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Lecture

Discrete-Time Systems Analysis

In course

ME-326: Control systems and discrete-time control

Ce cours inclut la modélisation et l'analyse de systèmes dynamiques, l'introduction des principes de base et l'analyse de systèmes en rétroaction, la synthèse de régulateurs dans le domain fréquentiel et dans l'espace d'état, et la commande de systèmes dis ...

Description

This lecture covers the analysis of discrete-time systems, focusing on the Z-transform and its applications in control systems. The instructor explains how to calculate the Z-transform for common signals like Dirac and step functions, and how to find the inverse Z-transform for rational functions. The lecture also delves into the decomposition of rational functions in Z, highlighting the differences with Laplace transforms. The instructor demonstrates methods for calculating Z-transform coefficients, stability analysis, and the concept of transfer functions in discrete-time systems.

Instructors (2)

Christophe Salzmann

Alireza Karimi

Alireza Karimi received his B. Sc. and M. Sc. degrees in Electrical Engineering in 1987 and 1990, respectively, from Amir Kabir University (Tehran Polytechnic). Then he received his DEA and Ph. D. degrees both on Automatic Control from Institut National Polytechnique de Grenoble (INPG) in 1994 and 1997, respectively. He was Assistant Professor at Electrical Engineering Department of Sharif University of Technology in Teheran from 1998 to 2000. Then he joined Automatic Laboratory of Swiss Federal Institute of Technology at Lausanne, Switzerland. He is currently Professor of Automatic Control and the head of "Data-Driven Modelling and Control" group. His research interests include data-driven controller tuning and robust control with application to mechatronic systems and electrical grids.

Official source

Related concepts (28)

Control system

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation.

Industrial control system

An industrial control system (ICS) is an electronic control system and associated instrumentation used for industrial process control. Control systems can range in size from a few modular panel-mounted controllers to large interconnected and interactive distributed control systems (DCSs) with many thousands of field connections. Control systems receive data from remote sensors measuring process variables (PVs), compare the collected data with desired setpoints (SPs), and derive command functions that are used to control a process through the final control elements (FCEs), such as control valves.

Z-transform

In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain (z-domain or z-plane) representation. It can be considered as a discrete-time equivalent of the Laplace transform (s-domain). This similarity is explored in the theory of time-scale calculus. Whereas the continuous-time Fourier transform is evaluated on the Laplace s-domain's imaginary line, the discrete-time Fourier transform is evaluated over the unit circle of the z-domain.

Distributed control system

A distributed control system (DCS) is a computerised control system for a process or plant usually with many control loops, in which autonomous controllers are distributed throughout the system, but there is no central operator supervisory control. This is in contrast to systems that use centralized controllers; either discrete controllers located at a central control room or within a central computer. The DCS concept increases reliability and reduces installation costs by localising control functions near the process plant, with remote monitoring and supervision.

Control engineering

Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering and mechanical engineering at many institutions around the world. The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance.

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