Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor

Sarah Makarem,Burhanettin Koc,Bülent Delibas

doi:10.3390/act10070148

Abstract

Ultrasonic motors employ resonance to amplify the vibrations of piezoelectric actuator, offering precise positioning and relatively long travel distances and making them ideal for robotic, optical, metrology and medical applications. As operating in resonance and force transfer through friction lead to nonlinear characteristics like creep and hysteresis, it is difficult to apply model-based control, so data-driven control offers a good alternative. Data-driven techniques are used here for iterative feedback tuning of a proportional integral derivative (PID) controller parameters and comparing between different motor driving techniques, single source and dual source dual frequency (DSDF). The controller and stage system used are both produced by the company Physik Instrumente GmbH, where a PID controller is tuned with the help of four search methods: grid search, Luus–Jaakola method, genetic algorithm, and a new hybrid method developed that combines elements of grid search and Luus–Jaakola method. The latter method was found to be quick to converge and produced consistent result, similar to the Luus–Jaakola method. Genetic Algorithm was much slower and produced sub optimal results. The grid search has also proven the DSDF driving method to be robust, less parameter dependent, and produces far less integral position error than the single source driving method.

Highlights

Ultrasonic motors rely on the vibration of piezoelectric actuator element at resonant frequency
The number of candidate solutions in each iteration remains the same throughout the process, but the search space is narrowed down and more thoroughly inspected for the optimal solution as iterations progress [27]. Another method used for tuning was genetic algorithm
As a starting point to the optimization problem presented, a grid search for the optimal among the evolutionary methods for parameter optimization and is a method for the proportional integral derivative (PID) parameters was run on the U-651 rotation stage

Summary

Introduction

Ultrasonic motors rely on the vibration of piezoelectric actuator element at resonant frequency. The geometry of the actuator is adapted to generate the two modes at the same operating frequency, and different regions of the actuator are selectively driven with one or more driving source [3,4] These motors are known to exhibit nonlinear dynamic characteristics due to the nature of force transfer through friction, such as hysteresis and creep [5]. To minimize these nonlinearities, friction models can be built to model and linearize the behavior of piezoelectric element [6,7,8]

Methods

Results

Conclusion