ELI2300 Dynamic Systems Course description

Knowledge of linear dynamic systems is important in many applications, including electronics, signal processing, communications, biomedical engineering, robotics and control systems. The course deals with analysis of linear dynamic systems in the time domain and the frequency domain. The course also is an introduction to modeling of systems as differential equations and solving them by application of the Laplace transform. The systems are analyzed by their transfer function and frequency response. The frequency response also reveals the filter characteristics of the system and how it affects the frequency content of a signal. 

Builds on ELPE1300 Electric Circuits, MEK1400 Physics, MEK1000 Mathematics 1000 and MEK2000 Mathematics 2000 should be taken in parallel.

Students will learn through a combination of interactive lectures, case studies, literature analyses, and guest lectures. Internal presenters in the course are from different departments. External presenters are from hospital, medical companies and interest organization with a cross-dissiplinary background.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge 

The student has knowledge of: 

• Modelling first and second order physical systems (e.g., mechanical, electrical, thermal, and fluid systems) as ordinary differential equations 
• Unilateral Laplace transformation and its main properties (including calculations of Laplace transformation of functions such as impulse, step, ramp, exponential, sinusoidal) 
• Inverse Laplace transform using partial fraction expansion to find the systems time response 
• Stability analysis of transfer functions 
• Frequency response analysis of stable systems 
• The Fourier transform and its main properties 
• Concepts of basic filter design (such as low-pass, band-pass, and high-pass) and how a signals changes after filtering (both time domain and frequency domain aspects) 
• Properties of first order and second order systems (such as time constant, rise-time, overshoot, settling time) 

Skills 

The student is capable of: 

• Setting up mathematical models of simple physical systems 
• Solving ordinary differential equations with the use of the unilateral Laplace transform 
• Finding the time response of linear time invariant systems (such as impulse response and step response) 
• Finding the frequency content of a signal by using the Fourier transform 
• Designing filters and finding their frequency response 
• Identifying first-order and second-order systems based on their response in time and frequency domain 
• Using MatLab to solve relevant problems 

General competence 

The student is capable of: 

• Setting up a mathematical model of a physical system in form of differential equations and solving them by application of the Laplace transform 
• Analyse linear systems both in the frequency and time domain 
• Design filters to limit the frequency content of a signal 

Individual assignment (report) counts for 70% of the final grade, and oral presentation of selected material (30 minutes per candidate) that counts 30 % of the final grade. Review assignment of report on a chosen subject, maximum 10 pages. To be submitted no more than two weeks after the end of the course.

Both individual assignment (report) and oral presentation must be passed in order to pass the course. The oral presentation cannot be appealed.

None.

Pass or fail.

A panel of all presenters in the course, and at least one external representative will evaluate the report and the presentation.

Grade scale A-F.

One internal examiner. The course may be selected for grading by external examiners.

For the continuation exam (resit), an oral exam can be used, with two internal examiners.