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Shape memory alloy (SMA) actuators have a number of appealing features, such as their low weight or their high force-to-weight ratio, that make them a potential alternative to traditional actuation technologies in fields such as space applications, surgical devices or wearable robotics. In this paper, a type of bilinear controller consisting of a conventional PID controller cascaded with a bilinear compensator, known as BPID, is proposed. Bilinear controllers are a subset of nonlinear controllers, which is why the BPID may be a promising alternative to control the position of a SMA actuator. Nonlinear control techniques are commonly applied to control SMA actuators, because of their nonlinear behavior caused by thermal hysteresis. The BPID controller is simpler and easier to implement than other nonlinear control strategies, which makes it a very appealing candidate to control SMA actuators. The performance of the BPID controller has been compared with other two controllers, a conventional PID and a commuted feed-forward PIPD, controlling a real SMA actuator. To this end, a set of five tests has been defined, in which the controlled actuator must follow a series of position references. From these tests, the position and error of the actuator have been plotted, and a series of metrics has been computed to have quantitative measurements of the performance of the three controllers. It is shown that, in most of the experiments, the BPID has a better performance than the other two tested controllers, especially tracking step references. However, the power consumption is slightly higher when the actuator is controlled with this strategy, although-the difference is minimal. Also, the BPID imposes greater energy variations to the SMA actuator, which might affect its service life. Overall, the BPID controller has proved to be a viable alternative to control SMA actuators.