Active Disturbance Rejection Control for Piezoelectric Beam

ABSTRACT Piezoelectric beam dynamics are characterized by elastic properties, nonlinearities, uncertainties, and unknown distur-bances, thus making vibration suppression a challenging control problem.To meet this challenge, a novel active control methodhas been designed and rigorously tested on actual hardware without the requirement of extensive modeling. In this uniqueapproach, the piezoelectric beam dynamics, known or unknown, linear or nonlinear, and all external disturbances are treated intheir totality as an input disturbance which is subsequently estimated and canceled in real time, reducing the challenging problemtoaverymanageableone.Simulationandexperimentalresultsdemonstratetheeffectivenessofthispracticalcontrolmethod.Thefrequency domain characteristics of the proposed method are analyzed using Bode and describing function methods. KeyWords: Piezoelectric beam control, extended state observer, active disturbance rejection control. I. INTRODUCTION Piezoelectricmaterialsareverysuitableforsensingandactuating applications because of their smaller size, lightweight, and higher bandwidth capabilities compared to otherdevices [1] which has caused them to receive considerableattention in the academic field. Piezoelectric actuators havebecomestandardoptionsinpositioningapplicationswherethedisplacementsmustbesmallandhighlyaccurate[2].Further-more, the materials are valued for their ability to directlyconvertelectricaltomechanicalforcesatnanometerresolutionwithout mechanical transmissions, which might introduceassembly or operating tolerances greater than the desirednanometerprecision.Recently,thesematerialshavebeenusedforactuatingdevicesofmicro-electro-mechanicalsystems[3],amicromechanicaldiskresonatorfortheultrahighfrequency(UHF) band [4], a micro-actuator for hard disk drives [5] andservo valves [6], a biomedical sensing technology [7], and atactile sensor for Braille pattern recognition [8].The complex dynamics of piezoelectric actuators, inparticular, the well-known phenomena of hysteresis, creep,and nonlinear voltage dependence affect the dynamicresponseandmakethecontroldesignagreatchallenge[2].Inaddition, piezoelectric beam vibration dynamics are uncer-tain and vary based on different mounting methods. Thesedynamics are difficult to measure, and may shift withtemperature changes. Often, control approaches use cali-brated models of the actuator to adjust their linear propor-tional integral (PI) control gains. Research in the past twodecades has focused almost exclusively on improving thesecalibration models and continued to use linear PI [9], loopshaping [10], and/or H-Infinity (

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