Paul Bourassa

TL;DR: In this paper, the stability of the vehicle/pilot system for two different models of human operator behaviour is investigated. But the results of these models are the outcome of various approximations of the precision model for single loop compensatory situations.

Abstract: The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincare maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries.

TL;DR: The mathematical model allows computation of the unmeasurable neurophysiological commands λ and μ that control the equilibrium position and stability and concludes that low-amplitude body sway during quiet stance is commanded by the central nervous system.

TL;DR: In this paper, the spectrum associated with a system of linear retarded functional differential equations is computed to determine the stability and chaotic motion of a time-delayed nonlinear vehicle system, which reveals that a loss of stability occurs following a Hopf bifurcation.

TL;DR: In this article, the simulation of a vehicle/pilot system experiencing external disturbances is dealt with, where the car is modeled with two degrees of freedom and the pilot is assumed to respond to the state vector with a time delay.