Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

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 (

Development and Optimization of a Nonlinear Multiparameter Human Operator Model

Abstract: A systematic method is proposed for the development, optimization, and comparison of human controller models. The method is suitable for any model, including multiparameter systems. The evaluation criteria for assessing model quality are based on three separate components: 1) the cost or criterion function, 2) the comparison between the input/output functions of the human operator and those of the model, and 3) characteristic values and functions of statistical signal theory (mean values, auto- and crosscorrelation functions, power spectral density functions, and histograms of time function data). A nonlinear multiparameter human operator model is presented which considers the complex input information rate in a single display. The nonlinear features of the model are brought about by a modified threshold element and a decision algorithm. A random search technique is used for parameter optimization. Different display content arrangements as well as various transfer functions of the controlled element are explained by different optimized parameter combinations. The comparison with the well-known quasi-linear describing function for the human operator shows a marked superiority of the nonlinear model.

Generation of periodic motions for underactuated mechanical system via second-order sliding-modes

Abstract: The generation of periodic motion for a simple underactuated manipulator, named Pendubot is made through second-order sliding-mode (SOSM) algorithms, particularly with twisting algorithm. This study is motivated by the fact that in the presence of an actuator, the transient process converge to a periodic solution. To obtain the desired amplitude and velocity of oscillations we use describing function and locus of a perturbed relay system approach to provide the corresponding gain parameters. Performance issue of the controller is illustrated in a simulation study.

Improving the accuracy of autotuning parameter estimates

Abstract: This paper discusses the inaccuracies involved in applying the describing function to obtaining plant information from autotuning measurements. Simple algorithms are given to improve the results for first order plus time delay plants (FOPTD). Attention is also drawn to the large errors which can occur when using autotuning for an unstable FOPTD plant.