Rate-dependent Modeling and Adaptive Inverse Control of Giant Magnetostrictive Actuators

A new adaptive inverse control strategy based on Hammerstein model is proposed to combat the rate-dependent hysteresis nonlinearity in Giant Magnetostrictive Actuators (GMA). In the Hammerstein model, a Modified Prandtl-Ishlinskii (MPI) model is used to represent the static hysteresis nonlinear part and an Autoregressive Model with Exogenous Input (ARX) is used to represent the linear dynamic part. The identified model can describe the rate-dependent hysteresis nonlinearity of GMA in the frequency range of 1-100Hz. The inverse of the Hammerstein model constructed off-line is taken as the initial controller, and the parameters of the inverse model are updated with Least-Mean-Square (LMS) algorithm to make the inverse model asymptotically converge to the real inverse of the GMA, thus cancel out the rate-dependent hysteresis nonlinearity. Trajectory tracking control results show that the proposed controller has good real-time performance, and it resulted in smaller steady-state errors compared with the compound control strategy based on feed-forward inverse compensation and PID feed-back.