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Chaotic dynamics of the vertical model in vehicles and chaos control of active suspension system via the fuzzy fast terminal sliding mode control

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Abstract

In this paper, the control of chaotic vibrations in vehicle suspension system is studied via a fuzzy fast terminal sliding mode method. Therefore, the nonlinear equations of motion in the vehicle half model are derived initially through the Newton-Euler laws and then these equations are solved by the fourth-order Runge-Kutta method. For analysis of chaos, some techniques including bifurcation diagrams, frequency response, power spectrum, phase plane trajectories, and Poincaré section are used to identify the chaotic behaviors. The chaotic zones are depicted with critical values on the uncontrolled model under the road surface force. In order to eliminate chaotic behavior, the control signals in the active suspension system are generated using the novel fuzzy fast terminal sliding mode control algorithm. The simulation results of the feedback system show that the suspension system can be stabilized the vibrations by efficient fuzzy fast terminal SMC while eliminating irregular chaotic behaviors.

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Abbreviations

m b :

Vehicle body mass

J :

Vehicle body inertia

m f :

Front unsprung mass

m r :

Rear unsprung mass

x b(t):

Displacement of mb

θ(t):

Angular displacement of mb

x f(t):

Displacement of mf

X r(t):

Displacement of mr

x fd(t):

Excitation to the front tire

x rd(t):

Excitation to the rear tire

l f :

Front length

l r :

Rear length

k f2 :

Front suspension spring stiffness

C f2 :

Front suspension damping coefficient

k r2 :

Rear suspension spring stiffness

C r2 :

Rear suspension damping coefficient

k f1 :

Front tire stiffness

C f1 :

Front tire damping coefficient

k r1 :

Rear tire stiffness

C r1 :

Rear tire damping coefficient

k s :

Stiffness of the suspension springs

Δs :

Relative variations in spring length potential

C u :

Damping coefficient in tension

C d :

Damping coefficient in compression

A :

Amplitude of the excitation force

f :

Frequency of the excitation force

α :

The time delay between the road roughness to the front and rear tires

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

    Yavar Nourollahi Golouje & Seyyed Mahdi Abtahi

Authors
  1. Yavar Nourollahi Golouje
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  2. Seyyed Mahdi Abtahi
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Corresponding author

Correspondence to Seyyed Mahdi Abtahi.

Additional information

Yavar Nourollahi Golouje received his B.S. and M.S. in Mechanical Engineering at Islamic Azad University of Tabriz, Iran. Now he is a Ph.D. candidate in Mechanical Engineering, Applied Solid Design, at Islamic Azad University of Qazvin, Iran from 2016. His research interests include nonlinear dynamic and control specialized chaotic systems.

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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 sliding mode control. J Mech Sci Technol 35, 31–43 (2021). https://doi.org/10.1007/s12206-020-1203-3

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  • DOI: https://doi.org/10.1007/s12206-020-1203-3

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