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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TME102 - Vehicle dynamics, advanced
Syllabus adopted 2014-02-17 by Head of Programme (or corresponding)
Owner: MPAUT
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Automation and Mechatronics Engineering, Mechanical Engineering, Engineering Physics
Department: 42 - APPLIED MECHANICS

Teaching language: English
Open for exchange students
Block schedule: B
Maximum participants: 40

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0111 Examination, part A 4,5 c Grading: TH   4,5 c   04 Jun 2015 am M,  13 Apr 2015 am M,  20 Aug 2015 am M
0211 Project, part B 3,0 c Grading: TH   3,0 c    

In programs



Docent  Mathias Lidberg


TME100   Advanced vehicle dynamics TME101   Advanced vehicle dynamics


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

MMF062 Vehicle dynamics and/or MMA092 Rigid body dynamics
ERE033 Control theory or similar


In this course the focus is put on the understanding of the coupled planar dynamics of road vehicles during steering and braking (or driving) including various non-linear effects from tires, suspension etc

Learning outcomes (after completion of the course the student should be able to)

* Identify and discuss factors (e.g. load transfer) that cause interactions between the different vehicle subsystems, e.g. braking and steering.

* Develop and implement computer models of vehicle dynamics behavior and critically analyze results from numerical simulations.

* Identify and mathematically characterize linear and nonlinear tire behavior and the influence of this behavior on vehicle performance using Handling Diagram.

* Identify suspension and tire characteristics influencing vehicle chassis performance and stability in both low and high-speed maneuvers, under both steady-state and transient maneuvers, with the ability to mathematically justify how changes in vehicle parameters (e.g. mass or weight distribution) can be stabilizing or destabilizing.

* Understand how to extend the mathematical analysis of the passenger car to heavy vehicles.

* Understand and characterize the change in vehicle performance and vehicle/roadway interaction due to automated subsystems such as e.g. ABS, ESP and Rear Wheel Steering.

* Construct specifications for vehicle control systems.


The mathematics and mechanics concepts and notations used in the course are reviewed.
The tire and vehicle models suitable for analyzing the coupled dynamics during steering and
braking or driving are developed and then used to evaluate handling performance in various
maneuvers. Some aspects about vehicle stability and the principles, basic implementation
and specifications for automated vehicle control systems are included. At the end the challenges
posed by heavy vehicles are discussed but not covered in detail. The course content is
separated in six modules:

Preliminaries (covered during the course)
Vehicle Dynamics Terminology & Notation
Fundamental Vehicle Dynamics
Relative Planar Motion, Rigid Body Kinematics & Dynamics (Newton 2.5D) 1
Linearization, Linear Analysis (Eigenvalues, Transfer Functions, Bode Plots)
Linear and Non-Linear Stability Concepts
Basic Signal Processing and Control Theory

Module 1: Vehicle Modeling for Planar Dynamics
Tire Properties Influence on Vehicle Dynamics
Tire Forces/Moments & Kinematics
Modified SAE Tire Axes & Terminology
Introduction to Tire Modeling (Magic Formula)
Definition of Effective Tire & Axle Characteristics
The Planar Rigid One Track Model (Bicycle Model)
Suspension and Steering Effects
The Planar Two Track Model Vehicle
Model Block Diagram

Module 2: Tire Modeling
Basic Tire Modeling Consideration
Brush Tire Model
Steady State Lateral/Longitudinal Slip Force Generation
Interaction between Lateral Slip and Longitudinal Slip (Combined Slip)
Transient Tire Forces
Review of Industry Standard Tire Models (Magic Formula, etc)

Module 3: Vehicle Handling and Stability
Steady State Cornering Stability Analysis
Handling Diagram
Quasi Steady State Cornering (Moderate Driving/Braking Milliken Moment Method
Straight Line Braking Stability Analysis
Transient Cornering (Step Steer, Throttle On/Off)
Dynamic Cornering (Double Lane Change, Sine with Dwell)
Principles for ABS and ESP

Module 4: Heavy Vehicles
Steady State Cornering of Single Unit Heavy Trucks
Effect of Tandem Axles and Dual Tires
Equivalent Wheelbase Handling Diagram of Complex Vehicles
V-Handling & R-Handling Curves
Steady State Cornering of a Tractor-Semitrailer
Tractor Jackknife & Trailer Swing

Module 5: Vehicle Stability Control
Vehicle Parameters and States Estimation
Road and Basic Driver Models Principles
Basic Powertrain Modeling
Brake System Modeling (Saturation and Delays)
Basic Implementation and Specifications for Vehicle Control Systems, e.g.:
- Anti-lock Braking System (ABS)
- Electronic Stability Control (ESC)


- Lectures
- Problem solving sessions
- Assignments
- Lab


Lidberg, M., Vehicle Dynamics, Stability and Controls (lecture notes).

* Pacejka, H.B., Tyre and Vehicle Dynamics, 2002.
* Abe M., Vehicle Handling Dynamics, 2009.
* Kiencke, U. and Nielsen, L., Automotive Control Systems, 2005
* Matlab/Simulink Users Guide, Mathworks Inc


* Marked assigment reports (50%)
* Graded written examination with problem solving (50%)

Page manager Published: Thu 04 Feb 2021.