Koopman Operator Linearization for Piezoceramic Hysteresis
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Solution Overview
Problem
Hysteresis nonlinearity in piezoelectric actuators significantly reduces positioning precision and stability in micro-displacement systems, and existing hysteresis modeling and control methods face challenges in accuracy, adaptability, and real-time performance.
Innovation Solution
A linearization identification method for hysteresis models of piezoceramics based on Koopman operators, involving building a hysteresis model structure, determining parameters, obtaining simulation data, performing deep learning training, and determining a linearization model using Koopman operators to achieve linear control and improve positioning precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional inverse model compensation control is used to eliminate hysteresis nonlinearity, then positioning precision is improved, but the solution of inverse model is difficult and calculation is complicated
Solution Approach 1:
The patent replaces the complex mechanical calculation process of traditional inverse model solution with a neural network-based computational system. The neural network is trained offline to learn the inverse hysteresis characteristics, and during operation, it directly provides compensation signals without requiring complex real-time mathematical inversion, thus substituting difficult analytical calculations with efficient numerical computation.
Solution Approach 2:
The patent performs preliminary training of the neural network offline using measured hysteresis data to establish the inverse compensation model before actual positioning operations. This preliminary action allows the system to store pre-computed compensation characteristics, eliminating the need for complex real-time calculations during positioning and enabling fast, accurate hysteresis compensation.
2Manufacturing precision
If inverse model compensation control is applied, then hysteresis influence is eliminated, but the sensitivity to changes of input signals, loads or working conditions is high and adaptability is lacked
Solution Approach 1:
The patent implements a dynamic neural network model that can adapt to changing operating conditions. The network is designed to learn from measured data under various loads and working conditions, and its structure allows it to dynamically adjust its compensation output based on the current state, making the system adaptable rather than static.
Solution Approach 2:
The patent incorporates feedback mechanisms where the neural network model is trained using measured input-output data from the piezoelectric actuator system. This feedback loop allows the model to learn actual system behavior including variations due to different loads and working conditions, thereby improving adaptability. The measured data is used to refine and update the compensation model.
3Manufacturing precision
If inverse model compensation control is used, then hysteresis nonlinearity is compensated, but the real-time performance under high dynamic conditions is poor
Solution Approach 1:
The patent performs all complex model training and inverse characteristic learning in advance during an offline training phase. The neural network is pre-trained using extensive measured data to capture the hysteresis behavior across the full operating range. During real-time positioning operations, the pre-trained network simply evaluates the current input to provide compensation, which is computationally efficient and suitable for high dynamic conditions.
Solution Approach 2:
The patent substitutes complex real-time mathematical inversion operations with a pre-trained neural network evaluation process. The neural network, once trained offline, can rapidly compute compensation signals during high-speed positioning operations without requiring the computationally intensive iterative solutions that traditional inverse models demand, thus achieving excellent real-time performance.
4Device complexity
If traditional linearization methods are used, then hysteresis model identification is simplified, but a great amount of simplification is applied which influences positioning precision
Solution Approach 1:
The patent replaces traditional mathematical linearization methods with a neural network-based identification approach. Instead of applying various simplification assumptions to linearize the hysteresis model analytically, the neural network directly learns the nonlinear hysteresis characteristics from measured data, achieving accurate model identification without simplification while maintaining computational efficiency.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method enables accurate identification of hysteresis nonlinear models in a linear framework, reducing errors from traditional linearization methods and ensuring higher positioning precision by avoiding complex derivation and approximation, thus enhancing the stability and adaptability of micro-displacement systems.
Implementation Method 1
based on the inverse piezoelectric effect, a piezoelectric actuator converts electric energy into elastic potential energy, and then converts the elastic potential energy into required mechanical energy
Data Source
AI summary
The disclosure provides a linearization identification method for a hysteresis model of piezoceramics based on Koopman operators, and belongs to the field of precision positioning. In order to solve the problem of hysteresis of a piezoelectric actuator in practical application, the disclosure further provides the linearization identification method for the hysteresis model of the piezoceramics based on Koopman operators. The method of the disclosure includes: Step I, building a structure of the hysteresis model of the piezoceramics; Step II, determining parameters of the hysteresis model of the piezoceramics; Step III, obtaining a great amount of simulation data by using simulation software; Step IV, performing deep learning training based on Koopman operators; and Step V, determining a linearization model for the hysteresis model of the piezoceramics based on Koopman operators. The disclosure is applicable to piezoelectric actuator control and precision positioning.