Course - Systems Theory, Introduction - TTK4225
TTK4225 - Systems Theory, Introduction
About
New from the academic year 2014/2015
Examination arrangement
Examination arrangement: Written examination
Grade: Letters
Evaluation | Weighting | Duration | Grade deviation | Examination aids |
---|---|---|---|---|
Skriftlig | 100/100 | 4 timer |
Course content
Fundamentals of complex algebra. The Laplace transform, applied to signals and linear systems. Convergence, inverse transform, properties.Impulse response and convolution. Transfer functions. Block diagrams and manipulation rules. "s" as a differentiation operator.
The Fourier transform, also as a special case of the Laplace transform. Fourier series and -transform of signals and for linear systems, common traits of signals and systems. Impulse and frequency response. Signal spectrum. Bilateral Fourier and Laplace transform. Convergence and existence. Impulse function in the frequency plane.
State space models with vector differential equations and use of linear algebra. Transition matrix, decoupling, similarity transformation. Relation to Laplace: resolvent matrix and transfer matrix.
Systems and signals in discrete time. Sampled systems. The sampling theorem. The zero-order hold and its phase effect. Analysis and synthesis via approximation in continuous time. Z as a time shift operator. Briefly and practically about stochastic signals and noise, analog and discrete filters.
Learning outcome
Knowledge: Basic knowledge about mathematical tools for describing and analysing linear time-continuous signals and dynamic systems described by time responses and differential equations. Basic knowledge about models of systems in the form of n-dimensional differential equations. Knowledge of concepts like vector differential equations, state space model, eigenvalues. Knowledge of concepts like impulse- and step response,poles and zeros, block diagram and feedback.
Basic knowledge about modeling and analysis of continuous dynamical systems with transfer functions and frequency analysis, and representation of signals in the frequency domain. Knowledge about the Laplace- and Fourier transformations, and their connections, applied to signals and systems. Knowledge about the connections between state space models and transfer function models, and the equivalences between signals and linear systems. Knowledge about the most important types of signals and their spectral (frequency domain) representation. Knowledge about stability in linear systems.
Skills: Be able independently to model, and analyse signals' and dynamical systems' properties algebraically, and also numerically with MATLAB. - To find system time responses using the Laplace transform, via tables or residue calculus. - To do elementary analysis of signals and filter design in continuous and discrete time.
General competence: Be able to think about and apply the concepts of systems theory when considering technical and also non-technical systems. Be conscious about how this theory may contribute when cooperating with other disciplines.
Learning methods and activities
Lectures, computer exercises and calculation exercises. Compulsory computer exercises in two-student groups, using MATLAB. Grades based 100% on the final written exam. If there is a re-sit examination, the examination form may change from written to oral.
Compulsory assignments
- Excersises
Recommended previous knowledge
Mathematics corresponding to B.Sc. in engineering.
Required previous knowledge
Mathematics corresponding to B.Sc. in engineering.
Course materials
Texbook and lecture notes, announced on its learning before start of semester.
No
Version: 1
Credits:
7.5 SP
Study level: Second degree level
Term no.: 1
Teaching semester: AUTUMN 2014
Language of instruction: Norwegian
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- Engineering Cybernetics
- Technological subjects
Department with academic responsibility
Department of Engineering Cybernetics
Examination
Examination arrangement: Written examination
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Autumn ORD Skriftlig 100/100 2014-12-03 09:00
-
Room Building Number of candidates
Examination arrangement: Oral examination
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Summer KONT Muntlig eksamen 100/100 2015-08-07
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Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"