Adaptive fuzzy sliding mode control for linear time-varying uncertain systems

In this paper, we propose an adaptive fuzzy sliding mode control scheme (AFSCS) for continuous-time multiple-input-multiple-output (MIMO) linear time-varying uncertain systems. The AFSCS consists of a fuzzy controller with adaptive mechanism to reconstruct the system states using the tracking error and to make the state error reach the equilibrium point in finite time period quickly. The sliding surface is first employed to represent the state error to reach the equilibrium point in a finite time period. Then, an adaptive fuzzy controller using sliding mode is developed to achieve the control performance and the state tracking errors performance quickly. The reaching mode of the uncertain system using the proposed adaptive fuzzy sliding mode controller is guaranteed. Moreover, the chattering around the sliding surface for the proposed adaptive fuzzy sliding mode control can be reduced. A 2-dof parallel robot system will be used to verify the effectiveness of the proposed method.