Abstract
A novel method-based fuzzy sliding mode (FSM) and linear matrix inequality (LMI) approach is presented in this paper to design a new robust adaptive fuzzy controller for a perturbed multi-input multi-output (MIMO) three-tank system with unknown dynamics and without chattering problem that is produced by the traditional sliding mode control. The proposed method uses the adaptive fuzzy system Takagi-Sugeno (TS) to approximate the unknown dynamics model of the three-tank system which is considered a very complicated system due to the high nonlinearity and cross coupling. Moreover, to overcome the external disturbance and the fuzzy approximation errors due to the modelling system, an auxiliary control term-based sliding mode is incorporated in the control law. Linear matrix inequality is used to determine the parameters of the dynamic compensator which is added to improve more performance of the closed-loop system in the sliding mode. The stability and robustness of the proposed method are proved, and the simulation is given to demonstrate the tracking performance of the proposed approach.
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