Nonlinear Dynamics of Giant Magnetostrictive Actuator Based on Fractional-Order Time-Lag Feedback Control

Investigating the nonlinear dynamic response of giant magnetostrictive actuator (GMA) is a valuable subject in the field of precision engineering. In order to effectively control the nonlinear dynamic response of a single-degree-of-freedom GMA, a fractional-order time-lag feedback controller is designed.

We model the nonlinear dynamics of the controlled GMA through the geometric nonlinearity imposed by the disc-spring mechanism and introduce the dimensionless for simplification. The flexible order adjustment capability of the Riemann–Liouville fractional-order derivatives is adopted to more accurately simulate the memory effects and nonlocal properties of the system. It effectively compensates its nonlinear dynamic behavior to optimize the system design and control. By using the averaging method, the amplitude–frequency response equations of the primary resonance in the system containing a fractional-order time-lag feedback control strategy are solved and the stability conditions are obtained.

Through detailed parametric studies, the effects of key structural parameters within the uncontrolled GMA and the adjustment of the parameters under fractional-order time-lag feedback control on the primary resonance response characteristics are researched. Moreover, the time-lag feedback gain and fractional-order are adjusted to effectively guide the system into the desired chaos, or to get the system out of the chaotic state and back to a stable periodic behavior.

The research results show that the unstable region of the primary resonance curve can be significantly reduced or eliminated by choosing suitable adjustment parameters, so as to better realize accurate and reliable motion control.