• 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 an engineering system using Matlab and Simulink.
• 1 lab where the student is given several data sets coming from a magnetic levitator, and where the goal is to use system identification tools to develop a mathematical model of the levitator.
• 2 online quizzes, to be given after approx. 50% and 90% of the course has passed.
• 1 final exam.

Schema HT-2021-344

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 and T. Glad, Modelling and Identification of Dynamic Systems, Studentliteratur, 2016.
• 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

• LAB1 - Lab 1, 0.5 credits, Grading scale: P, F
• LAB2 - Lab 2, 0.5 credits, Grading scale: P, F
• LAB3 - Lab 3, 2.0 credits, Grading scale: P, F
• TEN1 - Exam, 4.5 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, with deadlines Sept 10 and Sep 17, respectively, 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 up to 2 people. To pass this lab, the students need to submit a report by Oct 4, which needs to be successfully passed.

Lab 3:

For this lab, it is necessary to submit a report by Oct 20, 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 Nov 12.

Exam:

This examination is subdivided into 2 online quizzes and a final written exam. These three assessments should be done individually and without any help from others. The quizzes are scheduled for Sept 29 and Oct 19, respectively, and the exam will be on Oct 27.

In order to pass this examination, it is necessary to pass all three assessments. This means that a student can only get a grade A-B-C-D-E-Fx by passing both quizzes and receiving that respective grade in the final 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, only the following items are allowed:

1. Paper copy of lecture slides and notes

2. Ljung & Glad, “Modeling and Identification of Dynamic Systems”, 2016, or “Modelling of Dynamic Systems”, 1st/2nd Ed. in English or Swedish

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

4. Mathematical tables

5. Dictionary

To pass the course, all three 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 questions (1 point per correctly answered question), and 3.0 points are required to pass each of them. If the two quizzes have been passed, the following requirements hold for the final grade, in relation to the final exam:

• For grade E, a total of at least 17 points and at least 13 points is required on Tasks 1, 2 and 3
• For grade D, a total of at least 25 points and at least 13 points are required on Tasks 1, 2 and 3.
• For grade C, a total of at least 31 points and at least 13 points are required on Tasks 1, 2 and 3.
• For grade B, a total of at least 37 points and at least 13 points are required for Tasks 1, 2 and 3.
• For grade A, a total of at least 43 points and at least 13 points on Tasks 1, 2 and 3 are required.
• For Fx, a total of at least 15 points and at least 13 points are required on Tasks 1, 2 and 3.

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, or failed, some of the quizzes of the course, there will be another chance to re-take them the week before the re-exam. Check the course webpage for more information.
• 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 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.