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Giant magnetostrictive material (GMM) is gathering more interests due to its superior electromechanical properties. Though the strain of GMM is almost larger than PZT, it still needs to be amplified to match practical demands. A press-bend amplification based giant magnetostrictive actuator (GMA) is designed and the electromechanical system model is presented. The dynamic model consists of two subsystems, one is a rate-independent hysteretic model and the other is a linear transfer function. The Duhem hysteresis model was employed for analyzing of the hysteresis phenomena in the GMA. Based on thoroughly discussion of the properties of Duhem model, an adaptive variable structure controller was designed, which guaranteed global stability of the control system with certain accuracy of tracking desired trajectories. Both simulation and experiment results verified the effectiveness of the proposed electromechanical model and the applicable of the extracted control method.