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PhD Course in System Modelling and Simulation, 7.5 ECTS

April 25 @ 13:00 - June 18 @ 17:00

This course is about the simulation of complex technical systems. It covers the range from detailed equations to integration of multiple software for simulation. The course is based around the transmission line modelling (bi-directional delay lines) paradigm for partitioning of models, with application mainly in the Hopsan simulation package, and for co-simulation. However, it also includes more general topics applicable to simulation in general.

Course objective

After the course the participants should:

  • Have a broad orientation of simulation methods and tools.
  • Be able to use methods and tools for simulation and co-simulation.
  • Be able to develop system models.
  • Be able to develop component models at an equation level for system simulation.
  • Be able to match the level of detail with what is needed for a specific task.
  • Use simulation models for optimization.
  • Being prepared to use Large Language Models, LLMs for modelling.

Course content

  • Introduction and Basic Concepts of System Simulation
    • Course overview
    • Introduction to the Hopsan simulation package and relation to other simulation tools
  • Transmission Line Modelling
    • Simulation in the frequency domain
    • Frequency dependent friction.
      • Hydraulic and Electrical systems.
    • The Unit Transmission Line Element
  • Numerical Methods
    • Accuracy and stability analysis and characteristics of different methods
    • Differential Algebraic Equations
    • Algebraic solvers, Newton-Raphson
    • Variable time step
    • Event free systems
  • Equation Based Modelling
    • Object Oriented Modelling
    • Modelica
  • Connectivity
    • Co-simulation (e.g., Matlab/Simulink)
    • Simulation with FMI
  • Component modelling
    • Hopsan built-in editor and Mathematica/Compgen
    • Hydraulic components
    • Electrical components
    • Gas/pneumatic components
    • Mechanical components
      • Euler-Lagrange equation
      • Friction, multi-body systems, 2D-mechanics
    • Discrete event systems
    • Using LLM for modelling and simulation
  • Simulation based optimization.
    • Optimization methods
    • Objective function formulation
    • Parametrization
    • Optimizer performance
    • Macro functionality


  • Lecture Notes
  • Selected research publications
  • Dissertations from IEI/Flumes.


The course is examined through a project that is defined together with the examiner which is then executed and then presented at the end of the course.



Please register here!

Preliminary Schedule

Date Topic
April 25
13-17 CET
Introduction and Basic Concepts of System Simulation (PK, RB)

Transmission line dynamics (PK)

  • Simulation in the frequency domain
  • Frequency dependent friction

Electrical Systems

May 7
13-17 CET
Numerical methods (PK, RB)
May 8
13-17 CET
Equation based languages. (RB)
May 15
13-17 CET
Component Modelling (PK, RB)
May 16
13-17 CET
Component Modelling (PK)
May 21
13-17 CET
June 12
13-17 CET
Co-simulation (RB)
June 13
13-17 CET
Simulation based optimization (RB)
TBD Sept Examination (PK; RB)


April 25 @ 13:00
June 18 @ 17:00
Event Category: