A Non-linear Optimal Control Design using Narrowband Perturbation Feedback for Magnetostrictive Actuators

Abstract

Non-linear optimal and narrowband feedback control designs are developed and experimentally implemented on a magnetostrictive Terfenol-D actuator. The non-linear optimal control design incorporates a non-linear and hysteretic ferromagnetic homogenized energy model within an optimal control formulation to reduce displacement tracking errors and increase bandwidth. Improvements in robustness in the steady-state regime are achieved by utilizing narrowband feedback. A narrowband filter is implemented by treating the nonlinear and hysteretic magnetostrictive constitutive behavior as higher-order harmonic disturbances which are mitigated by tuning the narrowband filter to penalize these harmonics for displacement tracking control problems. The control designs are then combined into a hybrid optimal controller with perturbation narrowband feedback. Both transient and steady-state tracking control is assessed to illustrate performance attributes in different operating regimes. Narrowband perturbation feedback is shown to mitigate errors in the steady-state operating regime, while non-linear optimal control provides enhanced tracking control in the transient regime. The hybrid control design is relevant to a broad number of smart material actuators that exhibit non-linear and hysteretic field-coupled constitutive behavior.