Passivity and passivation of interconnected time-delay models of reheat power systems

Mahmoud, Magdi S.; Ismail, Abdulla

doi:https://doi.org/10.1155/MPE/2006/90416

Mathematical Problems in Engineering

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Volume 2006 | Article ID 090416 | https://doi.org/10.1155/MPE/2006/90416

Passivity and passivation of interconnected time-delay models of reheat power systems

Magdi S. Mahmoud¹and Abdulla Ismail²

Received10 Mar 2005

Accepted24 Jan 2006

Published01 Jun 2006

Abstract

This paper investigates the problems of delay-dependent passivity and passivation of a class of linear interconnected time-delay systems with particular emphasis on multiarea reheat power systems. This class contains state delay in the dynamics and observation at the subsystem (local) level. A new state transformation is developed to exhibit the delay dependence in the system dynamics and a less conservative passivity-bounding inequality is incorporated. Through the analytical development, it is established that the passivity condition can be cast in a linear matrix inequality (LMI) format at the subsystem level thereby facilitating decentralized passivity analysis. For state-feedback passivation, it is proven that it is indifferent to use instantaneous or delayed decentralized state feedback. The case of dynamic output-feedback passivation is also treated. The analytical developments are simulated to a typical multiarea power system and the ensuing results show satisfactory performance.

References

N. F. Al-Muthairi, M. Zribi, and M. S. Mahmoud, “Adaptive identification and control for a class of interconnected systems,” Systems Analysis Modelling Simulation, vol. 42, no. 6, pp. 851–877, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
B. O. D. Anderson and S. Vongpanitherd, Modern Analysis and Synthesis: A Modern Systems Theory Approach, Prentice-Hall, New Jersey, 1973.
A. A. Bahnasawi, A. S. Al-Fuhaid, and M. S. Mahmoud, “A new hierarchical control structure for a class of uncertain discrete systems,” Control Theory and Advanced Technology, vol. 6, no. 1, pp. 1–21, 1990.
View at: Google Scholar | MathSciNet
A. A. Bahnasawi, A. S. Al-Fuhaid, and M. S. Mahmoud, “Decentralized and hierarchical control of interconnected uncertain systems,” IEE Proceedings. Part D. Control Theory and Applications, vol. 137, pp. 311–321, 1990.
View at: Google Scholar
A. A. Bahnasawi and M. S. Mahmoud, Control of Partially-Known Dynamical Systems, vol. 124 of Lecture Notes in Control and Information Sciences, Springer, Berlin, 1989.
View at: Zentralblatt MATH | MathSciNet
A. R. Bergen and V. Vittal, Power Systems Analysis, Prentice-Hall, New Jersey, 2000.
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Pennsylvania, 1994.
View at: Zentralblatt MATH | MathSciNet
G. Escobar, A. J. van der Schaft, and R. Ortega, “A Hamiltonian viewpoint in the modeling of switching power converters,” Automatica, vol. 35, no. 3, pp. 445–452, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
E. Fridman and U. Shaked, “On delay-dependent passivity,” IEEE Transactions on Automatic Control, vol. 47, no. 4, pp. 664–669, 2002.
View at: Publisher Site | Google Scholar | MathSciNet
P. Gahinet, A. Nemirovski, A. L. Laub, and M. Chilali, LMI Control Toolbox, The MathWorks, Massachusetts, 1995.
J. C. Geromel, J. Bernussou, and P. L. D. Peres, “Decentralized control through parameter space optimization,” Automatica, vol. 30, no. 10, pp. 1565–1578, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
Z. Hu, “Decentralized stabilization of large scale interconnected systems with delays,” IEEE Transactions on Automatic Control, vol. 39, no. 1, pp. 180–182, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
T. N. Lee and U. L. Radovic, “Decentralized stabilization of linear continuous and discrete-time systems with delays in interconnections,” IEEE Transactions on Automatic Control, vol. 33, no. 8, pp. 757–761, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
R. Lozano, B. Brogliato, O. Egeland, and B. Maschke, Dissipative Systems Analysis and Control. Theory and Applications, Communications and Control Engineering Series, Springer, London, 2000.
View at: Zentralblatt MATH | MathSciNet
M. S. Mahmoud, “Stabilizing control for a class of uncertain interconnected systems,” IEEE Transactions on Automatic Control, vol. 39, no. 12, pp. 2484–2488, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
M. S. Mahmoud, “Guaranteed stabilization of interconnected discrete-time uncertain systems,” International Journal of Systems Science, vol. 26, no. 2, pp. 337–358, 1995.
View at: Google Scholar | Zentralblatt MATH
M. S. Mahmoud, “Adaptive stabilization of a class of interconnected systems,” Computers & Electrical Engineering, vol. 23, no. 4, pp. 225–238, 1997.
View at: Publisher Site | Google Scholar
M. S. Mahmoud, “Passive control synthesis for uncertain time-delay systems,” in Proceedings of the 37th IEEE Conference on Decision and Control, pp. 4139–4143, Florida, 1998.
View at: Google Scholar
M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems, vol. 5 of Control Engineering (New York), Marcel Dekker, New York, 2000.
View at: Zentralblatt MATH | MathSciNet
M. S. Mahmoud and N. F. Al-Muthairi, “Design of robust controllers for time-delay systems,” IEEE Transactions on Automatic Control, vol. 39, no. 5, pp. 995–999, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
M. S. Mahmoud and S. Bingulac, “Robust design of stabilizing controllers for interconnected time-delay systems,” Automatica, vol. 34, no. 6, pp. 795–800, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
M. S. Mahmoud and L. Xie, “Stability and positive realness of time-delay systems,” Journal of Mathematical Analysis and Applications, vol. 239, no. 1, pp. 7–19, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
M. S. Mahmoud and L. Xie, “Passivity analysis and synthesis for uncertain time-delay systems,” Mathematical Problems in Engineering, vol. 7, no. 5, pp. 455–484, 2001.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
M. S. Mahmoud and M. Zribi, “Robust and $\mathcal H_\infty$ stabilization of interconnected systems with delays,” IEE Proceedings. Part D. Control Theory and Applications, vol. 145, no. 6, pp. 559–567, 1998.
View at: Publisher Site | Google Scholar
M. S. Mahmoud and M. Zribi, “Passive control synthesis for uncertain systems with multiple-state delays,” Computers & Electrical Engineering, vol. 28, no. 3, pp. 195–216, 2002, (special issue on Time-Delay Systems).
View at: Publisher Site | Google Scholar | Zentralblatt MATH
C. J. Mao and J.-H. Yang, “Decentralized output tracking for linear uncertain interconnected systems,” Automatica, vol. 31, no. 1, pp. 151–154, 1995.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
W. Sun, P. P. Khargonekar, and D. Shim, “Solution to the positive real control problem for linear time-invariant systems,” IEEE Transactions on Automatic Control, vol. 39, no. 10, pp. 2034–2046, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
Z. Xi, G. Feng, D. Cheng, and Q. Lu, “Nonlinear decentralized saturated controller design for power systems,” IEEE Transactions on Control Systems Technology, vol. 11, no. 4, pp. 539–547, 2003.
View at: Publisher Site | Google Scholar
M. Zribi, M. S. Mahmoud, M. Karkoub, and T. Li, “ $\mathcal H_\infty$ controllers for linearised time-delay power systems,” IEE Proceedings - Generation, Transmission and Distribution, vol. 147, no. 6, pp. 401–408, 2000.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2006 Magdi S. Mahmoud and Abdulla Ismail. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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