Examination arrangement

Course content

As for the content, this course addresses mainly theoretical aspects that lie at the basis of state-space control. The focus is on that part of the theory that has direct consequences for modelling and characterizing linear systems and for understanding the differences that are present when dealing with nonlinear systems (not treated in this course). The course will not enter too much into practical aspects; at the same time we will have some insights on problems that may arise in practical scenarios (for example delays, and nonminimum-phase systems).

Referring to the "the map of control theory" (https://engineeringmedia.com/map-of-control), the topics covered in the course are:

- linear and nonlinear state-space;

- linearization;

- transfer functions;

- simulation;

- stability;

- Bode plots;

- phase plane;

- nonminimum phase.

If you want to see the detailed map of the intended learning flow of the course per content unit then search for the ``NTNU TTK4225 2022'' maps in the ``visualize learning flow maps'' tab of the https://faceit.pythonanywhere.com/ portal.

As for the purpose of the course, if we were to summarize it in one sentence then that would be: learn how to understand a system in terms of its time and frequency responses.

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 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

The lectures will be hybrid, thus both physical and digital. To enable to follow the course digitally, all the classes will be broadcast via dedicated Blackboard Collaborate Ultra sessions. For an overview of what Blackboard Collaborate is and enables, see for example https://www.youtube.com/watch?v=Qya2MrXNA1o. The classes will also be video-taped, and the videos will be then publicly in Blackboard immediately after each session.

The sessions can thus be taken both at home and at the main campus, but the latter is only if you wish. In each class session we will mix:

- classical frontal lesson elements, i.e., the ones you typically do in other courses. Note that we will do intermittent lecturing: it means that we break the lectures into smaller parts -- instead of lecturing for 45 or 90 straight, we stop after max 20-25 minutes and solve an exercise / answer a question to be discussed together, and then we continue;

- collective coding via dedicated Jupyter notebooks (https://jupyter.org/) where everybody can ``try'' things out live (and thus both get insights and the possibility of sharing intuitions with others);

- peer instruction sessions, where we answer together questions related to the teaching material.

At home, instead, you may (if you wish) execute self-assessment sessions consisting in questionnaires sessions, i.e., using the https://faceit.pythonanywhere.com/ to answer questions and get quantitative estimates of how well you know about the various contents in the course.

Note that the peer instructions and questionnaires sessions will not be used for assessing you but rather for you to self-assess, and for the teacher to aid and tailor the learning process.

Further on evaluation

Grades based 100% on the final oral exam.

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 the course webpage before the start of the semester.

Credit reductions