Sliding Mode Control of a Shape Memory Alloy Actuated Manipulator

This paper presents a two-part controller that uses a state variable estimator for control of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA) wire. A model for the SMA actuated manipulator is presented. The model includes nonlinear dynamics of the manipulator, a constitutive model of the Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. The estimator predicts the state vector at each time step and corrects its prediction based on the angular position measurements. The transformation temperatures of the SMA wire are stress dependent: this adds to complexity of the control of the position of the arm for certain angular positions. To overcome this problem a sliding mode controller is designed to calculate the desired stress of the wire based on the desired angular position of the arm. A classical feedback controller maintains this desired stress by regulating the input voltage to the SMA wire. The stress of the wire is a better set-point for the controller since the transformation temperatures and hence the Martensite fraction are functions of the wire’s stress. The stabilization and tracking performance of this two-part controller is presented and compared with a PID controller.