Abstract:

As an important component in the field of precision measurement, piezoelectric actuators boasts huge market potentials. The hysteresis nonlinearity of piezoelectric actuators is also a widely researched topic in the field of precision displacement control and piezoelectric driving technology. Currently, the modeling research on the hysteresis nonlinearity of piezoelectric actuators has been relatively well developed, but there are still some limitations. First, the physical model of hysteresis nonlinearity in piezoelectric actuators involves complex physical processes and exhibits uncertainties when applied to practical systems. Second, although the phenomenological models of hysteresis nonlinearity describe the hysteresis characteristics of piezoelectric actuators directly using input-output mapping relationships, which are more applicable, few of these models can simultaneously describe the asymmetry, rate dependency, and excitation generalization of hysteresis nonlinearity.

To address the low prediction accuracy and complexity of existing rate-dependent hysteresis models, this paper proposes a new modeling method for hysteresis nonlinearity in piezoelectric actuators. Based on the classical Duhem hysteresis model, hysteresis factors and inverse tangent functions are introduced to characterize the hysteresis behavior of piezoelectric actuators. To address the issue of low prediction accuracy, this paper analyzes the parameter identification characteristics of the Particle Swarm Optimization algorithm and proposes an improved Particle Swarm Optimization algorithm based on sine and cosine learning factors. This algorithm ensures population diversity while improving the global search capability, achieving precise identification of model parameters. To comprehensively evaluate the performance of the improved model and parameter identification method and ensure their effectiveness, experiments are conducted using ten sets of input signals with large amplitude and frequency spans, including sine, triangular, and mixed-frequency signals. The modeling errors of the proposed model are analyzed in detail.

The experimental results show the improved Particle Swarm Optimization algorithm effectively avoids the problem of getting trapped in local optima. The improved Duhem model accurately describes the rate-dependent hysteresis characteristics of piezoelectric actuators under high-frequency and high-amplitude excitations, and it exhibits good excitation generalization. This provides a new model choice and parameter identification method for the characterization of piezoelectric hysteresis nonlinearity and model parameter identification.