Modeling and Control of a Shape Memory Alloy Actuator

In this paper, we present a complete mathematical model of a spring-biased shape memory alloy (SMA) wire actuator driven by an electric current. The working of the SMA actuator is based on diverse physical phenomena, viz., heat convection, phase transformation, stress-strain variations and electrical resistance variation accompanying the phase transformation. The proposed model decomposes the operation of the actuator into these phenomena and comprises modules which represent each of these phenomena independently. The phase transformation involves significant temperature hysteresis. We model this hysteresis by a differential hysteresis model, which can conveniently represent both major and minor loops. We also propose a differential inverse of the hysteresis model, whereby, we obtain the differential inverse of the complete SMA actuator model. We propose a feedback control scheme with inverse compensation based on the inverse SMA model. Simulation results are presented, which demonstrate the effectiveness of the proposed control technique