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APM_4AUT2 (Mineures STIC / IAC et Méca / SI)

Introduction to a Control Theory

Program 2024-2025


Lecturer:
  • Elena VANNEAUX (ENSTA / U2IS)
  • Adnan SAOOD (ENSTA / U2IS)

Evaluation Modalities:

Each session will be divided into 1.5 hour of lecture followed by 1.5 hour of exercises. The exercise part will be done in Jupyter Notebooks.
Course grade breakdowns:
  • Labs: 40%
  • Final test: 30%
  • Final project: 30 %

This course will teach the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, you should be able to design controllers using state-space methods and evaluate whether these controllers are robust to certain types of modeling errors. The course will focus on linear control systems. You will learn to:

  • Linearize a nonlinear system and analyze controllability, observability, reachability, and stability.
  • Design controllers using state-space methods and analyze them using classical tools.
  • Design controllers for optimal control problems.
  • Assess the robustness of your control design.

Pre-requirements:

  • The course assumes a good working knowledge of linear algebra and differential equations. The class will cover new material in depth, but a strong background will be necessary.
  • Course material and practical exercises assume a good working knowledge of Python.

SESSION
CONTENT
LECTURER RESOURCES
Wednesday 5/2
9:00--12:15
  • CM1: Modeling
    • State-space models of systems. Linearization. Linear time-independent control systems.
Elena VANNEAUX
Adnan SAOOD
Wednesday 12/2
9:00--12:15
  • CM2: Controllability and Observability
    • Controllability and Observability. Kalman's criteria. Normal form.
Elena VANNEAUX
Adnan SAOOD
Wednesday 19/2
9:00--12:15
  • CM3: Stability and State Observer
    • State feedback  Stabilisator. Pole placement. Luenberger observer.
Elena VANNEAUX
Adnan SAOOD
Wednesday 5/3
9:00--12:15
  • CM4: Control design
    • Control design in the frequency domain. PID controller.
Elena VANNEAUX
Adnan SAOOD

Wednesday 12/3
9:00--12:15
  • CM5: Optimal control design
    • LQR controller.
Elena VANNEAUX
Adnan SAOOD

Wednesday 19/3
9:00--12:15
  • CM6: Advanced control techniques
Elena VANNEAUX
Adnan SAOOD

Wednesday 26/3
9:00--12:15
  • Project defense
Elena VANNEAUX
Adnan SAOOD