The purpose of this study is to design and control a thick shape memory alloys (SMA) actuator to achieve fast position control with two connected SMA wires. In the past, research had focused on position and force control of thin SMA wires, because they can be cooled fast in air and as it is easy to obtain fast response speeds for SMA actuators in this manner. However, the cooling time increases for thick SMA wires, making it difficult to obtain fast position responses. Phase resistance feedback control (PRFC) minimizes cooling time by shortening the long latency time of thick SMA wires. Compared with binary control, experimental results here show that a rate increase of 18% is achieved using this new method. A new displacement-resistance model which normalizes both resistance and displacement is used to estimate the total output displacement of this new SMA actuator.