Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Chaos Analysis and Control in Gear Transmission System using Model Predictive Sliding Mode Algorithm

Authors
1 Ph.D. Candidate, Department of Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 Assistant Professor, Department of Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Abstract
In this paper at first the chaotic behavior of a spur gear system is investigated by the use of numerical tools including phase plane trajectories, Poincare’ section and bifurcation diagrams. in order to eliminate the chaotic oscillations, a novel controller on the basis of the predictive sliding mode control is proposed in which the sliding surface is predicted using the model predictive control theory and the control input is obtained. The simulation results of the feedback system depict the effectiveness of the controller in elimination of the chaotic vibrations along with the reduction of settling time, overshoots, and energy consumption.
Keywords

Subjects


[1] S. L. de Souza, I. L. Caldas, R. L. Viana, A. M. Batista, and T. Kapitaniak, "Noise-induced Basin Hopping in a Gearbox Model," Chaos, Solitons & Fractals, Vol. 26, No. 5, pp. 1523-1531, 2005, doi: https://doi.org/10.1016/j.chaos.2005.04.033.
 
[2] X. Gou, L. Zhu, and C. Qi, "Nonlinear Dynamic Model of a Gear-rotor-bearing System Considering the Flash Temperature," Journal of Sound and Vibration, Vol. 410, pp. 187-208, 2017, doi: https://doi.org/10.1016/j.jsv.2017.08.014.
 
[3] M. Bozca, "Transmission Error Model-based Optimisation of the Geometric Design Parameters of an Automotive Transmission Gearbox to Reduce Gear-rattle Noise," Applied Acoustics, Vol. 130, pp. 247-259, 2018, doi: https://doi.org/10.1016/j.apacoust.2017.10.005.
 
[4] A. Farshidianfar and A. Saghafi, "Identification and Control of Chaos in Nonlinear Gear Dynamic Systems using Melnikov Analysis," Physics Letters A, Vol. 378, No. 46, pp. 3457-3463, 2014, doi: https://doi.org/10.1016/j.physleta.2014.09.060.
 
[5] H. Delavari and M. Mohadeszade, "Chaos Control in a Gear Transmission System via a Novel Adaptive Terminal Sliding Mode Control Approach with Nonlinearity in the Control Input," Journal of Control, Vol. 10, No. 4, pp. 45-53, 2017, doi: http://dorl.net/dor/20.1001.1.20088345.1395.10.4.3.9.
[6] Y. Wang, W. Chen, M. Tomizuka, and B. N. Alsuwaidan, "Model Predictive Sliding Mode Control: for Constraint Satisfaction and Robustness," in Dynamic Systems and Control Conference, 2013, Vol. 56147: American Society of Mechanical Engineers, p. V003T44A005, doi: https://doi.org/10.1115/DSCC2013-4067.
 
[7] G. P. Incremona, A. Ferrara, and L. Magni, "Hierarchical Model Predictive/Sliding Mode Control of Nonlinear Constrained Uncertain Systems," IFAC-PapersOnLine, Vol. 48, No. 23, pp. 102-109, 2015, doi: https://doi.org/10.1016/j.ifacol.2015.11.268.
 
[8] T. Temel, H. Ashrafiuon, C. Nataraj, and S. Yildirim, "A New Sliding-mode Model Predictive Controller for Output Tracking of Nonlinear Systems with Online Optimization," International Journal of Advanced Research, Vol. 3, No. 9, pp. 660-664, 2015, doi: 10.1109/TIE.2016.2618867.
 
[9] M. Spasic, M. Hovd, D. Mitic, and D. Antic, "Tube Model Predictive Control with an Auxiliary Sliding Mode Controller," Modeling, Identification and Control, Vol. 37, No. 3, pp. 181-193, 2016, doi: 10.4173/mic.2016.3.4.
 
[10] I. M.-B. Hassine, M. W. Naouar, and N. Mrabet-Bellaaj, "Model Predictive-sliding Mode Control for Three-phase Grid-connected Converters," IEEE Transactions on Industrial Electronics, Vol. 64, No. 2, pp. 1341-1349, 2016.
 
[11] S. M. Abtahi, "Suppression of Chaotic Vibrations in Suspension System of Vehicle Dynamics using Chattering-free Optimal Sliding Mode Control," Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 41, No. 5, p. 210, 2019, doi: https://doi.org/10.1007/s40430-019-1711-1.
 
[12] S. M. Abtahi, "Melnikov-based Analysis for Chaotic Dynamics of Spin-orbit Motion of a Gyrostat Satellite," Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 233, No. 4, pp. 931-941, 2019, doi: https://doi.org/10.1177/1464419319842024.
 
[13] C.-W. Chang-Jian and S.-M. Chang, "Bifurcation and Chaos Analysis of Spur Gear Pair with and without Nonlinear Suspension," Nonlinear Analysis: Real World Applications, Vol. 12, No. 2, pp. 979-989, 2011, doi: https://doi.org/10.1016/j.nonrwa.2010.08.021.
 
[14] S. Abtahi, S. Sadati, and A. Ghaffari, "Design of Sliding Mode and lQR Controllers for an HVAC System," Aerospace Mech. J, Vol. 9, No. 2, pp. 1-10, 2013.
 
[15] X. Cheng, P. Wang, L. Liu, and G. Tang, "Predictive Sliding Mode Control using Feedback Linearization for Hypersonic Vehicle," Procedia Engineering, Vol. 99, pp. 1076-1081, 2015, doi: https://doi.org/10.1016/j.proeng.2014.12.642.
 
[16] M. H. Gharagozloo and A. Shahmansoorian, "Chaos Control in Gear Transmission System using GPC and SMC‎ Controllers," Journal of Applied and Computational Mechanics, Vol. 8, no. 2, pp. 545-556, 2022, doi: 10.22055/JACM.2020.32499.2028
 
[17] P. C. Müller, "Popov and Circle Criterion," In Control System, Robotics and Automation-Volume III: System Analysis and Control: Classical Approaches-III, Encyclopedia of Life Support System, Vol. 3, H. Unbehauen, Ed., ed. Oxford, United Kingdom: EOLSS Publishers Co. Ltd., 2009, p. 154.

  • Receive Date 28 December 2021
  • Revise Date 15 May 2023
  • Accept Date 19 September 2023