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Shape memory alloy (SMA) actuators have found a wide range of applications due to their unique properties such as high force, long stroke, small size, light weight, and silent operation, etc. However, their strong nonlinear properties make them a challenge to achieve accurate actuations. A simple control strategy is presented based on the idea of adjusting the SMA wire temperature as rapidly as possible. This strategy is simple, stable, and requires no hysteresis model or thermal model. The strategy is tested first on tracking displacement outputs, and effects of updating rate and input current on control accuracy are also discussed. It is then used for active shape control of a membrane structure model by adjusting its boundary tensions. Results indicate that under the developed control strategy, SMA wire actuators can offer very good accuracy in tracking displacement outputs and tension outputs. For the membrane structure shape control, the structure shape precision is improved greatly.