Iterative Learning and Fractional Order PID Hybrid Control for a Piezoelectric Micro-Positioning Platform

Abstract

The piezoelectric micro-positioning platform(PMP) has advantages in high displacement resolution and fast response, however, the serious hysteresis nonlinearity in the PMP restricts its positioning accuracy. This paper presents a discretization of Krasnosel'skii-Pokrovskii model to describe the hysteresis nonlinearity of the PMP. Then, the density function is identified online by the adaptive linear neural network. To compensate the intrinsic hysteresis nonlinearity in the PMP, a feedforward compensation control method is implemented by an innovative iterative learning control algorithm. Moreover, a hybrid control method based on iterative learning and fractional order PID control is proposed to further improve the control accuracy. A series of comparative experiments are carried out to validate the feasibility and effectiveness of the proposed control method.INDEX TERMS Piezoelectric micro-positioning platform, hysteresis nonlinearity, iterative learning control, fractional order PID.

A Vision-Based Micro-Manipulation System

“…It introduces a Krasnosel'skii-Pokrovskii (KP) model to describe the hysteresis behavior, and involves an adaptive linear neural network for real-time model identification. To compensate for hysteresis, the paper presents a feed-forward control method and a hybrid approach combining iterative learning control and fractional order Proportional-Integral-Derivative (PID) control, which is validated through experiments and significantly enhances control accuracy [15].…”

A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller

“…To solve this problem, various optimization strategies have been applied, including particle swarm optimization [2]- [4], genetic algorithms [5], [6], differential evolution methods [5], chaotic firefly algorithms [7], extensions of classical tuning methods for PID controllers [8], [9], and other techniques [10]- [14]. Several implementations in control loops of various processes show that FOPID controllers can be effectively used, and their control performances can be much better than classical PID [14]- [23]. Additionally, the FOPID controllers can also apply fractional variable-order elements.…”

Mathematical modelling and theoretical research of micropositioning system

“…Simulation of systems behaviour under various operational conditions saves time required for their development and allows implementing modern control methods. To achieve the highest possible positioning accuracy of the system, machine learning can be used [8][9][10][11]. Many artificial intelligence developers agree that it is easier to train a system by showing its input and output behaviour by predicting the desired response to all implied inputs than programming them manually [12] since mathematically obtained results allow to determine system weaknesses and chose suitable control and positioning errors compensation methods [13,14].…”