Experimental investigation on rate-dependent vibration control of giant magnetostrictive actuators

The Hammerstein model was used to describe the rate-dependent hysteresis nonlinearity of giant magnetostrictive actuators (GMA). A modified Prandtl-Ishlinskii (MPI) model and the autoregressive model with exogenous input (ARX) represent respectively the static nonlinear part and the linear dynamic part of the Hammerstein model. Based on the proposed model, a new H_∞ robust control method was proposed for vibration control. The experimental results on a one degree-of-freedom vibration isolation platform with a GMA demonstrate that the H_∞ robust control method can attenuate 88%~92% of the vibration coming from the base in the frequency range of 1~100Hz in 1 vibration cycle, while the dual-filter-based adaptive filter x-LMS algorithm converges to the steady state in about 1 second, it can attenuate 90%~92% of the vibration in the frequency range of 40~100 Hz, but only 43%~74% in the frequency range of 10~30 Hz. Hence the proposed H_∞ robust vibration control method has a wider control band and a faster convergence rate compared to the dual-filter-based adaptive filter x-LMS algorithm, and does not require re-modeling the control channels under the excitation of different frequencies.