In this study, a novel adaptive nonsingular terminal sliding mode (ANTSM) control frame combined with a modified extended state observer (MESO) is presented to enhance the anti-interference performance of the permanent magnet synchronous motor (PMSM) system. In the face of time-varying disturbances with unknown upper bounds, traditional nonsingular terminal sliding mode (NTSM) controllers typically utilize the large control gain to counteract the total disturbance, which will cause unsatisfactory control performances. To address this tough issue, an ANTSM control technique was constructed for the PMSM system by tuning the control gain automatically without overestimation. On this basis, the MESO was adopted to estimate the unknown total disturbance, whose estimation was offset to the ANTSM control input. By applying finite-time techniques, the estimation error will finite-time converge to zero. The proposed MESO has a more rapid estimation speed than the traditional extended state observer (ESO). Finally, the validity of the ANTSM + ESO composite control algorithm is confirmed by comprehensive experiments.
Citation: Ying Shi, Keqi Mei. Adaptive nonsingular terminal sliding mode controller for PMSM drive system using modified extended state observer[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18774-18791. doi: 10.3934/mbe.2023832
In this study, a novel adaptive nonsingular terminal sliding mode (ANTSM) control frame combined with a modified extended state observer (MESO) is presented to enhance the anti-interference performance of the permanent magnet synchronous motor (PMSM) system. In the face of time-varying disturbances with unknown upper bounds, traditional nonsingular terminal sliding mode (NTSM) controllers typically utilize the large control gain to counteract the total disturbance, which will cause unsatisfactory control performances. To address this tough issue, an ANTSM control technique was constructed for the PMSM system by tuning the control gain automatically without overestimation. On this basis, the MESO was adopted to estimate the unknown total disturbance, whose estimation was offset to the ANTSM control input. By applying finite-time techniques, the estimation error will finite-time converge to zero. The proposed MESO has a more rapid estimation speed than the traditional extended state observer (ESO). Finally, the validity of the ANTSM + ESO composite control algorithm is confirmed by comprehensive experiments.
[1] | X. Chen, R. Chen, T. Deng, An investigation on lateral and torsional coupled vibrations of high power density PMSM rotor caused by electromagnetic excitation, Nonlinear Dyn., 99 (2020), 1975–1988. https://doi.org/10.1007/s11071-019-05436-1 doi: 10.1007/s11071-019-05436-1 |
[2] | T. Zhao, S. Wu, S. Cui, Multiphase PMSM with asymmetric windings for more electric aircraft, IEEE Trans. Transport. Electrific., 6 (2020), 1592–1602. https://doi.org/10.1109/TTE.2020.2997609 doi: 10.1109/TTE.2020.2997609 |
[3] | B. Xu, L. Zhang, W. Ji, Improved non-singular fast terminal sliding mode control with disturbance observer for PMSM drives, IEEE Trans. Transport. Electrific., 7 (2021), 2753–2762. https://doi.org/10.1109/TTE.2021.3083925 doi: 10.1109/TTE.2021.3083925 |
[4] | X. Li, D. W. C. Ho, J. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361–368. https://doi.org/10.1016/j.automatica.2018.10.024 doi: 10.1016/j.automatica.2018.10.024 |
[5] | X. Li, S. Song, J. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Trans. Autom. Control, 64 (2019), 4024–4034. https://doi.org/10.1109/TAC.2019.2905271 doi: 10.1109/TAC.2019.2905271 |
[6] | Q. Xie, C. Mu, G. Wu, Z. Yu, R. Jia, Method for flux linkage optimization of permanent magnet synchronous motor based on nonlinear dynamic analysis, Nonlinear Dyn., 97 (2019), 2068–2089. https://doi.org/10.1007/s11071-019-05104-4 doi: 10.1007/s11071-019-05104-4 |
[7] | X. Li, D. Peng, J. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Autom. Control, 65 (2020) 4908–4913. https://doi.org/10.1109/TAC.2020.2964558 doi: 10.1109/TAC.2020.2964558 |
[8] | F. Wang, H. Xie, Q. Chen, S. Davari, J. Rodriguez, R. M. Kennel, Parallel predictive torque control for induction machines without weighting factors, IEEE Trans. Power Electron., 35 (2020), 1779–1788. https://doi.org/10.1109/TPEL.2019.2922312 doi: 10.1109/TPEL.2019.2922312 |
[9] | F. Wang, S. Li, X. Mei, W. Xie, J. Rodrguez, R. M. Kennel, Model-based predictive direct control strategies for electrical drives: an experimental evaluation of PTC and PCC methods, IEEE Trans. Ind. Informat., 11 (2015), 671–681. https://doi.org/10.1109/TII.2015.2423154 doi: 10.1109/TII.2015.2423154 |
[10] | L. Shanmugam, Y. H. Joo, Design of interval type-2 fuzzy-based sampled-data controller for nonlinear systems using novel fuzzy lyapunov functional and its application to PMSM, IEEE Trans. Syst. Man Cybern. Syst., 51 (2021), 542–551. https://doi.org/10.1109/TSMC.2018.2875098 doi: 10.1109/TSMC.2018.2875098 |
[11] | R. Vadivel, Y. H. Joo, Reliable fuzzy $H_\infty$ control for permanent magnet synchronous motor against stochastic actuator faults, IEEE Trans. Syst., Man, Cybern., Syst., 51 (2021), 2232–2245. https://doi.org/10.1109/TSMC.2019.2957001 doi: 10.1109/TSMC.2019.2957001 |
[12] | L. Ma, K. Mei, S. Ding, T. Pan, Design of adaptive fuzzy fixed-time HOSM controller subject to asymmetric output constraints, IEEE Trans. Fuzzy Syst., 2023 (2023). https://doi.org/10.1109/TFUZZ.2023.3241147 doi: 10.1109/TFUZZ.2023.3241147 |
[13] | S. Ding, B. Zhang, K. Mei, J. H. Park, Adaptive fuzzy SOSM controller design with output constraints, IEEE Trans. Fuzzy Syst., 30 (2022), 2300–2311. https://doi.org/10.1109/TFUZZ.2021.3079506 doi: 10.1109/TFUZZ.2021.3079506 |
[14] | A. T. Woldegiorgis, X. Ge, H. Wang, M. Hassan, A new frequency adaptive second-order disturbance observer for sensorless vector control of interior permanent magnet synchronous motor, IEEE Trans. Ind. Electron., 68 (2021), 11847–11857. https://doi.org/10.1109/TIE.2020.3047065 doi: 10.1109/TIE.2020.3047065 |
[15] | K. Mei, S. Ding, C.-C. Chen, Fixed-time stabilization for a class of output-constrained nonlinear systems, IEEE Trans. Syst., Man, Cybern. Syst., 52 (2022), 6498–6510. https://doi.org/10.1109/TSMC.2022.3146011 doi: 10.1109/TSMC.2022.3146011 |
[16] | X. Jin, Y. Shi, Y. Tang, H. Werner, J. Kurths, Event-triggered fixed-time attitude consensus with fixed and switching topologies, IEEE Trans. Autom. Control, 67 (2022), 4138–4145. https://doi.org/10.1109/TAC.2021.3108514 doi: 10.1109/TAC.2021.3108514 |
[17] | K. Chen, W. He, Q. Han, M. Xue, Y. Tang, Leader selection in networks with switching topologies and antagonistic interactions, Automatica, 142 (2022), 110334. https://doi.org/10.1016/j.automatica.2022.110334 doi: 10.1016/j.automatica.2022.110334 |
[18] | L. Ma, C. Cheng, J. Guo, B. Shi, S. Ding, K. Mei, Direct yaw-moment control of electric vehicles based on adaptive sliding mode, Math. Biosci. Eng., 20 (2023), 13334–13355. https://doi.org/10.3934/mbe.2023594 doi: 10.3934/mbe.2023594 |
[19] | Q. Hou, S. Ding, X. Yu, K. Mei, A super-twisting-like fractional controller for SPMSM drive system, IEEE Trans. Ind. Electron., 69 (2022), 9376–9384. https://doi.org/10.1109/TIE.2021.3116585 doi: 10.1109/TIE.2021.3116585 |
[20] | S. Ding, Q. Hou, H. Wang, Disturbance-observer-based second-order sliding mode controller for speed control of PMSM drives, IEEE Trans. Energy Convers., 38 (2023), 100–110. https://doi.org/10.1109/TEC.2022.3188630 doi: 10.1109/TEC.2022.3188630 |
[21] | W. Dou, S. Ding, X. Yu, Event-triggered second-order sliding mode control of uncertain nonlinear systems, IEEE Trans. Syst. Man Cybern. Syst., 2023 (2023). https://doi.org/10.1109/TSMC.2023.3296681 doi: 10.1109/TSMC.2023.3296681 |
[22] | Q. Hou, S. Ding, GPIO based super-twisting sliding mode control for PMSM, IEEE Trans. Circuits Syst. II Exp. Briefs, 68 (2021), 747–751. https://doi.org/10.1109/TCSII.2020.3008188 doi: 10.1109/TCSII.2020.3008188 |
[23] | K. Mei, S. Ding, Second-order sliding mode controller design subject to an upper-triangular structure, IEEE Trans. Syst. Man, Cybern. Syst., 51 (2021), 497–507. https://doi.org/10.1109/TSMC.2018.2875267 doi: 10.1109/TSMC.2018.2875267 |
[24] | Y. Jiang, W. Xu, C. Mu, Y. Liu, Improved deadbeat predictive current control combined sliding mode strategy for PMSM drive system, IEEE Trans. Veh. Technol., 67 (2018), 251–263. https://doi.org/10.1109/TVT.2017.2752778 doi: 10.1109/TVT.2017.2752778 |
[25] | E. Lu, W. Li, X. Yang, Y. Liu, Anti-disturbance speed control of low-speed high-torque PMSM based on second-order non-singular terminal sliding mode load observer, ISA Trans., 88 (2019), 142–152. https://doi.org/10.1016/j.isatra.2018.11.028 doi: 10.1016/j.isatra.2018.11.028 |
[26] | M. Lv, Y. Li, W. Pan, S. Baldi, Finite-time fuzzy adaptive constrained tracking control for hypersonic flight vehicles with singularity-free switching, IEEE/ASME Trans. Mechatronics, 27 (2022), 1594–1605. https://doi.org/10.1109/TMECH.2021.3090509 doi: 10.1109/TMECH.2021.3090509 |
[27] | S. Li, M. Zhuo, X. Yu, Design and implementation of terminal sliding mode control method for PMSM speed regulation system, IEEE Trans. Ind. Informat., 9 (2013), 1879–1891. https://doi.org/10.1109/TII.2012.2226896 doi: 10.1109/TII.2012.2226896 |
[28] | H. Dong, X. Yang, H. Gao, X. Yu, Practical terminal sliding-mode control and its applications in servo systems, IEEE Trans. Ind. Electron., 70 (2023), 752–761. https://doi.org/10.1109/TIE.2022.3152018 doi: 10.1109/TIE.2022.3152018 |
[29] | S. Hou, C. Wang, Y. Chu, J. Fei, Neural network-based adaptive fractional-order terminal sliding mode control, Trans. Inst. Meas. Control, 44 (2022), 3107–3117. https://doi.org/10.1177/01423312221098486 doi: 10.1177/01423312221098486 |
[30] | J. C. Zhang, H. Wang, Z. H. Man, J. Jin, M. Y. Fu, Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode, IEEE/ASME Trans. Mechatron., 20 (2015), 1743–1752. https://doi.org/10.1109/TMECH.2014.2352647 doi: 10.1109/TMECH.2014.2352647 |
[31] | A. K. Junejo, W. Xu, C. Mu, M. M. Ismail, Y. Liu, Adaptive speed control of PMSM drive system based a new sliding-mode reaching law, IEEE Trans. Power Electron., 35 (2020), 12110–12121. https://doi.org/10.1109/TPEL.2020.2986893 doi: 10.1109/TPEL.2020.2986893 |
[32] | S. Ding, W. H. Chen, K. Mei, D. J. Murray-Smith, Disturbance observer design for nonlinear systems represented by input-output models, IEEE Trans. Ind. Electron., 67 (2020), 1222–1232. https://doi.org/10.1109/TIE.2019.2898585 doi: 10.1109/TIE.2019.2898585 |
[33] | K. Mei, C. Qian, S. Ding, Design of adaptive SOSM controller subject to disturbances with unknown magnitudes, IEEE Trans. Circuits Syst. I, Reg. Papers, 70 (2023), 2133–2142. https://doi.org/10.1109/TCSI.2023.3241291 doi: 10.1109/TCSI.2023.3241291 |
[34] | K. Mei, S. Ding, X. Yu, A generalized supertwisting algorithm, IEEE Trans. Cybern., 53 (2023), 3951–3960. https://doi.org/10.1109/TCYB.2022.3188877 doi: 10.1109/TCYB.2022.3188877 |
[35] | Y. A. I. Mohamed, Design and implementation of a robust current-control scheme for a PMSM vector drive with a simple adaptive disturbance observer, IEEE Trans. Ind. Electron., 54 (2007), 1981–1988. https://doi.org/10.1109/TIE.2007.895074 doi: 10.1109/TIE.2007.895074 |
[36] | Y. Zuo, X. Zhu, L. Quan, C. Zhang, Y. Du, Z. Xiang, Active disturbance rejection controller for speed control of electrical drives using phase-locking loop observer, IEEE Trans. Ind. Electron., 66 (2019), 1748–1759. https://doi.org/10.1109/TIE.2018.2838067 doi: 10.1109/TIE.2018.2838067 |
[37] | W. Xu, A. K. Junejo, Y. Liu, M. R. Islam, Improved continuous fast terminal sliding mode control with extended state observer for speed regulation of PMSM drive system, IEEE Trans. Veh. Technol., 68 (2019), 10465–10476. https://doi.org/10.1109/TVT.2019.2926316 \newpage doi: 10.1109/TVT.2019.2926316 |
[38] | F. Wang, D. Ke, X. Yu, D. Huang, Enhanced predictive model based deadbeat control for PMSM drives using exponential extended state observer, IEEE Trans. Ind. Electron., 69 (2022), 2357–2369. https://doi.org/10.1109/TIE.2021.3065622 doi: 10.1109/TIE.2021.3065622 |
[39] | K. Yu, Z. Wang, W. Hua, M. Cheng, Robust cascaded deadbeat predictive control for dual three-phase variable-flux PMSM considering intrinsic delay in speed loop, IEEE Trans. Ind. Electron., 69 (2022), 12107–12118. https://doi.org/10.1109/TIE.2022.3142400 doi: 10.1109/TIE.2022.3142400 |
[40] | Z. Liu, D. Yang, Y. Wang, M. Lu, R. Li, EGNN: Graph structure learning based on evolutionary computation helps more in graph neural networks, Appl. Soft Comput., 135 (2023), 110040. https://doi.org/10.1016/j.asoc.2023.110040 doi: 10.1016/j.asoc.2023.110040 |
[41] | Y. Wang, Z. Liu, J. Xu, W. Yan, Heterogeneous network representation learning approach for Ethereum identity identification, IEEE Trans. Comput. Social Syst., 10 (2023), 890–899. https://doi.org/10.1109/TCSS.2022.3164719 doi: 10.1109/TCSS.2022.3164719 |
[42] | Y. Shi, L. Li, J. Yang, Y. Wang, S. Hao, Center-based transfer feature learning with classifier adaptation for surface defect recognition, Mech. Syst. Signal Process., 188 (2023), 110001. https://doi.org/10.1016/j.ymssp.2022.110001 doi: 10.1016/j.ymssp.2022.110001 |
[43] | Y. Shi, H. Li, X. Fu, R. Luan, Y. Wang, N. Wang, et al., Self-powered difunctional sensors based on sliding contact-electrification and tribovoltaic effects for pneumatic monitoring and controlling, Nano Energy, 110 (2023), 108339. https://doi.org/10.1016/j.nanoen.2023.108339 doi: 10.1016/j.nanoen.2023.108339 |
[44] | C. Tian, Z. Xu, L. Wang, Y. Liu, Arc fault detection using artificial intelligence: Challenges and benefits, Math. Biosci. Eng., 20 (2023), 12404–12432. https://doi.org/10.3934/mbe.2023552 doi: 10.3934/mbe.2023552 |
[45] | Q. K. Hou, S. H. Ding, X. H. Yu, Composite super-twisting sliding mode control design for PMSM speed regulation problem based on a novel disturbance observer, IEEE Trans. Energy Convers., 36 (2021), 2591–2599. https://doi.org/10.1109/TEC.2020.2985054 doi: 10.1109/TEC.2020.2985054 |
[46] | S. Ding, L. Liu, J. H. Park, A novel adaptive nonsingular terminal sliding mode controller design and its application to active front steering system, Int. J. Robust Nonlinear Control, 29 (2019), 4250–4269. https://doi.org/10.1002/rnc.4625 doi: 10.1002/rnc.4625 |
[47] | J. Yang, T. Li, C. Liu, S. Li, W. H. Chen, Nonlinearity estimator-based control of a class of uncertain nonlinear systems, IEEE Trans. Autom. Control, 65 (2020), 2230–2236. https://doi.org/10.1109/TAC.2019.2940567 doi: 10.1109/TAC.2019.2940567 |
[48] | Y. Feng, X. Yu, Z. Man, Non-singular terminal sliding mode control of rigid manipulators, Automatica, 38 (2002), 2159–2167. https://doi.org/10.1016/S0005-1098(02)00147-4 doi: 10.1016/S0005-1098(02)00147-4 |
[49] | A. Levant, Principles of 2-sliding mode design, Automatica, 43 (2007), 576–586. https://doi.org/10.1016/j.automatica.2006.10.008 doi: 10.1016/j.automatica.2006.10.008 |
[50] | S. Yu, X. Yu, B. Shirinzadeh, Z. Man, Continuous finite-time control for robotic manipulators with terminal sliding mode, Automatica, 41 (2005), 1957–1964. https://doi.org/10.1016/j.automatica.2005.07.001 doi: 10.1016/j.automatica.2005.07.001 |