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In this paper we introduce a new approach to the sliding mode control design based on orthogonal models. First, we discuss the sliding mode control based on a model given in controllable canonical form. Then, we design almost orthogonal filters based on almost orthogonal polynomials of M¨untz-Legendre type. The advantage of the almost orthogonal filters is that they can be used for the modelling and analysis of systems with nonlinearities and imperfections. Herein, we use a designed filter to obtain several linearized models of an unknown system in different working areas. For each of these linearized models, corresponding sliding mode controller is designed and the switching between controls laws depends only on input signal. The experimental results and comparative analysis with relay control, already installed in laboratory equipment, verify the efficiency and excellent performance of such a control in the case of anti-lock braking system.

A NEW APPROACH TO THE SLIDING MODE CONTROL DESIGN: ANTI–LOCK BRAKING SYSTEM AS A CASE STUDY