Side 1 af 15 10 Digital Control Systems Sampling, Z-transform, transfer function Reg1_slide4 Chap. 13.1-3,4,(5) J.Nybo Rev.:14.04.04.

Slides:

Advertisements

Similar presentations

Chapter 13: Digital Control Systems 1 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e Chapter 13 Digital Control Systems.

Advertisements

FIGURE 2-1 Typical digital signal processing system. Joyce Van de Vegte Fundamentals of Digital Signal Processing Copyright ©2002 by Pearson Education,

Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin EE445S Real-Time Digital Signal Processing Lab Spring.

Digital Filters. A/DComputerD/A x(t)x[n]y[n]y(t) Example:

From Continuous Time System to Discrete Time System ES400 Jack Ou, Ph.D. Chapter 1.

Interfacing with the Analog World Wen-Hung Liao, Ph.D.

Modern Control Systems (MCS) Dr. Imtiaz Hussain Assistant Professor URL :

1 Figure 9.36 The process of periodically sampling an analog signal. (a) Sample-and-hold (S/H) circuit. The switch closes for a small part (  seconds)

EET260: A/D and D/A converters

President UniversityErwin SitompulSMI 7/1 Dr.-Ing. Erwin Sitompul President University Lecture 7 System Modeling and Identification

Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first.

Analog-to-Digital Converter Chapter 9. A/D Converter Analog-to-Digital Conversion The 68HC11 A/D Converter The 68HC12 A/D Converter Design of a Digital.

Analog-to-Digital Converters

Laplace Transforms 1. Standard notation in dynamics and control (shorthand notation) 2. Converts mathematics to algebraic operations 3. Advantageous for.

Science is organized knowledge. Wisdom is organized life.

© 2000 Prentice Hall Inc. Figure 12.1 Circuit symbol for the comparator. If v 1 > v 2, then v o is high; if v 1 < v 2, then v o is low.

Digital Control Systems

Digital Control Systems The z-Transform. The z Transform Definition of z-Transform The z transform method is an operational method that is very powerful.

Digital Communication Techniques

The sampling of continuous-time signals is an important topic It is required by many important technologies such as: Digital Communication Systems ( Wireless.

2. Z-transform and theorem

Chapter 2 Discrete System Analysis – Discrete Signals

Random signals. Histogram of the random signal Continuous Time Sinusoidal signals.

© The McGraw-Hill Companies, Inc McGraw-Hill 1 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I 15.

Properties of the z-Transform

Chapter 8 Discrete (Sampling) System

Properties and the Inverse of

©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.

Data Acquisition Systems

Robotics Research Laboratory 1 Chapter 3 Discrete System Analysis - Sampled Data Systems.

ECE 8443 – Pattern Recognition ECE 3163 – Signals and Systems Objectives: Modulation Summation Convolution Initial Value and Final Value Theorems Inverse.

Chapter 5 On-Line Computer Control – The z Transform.

1.1 Introduction Comparison between ACS and CCS. ACS CCS Process Actuator Measure Controller (correcting network) Structure: Process Actuator Measure.

Chapter 5 Z Transform. 2/45  Z transform –Representation, analysis, and design of discrete signal –Similar to Laplace transform –Conversion of digital.

HOMEWORK 08D Block diagrams Problem 1: Problem 2:

Chapter 6: Sampled Data Systems and the z-Transform 1.

數位控制（二）.

CHAPTER 19 Data Conversion. Objectives Describe and Analyze: Analog vs. Digital Signals Resolution Digital-to-Analog Conversion Analog-to Digital Conversion.

1 G. Baribaud/AB-BDI Digital Signal Processing March 2003 DISP-2003 The z-transform  The sampling process  The definition and the properties.

Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved. Figure 13.1 Conversion of antenna.

ES97H Biomedical Signal Processing

◦ We sometimes need to digitize an analog signal ◦ To send human voice over a long distance, we need to digitize it, since digital signals are less prone.

Digital Control CSE 421.

Figure Analog-to-digital conversion.. Figure The DAC output is a staircase approximation to the original signal. Filtering removes the sharp.

System Time Response Characteristics

Topics 1 Specific topics to be covered are: Discrete-time signals Z-transforms Sampling and reconstruction Aliasing and anti-aliasing filters Sampled-data.

Find f(kT) if Exercise 1. Solution 1 1 Begin by dividing F(z) by z and performing a partial-fraction expansion. For z = 0.5 For z = 0.7 For z = 0.9.

ECE 101 Exploring Electrical Engineering Chapter 7 Data Acquisition Herbert G. Mayer, PSU Status 11/30/2015 Derived with permission from PSU Prof. Phillip.

z-Plane Analysis of Discrete-Time Control Systems

Sampling. Introduction  Sampling refers to the process of converting a continuous, analog signal to discrete digital numbers.

Lecture 4: Sampling and Reconstruction

Chapter 4 Dynamical Behavior of Processes Homework 6 Construct an s-Function model of the interacting tank-in-series system and compare its simulation.

Figure 4.1 Computerized data-acquisition system.

Chapter 4 Dynamical Behavior of Processes Homework 6 Construct an s-Function model of the interacting tank-in-series system and compare its simulation.

Sezai Taskin, Ph.D. Assoc. Prof.

Chap2. Modeling in the Frequency Domain

Chapter4. Sampling of Continuous-Time Signals

Digital and Non-Linear Control

Digital Control Systems (DCS)

Data Acquisition Systems

Chapter 5 Z Transform.

لجنة الهندسة الكهربائية

The sampling of continuous-time signals is an important topic

The Z-Transform of a given discrete signal, x(n), is given by:

數位控制理論簡介.

CHAPTER-6 Z-TRANSFORM.

Example 1: Find the magnitude and phase angle of

Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first.

Laplace Transforms Important analytical method for solving linear ordinary differential equations. - Application to nonlinear ODEs? Must linearize first.

DIGITAL CONTROL SYSTEM WEEK 3 NUMERICAL APPROXIMATION

Presentation transcript:

Side 1 af Digital Control Systems Sampling, Z-transform, transfer function Reg1_slide4 Chap ,4,(5) J.Nybo Rev.:

Side 2 af 15 From analog to digital system Figure 13.1 Conversion of antenna azimuth position control system from: a. analog control to b. digital control

Side 3 af 15 Block-diagram of digital system Figure 13.2 a. Placement of the digital computer within the loop; b. detailed block diagram showing placement of A/D and D/A converters

Side 4 af 15 Digital-to-analog conver ter Figure 13.3 Digital-to-analog converter

Side 5 af 15 Steps in analog-to-digital conversion : Figure 13.4 Steps in analog-to-digital conversion: a. analog signal; b. analog signal after sample-and-hold; c. conversion of samples to digital numbers

Side 6 af 15 Two views of uniform-rate sampling: Figure 13.5 Two views of uniform-rate sampling: a. switch opening and closing; b. product of time waveform and sampling waveform

Side 7 af 15 Model of sampling with a uniform rectangular pulse train Figure 13.6 Model of sampling with a uniform rectangular pulse train

Side 8 af 15 Ideal sampling and the zero-order hold Figure 13.7 Ideal sampling and the zero-order hold

Side 9 af 15 Zero Order Hold

Side 10 af 15 Z-transform of a sampled signal

Side 11 af 15 Table 13.1 Partial table of z- and s-transforms

Side 12 af 15 Table 13.2 z-transform theorems

Side 13 af 15 Inverse z-transform Partial fraction expansion (partial brøker) Power series (polynomiers division) Tables

Side 14 af 15 Pulse Transfer Function Figure 13.8 Sampled-data systems: a. continuous; b. sampled input; c. sampled input and output

Side 15 af 15 Sampled-data systems and their z- transforms Figure 13.9 Sampled-data systems and their z-transforms

Side 16 af 15 Exercise Skill_assesment-Exercise 13.3