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. Since 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. Finally, the stability of the overall system is verified by the Lyapunov theory. Simulations and experiments of the velocity control of a four-bar-linkage system are presented to verify the usefulness of the proposed control