Experience With the Magic Formula Tyre Model

Lidner, Lars

doi:10.1080/00423119208969996

Cited by 16 publications

(11 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where B yc = n 1 cos {arctan [n 2 (α − n 3 )]}, C yc = n 4 (>0), D yc = µ y / cos[C yc arctan (B yc · x y )] and x y = n 5 . µ x and µ y are determined from equation (2) and equation (4) respectively.…”

Section: Combined Slipmentioning

confidence: 99%

“…One can distinguish theoretical models based on the physics of the tyre construction [1,2], and empirical or semiempirical models which are solely based on experimental results [3,4]. In this study, the Pacejka 'magic formula'tyre model [3] is adopted because it accurately describes the measured steady-state tyre behaviour and predicts the vehicle performance well [5]. The parameters of the 'magic formula' represent typical quantities of the tyre characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…The performance of those controllers is influenced by the accuracy of mathematical analysis of the vehicle dynamics and the tyre model. Tyre models [1][2][3][4][5][6][7][8][9][10][11][12][13] express the adhesive force and moment between the road and the tyre with some parameters such as the slip ratio, slip angle and normal force. One can distinguish theoretical models based on the physics of the tyre construction [1,2], and empirical or semiempirical models which are solely based on experimental results [3,4].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An experimental study on the longitudinal and lateral adhesive coefficients between the tyre and the road for a light motorcycle

Chenyuan

Shih

2005

Vehicle System Dynamics

View full text Add to dashboard Cite

The paper presents an analytical approach for estimating the longitudinal and the lateral adhesive coefficients between the tyre and the road surface through the Pacejka 'magic formula' tyre model for both pure-slip and combined-slip conditions. The Pacejka 'magic formula' tyre model describes the relationship between the normal force and the adhesive force. The relationship between the vehicle velocity and the parameters of the Pacejka 'magic formula' tyre model is discussed in the study. One may analyse the adhesive coefficient through genetic algorithm identification to search for the parameters of the Pacejka 'magic formula' tyre model from experimental data. A test stand is set up for adhesive force experiments. Only brake slip is studied in the experiments.

show abstract

Section: Combined Slipmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An experimental study on the longitudinal and lateral adhesive coefficients between the tyre and the road for a light motorcycle

Chenyuan

Shih

2005

Vehicle System Dynamics

View full text Add to dashboard Cite

show abstract

“…For modeling such interactions, various friction models were elaborated to describe e.g., the tire-road interaction ( [21], [22], [23].) The "magic formula" suggested in [24], [25], [26] contains complicated trigonometrical functions, the Rill model [27] applies polynomials in connected bounded sections to describe the slipping-skidding phenomenon. (Its essence is that with the increase of the velocity in the beginning, the friction forces increase, but following a limit they begin to decrease.)…”

Section: The Model Of the Plant To Be Controlledmentioning

confidence: 99%

Observation-based data driven adaptive control of an electromechanical device

Tar

Rudas

Kovács

et al. 2014

2014 IEEE International Symposium on Intelligent Control (ISIC)

View full text Add to dashboard Cite

Abstract-The model-based approach in control engineering works well when a reliable plant model is available. However, in practice, reliable models seldom exist: instead, typical "levels" of limited reliability occur. For instance, Computed Torque Control (CTC) in robotics assumes almost perfect models. The Adaptive Inverse Dynamics Controller (AIDC) and the Slotine Li Adaptive Robot Controller (SLARC) assume absolutely correct analytical model form, and only allows imprecise knowledge regarding the actual values of the model parameters. Neglecting the effects of dynamically coupled subsystems, and allowing the action of unknown external disturbances means a higher level of corrupted model reliability. Friction-related problems are typical examples of this case. In the traditional control literature, such problems are tackled by either drastic "robust" or rather intricate "adaptive" solutions, both designed by the use of Lyapunov's 2 nd method that is a complicated technique requiring advanced mathematical skills from the designer. As an alternative design methodology, the use of Robust Fixed Point Transformations (RFPT) was suggested, which concentrates on guaranteeing the prescribed details of tracking error relaxation via generation of iterative control signal sequences that converge on the basis of Banach's Fixed Point Theorem. This approach is essentially based on the fresh data collected by observing the behavior of the controlled systems, rather than in the case of the traditional ones. For the first time, this technique is applied for order reduction in the adaptive control of a strongly nonlinear plant with significant model imprecisions: the control of a DC motor driven arm in dynamic interaction with a nonlinear environment is demonstrated via numerical simulations.

show abstract

“…The inherent nonlinearity of these models were mathematically approximated in various manners. The "magic formula" invented in the '90s contained highly nonlinear trigonometrical functions with parameters for the identification [7], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Novel design of a Model Reference Adaptive Controller for soft tissue operations

Tar

Kovács

Takács

et al. 2014

2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

View full text Add to dashboard Cite

Abstract-Model Reference Adaptive Controllers (MRAC) have dual functionality: besides guaranteeing precise trajectory tracking of the controlled system, they have to provide an "external control loop" with the illusion that it controls a physical system of prescribed dynamic properties, i.e., the "reference system". The MRACs are designed traditionally by Lyapunov's 2 nd method that is mathematically complicated, requiring strong skills from the designer. Adaptive controllers alternatively designed by the use of Robust Fixed Point Transformations (RFPT) operate according to Banach's Fixed Point Theorem, and are normally simple iterative constructions that also have a standard variant for MRAC design. This controller assumes a single actuator that is driven adaptively. Master-Slave Systems form a distinct class of practical applications, in which two arms-the master and the slave-operate simultaneously. The movement of the master must be tracked precisely by the slave in spite of the quite different forces exerted by them. In the present paper, a soft tissue-cutting operation by a master-slave structure is simulated. The master arm has a simple torque-reference friction model, and is driven by the surgeon. The obtained master arm trajectory has to be precisely tracked by the electric DC motor driven slave system, which is in dynamic interaction with the actual tissue under operation. It is shown via simulations that the RFPT-based design can efficiently solve such tasks without considerable mathematical complexity.

show abstract

Experience With the Magic Formula Tyre Model

Cited by 16 publications

References 3 publications

An experimental study on the longitudinal and lateral adhesive coefficients between the tyre and the road for a light motorcycle

An experimental study on the longitudinal and lateral adhesive coefficients between the tyre and the road for a light motorcycle

Observation-based data driven adaptive control of an electromechanical device

Novel design of a Model Reference Adaptive Controller for soft tissue operations

Contact Info

Product

Resources

About