Linear control systems

This course offers a comprehensive introduction to linear control systems for beginners by focusing particularly on their application in industrial systems for controlling linear processes. At first, we start with an overview of control systems, introducing key definitions and concepts. The section covers the Laplace transformation of differential equations and their properties. After, we explore the concept of transfer functions in control systems, including open and closed loop systems. The course continues with an examination of the time-domain and frequency-domain responses of linear systems. To provide a solid understanding of the objectives of linear control, we cover stability and precision in detail. Finally, we conclude with a discussion of how controllers can be applied to improve system performance. By the end of the course, students will have a broad understanding of control systems, from physical modeling and differential equations to transfer functions. The course also offers insight into temporal and frequency analysis methods and explores techniques for enhancing the performance of systems in both open and closed loops, culminating in controller synthesis.

The following list outlines the key topics covered in by this course:

- Definition of system

- Definition of linear system

- The nature of the input and output signals

- Definition of command system

- The difference between regulation and control

- Laplace transformation

- Laplace transformation properties

- Famous Laplace transformation

- Example of Laplace's transformation

- Steps to get the transfer function

- Characteristic equation of first order system

- Characteristic equation of second order system

- Example of the RC circuit

- Example of a mechanical system

- Definition of the functional diagram

- Useful formalism

- A global view of the control scheme

- The Open-loop system FTBO

- The Closed-loop system FTBF

- Example of block diagram simplification

- Dynamics performance of the linear system

- Typical signals used in temporal analysis

- First-order system response

- Second-order system response

- Harmonic response

- The representation of A complex number (Nyquist, Black, and Bode)

- Bode diagram of the first-order system

- Nyquist diagram of the first-order system

- Black diagram of the first-order system

- Bode and Black diagram of a second-order system

- Precision

- Stability

- Algebraic criterion of Routh-Hurwitz

- Overview of the corrector

- Principle of poles placement corrector

- Phase advance corrector

- The PID corrector

- The PID parameters tuning corrector