{'fraction_non_alphanumeric': 0.017333333333333333, 'fraction_numerical': 0.0, 'mean_word_length': 5.949074074074074, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
System Identification of Micro Piezoelectric Actuators via Rate-Dependent Prandtl-Ishlinskii Hysteresis Model Based on a Modified PSO Algorithm

As one of the high-precision actuating mechanisms, the piezoelectric actuators show the advantage of micro/nano stage maneuverability in facilitating the actuating performance of the mechanical systems. To improve the actuating accuracy, it is important to predict the output behavior accurately under the wide operating range, particularly, the change of the driving frequency. The modeling method using the rate-dependent Prandtl-Ishlinskii (RDPI) model is subsequently adopted, which can show the strong nonlinearities relating to the coupling effects between the internal hysteresis and the actuating frequency. Considering the electromechanical characteristics of piezoelectric actuators, a modified particle swarm optimization (MPSO) algorithm is introduced for identifying the RDPI model using the experimental measurement data. The developed MPSO algorithm can overcome the local optimizing limitation of the classical particle swarm optimization (CPSO) algorithm and guarantee the accuracy of predicting the output. The utility and superiority of the MPSO are verified by fitting the identified model to the actual output of the piezoelectric actuators in the micro range at different actuating frequencies. The comparisons with available models using MPSO, CPSO and LS algorithms have examined the validity of the proposed identification method.