Model-Free Adaptive Sliding Mode Control of Parallel Platform Actuated by Shape Memory Alloys

This paper investigates the input coupling problem in a shape memory alloy (SMA) actuated parallel platform characterized by fully unknown nonlinear dynamics. In such a platform, the displacement of one actuator simultaneously affects the others owing to inherent coupling effects. The convergence of coupling phenomena and the nonlinear characteristics of SMA actuators renders bidirectional swing control exceptionally challenging, particularly under conditions of unknown dynamics. To address these limitations, a model-free adaptive sliding mode control (MFA-SMC) method is proposed to improve control accuracy for complex platform motions while avoiding the intricate modeling process typically required for SMA-actuated parallel platforms. Leveraging model-free adaptive control (MFAC) theory, a multiple-input, multiple-output (MIMO) dynamic linearized mathematical model of the parallel platform is developed using real-time input and output system data. Subsequently, a sliding mode controller is formulated based on this dynamic model. A rigorous theoretical analysis demonstrates that the proposed model-free adaptive sliding mode controller can effectively and stably manage the SMA-actuated parallel platform, with its tracking error being uniformly ultimately bounded (UUB). Lastly, experiments are performed on the developed SMA-actuated parallel platform. The results indicate that the proposed model-free controller is both feasible and effective, enabling precise control of the system to achieve complex bidirectional swing motion.