A fitness function for parameters identification of Bouc-Wen hysteresis model for piezoelectric actuators

Piezoelectric actuators (PA) are widely used in micro and nano positioning systems owing to their high stiffness, fast response, compact structure, and high precision. However, nonlinear behaviors of PAs, due to inherited hysteresis, tend to deteriorate their tracking performance. Therefore, many research works have been devoted to the modeling the hysteresis behavior in PAs. A number of nonlinear models were proposed in the literature such as Bouc-Wen (BW). The performance of identification of BW parameters is highly affected by the type of optimization algorithm and the adopted fitness function. One widely used fitness function is the mean square error (MSE). This choice often results in a relatively high error at the peaks and valleys of the displacement waveform. In this paper, a new optimization fitness function, based on the error in the signal peaks and valleys, is proposed. This fitness function is used to estimate the BW model parameters using the particle swarm optimization (PSO) technique. Experimental and simulation results show that this choice of fitness function improved the performance by up to 90% at the peaks and valleys.