(Created 2008-07-17.)

CONTROL THEORY | 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 (FRT110)

*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, Kalmans 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