Ill-conditioned dynamic hysteresis compensation for a low-frequency magnetostrictive vibration shaker

We report an adaptive feedforward controller to address the ill-conditioned dynamic hysteresis on a custom-developed magnetostrictive vibration shaker. The vibration shaker works within low-frequency bandwidth. Magnetostrictive-induced hysteresis is a main issue that affects excitation waveform replication. Generally, the shape of dynamic hysteresis loop depends on the amplitude and frequency of input current. Many studies, e.g., Prandtl–Ishlinskii (PI)-based feedforward control approach, are conducted to address nonlinear dynamics in the hysteresis. Particularly, the dynamic hysteresis loop characterizes non-positive gradient (i.e., ill condition) when the frequency of input current is increasing. Under the ill condition, traditional PI-based feedforward control is ineffective. In this paper, we investigate this phenomenon according to a few experiments. Then, a novel static hysteresis and dynamics hybrid compensator is presented to deal with the ill-conditioned dynamic hysteresis issue. The dynamic compensator is a finite-impulse-response-based model whose coefficients are updated by the modified filtered-x normalized least mean square (MFxNLMS) algorithm. The static hysteresis compensator is constructed with the polynomial-modified PI (PMPI) model. The parameters of PMPI model are acquired by particle swarm optimization. Two simulations are conducted to show (1) the convergence of the MFxNLMS algorithm; (2) the efficacy of proposed model to describe the ill-conditioned dynamic hysteresis. Furthermore, the experimental device is constructed and a couple of experiments are implemented. The experimental results show that, with the proposed controller, the magnetostrictive vibration shaker can replicate both narrowband and wideband waveforms accurately. Moreover, it is robust to load variation.