• model types
• overview of different physical domains (physics, mechanics, electronics)
• model simplification, differential-algebraic equations
• systematic modelling methods
• object-oriented modelling
• disturbances and disturbance models
• parameter estimation and statistical properties

After passing the course, the student should be able to

• formulate basic theory and definitions of important concepts in mathematical modelling of dynamic systems
• retrieve mathematical models for engineering systems based on fundamental physical relations and based on measurement data.

• 2 homework assignments, where the goal is to complete a Jupyter / Python notebook in order to simulate a given physical system.
• 1 lab consisting in simulating a physical system using Matlab and Simulink.
• 1 lab consisting in the estimation of a model for a real physical system using system identification tools.
• 1 final exam.
• 2 voluntary online quizzes that can give bonus points for the exam. 

Elementary physics and mathematical statistics, basic course or equivalent. Basic control course, EL1000 or equivalent.

Lecture slides, an exercise compendium, and other material will be made available online from the course website.

The course does not follow any specific book. However, supplementary (optional) material includes

• L. Ljung, T. Glad and A. Hansson, Modelling and Identification of Dynamic Systems, 2nd Ed. Studentliteratur, 2021.
• T. Söderström and P. Stoica, System Identification, Prentice Hall, 1989, in particular Chaps. 1-5. This book is out of print, but it is available online.

No special equipment is required for the course, besides a computer (with appropriate software; see next section) and internet access.

For the homework assignments, Python 3 + Jupyter is required, while for Labs 2 and 3 Matlab/Simulink will be used.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

A, B, C, D, E, FX, F

• LAB2 - Lab 2, 0.5 credits, Grading scale: P, F
• LAB3 - Lab 3, 2.0 credits, Grading scale: P, F
• LABA - Lab 1, 2.0 credits, Grading scale: P, F
• TENA - Written exam, 3.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Note: Specific information about the examinations is provided in the course website.

Lab 1:

This examination is divided into two homework assignments which can be performed in groups of up to 2 people. To pass Lab 1, both assignments should be successfully passed.

Lab 2:

This lab consists in following the steps described in the Lab instructions document, in a group of 2 people. To pass this lab, the students need to show to the TAs in a lab session that they have correctly solved all tasks for the lab.

Lab 3:

For this lab, it is necessary to submit a report by prescribed deadline (provided in the course webpage), written in groups of at most 2 people. The requirements for passing the Lab are described at the end of the Lab instructions document. In case the report does not fulfil all these requirements, the students can submit a completed report by a prescribed deadline (provided in the course webpage).

Exam:

The exam moment consists of one written exam. There will be also two voluntary quizzes whose combined score can give bonus points that can be added to the points in the exam.

For the quizzes, the students can use all the material from the course, but any contact with others during the quiz, or accessing the internet for answers, is strictly forbidden. For the final exam, to be done invidually, only the following items are allowed:

1. Paper copy of lecture slides and notes

2. L. Ljung, T. Glad and A. Hansson, Modeling of Dynamic Systems, 2nd Edition, or previous editions in English or Swedish

3. T. Söderström and P. Stoica, System Identification 

3. Mathematical handbook (“Beta”, CRC, etc.)

4. Mathematical tables

5. Dictionary

To pass the course, all four examinations should be passed.

Grading criteria

To achieve the grades as described below it is required to formulate basic theory and definitions in the mathematical modelling of dynamic systems, and to derive models of engineering systems based on fundamental physical relations and based on measurement data

• E: on simple problems
• D: on advanced problems within any part of the course
• C: on advanced problems in several parts of the course
• B: on advanced problems in all parts of the course or to solve problems that combine several parts of the course
• A: on advanced problems in all parts of the course and to solve problems that generalize several parts of the course.

The final exam consists of 5 tasks, each of which gives a maximum of 10 credits.

• Task 1 deals with simple problems.
• Tasks 2 and 3 deal with simple problems and advanced problems within physical modeling and system identification.
• Tasks 4 and 5 deal with advanced problems within physical modeling and system identification.

Grading requirements

Each quiz consists of 8 multiple choice / multiple answers questions at the level of an E grade, that is, enough to pass the course. Based on the sum of the scores of both quizzes, the number of bonus points to be added to the exam score according to the following conversion:

• Less than 3.0 points: 0 bonus points
• At least 3.0 points: 1 bonus points
• At least 6.0 points: 2 bonus points
• At least 9.0 points: 3 bonus points
• At least 12.0 points: 4 bonus points
• At least 15.0 points: 5 bonus points

The following requirements hold for the final grade, in relation to the final exam:

• For Fx, a total of at least 21 points and at least 15 points are required on Tasks 1, 2 and 3.
• For grade E, a total of at least 17 points and at least 15 points is required on Tasks 1, 2 and 3
• For grade D, a total of at least 25 points and at least 15 points are required on Tasks 1, 2 and 3.
• For grade C, a total of at least 31 points and at least 15 points are required on Tasks 1, 2 and 3.
• For grade B, a total of at least 37 points and at least 15 points are required for Tasks 1, 2 and 3.
• For grade A, a total of at least 43 points and at least 15 points on Tasks 1, 2 and 3 are required.

In the grading scale above, the total number of points includes the bonus points from the quizzes, but the required score on problems 1,2 and 3 does not include such bonus points.

A student who receives an Fx grade for the final exam can apply for a supplementary examination by contacting the teacher by email no later than 5 working days after the exam results are posted. The supplementary examination consists in a shorter written exam, focused on the topics the students failed to pass in the final exam, followed by an oral examination.

A student who passes the supplementary examination will receive an E grade for the final exam. Otherwise, a student who fails the supplementary examination, or who does not contact the examiner within the stipulated time frame, will receive an F grade for the final exam.

• There is a re-exam scheduled for December, and it can be taken by those who did not take the final exam, or who failed it and need to re-take it.
• In case of having missed an assignment or lab deadline, there will be an additional opportunity to submit the respective reports on November. Check the course webpage for the exact dates for re-submission.

The results of the exam will be posted under My Pages or Canvas no later than 15 working days after the exam is taken.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.