Adaptive Neural Indirect Inverse Control of Fractional-Order Rate-Dependent Hysteretic Nonlinear Systems and Its Application

Focusing on the high-precision motion control of nonlinear time-delay systems actuated by smart-material based actuators and motivated by flourishing development of fractional-order control theory, an adaptive fractional-order backstepping indirect inverse motion control (AFBIIMC) scheme is proposed to mitigate the rate-dependent hysteresis with the following features: 1) a new asymmetric rate-dependent hysteresis model, which can accurately depict the hysteresis in different smart-material based actuators such as magnetostrictive and dielectric elastomer actuators (DEA), is developed with the help of classical Prandtl–Ishlinskii hysteric model. 2) A novel hysteresis indirect inverse control algorithms of fractional-order hysteric nonlinear systems is designed, where the very difficult or even impossible work of construction of rate-dependent hysteresis direct inverse model are not required any more. Then, the rate-dependent hysteresis nonlinearity is effectively mitigated and the high-precision motion control performance is achieved. 3) The DEA motion platform is constructed, then, a new fractional-order model of the motion platform is proposed and motion control experiments are implemented to show the effectiveness of the proposed control scheme.