Cover
Vol. 6 No. 1 (2010)

Published: June 30, 2010

Pages: 1-6

Original Article

Singular Perturbation Method for Robust Control of Nonlinear Systems

Hadi Bafandegan Mogaver 1 Asef Zare Mohammad Rasoul Tanhatalab
1Dept. of Electrical & Control Engineering, Gonabad Univercity, Gonabad, Iran
History
  • Received: April 30, 2010
  • Available Online: June 30, 2010
DOI

https://doi.org/10.37917/ijeee.6.1.1

Abstract

In this paper, we consider robust control of nonlinear systems, via inclusion nonlinear systems solution and $H_{\infty}$ controller using singular perturbation method. First, using a technique for solving inclusion nonlinear systems, we transform the nonlinear system to an ordinary nonlinear system. Then using normal form equations, we eliminate the nonlinear part of the system matrix of equations of the system and transform it to a linear diagonal form. Separating new equations into slow and fast subsystems, due to the singular perturbation method and with the assumption of norm-boundedness of the fast dynamics, we can treat them as disturbance and design an $H_{\infty}$ controller for a system with a lower order than the original one that stabilizes the overall closed loop system. The proposed method is applied to a nominal system.

Keywords

References

  1. Bapurao C. Dhage," On Periodic Boundary Value Problems of First-Order Perturbed Impulsive Banach spaces, Dynamic Syst. Appl. 8 (1999), 119-126.
  2. J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.
  3. M. Benchohra and A. Boucherif, On first order initial value problems for impulsive differential inclusions in Banach spaces, Dynamic Syst. Appl. 8 (1999), 119-126.
  4. M. Benchohra, A. Boucherif and J. J. Nieto, On initial value problems for a class of first order impulsive differential inclusions, Discuss. Math. Differ. Incl. Control Optim. 21 (2001), 159-171.
  5. A. J. Van der Schaft, 2L-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H control," IEEE Trans. on Automatic Control, Vol. 37, No. 6, (1992).
  6. A. Khajepour, "Application of Center Manifold and Normal Form to Nonlinear Controller Design," Ph.D. thesis in Mechanical engineering, university of Waterloo, Canada, (1995).
  7. M. J. Yazdanpanah, H. R. Karimi, "The Design of H Controller for Robust Regulation of Singularly Perturbed Systems," Amir Kabir Journal, No. 49, (2002).
  8. J. C. Doyle, K. Glover, P. P. Khargonekar, B. A. Francis, "State Space Solutions to Standard 2 H and H control problems," IEEE Trans. on Automatic Control, Vol. 34, (1989).