A nonlinear disturbance observer for multivariable systems and its application to magnetic bearing systems

Xinkai Chen, Chun Yi Su, Toshio Fukuda

Research output: Contribution to journalArticle

110 Citations (Scopus)


This paper proposes a new nonlinear-disturbance observer for multivariable minimum-phase systems with arbitrary relative degrees. The model uncertainties and the system nonlinearities are treated as disturbances. The estimation of individual disturbances is independent of each other and the derivatives of the disturbances can be independently estimated. The proposed formulation is inspired by the variable structure-control method and adaptive algorithms where the a priori information concerning the upper bounds of the disturbances and their derivatives is not required. The nonlinear-disturbance observer is robust to the types of disturbances. Stability analysis shows that the estimation error decreases exponentially to a steady value, which is determined by the design parameters. To illustrate the method, the proposed design is applied to a vertical-shaft magnetic-bearing system where the rotational disturbances and their derivatives are estimated based on a linearized model of the rotational motion. Simulation results show the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)569-577
Number of pages9
JournalIEEE Transactions on Control Systems Technology
Issue number4
Publication statusPublished - 2004 Jul 1


ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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