Jump Phenomenon Analysis in Vehicle and Chaos Control of Active Suspension System via Extended Pyragas Algorithm
الموضوعات :yavar nourollahi 1 , Seyyed Mahdi Abtahi 2
1 - Department of Mechanical Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Department of Mechanical Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
الکلمات المفتاحية: Chaotic Dynamics, Chaos Control, Extended Pyragas, Jump Phenomenon,
ملخص المقالة :
In this paper, the nonlinear phenomenon including hump and chaos analysis along with chaos control of an active suspension in vehicles has been studied. The unstable periodic orbits of the system are stabilized using the novel developed delay feedback control algorithm based on the fuzzy sliding mode system. The chaotic Equations of motions are derived via Newton-Euler relations then, the nonlinear phenomenon such as jump and chaos in the vehicle dynamics has been confirmed using forcing frequency method. The results of the forcing frequency demonstrate the changes in system behaviour from the periodic to the irregular chaotic responses. In order to eliminate the chaotic responses in the vertical dynamics of the vehicle, a new fuzzy sliding delay feedback control algorithm is designed on the active suspension. The controller gain of the sliding feedback control is online estimated via fuzzy logic causing to rejection of the chattering phenomenon in the sliding mode algorithm besides the improvement in the responses of the feedback system. Simulation results of the control system depict a reduction of settling time and energy consumption along with eliminating the overshoots and chaotic vibrations.
[1] Ott, E., Grebogi, C., and Yorke, J. A., Controlling Chaos, Phys Rev Lett, Vol. 64, 1990, pp. 1196–1199.
[2] Pyragas, K., Continuous Control of Chaos by Self-Controlling Feedback, Physics Letters A, Vol. 170, 1992, pp. 421-428.
[3] Pyragas, K., Tamas, A., Experimental Control of Chaos by Delayed Self-Controlling Feedback, Phys. Lett. A, Vol. 180, 1993, pp. 99–102.
[4] Abtahi, M., Chaotic Study and Chaos Control in A Half-Vehicle Model with Semi-Active Suspension Using Discrete Optimal Ott–Grebogi–Yorke Method, J Multi-Body Dynamics, Vol. 231, 2017, pp. 148–155.
[5] Litak, G., Borowiec, M., Friswell, M., and Szabelski, K., Chaotic Vibration of a Quarter-Car Model Excited by The Road Surface Profile, Communications in Nonlinear Science and Numerical, Vol. 13, 2018, pp. 1373–1383.
[6] Litak, G., Borowiec, M., Friswell, M., and Przystupa, W., Chaotic Response of Quarter Car Model Forced by A Road Profile with A Stochastic Component, Chaos, Solutions and Fractals, Vol. 39, 2009, pp. 2448–2456.
[7] Naik, R., Singru, P., Resonance, Stability and Chaotic Vibration of a Quarter Car Vehicle Model with Time-Delay Feedback, Common Nonlinear Sci Numer Simulat, Vol. 16, 2011, pp. 3397–3410.
[8] Zhu, Q., Ishitobi, M., Chaotic Vibration of a Nonlinear Full-Vehicle Model, International Journal of Solids and Structures, Vol. 43, 2006, pp. 747-759.
[9] Zhong, S., Chen, Y., Bifurcation of Piecewise-Linear Nonlinear Vibration System of Vehicle Suspension, Applied Mathematics and Mechanics, Vol. 30, 2009, pp. 677–684.
[10] Fakheari, J., Khanlo, H., Ghayour, M., and Faramarzi, K., The Influence of Road Bumps Characteristics on The Chaotic Vibration of a Nonlinear Full-Vehicle Model with Driver, International Journal of Bifurcation and Chaos, Vol. 26, 2016, pp. 151-161.
[11] Dehghani, R., Khanlo, H., and Fakhraei, J., Active Chaos Control of a Heavy Articulated Vehicle Equipped with Magnetorheological Damper, Nonlinear Dyn, Vol. 87, 2017, pp. 1923–1942.
[12] Kucukefe, Y., Adnan, K., Delayed Feedback Control as Applied to Active Suspension of a Ground Vehicle, EUROCON 2009, IEEE.
[13] Zhang, Z., Chau, K., and Wang, Z., Analysis and Stabilization of Chaos in the Electric-Vehicle Steering System, IEEE Transactions on Vehicular Technology, Vol. 62, 2013, pp. 1-10.
[14] Koumen, G., Taffo, M., Siewe, S., and Tchawoua, C., Stability Switches and Bifurcation in A Two-Degrees-Of-Freedom Nonlinear Quarter-Car with Small Time-Delayed Feedback Control, Chaos, Solitons and Fractals, Vol. 87, 2016, pp. 226–239.
[15] Abtahi, M., Melnikov-Based Analysis for Chaotic Dynamics of Spin-Orbit Motion of a Gyrostat Satellite, Journal of Multi-Body Dynamics, Vol. 233, 2019, pp. 931-941.
[16] Chen, W,. Zhang, R,. Zhao, L,. Wang, H,. and Wei, Zh,. Control of Chaos in Vehicle Lateral Motion Using the Sliding Mode Variable Structure Control, Proc IMechE Part D: J. Automobile Engineering, 2018, pp. 1–14.
[17] Salarieh, H., Alasty, A., Chaos Control in Uncertain Dynamical Systems Using Nonlinear Delayed Feedback, Chaos, Solutions& Fractals, Vol. 41, 2009, pp. 67-71.
[18] Metered, H., Musaad Ibrahim, I., Vibration Mitigation of Commercial vehicle Active Tandem Axle Suspension System, SAE Internatiol Journal, Vol. 18, 2022, pp. 02- 15-03-0015.
[19] Abtahi, M., 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, 2019, pp. 209-219.
[20] Golouje, Y. N., Abtahi, S. M., Chaotic Dynamics of The Vertical Model in Vehicles and Chaos Control of Active Suspension System Via the Fuzzy Fast Terminal Slidin Mode Control, Journal of Mechanical Science and Technology, Vol. 35. No. 1, 2021, pp. 31-43.