2006.
[10]  X.M Sun, W. Wang, G.P. Liu, J. Zhao, "Stability analysis for linear switched systems with time varying delay," IEEE Systems, Man and Cybernetics, vol. 38, pp. 528-533, 2008.
[11]  X. Liu, W. Yu, L. Wang, "Stability analysis for continuous-time positive systems with time-varying delays," IEEE Transactions on Automatic Control, vol. 55, pp. 1024-1028, 2010.
[12]  A. Shariati, H.D. Taghirad, B. Labibi, "Delay-dependent H∞ control linear systems with time-varying delay using proportional-derivative state feedback," in proc. 2010 Mediterranean Conference on Control & Automation (MED), Marrakesh, Morocco, pp. 1006-1012.
[13]  G.J. Silva, A. Datta, S. P. Bhattacharyya, "New results on the synthesis of PID controllers," IEEE Transactions on Automatic Control, vol. 47, pp. 241-252, 2002.
[14]  H. Xu, A. Datta, S.P. Bhattacharyya, "PID stabilization of LTI plants with time-delay," in Proc. 2003 IEEE Conf. Dec. Cont., Maui, HI, pp. 4038-4043.
[15]  D.J. Wang, "Synthesis of PID controllers for high-order plants with time-delay," Journal of Process Control, vol. 19, pp. 1763–1768, 2009.
[16]  N. Hohenbichler, "All stabilizing PID controllers for time delay systems," Automatica, vol. 159, pp. 2678-2684, 2009.
[17]  P.E. Dupont, "Avoiding stick-slip through PD control, "IEEE Transactions on Automatic Control, vol. 39, pp. 1094-1097, 1994.
[18]  C. Yang, Q. Huang, H. Jiang, O.O. Peter, J. Han, "PD control with gravity compensation for hydraulic 6-DOF parallel manipulator," Mechanism and Machine Theory, vol. 45, pp. 666-677, 2010.
[19]  T. Häggland, "A predictive PI controller for processes with long dead times," IEEE Control System Magazine, vol. 12, pp. 57-60, 1992.
[20]  J.E. Normy-Rico, C. Bordons, E.F. Camacho, "Improving of dead-time compensating PI controllers," Control Engineering Practice, vol. 5, pp. 801-810, 1997.
[21]  J. Wei; H. Fang, H.O. Wang, "Consensus of multi-agent system with communication delays by self-delay PD control," in proc. 2010 World Congress on Intelligent Control and Automation, Jinan, China, pp. 2295-2300.
[22] J.E. Normy-Rico, C. Bordons, E.F. Camacho, "Unified approach for robust dead-time compensator design," Journal of Process Control, vol. 19, pp. 38-47, 2009.
[23]  K.T. Erickson, J.L. Hedrick, Plantwide Process Control, John-Wiley, 1999.
[24]  Y.S. Moon, P. Park, W.H. Kwon, Y.S. Lee, "Delay dependent robust stabilization of uncertain state delayed systems," International Journal of Control, vol. 74, pp. 1447-1455, 2001.
[25] A. Shariati, H.D. Taghirad, B. Labibi, "Delay-dependent H¥ control of linear systems with time-varying input delay using state derivative feedback" Journal of Control Engineering and Applied Informatics, to be published.

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