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Dynamic Systems 7.5 credits

Dynamiska system
Second cycle, R7016E
Course syllabus valid: Autumn 2020 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Education level
Second cycle
Grade scale
G U 3 4 5
Control Engineering
Subject group (SCB)
Automation Technology
Main field of study
Engineering Physics and Electrical Engineering

Entry requirements

Basic knowledge of physics, specifically mechanics, electric circuits and thermodynamics. Knowledge of mathematics, including linear algebra, differential equations, recurrence equations and the Laplace transform. These prerequisite knowledge correspond to F0004T Physics 1, M0031M Linear Algebra and Differential Equations, and one of M0018M Linear analysis, R0001E Basic automatic control, or R0002E Modeling and control. Good knowledge in English equivalent to English 6. More information about English requirements:

More information about English language requirements


The selection is based on 20-285 credits

Course Aim
After completing the course the student should be able to:       
  • Set up first principles models for basic mechanical, electrical, thermal, and fluid flow systems
  • Set up first principles models for other types of systems, such as chemical, biologic, economic, and sociologic, given a description of the system mechanisms.
  • Analyze dynamic systems regarding properties such as equilibrium, stability, oscillations, and chaotic behavior 
  • Implement simulation models for dynamic systems of different kinds, such as ordinary differential equation, partial differential equations, discrete-time systems, differential algebraic systems

  • Dynamic models for electric circuits, mechanical translation, rotation and for thermal and fluid flow systems
  • Some examples of models for chemical, biological, economic, sociologic, and population systems.
  • Phase portraits of dynamic systems
  • Stability analysis: Equilibrium, Introduction to Lyapunov stability, the circle criterion
  • Oscillation analysis: Poincare maps, Describing function
  • Introduction to chaotic behavior
  • Simulation of dynamic systems: Numerical solution of differential equations and differential-algebraic systems. Step length and stiffness

Lectures and group exercises on modeling and analysis of dynamic systems. Lab work on implementation and simulation of dynamic systems in software.

The examination consists of written exam with differentiated grades and written and oral reporting of lab and project work.

Andreas Johansson

Literature. Valid from Autumn 2020 Sp 1 (May change until 10 weeks before course start)
Title: Mathematics for Dynamic Modeling
Author: Edward Beltrami
Publisher: Academic Press, 1998

Course offered by
Department of Computer Science, Electrical and Space Engineering

CodeDescriptionGrade scaleHPStatusFrom periodTitle
0001Written examG U 3 4 54.50MandatoryA20
0002Laboratory workU G#3.00MandatoryA20

Syllabus established
by Jonny Johansson, HUL SRT 21 Feb 2020

Last revised
by Jonny Johansson, HUL SRT 21 Feb 2020