Study on Improved PI Model and Hysteresis Nonlinear of MSMA Sensor

Magnetically controlled shape memory alloy（MSMA） has significant hysteresis nonlinearity, which can affect the accuracy of MSMA sensor models. To establish an accurate MSMA sensor model and study its hysteresis nonlinearity, an improved Prandtl Ishlinskii model（PI model） is used to establish an input output model for the MSMA sensor. When modeling, improvements are made to the threshold, play operator, and density function of the traditional PI model to make the model output correlated with the frequency and amplitude of the input signal. Then, an improved particle swarm optimization algorithm is used to identify the unknown parameters in the MSMA sensor model; by introducing inertia weight adaptive wake-up probability, the convergence speed of the algorithm is accelerated, and a periodic escape operator is introduced to enhance the global search ability of the algorithm and avoid falling into local optima. Finally, the accuracy of the model is verified by the MSMA sensor experimental platform and the hysteresis nonlinearity of the MSMA sensor is explored. The experimental results show that compared with the traditional PI model, the improved PI model can dynamically describe the input-output relationship and the lag nonlinearity of the MSMA sensor more accurately. The larger the frequency or amplitude of the input sine force signal, the greater the peak to peak value of the induced voltage output by MSMA sensors, and the more obvious the hysteresis phenomenon between the input and output of MSMA sensors. This study lays a theoretical foundation for modeling sensors based on MSMA hysteresis nonlinearity.