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                <journal-meta>
                                                                <journal-id>saujs</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Sakarya University Journal of Science</journal-title>
            </journal-title-group>
                                        <issn pub-type="epub">2147-835X</issn>
                                                                                            <publisher>
                    <publisher-name>Sakarya University</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.16984/saufenbilder.1286774</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Electrical Engineering</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Elektrik Mühendisliği</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                        <article-title>Analysis and Control of Chaos in Permanent Magnet Synchronous Motor</article-title>
                                                                                                                                        </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0002-6746-3785</contrib-id>
                                                                <name>
                                    <surname>Moussa Yaya</surname>
                                    <given-names>Abdallah</given-names>
                                </name>
                                                                    <aff>SAKARYA UNIVERSITY</aff>
                                                            </contrib>
                                                    <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0001-5897-6274</contrib-id>
                                                                <name>
                                    <surname>Uyaroğlu</surname>
                                    <given-names>Yılmaz</given-names>
                                </name>
                                                                    <aff>SAKARYA ÜNİVERSİTESİ</aff>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20231218">
                    <day>12</day>
                    <month>18</month>
                    <year>2023</year>
                </pub-date>
                                        <volume>27</volume>
                                        <issue>6</issue>
                                        <fpage>1217</fpage>
                                        <lpage>1225</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20230425">
                        <day>04</day>
                        <month>25</month>
                        <year>2023</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20230727">
                        <day>07</day>
                        <month>27</month>
                        <year>2023</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 1997, Sakarya University Journal of Science</copyright-statement>
                    <copyright-year>1997</copyright-year>
                    <copyright-holder>Sakarya University Journal of Science</copyright-holder>
                </permissions>
            
                                                                                                <abstract><p>This paper explores the chaotic dynamics exhibited by a Permanent Magnet Synchronous Motors (PMSM) through an analysis of Lyapunov exponents and equilibrium points. Subsequently, the study focuses on controlling the motor&#039;s chaotic behavior under specific parameter conditions using a straightforward controller. The approach employed in this paper involves utilizing a single-state feedback controller as the resolution method. The derived control law enables the stabilization of the motor&#039;s state around a reference state, even in the presence of parameter uncertainties, thereby preventing chaotic behavior. To illustrate the proposed method, numerical simulations were conducted in MATLAB, showcasing the practical application of this approach. The simulation results demonstrate the success of the controller used.</p></abstract>
                                                                                    
            
                                                            <kwd-group>
                                                    <kwd>Chaos</kwd>
                                                    <kwd>  chaotic system</kwd>
                                                    <kwd>  chaos control</kwd>
                                                    <kwd>  PMSM</kwd>
                                            </kwd-group>
                                                        
                                                                                                                                                    </article-meta>
    </front>
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                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">[1] R. Krishnan, “Application Characteristics of Permanent Magnet Synchronous and Brushless dc Motors for Servo Drives,” IEEE Transactions on Industry Applications, vol. 27, no. 5, pp. 986–996, 1991.</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">[2] D. P. Iracleous, N. Mastorakis, and T. H. Piraeus, “Application of passivity control theory to chaotic systems,” 2004.</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">[3] M. Babaei, J. Nazarzadeh, and J. Faiz, “Nonlinear feedback control of chaos in synchronous reluctance motor drive systems,” 2008 IEEE International Conference on Industrial Technology, 2008.</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">[4] J. Hu, L. Liu, and D. Wei Ma, “Robust nonlinear feedback control of a chaotic permanent-magnet synchronous motor with a load torque disturbance,” Journal of the Korean Physical Society, vol. 65, no. 12, pp. 2132–2139, 2014.</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">[5] J. Hu, Y. Qiu, and H. Lu, “Adaptive robust nonlinear feedback control of chaos in PMSM system with modeling uncertainty,” Applied Mathematical Modelling, vol. 40, no. 19–20, pp. 8265–8275, Oct. 2016.</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">[6] (陈强) C. Q. et al., “Full-order sliding mode control of uncertain chaos in a permanent magnet synchronous motor based on a fuzzy extended state observer,” Chinese Physics B, vol. 24, no. 11, pp. 110504–110504, Nov. 2015.</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">[7] S. Luo, “Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain,” Chaos, vol. 24, no. 3, Sep. 2014.</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">[8] J. Yu, J. Gao, Y. Ma, H. Yu, and S. Pan, “Robust adaptive fuzzy control of chaos in the permanent magnet synchronous motor,” Discrete Dynamics in Nature and Society, vol. 2010, 2010.</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">[9] H. H. Choi, “Adaptive control of a chaotic permanent magnet synchronous motor,” Nonlinear Dyn, vol. 69, no. 3, pp. 1311–1322, Aug. 2012.</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">[10] L. Wang, J. Fan, Z. Wang, B. Zhan, and J. Li, “Dynamic Analysis and Control of a Permanent Magnet Synchronous Motor With External Perturbation,” Journal of Dynamic Systems Measurement and Control-transactions of The Asme, vol. 138, no. 1, 2016.</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">[11] M. Ataei, A. Kiyoumarsi, and B. Ghorbani, “Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement,” Phys Lett A, vol. 374, no. 41, pp. 4226–4230, 2010, Accessed: Apr. 22, 2023. [Online]. Available: https://www.academia.edu/9295607/C ontrol_of_chaos_in_permanent_magn et_synchronous_motor_by_using_opti mal_Lyapunov_exponents_placement</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">[12] Q. Donglian, W. Jia-jun, and Z. Guangzhou, “Passive control of Permanent Magnet Synchronous Motor chaotic systems,” Journal of Zhejiang University-SCIENCE A, 2005.</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">[13] X. Chen, J. Hu, Z. Peng, and C. Yuan, “Bifurcation and chaos analysis of torsional vibration in a PMSM-based driven system considering electromechanically coupled effect,” Nonlinear Dyn, vol. 88, no. 1, pp. 277– 292, Apr. 2017.</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">[14] D. Li, S. L. Wang, X. H. Zhang, D. Yang, and H. Wang, “Impulsive control of permanent magnet synchronous motors with parameters uncertainties,” Chinese Physics B, vol. 17, no. 5, pp. 1678–1684, May 2008.</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">[15] W. Du-Qu and Z. Bo, “Controlling chaos in permanent magnet synchronous motor based on finitetime stability theory,” Chinese Physics B, vol. 18, no. 4, pp. 1399–1403, 2009.</mixed-citation>
                    </ref>
                                    <ref id="ref16">
                        <label>16</label>
                        <mixed-citation publication-type="journal">[16] J. TU and Q. Zhou, “DESIGN AND IMPLEMENTATION OF THE CRYING VOICE DETECTION CIRCUIT IN THE BABY’S SUPERVISION SYSTEM,” Review of Computer Engineer Studies, vol. 1, no. 1, pp. 13–16, Sep. 2014.</mixed-citation>
                    </ref>
                                    <ref id="ref17">
                        <label>17</label>
                        <mixed-citation publication-type="journal">[17] J. Zhou, Y. Luo, Z. Li, and C. Kang, “ANALYSIS OF FOREST FIRE SURVEILLANCE &amp; PREWARNING APPLICATION SYSTEM BASED ON POWER GRID GIS,” Review of Computer Engineer Studies, vol. 1, no. 1, pp. 23–28, Sep. 2014.</mixed-citation>
                    </ref>
                                    <ref id="ref18">
                        <label>18</label>
                        <mixed-citation publication-type="journal">[18] U. J. Das, “Effects of non-newtonian parameter on unsteady MHD free convective mass transfer flow of a viscoelastic fluid past an infinite vertical porous plate with constant suction and heat, sink,” International Journal of Heat and Technology, vol. 31, no. 2, pp. 87–93, 2013.</mixed-citation>
                    </ref>
                                    <ref id="ref19">
                        <label>19</label>
                        <mixed-citation publication-type="journal">[19] B. Buonomo, O. Manca, S. Nardini, and P. Romano, “Thermal and fluid dynamic analysis of solar chimney building systems,” International Journal of Heat and Technology, vol. 31, no. 2, pp. 119–126, 2013.</mixed-citation>
                    </ref>
                                    <ref id="ref20">
                        <label>20</label>
                        <mixed-citation publication-type="journal">[20] L. Marietta and G. Evola, “Thermodynamic analysis of a hybrid photovoltaic/thermal solar collector,” International Journal of Heat and Technology, vol. 31, no. 2, pp. 135– 142, 2013.</mixed-citation>
                    </ref>
                                    <ref id="ref21">
                        <label>21</label>
                        <mixed-citation publication-type="journal">[21] M.G. Reddy, “Influence of thermal Radiation on Natural Convection Boundary Layer Flow of a Nanofluid Past a Vertical Plate with Uniform Heat Flux | IIETA,” International Journal of Heat and Technology, 2013. https://www.iieta.org/journals/ijht/pap er/10.18280/ijht.320101 (accessed Apr. 02, 2023).</mixed-citation>
                    </ref>
                                    <ref id="ref22">
                        <label>22</label>
                        <mixed-citation publication-type="journal">[22] K. Rajagopal, A. Karthikeyan, and P. Duraisamy, “Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems,” Nonlinear Engineering, vol. 6, no. 2, pp. 79–87, Jun. 2017.</mixed-citation>
                    </ref>
                                    <ref id="ref23">
                        <label>23</label>
                        <mixed-citation publication-type="journal">[23] Z. Li, J. B. Park, Y. H. Joo, B. Zhang, and G. Chen, “Bifurcations and chaos in a permanent-magnet synchronous motor,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 3, pp. 383–387, Mar. 2002.</mixed-citation>
                    </ref>
                                    <ref id="ref24">
                        <label>24</label>
                        <mixed-citation publication-type="journal">[24] X. Liao and P. Yu, “Absolute Stability of Nonlinear Control Systems,” vol. 25, 2008.</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
