Mixed H>sub<2</sub>/H>sub<&#8734;</sub> Control of Continuous-Time Singularly Perturbed System-State Feedback Computations

##plugins.themes.academic_pro.article.main##

S. A. Akbar
A. K. Singh
K. B. Datta

Abstract

This study brings out the scheme for the design of a mixed H>sub<2/H>sub<∞ >/subsub<2/H>sub<∞ control law was derived using the auxiliary cost minimisation approach and the feedback controller was formulated for a linear time invariant lower and higher order continuous-time singularly perturbed systems by solving iteratively coupled Riccati equations. The H>sub<∞-controller based on the mixed sensitivity approach and the Linear Quadratic Gaussian (LQG) controller were derived for the same system. The time responses for unit step input and robustness properties such as Gain and Phase margin were studied by formulating mixed H>sub<2/H>sub<∞, H>sub<∞ and LQG systems.

##plugins.themes.academic_pro.article.details##

How to Cite
Akbar, S. A., Singh, A. K., & Datta, K. B. (2009). Mixed H>sub<2</sub>/H>sub<&#8734;</sub> Control of Continuous-Time Singularly Perturbed System-State Feedback Computations. Power Research - A Journal of CPRI, 89–100. Retrieved from https://cprijournal.in/index.php/pr/article/view/965

References

  1. Kokotovic P V, H K Khalil and J O'Reilly, "Singular Perturbation Methods in Control: Analysis and Design", Academic Press, 1986.
  2. Chow J H and Kokotovic P V, "A Decomposition of Near Optimum Regulators for Systems with Slow and Fast Modes', IEEE Trans. Automat contr., Vol. AC-21, pp. 701-705, 1976.
  3. Kokotovic P V and R A Yackle, "Singular Perturbation of Linear Regulators: Basic Theorems", IEEE Trans. Automat. Contr., Vol. AC-17, pp. 29-37, 1976.
  4. Zames G., "Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Semi-norms and Approximate Inverses", IEEE Trans. Automat. Contr., Vol. AC-26, No.2, pp. 301-320, 1981.
  5. Khalil H K and F C Chen, "H∞ Control of Two Time Scale Systems, Systems and Control Lett.", Vol. 19, pp. 35-42, 1992.
  6. Pan Z and T Basar, "H∞ Optimal Control for Singularly Perturbed Systems-Part I: Perfect State Measurements", Automatica, Vol. 29, pp. 401-423, 1993.
  7. Pan Z and T Basar, "H∞ Optimal Control for Singularly Perturbed Systems-Part II: Imperfect State Measurements", IEEE Trans. Automat. Contr., Vol. AC-39, pp. 280-299, 1994.
  8. Petersen I R, "Disturbance Attenuation and H∞ Optimisation – A Design Method Based on the Algebraic Riccati Equation", IEEE Trans. Automat. Contr., Vol. AC-32, pp. 427-429, 1987.
  9. Doyle J C, Keith Glover, P P Khargonekar and B A Francis, "State Space Solutions to Standard H2 and H∞ Control Problems", IEEE Trans. Automat. Contr., Vol. 34, No. 8, 1989.
  10. Khargonekar P P, Petersen I R and Mario A Rotea, "H∞ Optimal Control with State Feedback", IEEE Trans. Automat. Contr., Vol. 33, pp. 786-788, 1988.
  11. M A Rotea and P P Khargonekar, "H2 Optimal Control with an H∞ Constraint: The State Feedback Case", Automatica., Vol. 27, pp. 307-316, 1991.
  12. D Mustafa and K Glover, "Controllers which Satisfy an H∞ Norm Bound and Minimise an Entropy Integral", Proc. of Conference on Decision and Control, 1988, Austin.
  13. Dennis S Bernstein and W M Haddad, "LQG Control with an H∞ Performance Bound: A Riccati Equation Approach", IEEE Trans. Automat. Contr., Vol. 34, No. 3, 1989.
  14. Yang C D, H C Tai and C C Lee, "Systematic Approach to Selecting H∞ Weighting Functions for DC Servos", Proc. of the 33rd Conf. on Decision and Control, pp. 1080-1085, Lake Buena Vista, FL-December, 1994.
  15. Postlethwaite I, M C Tsai and D W Gu, "Weighting Function Selection in H∞ Design", Proc. of IFAC Conference, Tallinn, Estonia.