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Automatic control: frequency domain analysis

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  • Lecturer: Mokrane Boudaoud (mokrane.boudaoud@sorbonne-universite.fr)
  • Course code: UM4RBR10-Freq
  • Student workload: 12h of lectures, 8h of tutorials, 8h of labs
  • Credits: 3 ECTS
  • Specialization tracks:
  • Semester offered: S1 S2 S3 S4
  • Language of instruction: French English
  • Targeted audience: Eng. Sc. department Other :
  • Localization : PMC Campus Other :

Course Overview

Introduction to the basic tools for modeling, analysis, and control of Linear Time Invariant (LTI) systems. Modeling of dynamic systems. Linear analysis of dynamic systems in the time and frequency domains. Output feedback control. Feedforward control. Design of multi-loop controllers.

Mots-clés : Linear Time Invariant (LTI) systems, Laplace transform, Bode diagram, output feedback control, feedforward control, design of multi-loop controllers.

Prerequisites

Students should have previously acquired the following prerequisites to follow this course:

  • Mathematics for signal processing

Intended Learning Outcomes

By the end of this course, students will be able to:

  1. Modeling of LTI systems in the time domain (differential equation) and the frequency domain (transfer function)
  2. Bode diagram of first order and second order LTI systems
  3. Determination of the static and dynamic properties of an LTI system in the time and frequency domains
  4. Modeling of a closed loop system
  5. Translation of control specifications into a system of equations
  6. Definition of a controller structure meeting the specifications and calculation of the controller gains
  7. Feedback control
  8. Feedforward control
  9. Disturbance observer
  10. Design of multi loop, multi objective controllers
  11. Implementation of a controller in an experimental setup

Indicative Teaching Sequence and Methods

Week C/TD/TP* Content Preparation Learn.\ outc.
S1 C1 (2h) Analysis of linear time-invariant systems in the time domain:
  • Definitions and properties of systems
  • Laplace Transform (LT)
  • Transfer function, poles and zeros
  • Temporal responses.
 AAV1
S2 C2 (2h) Analysis of linear time-invariant systems in the frequency domain:
  • Bode diagram: reminders and definitions
  • Bode diagram of elementary functions of first and second order
  • Nyquist diagram
 AAV2, AAV3
S2 TD1 (2h) Tutorial 1: Analysis of linear time-invariant systems in time and frequency domains (Modeling of a mechanical system, Bode plot, Time/frequency analysis, Quarter Car Suspension Model)
S3 C3 (2h) Output feedback control of linear systems: - Introduction
  • Regulation and control
  • Modeling of a closed loop system
  • Stability of a closed loop system
  • Stability margins
  • Precision and disturbance rejection
  • Correction structures
 AAV4, AAV5, AAV6, AAV7
S3 TD2 (2h) Tutorial 2: Output feedback control strategies for LTI systems (Proportional control, Phase-lead control, Dynamic controller with integral action)
S4 C4 (2h) Feedforward Control:
  • Wy Feedforward?
  • Disturbance feedforward
  • Application
 AAV8, AAV 9
S5 C5 (2h) Dynamic output feedback control:
  • Closed loop performance and specifications
  • Proportional control
  • Proportional Integral (PI) control
  • Ideal PI control
  • Approximate PI control
  • Lead and Lag Compensators
  • Design of a dynamic output feedback control based on stability, accuracy and bandwidth specifications
 AAV7
S5 TD3 (2h) Tutorial 3: Feedforward control for LTI systems (Tracking feedforward, Control of a hydraulic cylinder and disturbance rejection, Disturbance observer (DOB))
S6 C6 (2h) Multi-loop control:
  • Principle and advantages of Multi-loop control
  • Tachometric feedback
 AAV10
S6 TD4 (2h) Tutorial 4: Multiloop control for LTI systems (Control of a DC motor with tachometric feedback)
S7 TP (4h) Simulation work: Control of an active force sensor
S9 TP (4h) Experimental work: Control of DC motor and a Twin Rotor MIMO AAV11
  • C/TD/TP respectively corresponds to lectures, tutorials and lab sessions.

Indicative Assessment of Intended Learning Outcomes (1st session)

Week Individ./group In-person/remote Type of exam Evaluated outcomes Scale %
S10 Individual In-person Written AAV1-AAV10 70%
S11 Individual In-person Practical AAV11 30%

2nde session

Session Individ./group In-person/remote Type of exam Evaluated outcomes Scale %
2 Individual In-person Written AAV1-AAV10 70%
1 Individual In-person Practical AAV11 30%

Bibliographic references

  • Eric Ostertag, ”Systèmes et asservissements continus : Modélisation, analyse, synthèse des lois de commande”. ELLIPSES, ISBN-10 : 2-7298-2013-2

Logo SDI Date of generation of this unit description: 14/01/2026 Logo SDI