A stable adaptive fuzzy sliding-mode control for affine nonlinear systems with application to four-bar linkage systems

In this paper, a stable adaptive fuzzy sliding-mode control for affine highly nonlinear systems is developed. First, the external part of a transformed system via a feedback linearizing control evolves a linear dynamic system with uncertainties. A reference model with the desired amplitude and phase properties is given to obtain an error model. Because the uncertainties are assumed to be large, a fuzzy model is employed to model these uncertainties. A learning law with e-modification for the weight of a fuzzy model is considered to ensure the boundedness of learning weight without the requirement of persistent excitation condition. Then, an equivalent control using the known part of system dynamics and the learning fuzzy model is designed to achieve the desired control behavior. Furthermore, the uncertainties caused by the approximation of fuzzy model and the error of learning weight are tackled by a switching control. Under some mild conditions, the stability of the internal part of the transformed system is guaranteed. Finally, the stability of the overall system is verified by the Lyapunov theory so that the ultimately bounded tracking is accomplished. Simulations and experiments of velocity control of four-bar-linkage system are also presented to verify the usefulness of the proposed control.