Feedback Linearization of Nonlinear Singularly Perturbed Systems with State-dependent Coefficients

Abstract

The article examines a feedback linearization (FL) problem for a nonlinear singular perturbed (SP) system in a state-dependent coefficients form (SDC-form). The combination of the composite control technique of singular perturbation theory and a canonical similarity transformation approach for systems in a SDC-form are explored in this research. As a result, two FL problems for a fast state variables subsystem and a slow state variables subsystem are solved separately. The transformation matrix and feedback linearizing control for the entire nonlinear SP system are designed as a composition of solutions of these two FL problems. The composite stabilizing controller, based on feedback linearization and a pole placement method, is proposed for a nonlinear SP system in a SDC-form. Practical implementation of the proposed feedback linearizing composite stabilizing control is shown through an example (an inverted pendulum, controlled by a direct current motor).

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Correspondence to Aleksey A. Kabanov.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Shihua Li under the direction of Editor PooGyeon Park. This work was supported by the Russian Science Foundation (Project No.17-11-01220).

Aleksey A. Kabanov received his Ph.D. degree in Systems and Processes of Control from the Sevastopol National Technical University, Sevastopol, Ukraine in 2012. His current research interests include robotics, singular perturbation theory and methods in control, robust and adaptive control.

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Kabanov, A.A. Feedback Linearization of Nonlinear Singularly Perturbed Systems with State-dependent Coefficients. Int. J. Control Autom. Syst. 18, 1743–1750 (2020). https://doi.org/10.1007/s12555-019-0357-1

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Keywords

  • Feedback linearization
  • similarity transformation
  • singular perturbation
  • state-dependent coefficients