A Novel Rate-Dependent Hysteresis Framework for Piezoelectric Actuators: Modeling, Identification, and Control

Piezoelectric actuators (PEAs) offer significant advantages in resolution, response velocity, and immunity to magnetic interference, making them crucial for high-precision applications such as nanopositioning, semiconductor manufacturing, and space exploration. However, their performance is affected by hysteresis nonlinearity. To overcome the limitations of conventional models in capturing rate-dependent hysteresis, we propose a novel model (called nBW) that incorporates rate-dependent terms into both the output and evolution equations. This model adapts to frequency changes, providing a more accurate representation of hysteresis across a wide frequency range. We introduce an efficient nonlinear least squares technique for parameter identification, which outperforms traditional methods such as genetic algorithms (GAs) and particle swarm optimization (PSO) in terms of both accuracy and efficiency. At 10, 50, and 100 Hz, the nBW's relative error norms are 0.95%, 1.21%, and 2.12%, respectively, compared with 2.28%, 4.76%, and 7.07% for the classical Bouc–Wen model. The nBW also demonstrates robust performance under composite-frequency inputs, with a 0.99% relative error. A hybrid control strategy, combining inverse model-based feedforward and PI feedback control, effectively minimizes tracking errors, enhancing PEAs’ precision under dynamic conditions. These results highlight the superior accuracy and control performance of the nBW. Future work will explore its extension to other smart materials.