Corresponding author: Kabanov Aleksey A., Ph. D., Head of Department of Informatics and Control in Technical Systems, Sevastopol State University, 33, Universitetskaya St., Sevastopol, 299053, Russian Federation, e-mail: KabanovAleksey@gmail.com

Received on February 20, 2015
Accepted March 06, 2015

One of the most common methods of synthesis of the nonlinear control systems is the method of a feedback linearization (FL). The idea of this method consists in conversion of the original nonlinear system into a linear one by means of a state feedback and coordinate transformation. Then, the methods of control theory for the linear systems are used for the system design. If the original nonlinear system cannot be linearized exactly by the state feedback, the method of the approximate feedback linearization (AFL) is used. The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system (not of the entire system). In this paper, the author proposes a method of an approximate feedback linearization control of the nonlinear singularly perturbed (SP) systems. The proposed method is based on a decomposition of the original SP system and construction of AFL control in the form of composite FL controls for the slow and fast subsystems. In general, a nonlinear SP system cannot be easily separated into slow and fast subsystems, because the conditions of Tikhonov theorem are not complied. In order to overcome this, the author proposes to perform the feedback linearization method at first for the system's part, which describes the fast state variables. Thus, a fast control is chosen, so that the conditions of Tikhonov theorem would be met. Then, using a standard singular perturbation technique, we obtain a slow subsystem. Further the problem of FL control for a slow subsystem is solved. The resulting AFL control is obtained in the form of a composite control. Application of the proposed approach is illustrated with two examples.

Keywords: singularly perturbed system, approximate feedback linearization, composite control, robust stability

Acknowledgements: This work was supported by a grant from the Russian Foundation for Basic Research, project No. 15-08-06859.

For citation:
Kabanov A. A. Approximate Feedback Linearization Based on the Singular Perturbations Approach, Mekhatronika, Avtomatizatsiya, Upravlenie, 2015, vol. 16, no. 8, pp. 515—522.
DOI: 10.17587/mau.16.515-522

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