Shape Memory Alloy (SMA) driven actuation devices offer the potential for dramatic improvements in flight vehicle performance. Such actuators are ideally suited for the light-weight, low-bandwidth, compact size requirements associated with small changes in the vehicle geometry to enhance performance. Over the last 10+ years SMA-based actuation concepts have been considered for use on commercial aircraft, military aircraft, rotorcraft, and spacecraft. Many of these actuation concepts are driven by twisting SMA tubes which are under variable shear loading. This work extends previous quasi-static modeling work to provide a time-domain coupled thermo-mechanical model for SMA torque tubes. The model includes states associated with the material and states associated with peripheral dynamic systems, such as the heater. Approaches for obtaining the key parameters required by the model directly from experimental data are then described. Steps for developing controllers using these models are then reviewed including linearization and linear quadratic regulator (LQR) based control synthesis. The controller is implemented and tested in closed-loop position tracking experiments. These are completed in a lab setting and the results indicate a robust (in terms of gain and phase margin) and high-performance (in terms of settling time) tracking controller. The complete sequence described in this work illustrates the potential of model based optimal control applied to Shape Memory Alloy torque tubes.