Control Theory 2a (Digital Control Systems)

General Data
Academic program	Incoming Exchange Student Courses			:
Type d'EC	Classes (LIIEXP07EContTheo2a)
Lectures : 6h00 Tutorials : 6h00 Lab Work : 8h00 Total duration : 32h00	Status : Obligatoire	Period : Semester 7_Robotique and Automation	Education language : English

Learning Outcomes
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

Content
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

Content

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

Pre-requisites / co-requisites
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

Bibliography
• 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