actuators Article Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor Sarah Makarem 1 , Bülent Delibas 2, * and Burhanettin Koc 2   Citation: Makarem, S.; Delibas, B.; Koc, B. Data-Driven Tuning of PID Controlled Piezoelectric Ultrasonic Motor. Actuators 2021, 10, 148. https://doi.org/10.3390/act10070148 Academic Editors: André Preumont, Haim Abramovich and Kainan Wang Received: 25 February 2021 Accepted: 22 June 2021 Published: 29 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Institute for Applied Research, Karlsruhe University of Applied Sciences, 76133 Karlsruhe, Germany; sara.zaky@eu4m.eu 2 Physik Instrumente (PI) GmbH & Co. KG, 76228 Karlsruhe, Germany; b.koc@pi.de * Correspondence: b.delibas@pi.de; Tel.: +49-72148462426 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. Keywords: ultrasonic motor; PID controller; data-driven control; iterative feedback tuning; genetic algorithm; Luus-Jaakola 1. Introduction Ultrasonic motors rely on the vibration of piezoelectric actuator element at resonant frequency. For optimal operation of an ultrasonic motor, an elliptical or oblique motion is needed [1,2], which is produced through mode coupling of different vibrational modes. One example of mode coupling is the L1B2 ultrasonic motor where mode coupling occurs between the first longitudinal and second bending mode. 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 also known to exhibit nonlinear dynamic characteristics due to the nature of force transfer through friction, such as hysteresis and creep [5]. To minimize these nonlinear- ities, friction models can be built to model and linearize the behavior of piezoelectric element [6–8]. Different control methods can also be used to deal with the nonlinear behavior, such as a simple pulsed control relay [9], a hybrid control method of a traditional PID controller and a rule-based scheme [10], a fuzzy cerebella model articulation control (FCMAC) al- gorithm [11], state windows with adaptive PID [12], and recurrent fuzzy neural network algorithms [13]. The nonlinear characteristics pose a difficulty to produce exact mathematical models for ultrasonic motors [14]. In addition, some nonlinear systems can change when control is applied, so the mathematical model of the open loop system would not be beneficial for Actuators 2021, 10, 148. https://doi.org/10.3390/act10070148 https://www.mdpi.com/journal/actuators