Optimal position control of shape memory alloys actuator with nonlinear behavior by using states dependent Riccati equation (SDRE)

Several studies have been conducted to accurately control the deformation of Shape Memory Alloys (SMAs) as an actuator, however, due to the non-linear relationship between the change of mechanical structure, including stress and strain, they have often been associated with a challenge. In the current study, a wire made of intelligent memory alloy (Nitinol) is used as an actuator of one degree-of-freedom mechanism. In order to observe the operation of the wire under electrical stimuli, a laboratory set-up is implemented. Our main goal is to accurately control the position of this nonlinear system with high precision by using optimal control. So, the nonlinear system equations are extracted and sorted into state-dependent matrices and the State-Dependent Riccati Equation (SDRE) is used to find the optimal control value. To verify the experiment three inputs including multiple steps, a low-frequency sine wave and a high-frequency sine wave, are applied to the system. The results, show the good performance of the controller in sustainability, fast response, and tracking of the desired position with low overshoot.