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Artículos de revistas sobre el tema "Adaptive discrete-time sliding mode"

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Autor: Grafiati

Publicado: 6 de septiembre de 2023

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1

WATANABE, Kenichirou, Kenzo WADA y Fumitake FUJII. "Discrete-Time Sliding Mode Control with Adaptive Sliding Surface". Proceedings of Conference of Chugoku-Shikoku Branch 2004.42 (2004): 177–78. http://dx.doi.org/10.1299/jsmecs.2004.42.177.

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2

Sharma, Nalin Kumar, Spandan Roy, S. Janardhanan y I. N. Kar. "Adaptive Discrete-Time Higher Order Sliding Mode". IEEE Transactions on Circuits and Systems II: Express Briefs 66, n.º 4 (abril de 2019): 612–16. http://dx.doi.org/10.1109/tcsii.2018.2849975.

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3

Pieper, Jeff K. "A Discrete Time Adaptive Sliding Mode Controller". IFAC Proceedings Volumes 29, n.º 1 (junio de 1996): 5227–31. http://dx.doi.org/10.1016/s1474-6670(17)58511-0.

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4

Y.P., Patil. "Discrete Adaptive Model Following Sliding Mode Control Design for Improved Performance". Journal of Advanced Research in Dynamical and Control Systems 12, SP3 (28 de febrero de 2020): 557–69. http://dx.doi.org/10.5373/jardcs/v12sp3/20201293.

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5

Semba, Tetsuo y Katsuhisa Furuta. "Discrete-time adaptive control using a sliding mode". Mathematical Problems in Engineering 2, n.º 2 (1996): 131–42. http://dx.doi.org/10.1155/s1024123x96000270.

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Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs. We first prove the stability of a system in which the control inputs consist of equivalent control driven by the adaptive control law and bounded discontinuous control. The discontinuous control driven by the sliding control law is then obtained so that the output error quickly converges to zero. Finally, the performance improvements obtained by adding the sliding mode control input are shown through computer simulations.

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6

Jin, Shanhai, Yonggao Jin, Xiaodan Wang y Xiaogang Xiong. "Discrete-Time Sliding Mode Filter with Adaptive Gain". Applied Sciences 6, n.º 12 (1 de diciembre de 2016): 400. http://dx.doi.org/10.3390/app6120400.

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7

Bartolini, G., A. Ferrara y V. I. Utkin. "Adaptive sliding mode control in discrete-time systems". Automatica 31, n.º 5 (mayo de 1995): 769–73. http://dx.doi.org/10.1016/0005-1098(94)00154-b.

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8

Yang, Rong Jun y Yun Guo Shi. "Guided Rocket Control System Design Based on Discrete-Time Adaptive Sliding Mode". Applied Mechanics and Materials 541-542 (marzo de 2014): 1159–63. http://dx.doi.org/10.4028/www.scientific.net/amm.541-542.1159.

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The discrete-time adaptive sliding mode controller for spinning rockets in presence of parameter error is proposed. Considering the nonlinear characteristics for the system, input-output feedback linearization is utilized to transform the system model into two standard form subsystems. Then a discrete-time controller for guided rockets is designed based on discrete-time sliding mode control principle. In order to diminish the switch width of the discrete-time sliding mode system corresponding to parameter error, a dead-zone parameter adaptive law is designed. The stability of the uncertain closed-loop system is proved by Lyapunov theory, which make the controller have high robustness. Simulation result indicates that the proposed controller is robust with respect to large aerodynamic parametric uncertainty, and has excellent dynamic tracking performance.

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9

Dehri, Khadija y Ahmed Said Nouri. "A discrete repetitive adaptive sliding mode control for DC-DC buck converter". Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 235, n.º 9 (29 de marzo de 2021): 1698–708. http://dx.doi.org/10.1177/09596518211005576.

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The problem of sensitivity to uncertainties and disturbances is still a challenging task in the theory of discrete sliding mode controller. In this article, a discrete repetitive adaptive sliding mode control using only input-output measurements of linear time-varying system with periodic disturbances is proposed. A new indirect adaptive algorithm taken into account the periodicity of disturbances is used to identify parameter variations of the considered system. Based on this identification, discrete sliding mode controller is developed. Then, the structure of plug-in repetitive control is integrated into the previous controller to reject harmonic disturbances. A robustness analysis is achieved to ensure the asymptotic stability of the proposed controller. An example of time-varying DC-DC buck converter subject to harmonic disturbances is carried out to illustrate the effectiveness of the designed discrete repetitive adaptive sliding mode control.

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10

Zhong, Hua, Junhong Yu y Hanzheng Ran. "Characteristic Model-Based Discrete Adaptive Sliding Mode Control for System with Time Delay". International Journal of Automation Technology 10, n.º 2 (4 de marzo de 2016): 282–87. http://dx.doi.org/10.20965/ijat.2016.p0282.

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A novel characteristic model-based discrete sliding mode control (CMDSMC) for time delay system is presented in this paper. Firstly, to solve the challenge of establishing a accurate and simple model for time delay system, characteristic theory is applied to establish characteristic mode with time delay. Secondly, due to the uncertainties of time delay system, discrete sliding mode control based on characteristic model is proposed and stability analysis is done. At last, two illustrative examples taken from literatures are included to indicate the simplicity and superiority of the proposed method.

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11

Jin, Shanhai, Xiaodan Wang, Yonggao Jin y Xiaogang Xiong. "Enhanced Discrete-Time Sliding Mode Filter for Removing Noise". Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/3134987.

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This paper presents a new discrete-time sliding mode filter for effectively removing noise in control of mechatronic systems. The presented filter is an enhanced version of a sliding mode filter by employing an adaptive gain in determining a virtual desired velocity of the output. Owing to the use of backward Euler discretization, the discrete-time implementation of the filter does not produce chattering, which has been considered as a common problem of sliding mode techniques. Besides that, the state of the filter converges to the desired state in finite time. Numerical example and experimental position control of a mechatronic system are conducted for validating the effectiveness of the filter.

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12

Chan, C. Y. "Discrete adaptive quasi-sliding mode control". International Journal of Control 72, n.º 4 (enero de 1999): 365–73. http://dx.doi.org/10.1080/002071799221163.

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13

Chan, C. Y. "Discrete adaptive sliding-mode tracking controller". Automatica 33, n.º 5 (mayo de 1997): 999–1002. http://dx.doi.org/10.1016/s0005-1098(97)00001-0.

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14

Chen, Xinkai. "Adaptive quasi-sliding mode control for discrete-time multivariable systems". International Journal of Control 72, n.º 2 (enero de 1999): 133–40. http://dx.doi.org/10.1080/002071799221307.

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15

Monsees, G. y J. M. A. Scherpen. "Adaptive switching gain for a discrete-time sliding mode controller". International Journal of Control 75, n.º 4 (enero de 2002): 242–51. http://dx.doi.org/10.1080/00207170110101766.

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16

Chen, Xinkai y Toshio Fukuda. "Robust adaptive quasi-sliding mode controller for discrete-time systems". Systems & Control Letters 35, n.º 3 (octubre de 1998): 165–73. http://dx.doi.org/10.1016/s0167-6911(98)00048-6.

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17

Baruch, Ieroham S., P. Luis-Alberto Hernandez y Josefina Barrera-Cortes. "Adaptive discrete - time sliding mode control using recurrent neural identifier". IFAC Proceedings Volumes 37, n.º 21 (diciembre de 2004): 735–40. http://dx.doi.org/10.1016/s1474-6670(17)30558-x.

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18

Milbradt, Deise Maria Cirolini, Paulo Jefferson Dias de Oliveira Evald, Guilherme Vieira Hollweg y Hilton Abílio Gründling. "Discrete-time Analysis of a Robust Model Reference Adaptive Sliding Mode Control". International Journal of Control, Automation and Systems 21, n.º 5 (mayo de 2023): 1383–93. http://dx.doi.org/10.1007/s12555-022-0133-5.

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19

Zhang, Yong Jun, Yong Kang Zhang y Xiao Zhan Li. "Discrete Time Sliding Mode on Model Reference Adaptive System Based Sensorless Induction Motor Drive". Applied Mechanics and Materials 229-231 (noviembre de 2012): 2233–38. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.2233.

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Sensorless induction motor drives are widely used in industry for their reliability and flexibility. It’s very important to improve the performance of speed estimation in some cases, especial at low speed of IM drives. The authors have proposed and developed a model reference adaptive system (MRAS) based on discrete time sliding mode algorithm(DTSM), which has high performance for sensorless induction motor drive in low speeds. The new algorithm obtains the identification flux using the classic MRAS, and the PI adaptive law in MRAS is replaced with the sliding mode observer which is acquired by the error function. This paper presents the theory, modelling, simulation and experimental results of the proposed DTSM-MRAS based sensorless direct torque control induction motor drives.

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20

Zhou, Yuan, Zhe Sun, Bo Chen, Guangpu Huang, Xiang Wu y Tian Wang. "Human gait tracking for rehabilitation exoskeleton: adaptive fractional order sliding mode control approach". Intelligence & Robotics 3, n.º 1 (2023): 95–112. http://dx.doi.org/10.20517/ir.2023.05.

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To improve the rehabilitation training effect of hemiplegic patients, in this paper, a discrete adaptive fractional order fast terminal sliding mode control approach is proposed for the lower limb exoskeleton system to implement high-precision human gait tracking tasks. Firstly, a discrete dynamic model is established based on the Lagrange system discretization criterion for the lower limb exoskeleton robot. Then, in order to design a discrete adaptive fractional order fast terminal sliding mode controller, the Grünwald–Letnikov fractional order operator is introduced to combine with fast terminal attractor to construct a fractional order fast terminal sliding surface. An adaptive parameter adjustment strategy is proposed for the reaching law of sliding mode control, which drives the sliding mode to the stable region dynamically. Moreover, the stability of the control system is proved in the sense of Lyapunov, and the guidelines for selecting the control parameters are given. Finally, the simulations are tested on the MATLAB-Opensim co-simulation platform. Compared with the conventional discrete sliding mode control and discrete fast terminal sliding mode control, the results verify the superiority of the proposed method in improving lower limb rehabilitation training.

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21

Chai, Chang-Hyun. "Discrete-Time Sliding Mode Control with SIIM Fuzzy Adaptive Switching Gain". International Journal of Fuzzy Logic and Intelligent Systems 12, n.º 1 (30 de marzo de 2012): 47–52. http://dx.doi.org/10.5391/ijfis.2012.12.1.47.

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22

Xu, Qingsong. "Adaptive Discrete-Time Sliding Mode Impedance Control of a Piezoelectric Microgripper". IEEE Transactions on Robotics 29, n.º 3 (junio de 2013): 663–73. http://dx.doi.org/10.1109/tro.2013.2239554.

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23

Park, Young-Moon y Wook Kim. "Development of the Discrete-Time Adaptive Sliding Mode Power System Stabilizer". IFAC Proceedings Volumes 28, n.º 26 (diciembre de 1995): 43–48. http://dx.doi.org/10.1016/s1474-6670(17)44732-x.

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24

Rossomando, F. G. y C. M. Soria. "Discrete-time sliding mode neuro-adaptive controller for SCARA robot arm". Neural Computing and Applications 28, n.º 12 (24 de marzo de 2016): 3837–50. http://dx.doi.org/10.1007/s00521-016-2242-7.

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25

Weihong, Wang y Hou Zhongsheng. "New adaptive quasi-sliding mode control for nonlinear discrete-time systems". Journal of Systems Engineering and Electronics 19, n.º 1 (febrero de 2008): 154–60. http://dx.doi.org/10.1016/s1004-4132(08)60061-4.

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26

Xu, Fan Rong, Zheng Wang y Hong Zhi Yu. "Indirect Adaptive Fuzzy Sliding Mode Control and Application to Tank Pressurization System". Applied Mechanics and Materials 313-314 (marzo de 2013): 403–8. http://dx.doi.org/10.4028/www.scientific.net/amm.313-314.403.

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An indirect adaptive fuzzy sliding mode control scheme for a class of discrete-time systems with model uncertainty and external disturbance is developed. In this approach, a discrete-time exponential reaching law is used to obtain the ideal sliding mode control law. Then, two fuzzy systems and a third one are used to approximate unknown functions of the system and the switch-type control in the ideal control law, respectively, wherein the consequent parameters are adjusted by an on-line adaptation law with parameter projection. Towards to Tank pressurization system, experiment results have shown the effectiveness of the algorithm.

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27

Won, Mooncheol y J. K. Hedrick. "Disturbance Adaptive Discrete-Time Sliding Control With Application to Engine Speed Control". Journal of Dynamic Systems, Measurement, and Control 123, n.º 1 (16 de marzo de 1998): 1–9. http://dx.doi.org/10.1115/1.1349884.

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This paper presents a discrete-time adaptive sliding control method for SISO nonlinear systems with a bounded disturbance or unmodeled dynamics. Control and adaptation laws considering input saturation are obtained from approximately discretized nonlinear systems. The developed disturbance adaptation or estimation law is in a discrete-time form, and differs from that of conventional adaptive sliding mode control. The closed-loop poles of the feedback linearized sliding surface and the adaptation error dynamics can easily be placed. It can be shown that the adaptation error dynamics can be decoupled from sliding surface dynamics using the proposed scheme. The proposed control law is applied to speed tracking control of an automatic engine subject to unknown external loads. Simulation and experimental results verify the advantages of the proposed control law.

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28

Xia, Yuanqing, Zheng Zhu, Chunming Li, Hongjiu Yang y Quanmin Zhu. "Robust adaptive sliding mode control for uncertain discrete-time systems with time delay". Journal of the Franklin Institute 347, n.º 1 (febrero de 2010): 339–57. http://dx.doi.org/10.1016/j.jfranklin.2009.10.011.

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29

Ben Njima, Chakib, Anouar Benamor y Hassani Messaoud. "A New Robust Adaptive Sliding Mode Control for Discrete-Time Systems With Time-Varying State Delay". International Journal of Service Science, Management, Engineering, and Technology 12, n.º 2 (marzo de 2021): 132–53. http://dx.doi.org/10.4018/ijssmet.2021030108.

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This article proposes a novel robust adaptive sliding control mode law for time unknown varying delay in state uncertain systems. In this work, the upper limit of disruption and uncertainty is assumed to be unknown. The model is adjusted so that the system looks like a certain one with unknown added disturbances on the bounds of which are unknown too. Accordingly, new control law for this kind of systems has been defined based on a Lypunov function choice. The main results of this paper are that the conditions for the existence of linear sliding surfaces are derived within the linear matrix inequalities (LMIs) framework by employing the free weighting matrices and the determination of the control law based on a sliding surface will converge to zero. This proposed approach has been validated in simulation on an uncertain system with comparative study proved the efficiency of the proposed resulting methodology after has been validated in real system.

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30

Ma, Luning, Dongya Zhao, Shuzhan Zhang, Jiehua Feng y Lei Cao. "Discrete-time sliding mode control for a class of nonlinear process". IMA Journal of Mathematical Control and Information 37, n.º 2 (10 de abril de 2019): 513–34. http://dx.doi.org/10.1093/imamci/dnz011.

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Abstract The efficient control of nonlinear processes is generally considered to be challenging. The development of digital computers promotes the study of nonlinear process control technology. Due to the discrete sampling of digital computer, it is necessary to develop the corresponding control algorithms for nonlinear processes. In this paper, a new equivalent control-based discrete-time sliding mode control is proposed for a class of nonlinear process with uncertainty and external disturbance. An adaptive law and a disturbance observer are designed to estimate the uncertainty and the disturbance, respectively. By combining with them, the new discrete-time sliding mode control is developed with good performance. The corresponding theoretical analysis is well verified by using Lyapunov function. Finally, the proposed approach is demonstrated by case studies in light of MATLAB.

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31

Yoshimura, Toshio. "Discrete-time adaptive sliding mode controller for vehicle steering systems with preview". Journal of Vibration and Control 19, n.º 10 (22 de junio de 2012): 1587–600. http://dx.doi.org/10.1177/1077546312447835.

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32

Chen, Xinkai. "Adaptive sliding mode control for discrete-time multi-input multi-output systems". Automatica 42, n.º 3 (marzo de 2006): 427–35. http://dx.doi.org/10.1016/j.automatica.2005.10.008.

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33

Yoshimura, Toshio. "Discrete-time adaptive sliding mode control for a class of uncertain time delay systems". Journal of Vibration and Control 17, n.º 7 (11 de octubre de 2010): 1009–20. http://dx.doi.org/10.1177/1077546310367890.

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34

Almakhles, Dhafer. "The Complex Adaptive Delta-Modulator in Sliding Mode Theory". Entropy 22, n.º 8 (25 de julio de 2020): 814. http://dx.doi.org/10.3390/e22080814.

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In this paper, we consider the stability and various dynamical behaviors of both discrete-time delta modulator (Δ-M) and adaptive Δ-M. The stability constraints and conditions of Δ-M and adaptive Δ-M are derived following the theory of quasi-sliding mode. Furthermore, the periodic behaviors are explored for both the systems with steady-state inputs and certain parameter values. The results derived in this paper are validated using simulated examples which confirms the derived stability conditions and the existence of periodicity.

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35

Liu, Dong y Guang-Hong Yang. "Prescribed Performance Model-Free Adaptive Integral Sliding Mode Control for Discrete-Time Nonlinear Systems". IEEE Transactions on Neural Networks and Learning Systems 30, n.º 7 (julio de 2019): 2222–30. http://dx.doi.org/10.1109/tnnls.2018.2881205.

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36

Yoshimura, Toshio. "Design of adaptive fuzzy backstepping sliding mode control for MIMO uncertain discrete-time nonlinear systems based on noisy measurements". Journal of Vibration and Control 24, n.º 2 (13 de abril de 2016): 393–406. http://dx.doi.org/10.1177/1077546316642053.

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This paper presents an adaptive fuzzy backstepping sliding mode control for multi-input and multi-output uncertain nonlinear systems in semi-strict feedback form. The systems are described by a discrete-time state equation with uncertainties viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. Combining the adaptive fuzzy backstepping control with the sliding mode control approach for the comprehensive improvement in the stability and the robustness, the adaptive fuzzy backstepping sliding mode control is approximately designed where the design parameters are selected using an appropriate Lyapunov function. The uncertainities are approximated as fuzzy logic systems using the fuzzy inference approach based on the extended single input rule modules to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are taken by the proposed simplified weighted least squares estimator. It is proved that the trajectory of the tracking error and the sliding surface is uniformly ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

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37

Ren, Yan, Zhenghua Liu, Xiaodong Liu y Yu Zhang. "A Chattering Free Discrete-Time Global Sliding Mode Controller for Optoelectronic Tracking System". Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/951492.

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Aiming at the uncertainties including parameter variations and external disturbances in optoelectronic tracking system, a discrete-time global sliding mode controller (DGSMC) is proposed. By the design of nonlinear switching function, the initial state of control system is set on the switching surface. An adaptive discrete-time reaching law is introduced to suppress the high-frequency chattering at control input, and a linear extrapolation method is employed to estimate the unknown uncertainties and commands. The global reachability for sliding mode and the chattering-free property are proven by means of mathematical derivation. Numerical simulation presents that the proposed DGSMC scheme not only ensures strong robustness against system uncertainties and small tracking error, but also suppresses the high-frequency chattering at control input effectively, compared with the SMC scheme using conventional discrete-time reaching law.

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38

Wang, Zhihong, Yifei Wu, Wei Chen, Xiang Wang, Jian Guo y Qingwei Chen. "Discrete Second-Order Sliding Mode Adaptive Controller Based on Characteristic Model for Servo Systems". Journal of Control Science and Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/405376.

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Considering the varying inertia and load torque in high speed and high accuracy servo systems, a novel discrete second-order sliding mode adaptive controller (DSSMAC) based on characteristic model is proposed, and a command observer is also designed. Firstly, the discrete characteristic model of servo systems is established. Secondly, the recursive least square algorithm is adopted to identify time-varying parameters in characteristic model, and the observer is applied to predict the command value of next sample time. Furthermore, the stability of the closed-loop system and the convergence of the observer are analyzed. The experimental results show that the proposed method not only can adapt to varying inertia and load torque, but also has good disturbance rejection ability and robustness to uncertainties.

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39

Andrievsky, Boris y Yury Orlov. "Discrete-Time Sliding Mode Energy Control of sine-Gordon Chain with Adaptive Augmentation*". IFAC-PapersOnLine 55, n.º 12 (2022): 717–22. http://dx.doi.org/10.1016/j.ifacol.2022.07.397.

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40

Medhaffar, Hanene, Moez Feki y Nabil Derbel. "Adaptive Discrete-time Fuzzy Sliding Mode Control For a Class of Chaotic Systems". Advances in Science, Technology and Engineering Systems Journal 2, n.º 3 (mayo de 2017): 395–400. http://dx.doi.org/10.25046/aj020351.

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41

Yoshimura, Toshio. "Adaptive sliding mode control for non-linear discrete-time systems with mismatched uncertainty". International Journal of Modelling, Identification and Control 3, n.º 4 (2008): 427. http://dx.doi.org/10.1504/ijmic.2008.020551.

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42

Topalov, Andon V. y Okyay Kaynak. "ROBUST NEURAL IDENTIFICATION OF ROBOTIC MANIPULATORS USING DISCRETE TIME ADAPTIVE SLIDING MODE LEARNING". IFAC Proceedings Volumes 38, n.º 1 (2005): 336–41. http://dx.doi.org/10.3182/20050703-6-cz-1902.00277.

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43

Chan, C. Y. "Discrete-time adaptive sliding mode control of a linear system in statespace form". International Journal of Control 67, n.º 6 (enero de 1997): 859–68. http://dx.doi.org/10.1080/002071797223820.

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44

Rossomando, Francisco G. y Carlos M. Soria. "Adaptive Neural Sliding Mode Control in Discrete Time for a SCARA robot arm". IEEE Latin America Transactions 14, n.º 6 (junio de 2016): 2556–64. http://dx.doi.org/10.1109/tla.2016.7555218.

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45

Salhi, Houda, Samira Kamoun, Najib Essounbouli y Abdelaziz Hamzaoui. "Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models". International Journal of Control 89, n.º 3 (4 de octubre de 2015): 611–22. http://dx.doi.org/10.1080/00207179.2015.1088964.

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46

Park, Y. M. y W. Kim. "Discrete-time adaptive sliding mode power system stabilizer with only input/output measurements". International Journal of Electrical Power & Energy Systems 18, n.º 8 (noviembre de 1996): 509–17. http://dx.doi.org/10.1016/0142-0615(96)00011-7.

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47

Wang, Cong, Hongwei Xia, Yanmin Wang y Shunqing Ren. "Discrete-time Sliding Mode Control with Adaptive Reaching Law via Implicit Euler Method". International Journal of Control, Automation and Systems 21, n.º 1 (enero de 2023): 109–16. http://dx.doi.org/10.1007/s12555-021-0478-1.

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48

Hwang, Chih-Lyang y Bor-Sen Chen. "Constant Turning Force Adaptive Control Via Sliding Mode Control Design". Journal of Dynamic Systems, Measurement, and Control 112, n.º 2 (1 de junio de 1990): 308–12. http://dx.doi.org/10.1115/1.2896141.

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In the constant turning force adaptive control (CTFAC) system, the open-loop gain will vary and the stability cannot be assured when a cutting tool cuts a workpiece at various cutting depths or spindle operates in different speeds. In this paper, the spirit of sliding mode control is extended into discrete-time form to combine with parameter estimation having variable forgetting factor to stabilize the turning system against the variable gain and unmodeled dynamics, such as nonlinear perturbations, inaccurate measurements etc.

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49

Munoz, D. y D. Sbarbaro. "An adaptive sliding-mode controller for discrete nonlinear systems". IEEE Transactions on Industrial Electronics 47, n.º 3 (junio de 2000): 574–81. http://dx.doi.org/10.1109/41.847898.

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50

Sha, Daohang y Vladimir B. Bajic. "Robust discrete adaptive input-output-based sliding mode controller". International Journal of Systems Science 31, n.º 12 (enero de 2000): 1601–14. http://dx.doi.org/10.1080/00207720050217377.

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