Control Theory 2A (Digital Control Systems)

Données Générales
Programme Académique	ECAM LaSalle Mechanical and Electrical Engineering Programme			Responsable(s) Module : GHRAB Sonia,GIBERT Guillaume
Type d'EC : Cours	Control Theory 2A (Digital Control Systems) (LIIEEng07EContTheo2a)
TD : 6h00 TP : 8h00 Cours : 6h00 Travail personnel : 12h00 Durée totale: 32h00	Status	Periode Semester 7	Langue d'enseignement : English

Objectifs Généraux
By the end of this module, students will be able to : 1. Distinguish between continuous-sampled-discretized signals 2. Discretize the continuous LTI systems 3. Determine the Z-transform 4. Design of digital P, PI, PID controllers and implement them on real system 5. Analyze the system performances

Contenu
1. Introduction to signals : continuous/ sampled/ discrete 2. Distinction between Difference equation (used to describe Discrete systems) and differential equation (used to describe continuous systems) 3. Signal sampling and quantization Sampling of continuous signals Signal reconstruction Practical considerations for signal sampling : anti-aliasing filter Practical reconsiderations for signal reconstruction :anti-image filter and equalizer Analog to digital conversion digital to analog conversion/quantization 4. Determination of the z-transform Introduction to the z-transform and its properties Illustration of how we determine the inverse of z-transform using the partial fraction expansion The use of the z-transform to solve linear difference equations 5. Digital Proportional, PI and PID controllers Determination of the equation of the digital controller (case of P , PI and PID) *The implementation of digital P, PI and PID on real systems and the evaluation of the system performances

Contenu

1. Introduction to signals : continuous/ sampled/ discrete
2. Distinction between Difference equation (used to describe Discrete systems) and differential equation (used to describe continuous systems)
3. Signal sampling and quantization
*Sampling of continuous signals
*Signal reconstruction
*Practical considerations for signal sampling : anti-aliasing filter
*Practical reconsiderations for signal reconstruction :anti-image filter and equalizer
*Analog to digital conversion
*digital to analog conversion/quantization
4. Determination of the z-transform
*Introduction to the z-transform and its properties
*Illustration of how we determine the inverse of z-transform using the partial fraction expansion
*The use of the z-transform to solve linear difference equations
5. Digital Proportional, PI and PID controllers
*Determination of the equation of the digital controller (case of P , PI and PID)
*The implementation of digital P, PI and PID on real systems and the evaluation of the system performances

Prérequis
Introduction to control theory (S6) Electronic principles and technology (S2) : Kirshoff’s circuit laws Mathematics for engineers 1 and 2 (S1 & S2) : Partial fraction decomposition

Bibliographie
• Tan, L., Jiang, J. (2018) Digital signal processing : Fundamentals and applications • Franklin, G.F, Powell, J.D, Workman, M.L. (1998), Digital control of dynamic systems, 3d edition

Évaluation(s)
N°	Nature	Coefficient	Objectifs
1	Written exam	0,2	The written exam stands for a midterm. The students will be evaluated on some points that had been seen during the lectures and tutorials. The exact contents will be defined according to the progress on lectures and tutorials
2	Practical work	0,3	• First practical session (Use of Matlab/Simulink, 4 hours) : Discretization of systems using Matlab/Simulink : Initialisation with tf, zpk, c2d, pzmap,pole…,use of Simulink : closed-loop system , discretisation using different methods : ZOH, FOH, Tustin….Stability of Discrete LTI systems • Second practical session (Mainly Practical, 4 hours): Digital control of an aerotherm system (Automation + Electronic parts) * Understand the system setup (Electronics/automation parts : Identify the system input, output) and be able to write a code and plot the reference signal (desired temperature in our case), the error and the control input on the same figure using the serialplot. * Identification of the system : It is a delayed system (first order system subject to a constant delay) * Discretization of the system * Main Objective is to compare the performances of the aerotherm system when it is controlled by : * A proportional digital controller * a proportional-Integral digital controller * And a Digital PID controller * The advantages of each digital controller * The disadvantages of increasing/decreasing the proportial, derivative or integral actions (The results should be proved using Simulink as well as using the real practical system) * Compare the theoretic results (implementation of digital controllers using the Simulink block diagram) to the results issued from the practical setup.
3	Written exam	0,5	The exam will take all the parts the student had seen during lectures, tutorials and labs