Frequency-Dependent Sliding-Mode Control of Galfenol-Driven Unimorph Actuator Based on Finite-Element Model

A dynamic model is presented by coupling the structural dynamics of a Galfenol-driven unimorph beam with the magnetostriction generated by the active layer. Weak form equations are obtained by employing the virtual work principle, and finite-element representation of the model is implemented through a Galerkin discretization. In order to facilitate the design of the controller, a linearized constitutive law is used to describe the magnetostriction of Galfenol. A finite-dimensional sliding-mode controller is developed which accounts for the frequency-dependent deviations of structural damping and the piezomagnetic constant. A nonlinear switch controller, combined with the equivalent controller, is developed to guarantee Lyapunov stability at different frequencies, without changing the initial parameters of the controller. Since the model is finite-dimensional, model parameters are nonlinearly coupled in the state and output matrices in the state-space equation. A genetic algorithm is employed to solve the nonlinear estimation problem. Experimental results show that the model parameters are almost constant below 220 Hz. The model parameters are frequency dependent above 220 Hz. It is also found that significant performance enhancements are achieved by the proposed control relative to conventional Proportional-Integral (PI) control. The system remains stable for frequencies up to 400 Hz.