# Chaos Control of a Quarter-Car Vehicle Model with Hysteretic Nonlinear Suspension System

Topics: Chaos theory, Control theory, Nonlinear system Pages: 3 (858 words) Published: February 25, 2013
Chaos Control of a Quarter-car Vehicle Model with Hysteretic Nonlinear Suspension System

In this paper, chaotic motion in a nonlinear oscillator with nonsymmetric potential is examined. The strange chaotic attractor and its unstable periodic orbits for the system is investigated. By applying numerical results, phase diagrams, Lyapunov exponents and power spectrum are presented to observe periodic and chaotic motions. Chaos control using feedback methods are studied. Four chaos control methods are compared and most suitable method is found in this work. Keywords: Hysteretic nonlinear; Chaos; Quarter-car; feedback control Nomenclature

[pic]= the mass of the body, Kg. [pic]= nonlinear damping coefficient, Ns3m-3. g = acceleration due to gravity, ms-2. [pic] = the body’s vertical displacement, m. [pic]= Excitation frequency, Hz. k2 = Nonlinear stiffness, Nm-3. [pic] = Natural frequency, rads-1 [pic] = Linear damping coefficient, Nsm-1. k1 = suspension stiffness, Nm-1. [pic]= the road excitation, m.

1. Introduction

Chaos is interesting nonlinear phenomenon, having been studied over the past decades. There are two types of chaos control. One is OGY method, first introduce by Ott et al (1990) which uses some weak feedback control to make the chaotic trajectory approach and settle down finally to a desired stabilized periodic orbit. The second kind of chaos control belongs to non-feedback method, which usually uses given external or parametric excitations to control the system behavior. Both kinds of chaos control are still in nascent stage of development. In this paper, the results of an investigation of controlling chaos for a nonlinear oscillator with nonsymmetric potential are presented. The chaos in the system is determined by using periodic phase portraits, bifurcation diagram and Lyapunov exponents. The existence of chaos in the system is verified via power spectrum. A strange...