{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T11:44:05Z","timestamp":1778759045920,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,20]],"date-time":"2018-11-20T00:00:00Z","timestamp":1542672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In order to eliminate the influence of the joint torsional vibration on the system operation accuracy, the parameter identification and the elastic torsional vibration control of a flexible-joint robot are studied. Firstly, the flexible-joint robot system is equivalent to a rotor dynamic system, in which the mass block and the torsion spring are used to simulate the system inertia link and elasticity link, for establishing the system dynamic model, and the experimental prototype is constructed. Then, based on the mechanism method, the global electromechanical-coupling dynamic model of the flexible-joint robot system is constructed to clear and define the mapping relationship between the driving voltage of the DC motor and the rotational speed of joint I and joint II. Furthermore, in view of the contradiction between the system response speed and the system overshoot in the vibration suppression effect of the conventional PID controller, a fuzzy PID controller, whose parameters are determined by the different requirements in the vibration control process, is designed to adjust the driving voltage of the DC motor for attenuating the system torsional vibration. Finally, simulation and control experiments are carried out and the results show that the designed fuzzy PID controller can effectively suppress the elastic torsional vibration of the flexible-joint robot system with synchronization optimization of control accuracy and dynamic quality.<\/jats:p>","DOI":"10.3390\/a11110189","type":"journal-article","created":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T11:23:27Z","timestamp":1542799407000},"page":"189","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Vibration Suppression of a Flexible-Joint Robot Based on Parameter Identification and Fuzzy PID Control"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2713-7173","authenticated-orcid":false,"given":"Jinyong","family":"Ju","sequence":"first","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongrui","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, China University of Petroleum (East China), Qingdao 266000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunrui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0441-0528","authenticated-orcid":false,"given":"Yufei","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.rcim.2011.08.004","article-title":"Recent Progress on Programming Methods for Industrial Robots","volume":"28","author":"Pan","year":"2012","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1177\/0278364912455954","article-title":"Opportunities and Challenges with Autonomous Micro Aerial Vehicles","volume":"31","author":"Kumar","year":"2017","journal-title":"Int. J. Robot. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/s11071-018-4205-2","article-title":"Inverse dynamic analysis and position error evaluation of the heavy-duty industrial robot with elastic joints: An efficient approach based on Lie group","volume":"93","author":"Yang","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1016\/j.mechatronics.2009.05.004","article-title":"Fuzzy error governor: A practical approach to counter actuator saturation on flexible joint robots","volume":"19","author":"Ozgoli","year":"2009","journal-title":"Mechatronics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1109\/TRO.2015.2402511","article-title":"Torque Estimation for Robotic Joint with Harmonic Drive Transmission Based on Position Measurements","volume":"31","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Robot."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1007\/s11071-012-0596-7","article-title":"Fuzzy adaptive dynamic surface control for a single-link flexible-joint robot","volume":"70","author":"Li","year":"2012","journal-title":"Nonlinear Dyn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1016\/j.automatica.2013.01.042","article-title":"Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity","volume":"49","author":"Kostarigka","year":"2013","journal-title":"Automatica"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1007\/s11071-018-4242-x","article-title":"Dynamics analysis of 2-DOF complex planar mechanical system with joint clearance and flexible links","volume":"93","author":"Chen","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1007\/s11071-017-3726-4","article-title":"Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria","volume":"90","author":"Singh","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.mechatronics.2015.11.008","article-title":"A soft robotic spine with tunable stiffness based on integrated ball joint and particle jamming","volume":"33","author":"Wei","year":"2016","journal-title":"Mechatronics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10846-017-0741-0","article-title":"Analysis of Dynamic Characteristics of Water Hydraulic Rotating Angle Self-Servo Robot Joint Actuator","volume":"92","author":"Jiang","year":"2018","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3189","DOI":"10.1109\/TIE.2011.2160510","article-title":"Trajectory Planning and Second-Order Sliding Mode Motion\/Interaction Control for Robot Manipulators in Unknown Environments","volume":"59","author":"Capisani","year":"2012","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_13","first-page":"1381","article-title":"Data-Driven Multi-Stage Motion Planning of Parallel Kinematic Machines","volume":"18","author":"Khoukhi","year":"2010","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s11071-018-4193-2","article-title":"Dynamics and nonlinear feedback control for torsional vibration bifurcation in main transmission system of scraper conveyor direct-driven by high-power PMSM","volume":"93","author":"Ju","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.mechatronics.2014.06.001","article-title":"Semi-active and active magnetic stabilization of supercritical rotor dynamics by contra-rotating damping","volume":"24","author":"Brusa","year":"2014","journal-title":"Mechatronics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5744","DOI":"10.1109\/TIE.2016.2574299","article-title":"Compensation of Nonlinear Torsion in Flexible Joint Robots: Comparison of Two Approaches","volume":"63","author":"Ruderman","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1016\/j.mechmachtheory.2010.06.014","article-title":"Empirical model based optimization of gearbox geometric design parameters to reduce rattle noise in an automotive transmission","volume":"45","author":"Bozca","year":"2010","journal-title":"Mech. Mach. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1177\/1077546309359759","article-title":"Control of torsional rotor vibrations using an electrorheological fluid dynamic absorber","volume":"17","author":"Sun","year":"2010","journal-title":"J. Vib. Control"},{"key":"ref_19","first-page":"1","article-title":"Full-State Tracking Control for Flexible Joint Robots with Singular Perturbation Techniques","volume":"99","author":"Kim","year":"2017","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/S0045-7949(00)00155-3","article-title":"Modelling and \u03bc-synthesis control of flexible manipulators","volume":"79","author":"Karkoub","year":"2001","journal-title":"Comput. Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"51626","DOI":"10.1109\/ACCESS.2018.2870292","article-title":"Robust-Adaptive Controller Design for Robot Manipulators using the H\u221e Approach","volume":"6","author":"Hayat","year":"2018","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.ymssp.2015.07.002","article-title":"Mu-Synthesis robust control of 3D bar structure vibration using piezo-stack actuators","volume":"78","author":"Mystkowski","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3696","DOI":"10.1109\/TIA.2015.2424883","article-title":"Principle of a Novel Single-Drive Bearingless Motor with Cylindrical Radial Gap","volume":"51","author":"Sugimoto","year":"2015","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4539","DOI":"10.1109\/TIE.2016.2547858","article-title":"Dynamic Performance Evaluation of a Nine-Phase Flux-Switching Permanent-Magnet Motor Drive With Model Predictive Control","volume":"63","author":"Cheng","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.mechatronics.2008.07.003","article-title":"Design and control of a brushless DC limited-angle torque motor with its application to fuel control of small-scale gas turbine engines","volume":"19","author":"Tsai","year":"2009","journal-title":"Mechatronics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s11071-010-9662-1","article-title":"Simulation and hybrid fuzzy-PID control for positioning of a hydraulic system","volume":"61","author":"Cetin","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1016\/j.isatra.2014.02.007","article-title":"Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system","volume":"53","year":"2014","journal-title":"ISA Trans."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/11\/189\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:30:46Z","timestamp":1760196646000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/11\/11\/189"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,20]]},"references-count":27,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["a11110189"],"URL":"https:\/\/doi.org\/10.3390\/a11110189","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,20]]}}}