MATLAB Implementation of Hysteresis Models for Piezoelectric Ceramic Actuators

MATLAB implementation of hysteresis models for piezoelectric ceramic actuators involves modeling the dynamic characteristics of piezoelectric ceramic materials, particularly their hysteretic nonlinear behavior. Hysteresis is a common characteristic in piezoelectric actuators that can degrade control precision, making accurate modeling essential for both simulation and practical applications.

### Hysteresis Model Selection Common hysteresis models include Prandtl-Ishlinskii (PI) model, Preisach model, and Bouc-Wen model. The choice of appropriate model depends on specific application scenarios and computational complexity requirements. The Prandtl-Ishlinskii model is frequently used for real-time control due to its analytical expression and computational efficiency. In MATLAB implementation, each model requires different mathematical formulations - PI models typically use play/stop operators while Preisach models require more complex integral equations.

### MATLAB Implementation Approach Model Parameter Setting: First, determine hysteresis model parameters such as thresholds and weight functions, which can be obtained through experimental data fitting or theoretical derivation. MATLAB's Optimization Toolbox functions like `fmincon` or `lsqnonlin` can be used for parameter identification from measured input-output data. Input-Output Relationship Modeling: In MATLAB, define the hysteresis model's input-output mapping using functions. For example, implement piecewise linear approximations or integral operators to describe hysteresis loops. Key implementation steps include: - Creating function files for hysteresis operators (e.g., play operator for PI model) - Implementing recursive algorithms for real-time hysteresis calculation - Using matrix operations for efficient batch processing of input signals Simulation Verification: Apply typical input signals (such as sine waves or step signals) and observe whether the model output matches actual hysteresis characteristics. Adjust parameters using validation techniques like cross-validation to improve accuracy. MATLAB's plotting functions (`plot`, `subplot`) are essential for visualizing hysteresis loops and comparing with experimental data. Control Strategy Integration: If the model is used for closed-loop control, combine it with PID, fuzzy control, or adaptive algorithms for system simulation. Implement feedback compensation using inverse hysteresis models or adaptive controllers with online parameter update algorithms.

### Practical Recommendations Using MATLAB's Simulink tool enables more convenient construction of dynamic simulation models through graphical block diagrams. Combine experimental data with model parameter calibration using System Identification Toolbox functions to ensure simulation results closely match actual system behavior. For complex nonlinear hysteresis, consider hybrid modeling approaches such as neural network-assisted fitting using Deep Learning Toolbox, where neural networks can approximate the residual errors of conventional hysteresis models.

This modeling approach not only enhances the control precision of piezoelectric ceramic actuators but also provides a foundation for subsequent optimization control algorithms development. The implementation typically involves creating custom MATLAB classes or using existing toolboxes for nonlinear system identification and control design.