Linear Control

lepl1111  2026-2027  Louvain-la-Neuve

Linear Control
5.00 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Language
Prerequisites
Basic undergraduate background in mathematics and notions of signals and systems (e.g., as taught in LEPL1106).
Main themes
This course provides a comprehensive introduction to the modeling, analysis, and design of linear control systems. It begins by presenting techniques for modeling physical systems using differential equations and transfer functions, with examples drawn from robotics, mechanical, electrical, biological, and biomedical engineering. The course then explores methods for analyzing these models, focusing on key system properties such as stability, steady-state errors, disturbance rejection, and the role of feedback in ensuring robustness.
One part of the course is devoted to classical control design techniques using frequency-domain tools — such as PID tuning and frequency-domain methods — as well as robustness analysis. Another part focuses on system analysis and control synthesis using state-space methods, offering a modern framework that supports the study and design of controllers via state feedback. Particular emphasis is placed on the use of software tools for controller design
Learning outcomes

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

  • Model physical systems using both transfer function and state-space representations, with applications to mechanical, electrical, and process control systems.
  • Analyze system properties such as stability, transient response, steady-state error, and robustness using time-domain and frequency-domain techniques.
  • Translate design specifications into control specifications
  • Apply classical control design techniques, such as PID control, root locus, Bode plots, and Nyquist criterion, to meet specifications.
  • Design and analyze feedback control systems to ensure performance and robustness against disturbances, noise, and model uncertainties.
  • Develop and use state-space models for the analysis of dynamic systems, including the assessment of controllability, observability, and internal stability.
  • Synthesize state-feedback controllers and observers using, for example, pole placement and Linear Quadratic Regulator (LQR) methods.
  • Translate control design problems into practical implementations using software tools (for example, MATLAB and Simulink, leveraging the Control System Toolbox).
  • Solve practical control problems in lab settings, including fluid tank regulation, distillation process control, and robot control.
  • Autonomously run automatic control experiments, from the design level to the actual implementation and performance evaluations.
  • Communicate technical findings concisely through written reports and work in a team to develop control strategies in group settings.
  • Demonstrate the ability to independently apply learned concepts to solve unseen control problems under time constraints.
 
Content
The course is organized in 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.
Teaching methods
Learning will be based on lectures (in presence mode or in distance mode) 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 using laboratory equipment and MATLAB Simulink).
Evaluation methods
  • Written examination.
  • Continuous assessment: laboratory assessments and other assessments taking place during the semester (e.g. quizzes, assignments, etc.).
  • Let E be the written-examination mark, L the combined laboratory mark (arithmetic mean), and Q the combined quiz mark (arithmetic mean), all out of 20. The final mark will be calculated as follows:
    If E < 8: Final mark = E
    If E ≥ 8: Final mark = 65% E + 20% L + 15% Q
    This threshold reflects the requirement for students to demonstrate individual mastery of the learning outcomes at a minimum level corresponding to 8/20.
  • Laboratory sessions, laboratory assessments, and quizzes/assignments will not be organised during the second examination session (August) and cannot be completed outside the semester. In the event of a second examination attempt in August, the continuous-assessment marks will be retained. Consequently, the formula used to calculate the final grade in the second session remains the same as in the first session (with L and Q carried over).
  • In the second examination session, only the grade obtained in the second-session written examination is taken into account when calculating the final grade.
  • If a student re-enrols in the course in a subsequent academic year, the laboratory sessions and continuous assessments must be completed again, except in exceptional circumstances and only with the lecturer’s approval.
  • In specific circumstances, other activities, such as oral assessments or assignments, may be used in place of other assessments.
  • The language of the written examination and continuous assessments is the same as the language of instruction (English).
The use of AI and the distribution or exchange of solutions, whether in whole or in part, are strictly prohibited for all assessed activities.
Bibliography
Slides, notes, and laboratory manuals provided by the instructor
Suggested readings from the referenced books :
  • 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)
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Bachelor in Engineering

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