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.

No requirements over and above the admission requirements.

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

The teaching consists of lectures combined with exercises, laboratory work and a small project.

None

Individual written exam, 3 hours

The exam result can be appealed.

In the event of a resit or rescheduled exam, an oral examination may be used instead. In case an oral exam is used, the examination result cannot be appealed.

A handheld calculator that cannot be used for wireless communication or to perform symbolic calculations. If the calculator’s internal memory can store data, the memory must be deleted before the exam. Random checks may be carried out.

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.