Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator

Piezoelectric actuators (PEA) are extensively utilized in high-precision micro-measurement and operation. However, owing to the rate-dependent nature of its hysteresis, its accuracy in certain applications would suffer significantly, and the system would become unstable. To address this issue, a new method for developing a feedback control system that can reduce the rate-dependent impacts of PEA on the positioning system is provided using PEA as the research object. This strategy is based on the fractional order Hammerstein model (FO-Hammerstein). For the fractional order model, a novel fractional order integral sliding mode surface is proposed here that can accurately delineate the dynamic characteristics of PEA. This sliding mode surface is composed of a fractional polynomial and an integral term, which can better minimize static errors and monitor reference signals, and it is built using a fractional neural sliding mode control (BP-FSMC) method. The control technique can be extensively utilized in various systems, such as FO-Hammerstein and those described by the fractional transfer function. The research introduces a neural network and an artificial bee colony algorithm (DeC-ABC) that are used to alter the system's parameters. The study's findings reveal that a system with high resilience can follow the signals from both composite and single input sources. Compared with the fractional order sliding mode control approach on the basis of extended state observer, the fractional order sliding mode control method based on single parameter adaptive law and the proportional integral sliding mode control method on the basis of feedforward compensation, this method has a quicker response time and lower tracking error.