Sampled Control Systems

Mon, 01 Jan 0001 00:00:00 +0000

A digital-control course taught to the full year group (500 students) from April to June 2026: $z$-transform, discretisation, sampled PID, filtering and Kalman estimation.

I taught the second half of the course (sessions 5 to 9, digital control proper) along with its assessments. The first half, on continuous-time systems, was taught by another lecturer.

The documents below are the ones actually handed out to students. The course is taught in French, so the material is in French.

Lecture slides

#	Session	Topic	Pages
5	Continuous and discrete systems	Laplace and $\mathcal{Z}$ transforms	32
5 bis	Partial fractions	Decomposition of rational fractions, general case	10
6	Sampled systems	Sampling, zero-order hold, digital control	38
7	Digital PID controller	From the model to the real implementation	39
8	Filtering and the Kalman filter	From a noisy signal to optimal state estimation	26
9	Applications and revision	Data-based approaches, inverted-pendulum case study (student version)	19

Midterm quiz

A one-page, 20-minute quiz on sampled systems and filtering. Every student gets an individualised paper: papers are generated with auto-multiple-choice with a different random draw per group, then marked by optical recognition.

Sample paper (PDF)

Final exam

Rather than a set of disconnected questions, the exam is a single running case study: all four parts work on the same system, the altitude control of an agricultural observation drone, and each part picks up where the previous one left off. The paper is in French, as the course is taught in French.

Warm-up: five multiple-choice questions, an inverse Laplace transform, and the discretisation of a first-order plant behind a zero-order hold
Part 1, modelling: from Newton’s second law to the drone’s transfer functions, with the motor identified from a measured step response
Part 2, closed-loop control: steady-state error under gravity, integral action, and the risk of derivative action in gusty wind
Part 3, discretisation and implementation: the controller on an ESP32, recurrence equations for P, I and D, and a Python implementation to complete
Part 4, filtering: anti-aliasing, and fusing a 10 Hz GPS with a 100 Hz accelerometer

Duration: 1h30, calculator and documents not allowed. 20 points, plus 2 bonus points. Solutions are not published.

Other documents: answer sheet (PDF) · exam paper, full screen

Autonomous car and SLAM project

Wed, 01 Apr 2026 00:00:00 +0000

Autonomous car and SLAM - ECE Paris

Summary

From April to June 2026, supervision of a robotics project for 4th-year students at ECE Paris, focused on designing an autonomous car and implementing SLAM (Simultaneous Localization and Mapping).

ECE Paris | Etienne Chassaing