AMJAD HASOON Process Control Lec4.
|
|
- Anthony Pope
- 5 years ago
- Views:
Transcription
1 Multiple Inputs Control systems often have more than one input. For example, there can be the input signal indicating the required value of the controlled variable and also an input or inputs due to disturbances which affect the system. The procedure to obtain the relationship between the inputs and the output for such systems is: 1. Set all inputs except one equal to zero 2. Determine the output signal due to this one non-zero input 3. Repeat the above steps for each of the remaining inputs in turn 4. The total output of the system is the algebraic sum (superposition) of the outputs due to each of the inputs. Example1: Find the output Y(s) of the block diagram in the figure below Exercise: Determine the output Y(s) of the following system. 1
2 Modelling This lecture we will concentrate on how to do system modeling based on the most commonly used technique In frequency domain using Transfer Function (TF) representation 1. Modelling and electrical systems Basic laws governing electrical circuits are Kirchhoff's current law and voltage law. Mathematical model of an electrical circuit can be obtained by applying one or both of Kirchhoff's laws to it. Example 1: find the transfer function of the following R-C circuit if you know the input is v(t) and the output is v c (t) then find the transfer function if the output is i(t) 2
3 H.W. : for the same previous example find V R (t)/v(t) Example 1: find the transfer function of the following R-L-C circuit if you know the the input is v(t) and the output is v c (t) 3
4 2. Modelling Physical System Example1: find the transfer function, X(S)/F(S) for the system of figure below: SOLUTION: Begin the solution by drawing the free-body diagram shown in Figure: 4
5 Taking the Laplace transform, assuming zero initial conditions, Exercise: In the mechanical system shown in the figure, m is the mass, k is the spring constant, b is the friction constant, u(t) is an external applied force and y(t) is the resulting displacement. 1) Find the differential equation of the system 2) Find the transfer function between the input U(s) and the output Y(s). 5
6 3. Modelling and Control of Water Tank Model The mathematical model of most of the physical processes is nonlinear in nature. On the other hand, most of the analysis like in simulation and design of the controllers, assumes that the process is linear in nature. In order to build this gap, the linearization of the nonlinear model is needed. This linearization is always done with respect to a particular operating point of the system. From the above figure it is understood that qi is the inflow rate and qo is the outflow rate (in m3/sec) of the tank, and h is the height of the liquid level of the tank at any time instant. And also assume that the cross sectional area of the tank be A. In steady state condition, both qi and qo are same, and the height h of the liquid level of the tank will be constant. 1. RESISTANCE OF LIQUID LEVEL SYSTEM The resistance for liquid flow in such a pipe or restriction is defined as the change in the level difference to a unit change in flow rate; that is, 2. CAPACITANCE OF LIQUID-LEVEL SYSTEMS The capacitance of a tank is defined to be the change in quantity of stored liquid necessary to cause a unity change in the potential (head). The potential (head) is the quantity that includes the energy level of the system. Capacitance (C) is nothing but is cross sectional area (A) of the tank. 6
7 Rate of change of fluid volume in tank = flow in flow out Since volume is (area x height) And cross sectional area can be replaced by capacitance Where the resistance R may be written as Then rearranging the equation (8) we get Substitute equation (9) in equation (7), we get After simplifying above equation the equation (10) becomes Taking Laplace transform considering initial conditions to zero RCSH (s)+ H(s) =R Q i (s) (12) The transfer function can be obtained as Where, C=cross sectional area of the tank 7
8 First Order System What is a first order system? It is a system whose dynamic behavior is described by a first order differential equation. Standard form of first order transfer functions The first order system has only one pole as shown The important characteristics of the standard form are as follows: The denominator must be of the form τs + 1 The coefficient of the s term in the denominator is the system time constant τ 8
9 The numerator is the steady-state gain K or (DC gain) the system ration between the input signal and the steady state value of output. Example1: For the first order system given below DC gain (K) is equal 10 Time Constant (T) is equal 3 Example2: For the first order system given below find the DC gain and time constant ( ) DC gain (k)= Time Constant (T) is equal There are two methods to analyze functioning of a control system that are time domain analysis and frequency domain analysis. In time domain analysis the response of a system is a function of time. Response of first order systems to some common forcing functions To get the response to any input follow the following steps (scheme) [Input] (t) LT (s) TF (s) L 1 (t)[output] 1. Step response ((t) = A (t); (t) =?? ) ( ) ( ) (s) 9
10 (s) Solving by partial fractions A (s) (t) = [1 e t / τ] The above equation is the general form of first order system response to step change. اهم ميزتين بالفيرست اورد سيستم ريسبونس هي: No overshoot No oscillations 10
Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2)
Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2) For all calculations in this book, you can use the MathCad software or any other mathematical software that you are familiar
More information( ) ( = ) = ( ) ( ) ( )
( ) Vρ C st s T t 0 wc Ti s T s Q s (8) K T ( s) Q ( s) + Ti ( s) (0) τs+ τs+ V ρ K and τ wc w T (s)g (s)q (s) + G (s)t(s) i G and G are transfer functions and independent of the inputs, Q and T i. Note
More informationIntroduction to Controls
EE 474 Review Exam 1 Name Answer each of the questions. Show your work. Note were essay-type answers are requested. Answer with complete sentences. Incomplete sentences will count heavily against the grade.
More informationCHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System
CHAPTER 1 Basic Concepts of Control System 1. What is open loop control systems and closed loop control systems? Compare open loop control system with closed loop control system. Write down major advantages
More informationSchool of Engineering Faculty of Built Environment, Engineering, Technology & Design
Module Name and Code : ENG60803 Real Time Instrumentation Semester and Year : Semester 5/6, Year 3 Lecture Number/ Week : Lecture 3, Week 3 Learning Outcome (s) : LO5 Module Co-ordinator/Tutor : Dr. Phang
More informationCHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION. Professor Dae Ryook Yang
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 5-1 Road Map of the Lecture V Laplace Transform and Transfer
More informationModeling and Analysis of Dynamic Systems
Modeling and Analysis of Dynamic Systems by Dr. Guillaume Ducard Fall 2016 Institute for Dynamic Systems and Control ETH Zurich, Switzerland 1/22 Outline 1 Lecture 5: Hydraulic Systems Pelton Turbine:
More informationMODELING OF CONTROL SYSTEMS
1 MODELING OF CONTROL SYSTEMS Feb-15 Dr. Mohammed Morsy Outline Introduction Differential equations and Linearization of nonlinear mathematical models Transfer function and impulse response function Laplace
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #4 Monday, January 13, 2003 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Impulse and Step Responses of Continuous-Time
More informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 6 Mathematical Representation of Physical Systems II 1/67
1/67 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 6 Mathematical Representation of Physical Systems II State Variable Models for Dynamic Systems u 1 u 2 u ṙ. Internal Variables x 1, x 2 x n y 1 y 2. y m Figure
More informationDynamic Modeling. For the mechanical translational system shown in Figure 1, determine a set of first order
QUESTION 1 For the mechanical translational system shown in, determine a set of first order differential equations describing the system dynamics. Identify the state variables and inputs. y(t) x(t) k m
More informationChapter three. Mathematical Modeling of mechanical end electrical systems. Laith Batarseh
Chapter three Mathematical Modeling of mechanical end electrical systems Laith Batarseh 1 Next Previous Mathematical Modeling of mechanical end electrical systems Dynamic system modeling Definition of
More information8 sin 3 V. For the circuit given, determine the voltage v for all time t. Assume that no energy is stored in the circuit before t = 0.
For the circuit given, determine the voltage v for all time t. Assume that no energy is stored in the circuit before t = 0. Spring 2015, Exam #5, Problem #1 4t Answer: e tut 8 sin 3 V 1 For the circuit
More informationChapter 10 Sinusoidal Steady State Analysis Chapter Objectives:
Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steady-state analysis. Learn how to apply nodal and mesh analysis in the frequency
More informationLab Experiment 2: Performance of First order and second order systems
Lab Experiment 2: Performance of First order and second order systems Objective: The objective of this exercise will be to study the performance characteristics of first and second order systems using
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review
Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationModeling. Transition between the TF to SS and SS to TF will also be discussed.
Modeling This lecture we will consentrate on how to do system modeling based on two commonly used techniques In frequency domain using Transfer Function (TF) representation In time domain via using State
More informationControl of Manufacturing Processes
Control of Manufacturing Processes Subject 2.830 Spring 2004 Lecture #18 Basic Control Loop Analysis" April 15, 2004 Revisit Temperature Control Problem τ dy dt + y = u τ = time constant = gain y ss =
More informationMATHEMATICAL MODELING OF DYNAMIC SYSTEMS
MTHEMTIL MODELIN OF DYNMI SYSTEMS Mechanical Translational System 1. Spring x(t) k F S (t) k x(t) x i (t) k x o (t) 2. Damper x(t) x i (t) x o (t) c c 3. Mass x(t) F(t) m EXMPLE I Produce the block diagram
More information(a) Find the transfer function of the amplifier. Ans.: G(s) =
126 INTRDUCTIN T CNTR ENGINEERING 10( s 1) (a) Find the transfer function of the amplifier. Ans.: (. 02s 1)(. 001s 1) (b) Find the expected percent overshoot for a step input for the closed-loop system
More informationGiven: We are given the drawing above and the assumptions associated with the schematic diagram.
PROBLEM 1: (30%) The schematic shown below represents a pulley-driven machine with a flexible support. The three coordinates shown are absolute coordinates drawn with respect to the static equilibrium
More information130 CHAP. 4 Systems of ODEs. Phase Plane. Qualitative Methods. Find the eigenvalues and eigenvectors of the matrix
3 CHAP. 4 Systems of ODEs. Phase Plane. Qualitative Methods This quadratic equation in l is called the characteristic equation of A. Its solutions are the eigenvalues l and l of A. First determine these.
More informationProfessor Fearing EE C128 / ME C134 Problem Set 2 Solution Fall 2010 Jansen Sheng and Wenjie Chen, UC Berkeley
Professor Fearing EE C128 / ME C134 Problem Set 2 Solution Fall 21 Jansen Sheng and Wenjie Chen, UC Berkeley 1. (15 pts) Partial fraction expansion (review) Find the inverse Laplace transform of the following
More informationQUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)
QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34) NOTE: FOR NUMERICAL PROBLEMS FOR ALL UNITS EXCEPT UNIT 5 REFER THE E-BOOK ENGINEERING CIRCUIT ANALYSIS, 7 th EDITION HAYT AND KIMMERLY. PAGE NUMBERS OF
More informationControl Engineering BDA30703
Control Engineering BDA30703 Lecture 3: Performance characteristics of an instrument Prepared by: Ramhuzaini bin Abd. Rahman Expected Outcomes At the end of this lecture, students should be able to; 1)
More informationLecture 39. PHYC 161 Fall 2016
Lecture 39 PHYC 161 Fall 016 Announcements DO THE ONLINE COURSE EVALUATIONS - response so far is < 8 % Magnetic field energy A resistor is a device in which energy is irrecoverably dissipated. By contrast,
More informationFirst and Second Order Circuits. Claudio Talarico, Gonzaga University Spring 2015
First and Second Order Circuits Claudio Talarico, Gonzaga University Spring 2015 Capacitors and Inductors intuition: bucket of charge q = Cv i = C dv dt Resist change of voltage DC open circuit Store voltage
More informationNETWORK ANALYSIS WITH APPLICATIONS
NETWORK ANALYSIS WITH APPLICATIONS Third Edition William D. Stanley Old Dominion University Prentice Hall Upper Saddle River, New Jersey I Columbus, Ohio CONTENTS 1 BASIC CIRCUIT LAWS 1 1-1 General Plan
More informationProblem Value Score Total 100/105
RULES This is a closed book, closed notes test. You are, however, allowed one piece of paper (front side only) for notes and definitions, but no sample problems. The top half is the same as from the first
More informationIndex. Index. More information. in this web service Cambridge University Press
A-type elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 A-type variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,
More informationDr. Ian R. Manchester
Dr Ian R. Manchester Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus
More information(a) Torsional spring-mass system. (b) Spring element.
m v s T s v a (a) T a (b) T a FIGURE 2.1 (a) Torsional spring-mass system. (b) Spring element. by ky Wall friction, b Mass M k y M y r(t) Force r(t) (a) (b) FIGURE 2.2 (a) Spring-mass-damper system. (b)
More informationBasic Procedures for Common Problems
Basic Procedures for Common Problems ECHE 550, Fall 2002 Steady State Multivariable Modeling and Control 1 Determine what variables are available to manipulate (inputs, u) and what variables are available
More informationEC Control Systems- Question bank
MODULE I Topic Question mark Automatic control & modeling, Transfer function Write the merits and demerits of open loop and closed loop Month &Year May 12 Regula tion Compare open loop system with closed
More informationExercise 1a: Transfer functions
Exercise 1a: Transfer functions Transfer functions are a model form based on the Laplace transform. Transfer functions are very useful in analysis and design of linear dynamic systems. A general Transfer
More informationExercise 5 - Hydraulic Turbines and Electromagnetic Systems
Exercise 5 - Hydraulic Turbines and Electromagnetic Systems 5.1 Hydraulic Turbines Whole courses are dedicated to the analysis of gas turbines. For the aim of modeling hydraulic systems, we analyze here
More informationDynamic Behavior. Chapter 5
1 Dynamic Behavior In analyzing process dynamic and process control systems, it is important to know how the process responds to changes in the process inputs. A number of standard types of input changes
More informationYTÜ Mechanical Engineering Department
YTÜ Mechanical Engineering Department Lecture of Special Laboratory of Machine Theory, System Dynamics and Control Division Coupled Tank 1 Level Control with using Feedforward PI Controller Lab Report
More informationTime Response Analysis (Part II)
Time Response Analysis (Part II). A critically damped, continuous-time, second order system, when sampled, will have (in Z domain) (a) A simple pole (b) Double pole on real axis (c) Double pole on imaginary
More informationYTÜ Mechanical Engineering Department
YTÜ Mechanical Engineering Department Lecture of Special Laboratory of Machine Theory, System Dynamics and Control Division Coupled Tank 1 Level Control with using Feedforward PI Controller Lab Date: Lab
More informationControl Systems Engineering (Chapter 2. Modeling in the Frequency Domain) Prof. Kwang-Chun Ho Tel: Fax:
Control Systems Engineering (Chapter 2. Modeling in the Frequency Domain) Prof. Kwang-Chun Ho kwangho@hansung.ac.kr Tel: 02-760-4253 Fax:02-760-4435 Overview Review on Laplace transform Learn about transfer
More informationBasic RL and RC Circuits R-L TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri
st Class Basic RL and RC Circuits The RL circuit with D.C (steady state) The inductor is short time at Calculate the inductor current for circuits shown below. I L E R A I L E R R 3 R R 3 I L I L R 3 R
More informationDr Ian R. Manchester
Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign
More informationChapter 4 Transients. Chapter 4 Transients
Chapter 4 Transients Chapter 4 Transients 1. Solve first-order RC or RL circuits. 2. Understand the concepts of transient response and steady-state response. 1 3. Relate the transient response of first-order
More informationHydraulic (Fluid) Systems
Hydraulic (Fluid) Systems Basic Modeling Elements Resistance apacitance Inertance Pressure and Flow Sources Interconnection Relationships ompatibility Law ontinuity Law Derive Input/Output Models ME375
More informationMAE106 Homework 2 - Solution DC Motors & Intro to the frequency domain
MAE06 Homework 2 - Solution DC Motors & Intro to the frequency domain University of California, Irvine Department of Mechanical and Aerospace Engineering Problem You are given the circuit shown in Figure.
More informationProcess Control and Instrumentation Prof. A. K. Jana Department of Chemical Engineering Indian Institute of Technology, Kharagpur
Process Control and Instrumentation Prof. A. K. Jana Department of Chemical Engineering Indian Institute of Technology, Kharagpur Lecture - 10 Dynamic Behavior of Chemical Processes (Contd.) (Refer Slide
More informationChapter 3 - Solved Problems
Chapter 3 - Solved Problems Solved Problem 3.. A nonlinear system has an input-output model given by dy(t) + ( + 0.2y(t))y(t) = u(t) + 0.2u(t) 3 () 3.. Compute the operating point(s) for u Q = 2. (assume
More informationExercise 8: Level Control and PID Tuning. CHEM-E7140 Process Automation
Exercise 8: Level Control and PID Tuning CHEM-E740 Process Automation . Level Control Tank, level h is controlled. Constant set point. Flow in q i is control variable q 0 q 0 depends linearly: R h . a)
More informationMixing Problems. Solution of concentration c 1 grams/liter flows in at a rate of r 1 liters/minute. Figure 1.7.1: A mixing problem.
page 57 1.7 Modeling Problems Using First-Order Linear Differential Equations 57 For Problems 33 38, use a differential equation solver to determine the solution to each of the initial-value problems and
More informationAs in the previous problem, the height of a object thrown straight up is given by
WebAssign Lesson 2-1 Basic Hw (Homework) Current Score : / 36 Due : Wednesday, January 29 2014 07:30 AM MST Shari Dorsey Sp 14 Math 170, section 001, Spring 2014 Instructor: Doug Bullock 1. /2 points An
More informationTopic 4 Formula. Introduction: V = IR Write down the formula being used. V = (5)(10) Substitute I with 5 and R with 10
Topic 4 Formula Introduction: In many situations in science and business we use formulas. these formula are essentially just an algebraic expression where the variables used have very specific meanings.
More informationI. Frequency Response of Voltage Amplifiers
I. Frequency Response of Voltage Amplifiers A. Common-Emitter Amplifier: V i SUP i OUT R S V BIAS R L v OUT V Operating Point analysis: 0, R s 0, r o --->, r oc --->, R L ---> Find V BIAS such that I C
More informationSeries RC and RL Time Domain Solutions
ECE2205: Circuits and Systems I 6 1 Series RC and RL Time Domain Solutions In the last chapter, we saw that capacitors and inductors had element relations that are differential equations: i c (t) = C d
More informationMATHEMATICAL MODELING OF CONTROL SYSTEMS
1 MATHEMATICAL MODELING OF CONTROL SYSTEMS Sep-14 Dr. Mohammed Morsy Outline Introduction Transfer function and impulse response function Laplace Transform Review Automatic control systems Signal Flow
More informationAC&ST AUTOMATIC CONTROL AND SYSTEM THEORY SYSTEMS AND MODELS. Claudio Melchiorri
C. Melchiorri (DEI) Automatic Control & System Theory 1 AUTOMATIC CONTROL AND SYSTEM THEORY SYSTEMS AND MODELS Claudio Melchiorri Dipartimento di Ingegneria dell Energia Elettrica e dell Informazione (DEI)
More informationMATHEMATICAL MODELLING OF TWO TANK SYSTEM
MATHEMATICAL MODELLING OF TWO TANK SYSTEM 1 KHELE SWARADA, ELECTRICAL, AISSMS IOIT, MAHARASHTRA, INDIA 2 AARTI WALVEKAR, ELECTRICAL, AISSMS IOIT, MAHARASHTRA, INDIA 3 AMITA THORAT, ELECTRICAL, AISSMS IOIT,
More informationLecture Fluid system elements
Lecture 8.1 Fluid system elements volumetric flowrate pressure drop Detailed distributed models of fluids, such as the Navier-Stokes equations, are necessary for understanding many aspects of fluid systems
More informationET3-7: Modelling II(V) Electrical, Mechanical and Thermal Systems
ET3-7: Modelling II(V) Electrical, Mechanical and Thermal Systems Agenda of the Day 1. Resume of lesson I 2. Basic system models. 3. Models of basic electrical system elements 4. Application of Matlab/Simulink
More informationStep Response of First-Order Systems
INTRODUCTION This tutorial discusses the response of a first-order system to a unit step function input. In particular, it addresses the time constant and how that affects the speed of the system s response.
More informationEE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation
EE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation Tim Davidson Ext. 27352 davidson@mcmaster.ca Objective To use the root locus technique to design a lead compensator for a marginally-stable
More informationsc Control Systems Design Q.1, Sem.1, Ac. Yr. 2010/11
sc46 - Control Systems Design Q Sem Ac Yr / Mock Exam originally given November 5 9 Notes: Please be reminded that only an A4 paper with formulas may be used during the exam no other material is to be
More informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING MSC SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2016/2017
UNIVERSITY OF BOLTON TW16 SCHOOL OF ENGINEERING MSC SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2016/2017 ADVANCED CONTROL TECHNOLOGY MODULE NO: EEM7015 Date: Monday 15 May 2017
More informationBasic Electronics. Introductory Lecture Course for. Technology and Instrumentation in Particle Physics Chicago, Illinois June 9-14, 2011
Basic Electronics Introductory Lecture Course for Technology and Instrumentation in Particle Physics 2011 Chicago, Illinois June 9-14, 2011 Presented By Gary Drake Argonne National Laboratory Session 2
More informationIntroduction to Process Control
Introduction to Process Control For more visit :- www.mpgirnari.in By: M. P. Girnari (SSEC, Bhavnagar) For more visit:- www.mpgirnari.in 1 Contents: Introduction Process control Dynamics Stability The
More informationEXAMINATION INFORMATION PAGE Written examination
EXAMINATION INFORMATION PAGE Written examination Course code: Course name: PEF3006 Process Control Examination date: 30 November 2018 Examination time from/to: 09:00-13:00 Total hours: 4 Responsible course
More informationTime Response of Systems
Chapter 0 Time Response of Systems 0. Some Standard Time Responses Let us try to get some impulse time responses just by inspection: Poles F (s) f(t) s-plane Time response p =0 s p =0,p 2 =0 s 2 t p =
More informationDifferential Equations Spring 2007 Assignments
Differential Equations Spring 2007 Assignments Homework 1, due 1/10/7 Read the first two chapters of the book up to the end of section 2.4. Prepare for the first quiz on Friday 10th January (material up
More informationECE Circuit Theory. Final Examination. December 5, 2008
ECE 212 H1F Pg 1 of 12 ECE 212 - Circuit Theory Final Examination December 5, 2008 1. Policy: closed book, calculators allowed. Show all work. 2. Work in the provided space. 3. The exam has 3 problems
More information(Refer Slide Time: 00:01:30 min)
Control Engineering Prof. M. Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Introduction to Control Problem (Contd.) Well friends, I have been giving you various
More informationEE 422G - Signals and Systems Laboratory
EE 4G - Signals and Systems Laboratory Lab 9 PID Control Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 April, 04 Objectives: Identify the
More informationLecture 7: Laplace Transform and Its Applications Dr.-Ing. Sudchai Boonto
Dr-Ing Sudchai Boonto Department of Control System and Instrumentation Engineering King Mongkut s Unniversity of Technology Thonburi Thailand Outline Motivation The Laplace Transform The Laplace Transform
More informationFATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY
FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY Senkottai Village, Madurai Sivagangai Main Road, Madurai - 625 020. An ISO 9001:2008 Certified Institution DEPARTMENT OF ELECTRONICS AND COMMUNICATION
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Steady-state error Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling Analysis Design Laplace
More informationEEE105 Teori Litar I Chapter 7 Lecture #3. Dr. Shahrel Azmin Suandi Emel:
EEE105 Teori Litar I Chapter 7 Lecture #3 Dr. Shahrel Azmin Suandi Emel: shahrel@eng.usm.my What we have learnt so far? Chapter 7 introduced us to first-order circuit From the last lecture, we have learnt
More informationSubject: BT6008 Process Measurement and Control. The General Control System
WALJAT COLLEGES OF APPLIED SCIENCES In academic partnership with BIRLA INSTITUTE OF TECHNOLOGY Question Bank Course: Biotechnology Session: 005-006 Subject: BT6008 Process Measurement and Control Semester:
More information0 t < 0 1 t 1. u(t) =
A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 13 p. 22/33 Step Response A unit step function is described by u(t) = ( 0 t < 0 1 t 1 While the waveform has an artificial jump (difficult
More informationD C Circuit Analysis and Network Theorems:
UNIT-1 D C Circuit Analysis and Network Theorems: Circuit Concepts: Concepts of network, Active and passive elements, voltage and current sources, source transformation, unilateral and bilateral elements,
More informationFlow Rate is the NET amount of water passing through a surface per unit time
Electric Current An Analogy Water Flow in a Pipe H 2 0 gallons/minute Flow Rate is the NET amount of water passing through a surface per unit time Individual molecules are bouncing around with speeds of
More informationCapacitors. Chapter How capacitors work Inside a capacitor
Chapter 6 Capacitors In every device we have studied so far sources, resistors, diodes and transistors the relationship between voltage and current depends only on the present, independent of the past.
More information3. Mathematical Modelling
3. Mathematical Modelling 3.1 Modelling principles 3.1.1 Model types 3.1.2 Model construction 3.1.3 Modelling from first principles 3.2 Models for technical systems 3.2.1 Electrical systems 3.2.2 Mechanical
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 14 121011 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review Steady-State Analysis RC Circuits RL Circuits 3 DC Steady-State
More informationSome of the different forms of a signal, obtained by transformations, are shown in the figure. jwt e z. jwt z e
Transform methods Some of the different forms of a signal, obtained by transformations, are shown in the figure. X(s) X(t) L - L F - F jw s s jw X(jw) X*(t) F - F X*(jw) jwt e z jwt z e X(nT) Z - Z X(z)
More informationCourse roadmap. ME451: Control Systems. Example of Laplace transform. Lecture 2 Laplace transform. Laplace transform
ME45: Control Systems Lecture 2 Prof. Jongeun Choi Department of Mechanical Engineering Michigan State University Modeling Transfer function Models for systems electrical mechanical electromechanical Block
More informationSingle-Time-Constant (STC) Circuits This lecture is given as a background that will be needed to determine the frequency response of the amplifiers.
Single-Time-Constant (STC) Circuits This lecture is given as a background that will be needed to determine the frequency response of the amplifiers. Objectives To analyze and understand STC circuits with
More informationIntroduction to Feedback Control
Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System
More informationSolutions for Tutorial 4 Modelling of Non-Linear Systems
Solutions for Tutorial 4 Modelling of Non-Linear Systems 4.1 Isothermal CSTR: The chemical reactor shown in textbook igure 3.1 and repeated in the following is considered in this question. The reaction
More informationSystem Modeling. Lecture-2. Emam Fathy Department of Electrical and Control Engineering
System Modeling Lecture-2 Emam Fathy Department of Electrical and Control Engineering email: emfmz@yahoo.com 1 Types of Systems Static System: If a system does not change with time, it is called a static
More informationPower System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur. Module 3 Lecture 8
Power System Operations and Control Prof. S.N. Singh Department of Electrical Engineering Indian Institute of Technology, Kanpur Module 3 Lecture 8 Welcome to lecture number 8 of module 3. In the previous
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 Electrical and Electronics Engineering TUTORIAL QUESTION BAN Course Name : CONTROL SYSTEMS Course Code : A502 Class : III
More information2.004 Dynamics and Control II Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 or information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 2 I C + 4 * Massachusetts
More informationLecture 14: Ordinary Differential Equation I. First Order
Lecture 14: Ordinary Differential Equation I. First Order 1. Key points Maple commands dsolve 2. Introduction We consider a function of one variable. An ordinary differential equations (ODE) specifies
More informationProcess Control J.P. CORRIOU. Reaction and Process Engineering Laboratory University of Lorraine-CNRS, Nancy (France) Zhejiang University 2016
Process Control J.P. CORRIOU Reaction and Process Engineering Laboratory University of Lorraine-CNRS, Nancy (France) Zhejiang University 206 J.P. Corriou (LRGP) Process Control Zhejiang University 206
More informationEE102 Homework 2, 3, and 4 Solutions
EE12 Prof. S. Boyd EE12 Homework 2, 3, and 4 Solutions 7. Some convolution systems. Consider a convolution system, y(t) = + u(t τ)h(τ) dτ, where h is a function called the kernel or impulse response of
More information(Refer Slide Time 1:25)
Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Module - 2 Lecture - 24 Transient Response of Pressure Transducers
More informationLecture 9 Time-domain properties of convolution systems
EE 12 spring 21-22 Handout #18 Lecture 9 Time-domain properties of convolution systems impulse response step response fading memory DC gain peak gain stability 9 1 Impulse response if u = δ we have y(t)
More informationSteady State Errors. Recall the closed-loop transfer function of the system, is
Steady State Errors Outline What is steady-state error? Steady-state error in unity feedback systems Type Number Steady-state error in non-unity feedback systems Steady-state error due to disturbance inputs
More informationSolving a RLC Circuit using Convolution with DERIVE for Windows
Solving a RLC Circuit using Convolution with DERIVE for Windows Michel Beaudin École de technologie supérieure, rue Notre-Dame Ouest Montréal (Québec) Canada, H3C K3 mbeaudin@seg.etsmtl.ca - Introduction
More information06 Feedback Control System Characteristics The role of error signals to characterize feedback control system performance.
Chapter 06 Feedback 06 Feedback Control System Characteristics The role of error signals to characterize feedback control system performance. Lesson of the Course Fondamenti di Controlli Automatici of
More informationLecture 1. Electrical Transport
Lecture 1. Electrical Transport 1.1 Introduction * Objectives * Requirements & Grading Policy * Other information 1.2 Basic Circuit Concepts * Electrical l quantities current, voltage & power, sign conventions
More information