Linear Control

Teacher(s)

Bianchin Gianluca;

Language

English
> French-friendly

Prerequisites

Notions of signals and systems as taught in LEPL1106.

Main themes

Development of mathematical models for linear dynamical systems (state-space representation, transfer functions) allowing to represent the dynamics in a unified way for a diversity of engineering applications (e.g. electromechanical, mechanical, electrical, chemical, biological, computer science)
Design of control schemes that meet specifications related to stability, transient and steady state performance (accuracy), and robustness. PI and PID controllers, Linear Quadratic Control, Smith predictor, feedforward control, cascade control. Use of software to design controllers.

Learning outcomes

At the end of this learning unit, the student is able to :

With respect to the referentiel AA, this courses contributes to the development,  the acquisition and the evaluation of the following learning outcomes : AA1.1, AA1.2, AA1.3 AA5.3, AA5.4, AA5.5 At the end of the course, the student will be able : design control systems based on linear models; design of control schemes that meet specifications on related to stability, transient and steady state performance (accuracy), and robustness. PI and PID regulators, Linear Quadratic Control, Smith predictors, feedforward control, cascade control; use software to design controllers; implement closed-loop control system in laboratory experiments under conditions similar to those in industrial applications; use industrial PID controller; autonomously run automatic control experiments, from the design level to the actual implementation and performance evaluations;

Content

The course is organized into two main parts:
Part 1 - Analysis of systems using frequency-domain tools: Laplace transforms, dynamic response, transfer functions, system poles, block diagrams, stability, PID control, Bode and Nyquist diagrams, lead and lag compensators.
Part 2 - Analysis of systems using time-domain tools: state-space models, matrix exponentials, linearization, linear time-varying systems, Lyapunov stability, controllability and observability, pole placement, advanced control via state feedback.
The course presumes a basic undergraduate background in mathematics and introductory concepts from signals and systems (e.g., as covered in LEPL1106). It is designed to be self-contained with respect to complex analysis, as the essential topics required throughout the course will be introduced as needed.
The course integrates aspects of transition and sustainable development by exploring sustainable control strategies, including minimum-energy control techniques and lifecycle-aware system design.

Teaching methods

Learning will be based on lectures (in presence mode or virtual) interlaced with exercise sessions (offered in class with the support of TAs) and laboratory sessions (to be realized in the laboratory room by groups of 2-5 students).

Evaluation methods

• Written exam
• Laboratory evaluations taking place during the semester
• Evaluations during the semester (e.g., quizzes)
• The laboratory experiences or quizzes cannot be accomplished outside the semester. 
• The grades of labs and semester evaluations (e.g., quizzes) cannot be carried over from previous years, except in exceptional cases and only with the instructor's approval.
• Other activities, such as oral evaluations or homework, may be used in place of other evaluations under special circumstances

Let `E' denote the grade of the written exam, `L' denote the combined grade for the laboratory, and `Q' denote the combined grade for the quiz (base 20). The final grade will be computed as follows:
If E < 8: Final Grade= E
If E >= 8: Final Grade = 0,65*E+0,2*L+0,15*Q
 

Other information

The main language used during lectures, exercise sessions, and the laboratory is English. Examinations can be made French-friendly, upon request. 

Online resources

https://moodleucl.uclouvain.be/course/view.php?id=7834

Bibliography

Khalil, H. K. (2023). Control Systems: An Introduction. Michigan Publishing.
J. P. Hespanha, "Linear systems theory," Princeton University Press, 2018 (available in the library)
G. F. Franklin, J. D. Powell, E. Emami-Naeini, "Feedback control of dynamic systems," Prentice Hall, 2019 (available in the library)

Teaching materials

• Slides, notes, and laboratory manuals provided by the instructor
• Suggested readings from the referenced books

Faculty or entity

> MAP