Multivarable and Robust Control Systems 7.5 Credits

Multivariabla och robusta reglersystem
Second cycle, R7005E
Course syllabus valid: Spring 2017 Sp 3 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

Syllabus established
by Department of Computer Science and Electrical Engineering 17 Dec 2007

Last revised
by Jonny Johansson, HUL SRT 15 Jun 2016

Education level
Second cycle
Grade scale
G U 3 4 5
Control Engineering
Subject group (SCB)
Automation Technology

Entry requirements

Intermediate level knowledge in the subject of Automatic control, specifically regarding transfer functions, frequency response, state-space form, state feedback, and the Nyquist criterion. Experience with using Matlab for analysis of control systems is also presumed (R7003E).

More information about English language requirements


The selection is based on 20-285 credits

Course Aim

The course aim is for students to acquire in-depth knowledge of feedback systems, their design and their use in control engineering applications.

The students should be able to:

  • show a deep knowledge of control engineering methods and terminology for multivariable and robust control
  • show deep understanding of mathematical methods to analyze multivariable dynamic systems and dynamic systems with uncertainty descriptions
  • demonstrate the ability to model multivariable dynamic systems based on empirical data and formulate uncertainty descriptions of dynamical systems
  • demonstrate an ability to formulate performance requirements for control systems and determine what performance is achievable
  • use standard methods for designing and analyzing robust controllers and controllers for multivariable systems
  • demonstrate an ability to, in a group, simulate, analyze, evaluate and implement multivariable controllers for a real process and toreport on this work, both orally and in writing
  • ability to identifyconstraints of simplecontroller s and the need for more advanced methods.

When attempting to apply control to a complex real-world process, a number of problems appear that this course provides theoretical methods to handle. The first problem treated in the course is that the process model that is available can never be an exact description of the process in question. How to describe model uncertainty is treated, as well as methods for designing robust controllers that maintain stability and performance despite variations in the process. The second problem is that many processes that are interesting to be able to control are in practice multivariable, i.e. that several inputs affect several outputs. Basic notions, such as poles and zeros, controllability and observability are treated for multivariable systems, as well as methods to determine when single variable controllers can be used on the multivariable process with acceptable performance. Controllers, based on optimization in the H-infinity norm, are treated for the situation where multivariable control must be used. The third problem is fundamental limitation regarding the performance that can be achieved in a control system. Such limitations appear in particular when the process is unstable or has nonminimum phase character. Tools to analyze this are also provided in this course. The theoretical parts of the course are supplemented with practical lab work and a project assignment on an experimental setup in the laboratory of the Department of Computer Science and Electrical Engineering.

The teaching consists of lectures and laboratory exercises

Written exam with differentiated grades and approved lab and project work

The course will not be given every year.

Wolfgang Birk

Transition terms
The course R7005E is equal to SMR047

Literature. Valid from Autumn 2008 Sp 1 (May change until 10 weeks before course start)
Skogestad, S. and Postlethwaite, I.: Multivariable Feedback Control. Analysis and Design. Wiley 2005

Course offered by
Department of Computer Science, Electrical and Space Engineering

0001Written exam4.5G U 3 4 5
0002Laboratory work3.0U G#

Study guidance
Study guidance for the course is to be found in our learning platform Canvas before the course starts. Students applying for single subject courses get more information in the Welcome letter. You will find the learning platform via My LTU.