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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Content and learning outcomes
The course introduces basic theory and methods for analysis and design of advanced multivariable control systems.
• Basic properties of multivariable linear dynamic systems, such as poles, zeros, system gain, input and output directions
• Calculation of signal norms and system gain
• Analysis of stability with the Small Gain Theorem
• Analysis of feedback systems in terms of critical transfer functions, such as the sensitivity function and the complementary sensitivity function.
• Quantification of fundamental limitations in feedback control systems
• Modelling of uncertainty and analysis of robust stability in feedback systems
• Analysis of interactions and design of decentralised control structures based on the Relative Gain Array
• Design of LQG optimal controllers, effect of design parameters on properties of the closed loop system
• Design of H_2 and H_infinity-optimal controllers, effect of choice of weights on properties of the closed loop system
• Strategies for anti-windup to handle limitations in control inputs
• Basic principles behind Model Predictive Control
Intended learning outcomes
On completion of the course, the student should be able to
• formulate basic theory and definitions of important concepts in multivariable control
• apply analysis and design methods in multivariable control.
Literature and preparations
Automatic Control, General Course (EL1000 or EL1110) or similar.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- 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
Opportunity to raise an approved grade via renewed examination
- 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 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
Main field of study
In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.