Force tracking control of a flexible gripper featuring shape memory alloy actuators

Abstract

This paper presents a robust force tracking control of a flexible gripper using shape memory alloy (SMA) actuators. The governing equation of a partial differential form for the flexible gripper is derived by employing Hamilton’s principle, and a state-space control model is obtained by retaining a finite number of vibration modes. In the formulation of the control model, time constant of the SMA actuator is treated as uncertain parameter. This is adopted due to the fact that the SMA actuator has different time constant at the heating and cooling stage, respectively. The H ∞-controller is then synthesized by treating the uncertain parameter as coprime factor. The specifications of stability margin and steady state error to achieve robust performance are imposed, and the first-order reference model is augmented to avoid excessive overshoot. After analyzing the robust stability of the system using the singular value plot, the controller is experimentally realized and force tracking control responses for step and sinusoidal force trajectories are presented in time domain to demonstrate the effectiveness of the proposed methodology.