Two-time-scale averaging of systems involving operators and its application to adaptive control of hysteretic systems

  • Authors:

  • Xiaobo Tan;Hassan K. Khalil

  • Affiliations:

  • Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI;Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

Motivated by the adaptive control problem for systems with hysteresis, a two-time-scale averaging framework is presented in this paper for systems involving operators, by extending the work of Teel and co-workers. The developed averaging theory is applied to the analysis of a model reference adaptive inverse control scheme for a system consisting of linear dynamics preceded by a Prandtl-Ishlinkskii (PI) hysteresis operator. The fast component of the closed-loop system involves the coupling of an ordinary differential equation and a hysteresis operator derived from the PI operator and its inverse, while the slow component is the parameter update rule. The stability of the boundary-layer system and that of the average system are established under suitable conditions, which implies practical regulation of the parameter error and tracking error under the adaptive scheme.