Tracking control of an SMA-driven actuator with rate-dependent behavior using an inverse model of hysteresis

Hysteresis is a nonlinear phenomenon which may cause inaccuracies and delay in control applications. Shape memory alloys (SMAs) have an asymmetric saturated hysteresis. In addition, the excitation frequency changes the hysteresis behavior of SMA-driven systems and makes them challenging to track reference inputs at different frequencies. In this study, a rate-dependent Prandtl–Ishlinskii model coupled with a deadband function is proposed to characterize the asymmetric and saturated hysteresis behavior as well as its rate-dependency. Unknown parameters of the model are identified using genetic optimization algorithm in MATLAB Toolbox based on measured data. The identified model is validated to consider the excitation frequency effect with a different measured data set. The inverse model is also proposed as a compensator to mitigate hysteresis nonlinearity effects especially the frequency effect in tracking control. Although the proposed compensator cannot fully compensate for hysteresis effects, it can reduce the input–output hysteresis. The proposed rate-dependent compensator as a feedforward controller combined with a proportional–integral–derivative (PID) controller as a feedback mitigates hysteresis effects. The PID controller is used to improve the accuracy of compensated system and remove the steady-state error. Experimental results illustrate that the proposed controller has a great accuracy in tracking control to consider the excitation frequency effect as well as the asymmetric saturated hysteresis.