# MTAT.03.241 Modelling and Control of Dynamic Systems

MTAT.03.241 Dünaamiliste süsteemide modelleerimine ja juhtimine

- The seminar starts on the 4th study week (22. september).
- All seminars are held on Mondays in Liivi 404.
- First seminars are lectures that cover basics of
system indentification.

After that students must prepare a presentations on specific topics. - The seminar ends with a project, where students must
demonstrate their expertise

by solving a system identification and control task. - Lectures and seminar sessions are held in English or in Estonian depending on circumstances.
- Final reports should be written in English.

## Requirements

There are no formal prerequisites to the seminar. However, basic knowledge in linear algebra and calculus is essential. Also, one needs reasonable English skills to complete the course report.

If the formal requirements of
the
ÕIS do not permit registration then write me an email
or talk with me. After that we decide whether to enrol you
or not. Secondly, active participation in the course is
absolute necessity. You must participate in most seminars
or otherwise you **do not pass** the seminar. Namely,
student gets grade **F** if he or she misses 4 or more
seminars.

In reasonable circumstances, it is possible
to compensate missed seminars by extra work. Details are
determined by individual agreements with the lecturer.

The seminar grade is determined by the final research report and the corresponding discussion with the student. The written report gives a base level grade and the discussion can either increase or decrease the base level grade by one grade point. As usual grades range from A to F.

## Brief Summary of Covered Topics

The main aim of the seminar is to give a basic principles of system identification and control. As usual, we start with linear models, as they are relatively simple and their behaviour is well known. Linear models form also a good baseline case for other more complex models, since in they often provide a good precision and control over the dynamic system. If the time resolution between consecutive measurements is high enough, then any complex correspondence can be linearised with relatively small error. Nevertheless, non-linear models are important, as they can improve the prediction precision and control. Therefore, we study standard prediction models:

- FIR
- ARX
- ARMAX
- OE
- SSIF

- PID
- Direct Inverse Control
- Internal Model Control
- Feedback linearisation with neural networks
- Feedforward Control
- Optimal Control

**Motivation for BIIT group.** Although the main
application areas of control are in robotics,
identification of various control mechanisms is important
in many other areas. In particular, chemical processes
taking part in a cell form a complex feedback
system. Hence, the analysis of the gene expression data is
indeed system identification task. Although the expression
data is too scarce for proper analysis, many statistical
techniques discussed in this seminar are usable in other
biological contexts, as well. For instance, inferring
binding cites from ChIP data can be naturally recast to
system identification task. Hence, we consider also some
semi-discrete control mechanisms such as hidden Markov
Models.

## Course Books

- Magnus Nørgaard, O. Ravn, N. K. Poulsen,
L. K. Hansen.
*Neural Networks for Modelling and Control of Dynamic Systems.*Springer. 2000 - Chi-Tsong Chen.
*Linear System Theory and Design*, Oxford University Press. 1999.

## Tentative Schedule

- 22nd Sep. Introductory Lecture (Sven, slides, slides)
- 29th Sep. Linear Systems (Sven, slides, materials)
- 6th Oct. Stability of Linear Systems (Sven, slides, materials, r-code)
- 13th Oct. Controllability and Observability of Linear Systems (Sven, slides, materials, r-code)
- 20th Oct. Model Structure Selection (p. 18--37 + paper, Maria & Oskar, slides)
- 27th Oct. Experimental Data and Training (p. 38--84, Alo & Mihkel, slides)
- 3rd Nov. Validation and Re-evaluation of Inference Steps (p. 85--119, Darja & Konstantin, slides, slides)
- 10th Nov. PID Controllers (Sven, slides, r-code)
- 17th Nov. Direct Inverse Control and Internal Model Control (p. 121--142, Jürgen & Andres, slides)
- 24th Nov. Feedback Linearisation and Optimal Control (p. 143--175, Konstantin)
- 8st Dec. Predictive Control and Case Studies (p. 178--233, Raivo & Roland, slides, slides)
- 15th Dec. Kalman Filters as Discrete Hidden Markov Models (Raivo, slides)
- 15th Dec. Questions & Answes session about course projects (Sven & Co)
- 22nd Dec. Q & A through email (Sven & Co)

## Important Deadlines

5th January 23:59 Tuvalu time the first deadline for course reports.

7th January 23:59 Estonian time deadline for the initial grade proposals.

8th January 10:15 Estonian time discussions and final grading (provided that you accept the grade).

27th January 23:59 Hyderabad time the second and **absolutely final** deadline for course reports.

29th January 23:59 Estonian time deadline for the corresponding grade proposals.

30th January 10:15 Estonian time discussions and final grading.

## Course Assignments

Matlab toolboxes for system identification and control### Datasets for system identification

- Zlog Data pdf data
- Inverteeritud pendel pdf
Initial dataset

Andmete kirjeldus ning uued andmed on kättesaadavad aadressilt

http://digi.physic.ut.ee/mw/index.php/Inverteeritud_kaheastmeline_pendel - Litter tasandil pdf (simulators)
- Chip-chip andmete analüüs (Raivo teema)

### Models for the control task

- Proovida kolme erinevat kontrolleri ehitamise strateegiat kas pöördpendli või litri ülesande jaoks (pdf)

## Best course reports

- Mihkel Pajusalu, Alo Peets. Inverteeritud pendli süsteemi identifitseerimine ja juhtimine. Good layout, excellent content.
- Konstantin Tretjakov, Darja Krushevskaja. Control of a Ball on a Tilted Rail Using Neural Networks. Exellent layout, good content.