Research on Chaotic Threshold of Giant Magnetostrictive Actuator With Fractional-Order Time-Delay Feedback - Xin Fu; Hongbo Yan; Chaohui Ai; Jianxin Wang (Shock and Vibration)
To reduce the giant magnetostrictive actuator’s (GMA) irregular vibration caused by system parameter changes, we innovatively apply fractional-order time-delay feedback to control bifurcation and chaos in the GMA’s nonlinear dynamics. The GMA dynamic equation with feedback control is established using the quadratic domain rotation model, the Jiles–Atherton model, and the structural dynamic. First, the concepts of equivalent stiffness and damping are introduced to deal with the feedback control term. Second, using the Melnikov method, the threshold condition for the controlled system to enter the Smale horseshoe chaos is established, and a numerical solution verifies the accuracy of the analytical solution. Finally, the influence of excitation frequency, damping coefficient, and control parameters on the chaotic threshold of the system is studied by numerical simulation. The results show that complex motion patterns, including jump, period-doubling bifurcation, and chaos behavior, will occur when the system parameters are improperly chosen. After introducing the controller, the bifurcation and chaos phenomena of the system can be effectively eliminated. By adequately adjusting the feedback parameters, the system’s vibration displacement response can be adjusted from chaotic to stable periodic motion.