Direct PID tuning for systems with hysteresis and its application to shape memory alloy actuators

Shape memory alloy (SMA) actuators intrinsically have hysteresis, which often leads to inferior control performance when using simple control methods such as proportional-integral-derivative (PID) control. To overcome this difficulty, this paper proposes a simple controller parameter tuning method that can compensate for hysteresis. The proposed method is based on the so-called fictitious reference iterative tuning (FRIT) technique which can easily tune controller parameters using a one-shot closed-loop experiment. In the proposed framework, a simple hysteresis model is introduced to a control system, and its inverse is used as a hysteresis compensator. Since the hysteresis model is characterized with only three parameters, the related computational burden is moderate in the parameter tuning process. Also, the proposed FRIT method needs an only one-shot experiment as in the standard FRIT one, which implies that the feature of FRIT is well-maintained. In the optimization process, the so-called covariance matrix adaptation evolution strategy (CMA-ES) is used for simultaneously searching hysteresis parameters as well as controller parameters. CMA-ES is a kind of stochastic multi-point search techniques and is effective for nondifferentiable and nonconvex optimization problems. The proposed FRIT method is applied to an experimental control system that comprises an SMA actuator, and its effectiveness is verified.