Limit cycles at oversteer vehicle

Steindl, Alois; Edelmann, Johannes; Plöchl, Manfred

doi:10.1007/s11071-019-05081-8

Cited by 19 publications

(12 citation statements)

References 17 publications

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“…This approximation suggests the reduction of the dynamics onto the critical manifold, like it is often assumed (e.g. [27]). Interestingly, this approximation is not sufficient to study the inversion phenomenon of the tippedisk.…”

Section: Discussionmentioning

confidence: 86%

Singularly perturbed dynamics of the tippedisk

Sailer

Leine

2021

Proc. R. Soc. A.

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The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow–fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.

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Section: Discussionmentioning

confidence: 86%

Singularly perturbed dynamics of the tippedisk

Sailer

Leine

2021

Proc. R. Soc. A.

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“…Depending on the specific use-case and the accuracy needed, there exist many variations of this model [34,39]: The simplest vehicle models assume rigid wheels with no tire deformation [19,26], but a wide range of tire models are also available in the literature to describe the tire-road interaction [33]. The arising side forces and self-aligning moments are commonly considered as different linear and nonlinear functions of the side slip angles [21,45], but more involved tire models can also be applied [5]. Additional modeling aspects include the consideration of geometrical nonlinearities [10,30,45], the drive type of the vehicle [30], the inertia of the steering system [49] and the caster length of the steered wheel [48].…”

Section: Introductionmentioning

confidence: 99%

“…The arising side forces and self-aligning moments are commonly considered as different linear and nonlinear functions of the side slip angles [21,45], but more involved tire models can also be applied [5]. Additional modeling aspects include the consideration of geometrical nonlinearities [10,30,45], the drive type of the vehicle [30], the inertia of the steering system [49] and the caster length of the steered wheel [48]. When selecting the appropriate vehicle model, a balance needs to be found between model complexity and fidelity.…”

Section: Introductionmentioning

confidence: 99%

On the global dynamics of path-following control of automated passenger vehicles

Vörös¹,

Orosz

Takács³

2023

Nonlinear Dyn

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The nonlinear dynamics of the path-following control of passenger cars is analyzed in this paper. The effect of specific modeling aspects, such as tire deformation, steering dynamics, feedback delay and controller saturation, is considered. Possible equilibrium points and singularities in the state space are uncovered and analyzed for different vehicle model and controller designs. The equilibrium of stable path following is then analyzed in greater detail: The domains of stabilizing control gains are presented in stability charts and the basin of attraction of the equilibrium along the stable domain is approximated with the help of numerical continuation. Unsafe zones of control gains are highlighted, where the stable equilibrium is surrounded by low-amplitude unstable limit cycles. Finally, it is shown how specific modifications of the control law can remove unwanted equilibrium points and increase the basin of attraction of stable path following, resulting in safer and more reliable control of the vehicle.

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“…By analyzing the linear stability of equilibria, Varszegi et al 20 found that the vehicle may lose stability in oscillatory and non-oscillatory ways corresponding to Hopf and pitchfork bifurcations, respectively. Steindl et al 21 found that small amplitude limit cycles close to the Hopf bifurcation point emerge with the steering angle (drive torque) as bifurcation parameter, followed by large amplitude relaxation cycles.…”

Section: Introductionmentioning

confidence: 99%

Vehicle coupled bifurcation analysis of steering angle and driving torque

Xian-bin

Shi

2021

Proceedings of the Institution of Mechanical Engineers, Part D:

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The mechanism of vehicle dynamics steering bifurcation has almost been confirmed. But the present steering bifurcation mechanism cannot explain the bifurcation phenomena caused by the driving torque. As a result, the vehicle coupled bifurcation analysis of the steering angle and driving torque has not been studied. Based on the five degrees of freedom (5DOF) vehicle system dynamics model with driving torque involved, the vehicle dynamics equilibriums under different driving torque and driving mode were searched by a hybrid method in this paper. The hybrid method combined the real-coded Genetic Algorithm with Quasi-Newton gradient method. According to the definition of static bifurcation of nonlinear systems, the equilibrium bifurcation of 5DOF vehicle system was confirmed. Then, the 5DOF vehicle system model was transformed into autonomous equation with the front wheel steering angle as intermediate variable. From the two aspects of constant steering angle amplitude and constant driving torque, the bifurcation diagrams of different driving mode were calculated. The vehicle coupled bifurcation characteristics of steering angle and driving torque were analyzed. The results show that the values of the driving torque will directly affect the bifurcation characteristics of vehicle dynamics system. The coupled feature of the front wheel steering angle and driving torque effect on vehicle bifurcation is obvious.

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Limit cycles at oversteer vehicle

Cited by 19 publications

References 17 publications

Singularly perturbed dynamics of the tippedisk

Singularly perturbed dynamics of the tippedisk

On the global dynamics of path-following control of automated passenger vehicles

Vehicle coupled bifurcation analysis of steering angle and driving torque

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