Fractional order time-delayed feedback control of hysteresis dynamics in giant magnetostrictive actuators

In order to effectively control the nonlinear dynamic response of the giant magnetostrictive actuator, a design scheme based on fractional-order time-delayed feedback control is proposed in this study. The J-A hysteresis nonlinear mathematical model of the GMA system is established considering the geometric nonlinearity introduced by the precompressed disc spring mechanism. On this basis, the amplitude-frequency response equation of the main resonance of the system under the fractional-order time-delayed feedback control strategy is solved using the averaging method, and the stability conditions of the system are determined based on the Routh-Hurwitz criterion. The influence of key structural parameters on the amplitude-frequency response characteristics of the GMA system is investigated by numerical simulation, and the laws of the main resonance peak and system stability with each time-delayed feedback parameter are obtained. Further, the influence of the excitation amplitude on the chaotic motion of the system is investigated by bifurcation diagram and Lyapunov exponential diagram. Finally, the chaotic motion of the system is suppressed by adjusting the time-delayed feedback gain and fractional order. The results show that the time-delayed feedback gain and fractional order have significant effects on suppressing the main resonance peak and the unstable region of the system, and can adjust the system response from chaotic motion to stable periodic motion, thus improving the stability of the system.