{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T05:00:45Z","timestamp":1775365245167,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,3]],"date-time":"2024-08-03T00:00:00Z","timestamp":1722643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSPD2024R588"],"award-info":[{"award-number":["RSPD2024R588"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The primary goal of this research is to lessen the high vibration that the model causes by using an appropriate vibration control. Thus, we begin by implementing various controller types to investigate their impact on the system\u2019s reaction and evaluate each control\u2019s outcomes. The controller types are presented as proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers. We employed PID control to regulate the torsional vibration behavior on a dynamical system. The PID controller aims to increase system stability after seeing the impact of P and PI control. This kind of control ensures that there are no unstable components in the system. By using the multiple time scale perturbation (MTSP) technique, a first-order approximate solution has been obtained. Using the frequency response function approach, the stability and steady-state response of the system at the primary resonance scenario (\u03a91\u2245\u03c91,\u03a92\u2245\u03c92) are considered as the worst resonance and addressed. Additionally examined are the nonlinear dynamical system\u2019s chaotic response and the numerical solution for various parameter values. The MATLAB programs are utilized to attain simulation outcomes.<\/jats:p>","DOI":"10.3390\/computation12080157","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T07:37:30Z","timestamp":1722843450000},"page":"157","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["The Effect of Proportional, Proportional-Integral, and Proportional-Integral-Derivative Controllers on Improving the Performance of Torsional Vibrations on a Dynamical System"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9995-8520","authenticated-orcid":false,"given":"Khalid","family":"Alluhydan","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, College of Engineering, King Saud University, P.O Box 800, Riyadh 11421, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3280-7549","authenticated-orcid":false,"given":"Ashraf Taha","family":"EL-Sayed","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Modern Academy for Engineering and Technology, Elmokattam 11439, Egypt"}]},{"given":"Fatma Taha","family":"El-Bahrawy","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Modern Academy for Engineering and Technology, Elmokattam 11439, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,3]]},"reference":[{"key":"ref_1","first-page":"32","article-title":"Application of various PID controller tuning techniques for a temperature system","volume":"103","author":"Sowmya","year":"2014","journal-title":"Int. J. Comput. Appl."},{"key":"ref_2","first-page":"93","article-title":"Implementation of Gain Scheduled PID Controller for a Nonlinear Coupled Spherical Tank Process","volume":"14","author":"Pradeepkannan","year":"2014","journal-title":"Int. J. Mech. Mechatron. Eng."},{"key":"ref_3","first-page":"6","article-title":"Implementation of fuzzy and PID controller to water level system using LabView","volume":"116","author":"Sabri","year":"2015","journal-title":"Int. J. Comput. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e29749","DOI":"10.1016\/j.heliyon.2024.e29749","article-title":"Empirical study of robust\/developed PID control for nonlinear time-delayed dynamical system in discrete time domain","volume":"10","author":"Bashiri","year":"2024","journal-title":"Heliyon"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1007\/s40435-015-0199-5","article-title":"Design and implementation of discrete PID control applied to Bitumen tank based on new approach of pole placement technique","volume":"5","author":"Hamed","year":"2017","journal-title":"Int. J. Dynam. Control"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shaban, E.M., Hamed, A., Darwish, R.R., and Abdel Ghany, A.M. (2015, January 24\u201326). New tuning approach of discrete PI\/PID controller applied to bitumen system based on non-minimal state space formulation. Proceedings of the 25th International Conference on Computer Theory and Applications (ICCTA), Alexandria, Egypt.","DOI":"10.1109\/ICCTA37466.2015.9513435"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1007\/s40998-022-00488-3","article-title":"Industrial implementation of state dependent parameter PID+ control for nonlinear time delayed bitumen tank system","volume":"46","author":"Hamed","year":"2022","journal-title":"Iran J. Sci. Technol. Trans. Electr. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Farouk, M., and Hassanein, M. (2020). State-Dependent Parameter PID+ Control Applied to A Nonlinear Manipulator Arm. Recent Advances in Engineering Mathematics and Physics, Springer.","DOI":"10.1007\/978-3-030-39847-7"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2315","DOI":"10.1088\/0964-1726\/16\/6\/035","article-title":"Active control of thermally induced distortion in composite structures using macro fiber composite actuators","volume":"16","author":"Dano","year":"2007","journal-title":"Smart Mater. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.compstruct.2013.03.010","article-title":"Active control of geometrically nonlinear vibrations of doubly curved smart sandwich shells using 1\u20133 piezoelectric composites","volume":"105","author":"Kumar","year":"2013","journal-title":"Compos. Struct."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.ijnonlinmec.2016.10.003","article-title":"Nonlinear PD-controller to suppress the nonlinear oscillations of horizontally supported Jeffcott-rotor system","volume":"87","author":"Saeed","year":"2016","journal-title":"Int. Non-Linear Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/s11071-009-9613-x","article-title":"Proportional and derivative control for steady-state vibration mitigation in a piecewise linear beam system","volume":"60","author":"Fey","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1007\/s11071-014-1738-x","article-title":"Analysis of a nonlinear magnetic levitation system vibrations controlled by a time-delayed proportional derivative controller","volume":"79","author":"Eissa","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s11012-014-0069-9","article-title":"On controlling the response of primary and parametric resonances of a nonlinear magnetic levitation system","volume":"50","author":"Eissa","year":"2015","journal-title":"Meccanica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"095210","DOI":"10.1088\/1402-4896\/abaa7c","article-title":"Act of nonlinear proportional derivative controller for MFC laminated shell","volume":"95","author":"Bauomy","year":"2020","journal-title":"Phys. Scr."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1016\/j.ifacol.2018.06.162","article-title":"PID controller design for load frequency control: Past, Present and future challenges","volume":"51","author":"Hote","year":"2018","journal-title":"IFAC-Pap. Online"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1177\/0142331216675400","article-title":"PID controller design in the frequency domain for time-delay systems using direct method","volume":"40","author":"Darwish","year":"2018","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"022201","DOI":"10.1007\/s11432-016-0879-3","article-title":"PID controller design for second order nonlinear uncertain systems","volume":"60","author":"Zhao","year":"2017","journal-title":"Sci. China Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hanafi, D. (2010, January 19\u201321). PID controller design for semi-active car suspension based on model from intelligent system identification. Proceedings of the IEEE Computer Society, Second International Conference on Computer Engineering and Applications, Bali, Indonesia.","DOI":"10.1109\/ICCEA.2010.168"},{"key":"ref_20","first-page":"74","article-title":"Testing and simulation of motor vehicle suspension","volume":"3","author":"Constantin","year":"2009","journal-title":"Int. J. Syst. Appl. Eng. Dev."},{"key":"ref_21","unstructured":"Kumar, M.S. (2008, January 2\u20134). Development of Active System for Automobiles using PID Controller. Proceedings of the World Congress on Engineering, London, UK."},{"key":"ref_22","first-page":"012085","article-title":"Enhancing the Closed Loop Performance of Semi-active Suspension System with I-PD Controller","volume":"561","author":"Govinda","year":"2019","journal-title":"Mater. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1007\/s12206-015-0330-8","article-title":"Torsional vibration reduction for rolling mill\u2019s main drive system via negative velocity feedback under parametric excitation","volume":"29","author":"Amer","year":"2015","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1326","DOI":"10.1016\/j.mechmachtheory.2010.04.005","article-title":"Active control and simulation test study on torsional vibration of large turbo-generator rotor shaft","volume":"45","author":"Wenzhi","year":"2010","journal-title":"Mech. Mach. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2616","DOI":"10.1177\/1077546313514762","article-title":"Passive and active controllers for suppressing the torsional vibration of multiple degree-of-freedom system","volume":"21","author":"Bauomy","year":"2015","journal-title":"J. Vib. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"120817","DOI":"10.1016\/j.ins.2024.120817","article-title":"Adaptive PI event-triggered control for MIMO nonlinear systems with input delay","volume":"677","author":"Jianhui","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"119005","DOI":"10.1016\/j.ces.2023.119005","article-title":"An adaptive P\/PI control strategy for a solar volumetric methane\/steam reforming reactor with passive thermal management","volume":"281","author":"Yang","year":"2023","journal-title":"Chem. Eng. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kevorkian, J., and Cole, J.D. (1996). Multiple Scale and Singular Perturbation Methods. Applied Mathematical Sciences, Springer.","DOI":"10.1007\/978-1-4612-3968-0"},{"key":"ref_29","unstructured":"Nayfeh, A. (1973). Perturbation Methods, Wiley."},{"key":"ref_30","unstructured":"Dukkipati, R.V. (2007). Solving Vibration Analysis Problems Using Matlab, New Age International Pvt Ltd Publishers."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1177\/0020294020964243","article-title":"Mixed controller (IRC+ NSC) involved in the harmonic vibration response cantilever beam model","volume":"53","author":"Bauomy","year":"2020","journal-title":"Meas. Control"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"025005","DOI":"10.1088\/0031-8949\/80\/02\/025005","article-title":"Vibration reduction of a nonlinear spring pendulum under multi-parametric excitation via a longitudinal absorber","volume":"80","author":"Kamel","year":"2009","journal-title":"Phys. Scr."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"16864","DOI":"10.3934\/math.2023862","article-title":"The improved giant magnetostrictive actuator oscillations via positive position feedback damper","volume":"8","author":"Bauomy","year":"2023","journal-title":"AIMS Math."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.aej.2022.12.050","article-title":"Safety of a continuous spinning Shaft\u2019s structure from nonlinear vibration with NIPPF","volume":"67","author":"Bauomy","year":"2023","journal-title":"Alex. Eng. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1349","DOI":"10.1007\/s00419-018-1375-9","article-title":"Vibration performance of a vertical conveyor system under two simultaneous resonances","volume":"88","author":"Bauomy","year":"2018","journal-title":"Arch. Appl. Mech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"111778","DOI":"10.1016\/j.chaos.2021.111778","article-title":"NIPPF versus ANIPPF controller outcomes on semi- direct drive cutting transmission system in a shearer","volume":"156","author":"Bauomy","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_37","unstructured":"(2013, January 01). Forming Equations of Motion for Multiple Degree-of-Freedom Systems. Available online: www.efunda.com\/formulae\/vibrations\/mdof_eom.cfm."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/8\/157\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:29:34Z","timestamp":1760110174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/8\/157"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,3]]},"references-count":37,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["computation12080157"],"URL":"https:\/\/doi.org\/10.3390\/computation12080157","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,3]]}}}