Model Predictive Control for an SMA Actuator Based on an SGPI Model

Shape memory alloy (SMA) actuators possess unique advantages for aerospace applications, including significant deformation, a high work-to-weight ratio, and structural simplicity. However, SMA actuators exhibit inherently strongly saturated and asymmetric hysteresis characteristics, which cause significant hysteresis in the output response. These hysteresis nonlinearities, compounded by process and measurement noise, severely degrade control precision. To overcome these issues, this study proposes a Smoothed Generalized Prandtl–Ishlinskii (SGPI) model to characterize such hysteresis behavior. Based on the SGPI model, we developed a state-space representation for the SMA actuator. Furthermore, an Extended Kalman Filter (EKF) is employed to estimate unmeasurable internal hysteresis states, and these estimates are subsequently utilized as input states for Model Predictive Control (MPC). The simulation results demonstrate that the proposed EKF-MPC approach achieves both rapid dynamic response and high-precision tracking control, effectively compensating for hysteresis nonlinearity while rejecting noise disturbances.