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This brief describes a new model for shape memory alloy (SMA) actuators based on the physics of the process and develops control strategies using the model. The model consists of three equations - the temperature dynamics described by Joules heating-convectional cooling, the mole fraction distribution with temperature given by statistics to describe a two state system, and a constitutive equation relating the changes in temperature and mole fraction to the stress and strain induced in the SMA. This model is used to develop two control schemes for controlling the strain in an SMA actuator. The first control scheme describes a gain-scheduled proportional-integral (PI) controller, the gains of which are obtained by means of linear quadratic regulator (LQR) optimization. The second control scheme is an Hinfin loop-shaping controller using normalized coprime stabilization which ensures robust stability by minimizing the effect of unmodeled dynamics at high frequencies. Simulation and experimental results show fast and accurate control of the strain in the SMA actuator for both control schemes.