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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TME100 - Advanced vehicle dynamics
Syllabus adopted 2008-02-20 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

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0107 Examination 7,5c Grading: TH   7,5c   25 May 2009 pm V,  Contact examiner

In programs

MPAUT AUTOMOTIVE ENGINEERING, MSC PROGR - Vehicle Dynamics specialization, Year 1 
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR - Control specialization, Year 1 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR - Mechatronics specialization, Year 1 (elective)


Docent  Mathias Lidberg

Course evaluation:


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Vehicle dynamics, Control theory


The course aims to extend the student's existing knowledge in vehicle dynamics beyond investigating the longitudinal, lateral and vertical dynamics independently using linear models. In this course the focus is put on the understanding of the coupled dynamics of the vehicle including non-linear effects. The course also aims to introduce some vehicle-specific signal processing and automatic control used in automated subsystems.

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

- Identify and discuss factors that cause interactions between the different vehicle subsystems
- Develop and implement computer models of vehicle dynamics behaviour and critically analyze results from numerical simulations.
- Identify and mathematically characterize linear and nonlinear tire behaviour and the influence of this behaviour on vehicle performance.
- Determine the limits of acceleration and braking and also select the best vehicle setup in terms of weight distribution, wheel usage, etc. for optimized vehicle stability and braking performance.
- Identify suspension and tire characteristics influencing vehicle chassis performance and stability in both low and high-speed manoeuvres, under both steady-state and transient manoeuvres, with the ability to mathematically justify how changes in lumped vehicle parameters 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 ABS, ESC, rear-wheel steering, and active suspension.
- Construct specifications for vehicle control systems.


The course starts with a review of the advanced mathematics and mechanics concepts and notations used in the course. The tire and vehicle models suitable for analyzing the coupled dynamics during steering/braking are developed and then used to evaluate handling performance evaluation 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 material is separated in five modules.

Mathematics and Mechanics Terminology & Notations
Relative Motion, Rigid Body Kinematics & Dynamics (Newton 2.5D)
Linearization, Linear Analysis (Eigenvalues, Transfer Functions, Bode Plots)
Linear and Non-Linear Stability Concepts
Vehicle Dynamics Terminology & Notation
Fundamental Vehicle Dynamics
Importance of Tires
Tire Forces/Moments & Kinematics
ISO Tire Axes & Terminology
Mathematics and Mechanics Notations
Module 1: Vehicle Modeling
The Planar Non-Linear One Track Model (Bicycle Model)
The Planar Non-Linear Two Track Model
Nonlinear tire and suspension effects to be considered:
- The Effect of Roll and Pitch Motions
- Load Transfer Effect on Cornering Stiffness
- Combined Slip Tire Forces
- Effective Axle Characteristics
- Braking/Steering Actuator Saturation and Delays
Module 2: Tire Modeling
Tire Forces/Moments & Kinematics
ISO Tire Axes & Terminology
Longitudinal/ Lateral/ Combined Slip
Stationary and Transient Tire Forces
Review of Industry Standard Tire Models (TMEasy, Brush Tire, Magic Formula)
Module 3: Handling Performance Evaluation
Steady State Cornering
The Handling Diagram
Millikens Moment Method (MMM)
Transient Maneuvers (Step steer, Throttle on/off during Cornering)
Dynamic Maneuvers (Lane Change, Sine with Dwell)
Module 4: Vehicle Stability Control
Basic Signal Processing Theory
Basic Control Theory
Vehicle Parameters and States
Road and Basic Driver Models
Principles, Basic Implementation and Specifications for Vehicle Control Systems:
- Anti-Lock Braking System (ABS)
- Traction Control Systems (TCS)
- Electronic Stability Control (ESC)
- Active Front/Rear Steering (AFS/RAS)
- Active Suspension & Damping
Module 5: Heavy Vehicles
- Steady State Cornering of Single Unit Heavy Trucks and a
Tractor-Semitrailer Combination
- Effect of Tandem Axles and Dual Tires
- The Equivalent Wheelbase Concept
- Handling Diagram of Complex Vehicles
- Tractor Jackknife & Trailer Swing


The course includes formal lectures, assignments and a measurement lab.


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

Pacejka, H.B., Tyre and Vehicle Dynamics, 2002.
Kiencke, U. and Nielsen, L., Automotive Control Systems, 2005
Wong, J.Y., Theory of Ground Vehicle, 2001.
Gillespie, T.D., Fundamentals of Vehicle Dynamics, 1992.
Dixon, J.C., Tires, Suspension and Handling, 2nd Edition, SAE Press, 1996.
Ellis, J.R., Vehicle Handling Dynamics, Mechanical Engineering Publication Limited, London, 1993.
Adams, H., Chassis Engineering: Chassis Design, Building, & Tuning for High Performance Handling.
Matlab/Simulink Users Guide, Mathworks Inc.


A final written examination will comprise 40% of the course grade. Submitted assignments will make up the remainder of the grade.

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