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Feedback systems


Programme (detailed contents):

The course presents the models for linear time-invariant systems, in particular the differential equation and the transfer function. The main methods for analysis of linear systems are then studied (frequency and time responses) and the concepts of open loop and closed loop stability introduced. After defining the main indicators in terms of transient and steady-state behaviours, the design of lead and lag control laws are developed. The PID controller with the main methods of design are then presented



1) Introduction

2) Models

3) Responses

4) Stability

5) Specifications

6) Lead and lag controllers

7) PID


Main difficulties for students:

No particular difficulty



At the end of this module, the student will have understood and be able to explain (main concepts):

The design of closed-loop control laws for linear time-invariant systems described by their transfer function


The student will be able to:

To design closed-loop control laws based on specifications of

steady state behaviour (precision) and on transient behaviour (settling time)

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...


B. Pradin et G. Garcia : Modélisation, analyse et commande des systèmes linéaires. PUM (presses universitaires du Mirail. 2010
H. Bourlès : Linear systems - ISTE ; Hoboken, NJ , Wiley - ISBN : 978-1-8482-1162-9