Linear control systems - KAEL6M02

Goal(s)

This is a basic course on control of linear system. The course will cover the automatic control of linear systems from modeling until the synthesis of analog correctors. At first, we will study how to model a physical system by a differential equation. Then, the concept of Transfer Function is introduced.
The special cases of first and second order systems is studied with temporal and frequency analysis. The need for a closed loop system is studied by means of the performances: accuracy - precision and stability (algebraic and geometric criteria). The last part is dedicated to the controller synthesis.
The aim is to :

• Model a physical system
• Identify the parameters of a linear system.
• Study the first and second order systems.
• Analyze the stability and performance of a dynamic system.
• Propose a correction adapted to improve system performance.

Content(s)

Introduction
Chapter 1. Modeling and equation of dynamic systems
Chapter 2. Response of a linear system - Transfer function
Chapter 3. Temporal response for the 1st and 2nd order systems
Chapter 4. Frequency response of linear systems
Chapter 5. System control - Closed loop
Chapter 6. Performance of servo systems - Stability - Accuracy and Precision
Chapter 7. Temporal and frequency correction of linear system

Laplace transformations
Elementary laws of physics (fundamental principle of dynamics, Fourier's law, conservation of matter, electromagnetism ...)