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Friction: Problem Solving

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Friction is an essential force that influences the motion of objects in daily life. Depending on the situation, it can be either beneficial or problematic. Consider a bus with a mass of three megagrams and its center of mass at a specific point, moving along a banked road at a constant speed. The coefficient of static friction between the tires and the road is 0.5. Find the maximum angle of the banked road at which the bus would not slip or tip.
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Determination of the Friction Coefficients of Icy Pavements Under Different Amounts of Snowfall

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Tire Slip H_∞ Control for Optimal Braking Depending on Road Condition.

Miguel Meléndez-Useros¹, Manuel Jiménez-Salas¹, Fernando Viadero-Monasterio¹

¹Mechanical Engineering Department, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain.

Sensors (Basel, Switzerland)

|February 11, 2023

Summary

This study introduces an H∞ controller for optimal tire slip control, enhancing vehicle braking performance across various road conditions by adapting to friction levels. The controller ensures accurate slip tracking for improved safety and efficiency.

Keywords:

H∞ control anti-lock brake system tire slip control vehicle dynamics

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Area of Science:

Vehicle Dynamics and Control
Automotive Engineering
Robotics

Background:

Tire slip control is crucial for vehicle safety systems like ABS, TCS, and ESP.
The nonlinear nature of tire-road interactions and varying road conditions complicate robust controller design.
Optimal braking performance is directly influenced by the tire-road friction coefficient.

Purpose of the Study:

To develop an H∞ controller for tire slip control.
To maximize vehicle braking forces by adapting to different road conditions.
To improve the robustness and performance of vehicle dynamics control systems.

Main Methods:

Design of an H∞ controller for tire slip control.
Utilizing the CarSim software for vehicular dynamics simulations.
Implementing a control strategy that adjusts slip ratio reference based on the friction coefficient.

Main Results:

The proposed H∞ controller effectively manages tire slip according to road conditions.
The controller achieved a small reference error in tire slip tracking.
Demonstrated good transient response during simulations across various tested road conditions.

Conclusions:

The H∞ controller provides an effective solution for tire slip control.
Adapting the slip ratio reference based on the friction coefficient maximizes braking performance.
The developed controller enhances vehicle stability and braking efficiency on diverse road surfaces.