It is a complete course in linear control systems dedicated to beginners. This field is very useful in industrial systems, especially for the control and command of a linear process. In the present course, we start by giving general information on control systems, in which the different definitions and concepts are presented. In this part, we see the Laplace transformation of differential equations and their proprieties. After this, we present the concept of transfer functions in control systems in which the notion of the open and closed loop is viewed. Next, we move to the temporal and frequency response of linear systems. In this course, the stability and precision of systems are explicated in detail in order to get an idea of linear control aims, and following that, we finish with the presentation of the manner of improving performances of systems using correctors. This course provides a general overview of linear control systems, and after learning this course, the student will get general information on the control systems field and also be able to study a physical system starting from physical modeling and differential equations until arriving at to transfer function. This list can be studied based on temporal and frequency approaches. In the end, the student tackles the corrector synthesis to improve the response performance of systems in an open and closed loop.
The essential points tackled in this course are given as follows:
- 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 1st order system
- Characteristic equation of 2nd 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
- Open-loop system
- Closed-loop system
- 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
- Introduction to corrector
- Poles placement corrector
- Phase advance corrector
- The PID corrector
- The PID parameters tuning corrector
