Stress-based sliding mode control of a rotary SMA-actuated manipulator

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Abstract
This paper presents a sliding mode 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 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 current experimental setup allows for the measurement of only one state variable which is the angular position of the arm. This 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, adding to complexity of the control of the position of the arm for certain angular positions. To overcome thais problem a sliding mode controller is designed to calculate the desired stress of the wire based on the desired angular position of the arm. 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. A feedback controller maintains this desired stress by regulating the input voltage to the wire. The stabilization and tracking performance of this controller is presented and compared with a PID controller.

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