EL2520 Control Theory and Practice, Advanced Course 7.5 credits

Reglerteknik, fortsättningskurs

The aim of this course is to provide the basic theory required for solving complex control problems. The course presents theory and methodology for analysis and modelling of systems and signals, and methods for design and synthesis of feedback controllers. Special emphasis is placed on:

  • Control of systems with multiple inputs and outputs.
  • Fundamental limitations for control performance.
  • Sensitivity and robustness in feedback systems.
  • Synthesis of controllers through optimization.
  • Predictive control with constraints.

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Course information

Content and learning outcomes

Course contents *

Mathematical descriptions of linear multivariable systems, design of multivariable controllers, fundamental limitations on achievable performance, robustness to model uncertainties, design of multivariable controllers, linear quadratic control, H2- och H8-optimal control, model predictive control.

Intended learning outcomes *

This course introduces basic theories and methodologies required for analyzing and designing advanced control systems. After the course, you should be able to

  • Understand basic properties of multivariable linear systems, such as multivariable poles, zeros, system gains and associated critical input and output directions.
  • Compute signal norms and system gains, and analyze closed-loop stability using the small gain theorem.
  • Perform a thorough analysis of a closed-loop control system in terms of the critical transfer functions, including the sensitivity and complementary sensitivity function.
  • Quantify fundamental limitations on control system performance due to time-delays, right-half plane zeros and poles and understand their implications on controller design.
  • Derive frequency-dependent description of model uncertainty using the multiplicative uncertainty model and analyze robust stability and performance.
  • Use the relative gain array to analyze interactions and propose decentralized control structures.
  • Derive LQG-optimal controllers for scalar systems, and understand how the design parameters influence the closed-loop system properties.
  • Understand how mixed H_inf control can be formulated in terms of an extended system, and propose reasonable performance weights.
  • Develop anti-windup control strategies to deal with control signal limitations
  • Understand the basic principles behind model-predictive control, including how the design parameters influence the closed-loop performance and how the basic problem can be transformed into an associated optimization problem.

Course Disposition

Lectures, Exercises, Computer exercises, Laboratory work. Homeworks

Literature and preparations

Specific prerequisites *

For single course students: 120 credits and documented proficiency in English B or equivalent.

Recommended prerequisites

Automatic Control, General Course (EL1000 or EL1110) or similar.


No information inserted


Torkel Glad and Lennart Ljung, Control Theory - Multivariable and Nonlinear Methods, Taylor and Francis Ltd, ISBN 0748408789
(Swedish version: T. Glad and L. Ljung, Reglerteori, flervariabla och olinjära metoder, Studentliteratur, 2:a upplagan, ISBN 91-44-03003-7

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale *

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

Examination *

  • LAB1 - Laboratory Work, 1.5 credits, Grading scale: P, F
  • LAB2 - Laboratory Work, 1.5 credits, Grading scale: P, F
  • TEN1 - Examination, 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.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted


Elling W Jacobsen

Ethical approach *

  • 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.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web EL2520

Offered by

EECS/Intelligent Systems

Main field of study *

Electrical Engineering

Education cycle *

Second cycle

Add-on studies

No information inserted


Elling W Jacobsen

Supplementary information

TEN, 4,5 cr, LAB, 1,5 cr, PROJ, 1,5 cr

Replaces 2E1252.

In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.