(Created 2011-09-01.)
 CONTROL THEORY FRT130
Credits: 3. Grading scale: UG. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course might be given in English. Alternative for: Pi2. Optional for: D4, F2. Course coordinator: Dr Anders Robertsson, anders.robertsson@control.lth.se and Professor Karl-Erik Årzén, karl-erik.arzen@control.lth.se, Automatic Control. Prerequisites: FMAF01 Mathematics - Analytic Functions and FMAF05 Mathematics - Systems and Transforms. The course might be cancelled if the number of applicants is less than 10. Assessment: One problem-oriented hand-in problem and one mini-project with opposition that is presented in oral and written form. Home page: http://www.control.lth.se/course/FRT130/.

Aim
The aim of the course is to give a deeper knowledge and understanding for the mathematical theory behind many of the concepts and methods taught in the Basic Course in Automatic Control (FRT010)

Knowledge and understanding
For a passing grade the student must

• understand the matematical definition of the Laplace transform and frequency response curves

• understand the interpretation of the general solution to the state-space description as a mapping and how this can be used to define controllability and observability

Skills and abilities
For a passing grade the student must

• be able to use the argument principle, the Nyquist theorem, and Bode's relations to decide stability and robustness

• master the sensitivity functions and its properties

• be able to use coordinate changes in state-space to show properties of zeros, state feedback, and observers

• be able to use the relationships between different criteria for controllability and observability

• be able to apply Kalman's decomposition formula in order to understand series connections, and cancellations and non observability in state feedback

• be able to present concepts from automatic control on oral and written form

Judgement and approach
For a passing grade the student must

• understand the value of mathematical reasoning as a tool for solving control problems

• be able to grasp a mathematical proof as a part of understanding, e.g., the proof of the Nyquist theorem and Bode's relations

• be able to discuss and present group work in the form of the solution to a hand-in problem

Contents
The course is given in parallel with the Basic Course in Automatic Control (FRT010). It brings up many of the concepts that are being taught in the basic course from a more mathematical perspective. Some examples are: Solutions to the system equations, deduction of controllability and observability criteria, Kalmans decomposition formula, the argument principle, robustness analysis.

Literature
Åström K.J: Reglerteori, Almqvist & Wiksell, 1976 or
Åström K J: Introduction to Control, 2004 (book manuscript)
Handout material