Course syllabus

# Flervariabel reglering Multivariable Control

## FRTN10, 7,5 credits, A (Second Cycle)

Valid for: 2019/20
Decided by: PLED F/Pi
Date of Decision: 2019-03-26

## General Information

Elective for: B5, C4, D4-ssr, E4-ra, F4, F4-r, I4-pvs, K5, Pi4-ssr
Language of instruction: The course will be given in English on demand

## Aim

To teach the basic principles for control of systems with multiple inputs and outputs. The course will provide insight on fundamental limitation and on the use of mathematical optimization as a design tool. The course covers linear continuous-time systems.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to define and explain basic concepts for multivariable systems
• be able to translate between, and intelligently select among, different representations for multivariable systems, in particular transient responses, transfer function matrices, and state-space descriptions
• be able to derive properties of interconnected systems from the properties of their subsystems, and to characterize and quantify the role of the different subsystems
• be able to formulate constraints on input signals and output signals of a control system and to relate these to conditions on the matrices that describe the system
• be able to analyse how process characteristics put limitatoins on the control performance that can be achieved

Competences and skills
For a passing grade the student must

• be able to independently formulate technical specifications based on understanding of the control system should be used and interact with the external environment
• be able to select control design methods and model structures, and translate specifications into mathematical optimization problems
• draw conclusions from numerical calculations about the correctness of models and specifications, and about the consequences for the interaction between the system and the environment

Judgement and approach
For a passing grade the student must

• understand relationships and limitations when simplified models are used to describe a complex and dynamic reality
• show ability to teamwork and group collaboration at laboratories

## Contents

The control design process, signal size, gain, stability, sensitivity, robustness, the small-gain theorem, transfer function matrices, multivariable zeros, non-minimum-phase systems, disturbance models in the time domain and frequency domain, frequency-domain specifications, fundamental limitations and trade-offs, controller structures, the Youla parameterization and internal model control, linear-quadratic optimization of state feedback and Kalman filter, synthesis using convex optimization, model reduction.

## Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam (5 hours), three laboratory exercises. In case of less than 5 registered students the retake exams may be given in oral form.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts
Code: 0114. Name: Examination.
Credits: 6. Grading scale: TH. Assessment: Passed exam
Code: 0214. Name: Laboratory Work 1.
Credits: 0,5. Grading scale: UG. Assessment: Preparation exercises and approved participation in laboratory
Code: 0314. Name: Laboratory Work 2.
Credits: 0,5. Grading scale: UG. Assessment: Preparation exercises and approved participation in laboratory
Code: 0414. Name: Laboratory Work 3.
Credits: 0,5. Grading scale: UG. Assessment: Preparation exercises and approved participation in laboratory

Required prior knowledge: FRTF05 Automatic Control, Basic Course or FRTN25 Automatic Process Control
The number of participants is limited to: No
The course overlaps following course/s: FRT020

• Lecture Notes in Multivariable Control. Department of Automatic Control, LTH (compendium).
• Torkel Glad, Lennart Ljung: Control Theory: Multivariable and Nonlinear Methods, Taylor & Francis, 2000, ISBN 0748408789 (optional reading).
• Lecture slides, exercise material and laboratory manuals are available on the course homepage.

## Contact and other information

Course coordinator: Anton Cervin, anton.cervin@control.lth.se
Director of studies: Anton Cervin, anton.cervin@control.lth.se
Course homepage: http://www.control.lth.se/course/FRTN10
Further information: The course may not be part of an exam together with the course FRT020.