Reduction of Multiple Subsystems
|
|
- Paul Barton
- 6 years ago
- Views:
Transcription
1 Reduction of Multiple Subsystems Ref: Control System Engineering Norman Nise : Chapter 5 Chapter objectives : How to reduce a block diagram of multiple subsystems to a single block representing the transfer function from input to output How to analyze and design transient response for a system consisting of multiple subsystems How to represent in state space a system consisting of multiple subsystems Multiple subsystems - 2 1
2 1. Block Diagrams for Dynamic Systems Block diagram an interconnection of blocks representing basic mathematical operations in such a way that the overall diagram is equivalent to the system s mathematical model. In such a diagram, the lines interconnecting the blocks represent the variables describing the system behaviour. x K f A block diagram representing f = Kx Multiple subsystems - 3 Antenna position control Multiple subsystems - 4 2
3 Block Diagram Reduction Block diagram reduction involves algebraic manipulations of the transfer functions of the subsystems or blocks, which in effect reduce the diagram to a single block. This gives the overall transfer function relating the input r and output c in a block diagram and hence permits, for example, calculation of system transient responses. Multiple subsystems - 5 Summer addition and subtraction of variables x 2 x x 3 y A summer representing y = x 1 + x 2 - x 3 Gain multiplication of a single by a constant (exp. spring) Integrator integration with respect to time u y y y dt dt The block diagram for an integrator Multiple subsystems - 6 3
4 Constant has no input, and its output never changes c y Combining block diagram Consider the following equation : x fa t Ax Steps (for input output equations) - Solve the given equation for the highest derivative of the unknown output variables - Connect one or more integrator blocks in series to integrate that derivative successively as many times as necessary to produce the output var. - Use the result of step 1 to form the highest output derivatives as the output of a summer and a gain block. Multiple subsystems - 7 Construct block diagrams for the following systems 1. Mx Bx Kx fa t iv 2. M M x M K M K K x1 K1K2x1 K2 fa t 3. M x Bx K K x Bx K2x2 0 Bx K x M x Bx K x f t Rules for altering diagram structure Transfer functions which are generally the ratio of two polynomials are often denoted by F(s), G(s) or H(s). When the transfer function is a constant, then that block reduces to a gain block. Series combination 2 a X(s) F 1 (s) V(s) F 2 (s) Y(s) Multiple subsystems - 8 4
5 Parallel combination X(s) F 1 (s) F 2 (s) V 1 (s) V 2 (s) + + Y(s) Example 1 Evaluate the transfer functions Y(s)/U(s) and Z(s)/U(s) for the block diagram below give the results as rational functions of s Multiple subsystems - 9 Equivalent diagrams for the diagram shown in Example 1 Multiple subsystems
6 Moving block to create familiar forms Moving a pick off point a point where an incoming variable in the diagram is directed into more than one block (1) (2) (3) 1 Original diagram, 2 & 3 equivalent diagrams Multiple subsystems - 11 Block diagram algebra for pickoff points - equivalent forms for moving a block a. to the left past a pickoff point; b. to the right past a pickoff point Multiple subsystems
7 Moving a summing junction Ahead of a block After a block Multiple subsystems - 13 Block diagram algebra for summing junctions - equivalent forms for moving a block a. to the left past a summing junction; b. to the right past a summing junction Multiple subsystems
8 Example 2 Modify the bock diagram in (a) to remove the right summing junction, leaving only the left summing junction (a) Original diagram, (b), (c) & (d) equivalent diagrams Multiple subsystems - 15 Reducing diagrams for feedback systems G(s) = Y(s)/E(s) forward transfer function Y(s) H(s) = Z(s)/Y(s) feedback transfer function G(s)H(s) function open-loop transfer Y(s) T(s) = Y(s)/R(s) closed-loop transfer function Z(s) H(s) = 1 system unity feedback Y(s) Multiple subsystems
9 Obtaining the CLTF E()()() s R s YH s Y ()()() s E s G s Y () s G() S R()() s YH s Y () s 1()() GH S GR s Y ()()() s G s1 E s ; R() s 1()() GH1() S R s GH S Y () s R() s is the closed loop TF Multiple subsystems - 17 Unity feedback For a unity feedback, the CLTF is Y ()() s G s R() s 1() G S 1() GH0 S This equation is called the characteristic equation of the closed loop system, giving the root or poles of the TF on the s-plane. Multiple subsystems
10 Consider the cascade or series connection of two blocks in the Fig. By definition, C = G 2 M M = G 1 R Substituting the second into the first yields C = GR G = G 1 G 2 By direct extension it follows that The overall transfer function of a series of blocks equals the product of the individual transfer functions. Multiple subsystems - 19 Multiple subsystems
11 Multiple subsystems - 21 Loop Gain In words, and in somewhat generalized form, this may be stated as follows: The closed-loop transfer function of the standard loop equals the product of the transfer functions in the forward path divided by the sum of 1 and the loop gain function. The loop gain function is defined as the product of the transfer functions around the loop. Multiple subsystems
12 For the present system, the Loop gain function = G 1 G 2 H(s) If H = 1, then E = R - C is the system error, then E/R is the input-to-error transfer function. This will permit the error response for a given input r(t) to be found directly. Multiple subsystems - 23 Error to input TF Since C = G 1 G 2 E(s), then the error to input TF is E() s 1 R() s 1() G G H S 1 2 If the feedback H = 1 and G = G1G2 E() s 1 R() s 1 G Note that the characteristic equation here is 1+G = 0. Multiple subsystems
13 Reducing TF blocks Multiple subsystems - 25 Multiple subsystems
14 Multiple subsystems - 27 Example 3 Multiple subsystems
15 Multiple subsystems - 29 Multiple subsystems
16 Multiple subsystems - 31 Block diagram reduction via familiar form Example 4 reduce the block diagram shown below to a single transfer function Multiple subsystems
17 Steps in solving Example 4: a. collapse summing junctions; b. form equivalent cascaded system in the forward path and equivalent parallel system in the feedback path; c. form equivalent feedback system and multiply by cascaded G1(s) Multiple subsystems - 33 Block diagram reduction by moving blocks Example 5 reduce the block diagram shown below to a single transfer function Multiple subsystems
18 Steps in the block diagram reduction for Example 5 Multiple subsystems - 35 Example 6 reduce the block diagram shown below to a single transfer function Multiple subsystems
19 Example 7 find the equivalent transfer function T(s)=C(s)/R(s) Multiple subsystems - 37 Example 8 Find the closed-loop transfer function for the feedback system below. Compare the locations of the poles of the open-loop and closed-loop transfer function in s-plane. Multiple subsystems
20 Example 9 Find the closed-loop transfer function of the two-loop feedback system in Fig 1. Also express the damping ratio and the un-damped natural frequency of the closedloop system in terms of the gains a 0 and a 1. Figure 1 Equivalent block diagrams Multiple subsystems - 39 Second order system Example 10 construct the block diagram for the system described by the differential equation a y a y a y f t which involves no input derivatives in its input function. Then use the block diagram to find a state-variable model for the system Multiple subsystems
21 2. Analysis and Design of Feedback System Immediate application of the principles of block diagram. Example 11 find the peak time, percent overshoot and settling time. Example 12 design the value gain K for the system below so that the system will respond with a 10 % overshoot Multiple subsystems - 41 Two or more inputs Multiple subsystems
22 Since the plant is assumed linear, the total output c(t) can be independently evaluated due to the disturbance or load D the input R and then added together The same concept can be applied for transfer functions Multiple subsystems - 43 First set D(s) = 0 to evaluate C 1 /R C1 () s G1G 2 R() s 1() G G H S 1 2 Second set R(s) = 0 to evaluate C2/D C 2 () s 2 G L D() s 1() G G H S 1 2 The characteristic equations are the same Multiple subsystems
23 3. Signal-Flow Graphs Signal flow graphs are alternative to block diagram. A signal flow graph consists only of branches, which represent systems, and nodes, which represent signals. Signal-flow graph components: a. system; b. signal; c. interconnection of systems and signals Multiple subsystems - 45 Converting common block diagrams to signal-flow graphs a. cascaded system nodes; b. cascaded system signal-flow graph; Multiple subsystems
24 c. parallel system nodes; d. parallel system signal-flow graph; Multiple subsystems - 47 e. feedback system nodes; f. feedback system signal-flow graph; Multiple subsystems
25 Example 13 Convert the block diagram in Example 4 to signal-flow graph. Signal-flow graph development: a. signal nodes; b. signal-flow graph; c. simplified signal-flow graph Multiple subsystems - 49 Example 14 Convert the block diagram below to signal-flow graph Multiple subsystems
Unit 4: Block Diagram Reduction. Block Diagram Reduction. Cascade Form Parallel Form Feedback Form Moving Blocks Example
Engineering 5821: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland February 15, 2010 1 1 Subsystems are represented in block diagrams as blocks, each representing
More informationANNA UNIVERSITY :: CHENNAI MODEL QUESTION PAPER(V-SEMESTER) B.E. ELECTRONICS AND COMMUNICATION ENGINEERING EC334 - CONTROL SYSTEMS
ANNA UNIVERSITY :: CHENNAI - 600 025 MODEL QUESTION PAPER(V-SEMESTER) B.E. ELECTRONICS AND COMMUNICATION ENGINEERING EC334 - CONTROL SYSTEMS Time: 3hrs Max Marks: 100 Answer all Questions PART - A (10
More informationLECTURE FOUR Time Domain Analysis Transient and Steady-State Response Analysis
LECTURE FOUR Time Domain Analysis Transient and Steady-State Response Analysis 4.1 Transient Response and Steady-State Response The time response of a control system consists of two parts: the transient
More informationME 375 System Modeling and Analysis
ME 375 System Modeling and Analysis G(s) H(s) Section 9 Block Diagrams and Feedback Control Spring 2009 School of Mechanical Engineering Douglas E. Adams Associate Professor 9.1 Key Points to Remember
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 informationDr Ian R. Manchester Dr Ian R. Manchester Amme 3500 : Root Locus Design
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 informationLab 11. Speed Control of a D.C. motor. Motor Characterization
Lab 11. Speed Control of a D.C. motor Motor Characterization Motor Speed Control Project 1. Generate PWM waveform 2. Amplify the waveform to drive the motor 3. Measure motor speed 4. Estimate motor parameters
More informationEC6405 - CONTROL SYSTEM ENGINEERING Questions and Answers Unit - II Time Response Analysis Two marks 1. What is transient response? The transient response is the response of the system when the system
More informationEC CONTROL SYSTEMS ENGINEERING
1 YEAR / SEM: II / IV EC 1256. CONTROL SYSTEMS ENGINEERING UNIT I CONTROL SYSTEM MODELING PART-A 1. Define open loop and closed loop systems. 2. Define signal flow graph. 3. List the force-voltage analogous
More informationLab 1: Simulating Control Systems with Simulink and MATLAB
Lab 1: Simulating Control Systems with Simulink and MATLAB EE128: Feedback Control Systems Fall, 2006 1 Simulink Basics Simulink is a graphical tool that allows us to simulate feedback control systems.
More informationIntroduction to System Block Algebra
Introduction to System lock lgebra Course No: E0203 Credit: 2 PDH Jeffrey Cwalinski, P.E. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, N 0980 P: (877) 3225800 F: (877)
More informationLecture 18 Stability of Feedback Control Systems
16.002 Lecture 18 Stability of Feedback Control Systems May 9, 2008 Today s Topics Stabilizing an unstable system Stability evaluation using frequency responses Take Away Feedback systems stability can
More informationT.J.Moir AUT University Auckland. The Ph ase Lock ed Loop.
T.J.Moir AUT University Auckland The Ph ase Lock ed Loop. 1.Introduction The Phase-Locked Loop (PLL) is one of the most commonly used integrated circuits (ICs) in use in modern communications systems.
More informationi + u 2 j be the unit vector that has its initial point at (a, b) and points in the desired direction. It determines a line in the xy-plane:
1 Directional Derivatives and Gradients Suppose we need to compute the rate of change of f(x, y) with respect to the distance from a point (a, b) in some direction. Let u = u 1 i + u 2 j be the unit vector
More information1. Consider the closed loop system shown in the figure below. Select the appropriate option to implement the system shown in dotted lines using
1. Consider the closed loop system shown in the figure below. Select the appropriate option to implement the system shown in dotted lines using op-amps a. b. c. d. Solution: b) Explanation: The dotted
More informationLECTURE 2: PD, PID, and Feedback Compensation. ( ) = + We consider various settings for Zc when compensating the system with the following RL:
LECTURE 2: PD, PID, and Feedback Compensation. 2.1 Ideal Derivative Compensation (PD) Generally, we want to speed up the transient response (decrease Ts and Tp). If we are lucky then a system s desired
More informationLesson 1 6. Algebra: Variables and Expression. Students will be able to evaluate algebraic expressions.
Lesson 1 6 Algebra: Variables and Expression Students will be able to evaluate algebraic expressions. P1 Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable
More informationProcess. Controller. Output. Measurement. Comparison FIGURE 4.1. A closed-loop system. Dorf/Bishop Modern Control Systems 9/E
Controller Process Output Comparison Measurement FIGURE 4. A closed-loop system. R(s) E a (s) G(s) Y(s) R(s) E a (s) G(s) Y(s) H(s) H(s) FIGURE 4.3 A closed-loop control system (a feedback system). v in
More informationJNTUWORLD. 6 The unity feedback system whose open loop transfer function is given by G(s)=K/s(s 2 +6s+10) Determine: (i) Angles of asymptotes *****
Code: 9A050 III B. Tech I Semester (R09) Regular Eaminations, November 0 Time: hours Ma Marks: 70 (a) What is a mathematical model of a physical system? Eplain briefly. (b) Write the differential equations
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder Construction of transfer function v 2 (s) v (s) = Z 2Z Z Z 2 Z = Z out Z R C Z = L Q = R /R 0 f
More information1.What is frequency response? A frequency responses the steady state response of a system when the input to the system is a sinusoidal signal.
Control Systems (EC 334) 1.What is frequency response? A frequency responses the steady state response of a system when the input to the system is a sinusoidal signal. 2.List out the different frequency
More informationEE 3TP4: Signals and Systems Lab 5: Control of a Servomechanism
EE 3TP4: Signals and Systems Lab 5: Control of a Servomechanism Tim Davidson Ext. 27352 davidson@mcmaster.ca Objective To identify the plant model of a servomechanism, and explore the trade-off between
More informationKaradeniz Technical University Department of Electrical and Electronics Engineering Trabzon, Turkey
Karadeniz Technical University Department of Electrical and Electronics Engineering 61080 Trabzon, Turkey Chapter 3-2- 1 Modelling and Representation of Physical Systems 3.1. Electrical Systems Bu ders
More information2.3 BUILDING THE PERFECT SQUARE
16 2.3 BUILDING THE PERFECT SQUARE A Develop Understanding Task Quadratic)Quilts Optimahasaquiltshopwhereshesellsmanycolorfulquiltblocksforpeoplewhowant tomaketheirownquilts.shehasquiltdesignsthataremadesothattheycanbesized
More informationBiomedical Control Systems. Lecture#01
1 Biomedical Control Systems Lecture#01 2 Text Books Modern Control Engineering, 5 th Edition; Ogata. Feedback & Control Systems, 2 nd edition; Schaum s outline, Joseph J, Allen R. Control Systems Engineering,
More informationTennessee Senior Bridge Mathematics
A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10 A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts
More informationPoles and Zeros of H(s), Analog Computers and Active Filters
Poles and Zeros of H(s), Analog Computers and Active Filters Physics116A, Draft10/28/09 D. Pellett LRC Filter Poles and Zeros Pole structure same for all three functions (two poles) HR has two poles and
More informationECE317 : Feedback and Control
ECE317 : Feedback and Control Lecture : Frequency domain specifications Frequency response shaping (Loop shaping) Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University
More informationSRI VENKATESWARA COLLEGE OF ENGINEERING AND TECHNOLOGY
SRI VENKATESWARA COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING IC 6501 CONTROL SYSTEMS UNIT I - SYSTEMS AND THEIR REPRESETNTATION` TWO MARKS QUESTIONS WITH
More informationChapter 8. Natural and Step Responses of RLC Circuits
Chapter 8. Natural and Step Responses of RLC Circuits By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits1.htm
More information[ á{tå TÄàt. Chapter Four. Time Domain Analysis of control system
Chapter Four Time Domain Analysis of control system The time response of a control system consists of two parts: the transient response and the steady-state response. By transient response, we mean that
More informationLecture 9. Lab 16 System Identification (2 nd or 2 sessions) Lab 17 Proportional Control
246 Lecture 9 Coming week labs: Lab 16 System Identification (2 nd or 2 sessions) Lab 17 Proportional Control Today: Systems topics System identification (ala ME4232) Time domain Frequency domain Proportional
More information(1) Identify individual entries in a Control Loop Diagram. (2) Sketch Bode Plots by hand (when we could have used a computer
Last day: (1) Identify individual entries in a Control Loop Diagram (2) Sketch Bode Plots by hand (when we could have used a computer program to generate sketches). How might this be useful? Can more clearly
More informationCHAPTER 9 FEEDBACK. NTUEE Electronics L.H. Lu 9-1
CHAPTER 9 FEEDBACK Chapter Outline 9.1 The General Feedback Structure 9.2 Some Properties of Negative Feedback 9.3 The Four Basic Feedback Topologies 9.4 The Feedback Voltage Amplifier (Series-Shunt) 9.5
More informationAndrea Zanchettin Automatic Control 1 AUTOMATIC CONTROL. Andrea M. Zanchettin, PhD Spring Semester, Linear control systems design
Andrea Zanchettin Automatic Control 1 AUTOMATIC CONTROL Andrea M. Zanchettin, PhD Spring Semester, 2018 Linear control systems design Andrea Zanchettin Automatic Control 2 The control problem Let s introduce
More informationAndrea Zanchettin Automatic Control 1 AUTOMATIC CONTROL. Andrea M. Zanchettin, PhD Winter Semester, Linear control systems design Part 1
Andrea Zanchettin Automatic Control 1 AUTOMATIC CONTROL Andrea M. Zanchettin, PhD Winter Semester, 2018 Linear control systems design Part 1 Andrea Zanchettin Automatic Control 2 Step responses Assume
More informationClosed-loop System, PID Controller
Closed-loop System, PID Controller M. Fikar Department of Information Engineering and Process Control Institute of Information Engineering, Automation and Mathematics FCFT STU in Bratislava TAR MF (IRP)
More informationElectrical Drives I. Week 4-5-6: Solid state dc drives- closed loop control of phase controlled DC drives
Electrical Drives I Week 4-5-6: Solid state dc drives- closed loop control of phase controlled DC drives DC Drives control- DC motor without control Speed Control Strategy: below base speed: V t control
More informationEES42042 Fundamental of Control Systems Bode Plots
EES42042 Fundamental of Control Systems Bode Plots DR. Ir. Wahidin Wahab M.Sc. Ir. Aries Subiantoro M.Sc. 2 Bode Plots Plot of db Gain and phase vs frequency It is assumed you know how to construct Bode
More informationCourse Outline. Time vs. Freq. Domain Analysis. Frequency Response. Amme 3500 : System Dynamics & Control. Design via Frequency Response
Course Outline Amme 35 : System Dynamics & Control Design via Frequency Response Week Date Content Assignment Notes Mar Introduction 2 8 Mar Frequency Domain Modelling 3 5 Mar Transient Performance and
More informationExperiment 9. PID Controller
Experiment 9 PID Controller Objective: - To be familiar with PID controller. - Noting how changing PID controller parameter effect on system response. Theory: The basic function of a controller is to execute
More informationBode Plot for Controller Design
Bode Plot for Controller Design Dr. Bishakh Bhattacharya Professor, Department of Mechanical Engineering IIT Kanpur Joint Initiative of IITs and IISc - Funded by This Lecture Contains Bode Plot for Controller
More informationAn Introduction to Proportional- Integral-Derivative (PID) Controllers
An Introduction to Proportional- Integral-Derivative (PID) Controllers Stan Żak School of Electrical and Computer Engineering ECE 680 Fall 2017 1 Motivation Growing gap between real world control problems
More informationCourse Syllabus - Online Prealgebra
Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 1.1 Whole Numbers, Place Value Practice Problems for section 1.1 HW 1A 1.2 Adding Whole Numbers Practice Problems for section 1.2 HW 1B 1.3 Subtracting Whole Numbers
More informationReadings: FC: p : lead compensation. 9/9/2011 Classical Control 1
MM0 Frequency Response Design Readings: FC: p389-407: lead compensation 9/9/20 Classical Control What Have We Talked about in MM9? Control design based on Bode plot Stability margins (Gain margin and phase
More informationBSNL TTA Question Paper Control Systems Specialization 2007
BSNL TTA Question Paper Control Systems Specialization 2007 1. An open loop control system has its (a) control action independent of the output or desired quantity (b) controlling action, depending upon
More informationSMJE 3153 Control System. Department of ESE, MJIIT, UTM 2014/2015
SMJE 3153 Control System Department of ESE, MJIIT, UTM 2014/2015 1 Course Outline Course Instructors Prof Nozomu Hamada (hamada@utm.my)and Dr. Mohd Azizi Abdul Rahman Course Web site UTM e-learning site
More informationModule 08 Controller Designs: Compensators and PIDs
Module 08 Controller Designs: Compensators and PIDs Ahmad F. Taha EE 3413: Analysis and Desgin of Control Systems Email: ahmad.taha@utsa.edu Webpage: http://engineering.utsa.edu/ taha March 31, 2016 Ahmad
More informationVer. 4/5/2002, 1:11 PM 1
Mechatronics II Laboratory Exercise 6 PID Design The purpose of this exercise is to study the effects of a PID controller on a motor-load system. Although not a second-order system, a PID controlled motor-load
More informationBranch Current Method
Script Hello friends. In this series of lectures we have been discussing the various types of circuits, the voltage and current laws and their application to circuits. Today in this lecture we shall be
More informationModular arithmetic Math 2320
Modular arithmetic Math 220 Fix an integer m 2, called the modulus. For any other integer a, we can use the division algorithm to write a = qm + r. The reduction of a modulo m is the remainder r resulting
More informationEECE251 Circuit Analysis I Set 5: Operational Amplifiers
EECE251 Circuit Analysis I Set 5: Operational Amplifiers Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca 1 Amplifiers There are various
More informationJUNE 2014 Solved Question Paper
JUNE 2014 Solved Question Paper 1 a: Explain with examples open loop and closed loop control systems. List merits and demerits of both. Jun. 2014, 10 Marks Open & Closed Loop System - Advantages & Disadvantages
More informationToday s topic: frequency response. Chapter 4
Today s topic: frequency response Chapter 4 1 Small-signal analysis applies when transistors can be adequately characterized by their operating points and small linear changes about the points. The use
More informationA slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal
More informationelectronics fundamentals
electronics fundamentals circuits, devices, and applications THOMAS L. FLOYD DAVID M. BUCHLA chapter 6 Identifying series-parallel relationships Most practical circuits have combinations of series and
More informationLINEAR EQUATIONS IN TWO VARIABLES
LINEAR EQUATIONS IN TWO VARIABLES What You Should Learn Use slope to graph linear equations in two " variables. Find the slope of a line given two points on the line. Write linear equations in two variables.
More informationEE228 Applications of Course Concepts. DePiero
EE228 Applications of Course Concepts DePiero Purpose Describe applications of concepts in EE228. Applications may help students recall and synthesize concepts. Also discuss: Some advanced concepts Highlight
More informationMATLAB and Simulink in Mechatronics Education*
Int. J. Engng Ed. Vol. 21, No. 5, pp. 896±905, 2005 0949-149X/91 $3.00+0.00 Printed in Great Britain. # 2005 TEMPUS Publications. MATLAB and Simulink in Mechatronics Education* A. ALBAGUL, OTHMAN O. KHALIFA
More informationOutcome 9 Review Foundations and Pre-Calculus 10
Outcome 9 Review Foundations and Pre-Calculus 10 Level 2 Example: Writing an equation in slope intercept form Slope-Intercept Form: y = mx + b m = slope b = y-intercept Ex : Write the equation of a line
More information4-7 Point-Slope Form. Warm Up Lesson Presentation Lesson Quiz
Warm Up Lesson Presentation Lesson Quiz Holt Algebra McDougal 1 Algebra 1 Warm Up Find the slope of the line containing each pair of points. 1. (0, 2) and (3, 4) 2. ( 2, 8) and (4, 2) 1 3. (3, 3) and (12,
More informationLecture 48 Review of Feedback HW # 4 Erickson Problems Ch. 9 # s 7 &9 and questions in lectures I. Review of Negative Feedback
Lecture 48 Review of Feedback HW # 4 Erickson Problems Ch. 9 # s 7 &9 and questions in lectures I. Review of Negative Feedback A. General. Overview 2. Summary of Advantages 3. Disadvantages B. Buck Converter
More informationPYKC 13 Feb 2017 EA2.3 Electronics 2 Lecture 8-1
In this lecture, I will cover amplitude and phase responses of a system in some details. What I will attempt to do is to explain how would one be able to obtain the frequency response from the transfer
More informationEEL2216 Control Theory CT2: Frequency Response Analysis
EEL2216 Control Theory CT2: Frequency Response Analysis 1. Objectives (i) To analyse the frequency response of a system using Bode plot. (ii) To design a suitable controller to meet frequency domain and
More informationFigure 1: Unity Feedback System. The transfer function of the PID controller looks like the following:
Islamic University of Gaza Faculty of Engineering Electrical Engineering department Control Systems Design Lab Eng. Mohammed S. Jouda Eng. Ola M. Skeik Experiment 3 PID Controller Overview This experiment
More informationAdvances in Averaged Switch Modeling
Advances in Averaged Switch Modeling Robert W. Erickson Power Electronics Group University of Colorado Boulder, Colorado USA 80309-0425 rwe@boulder.colorado.edu http://ece-www.colorado.edu/~pwrelect 1
More informationPhys Lecture 5. Motors
Phys 253 Lecture 5 1. Get ready for Design Reviews Next Week!! 2. Comments on Motor Selection 3. Introduction to Control (Lab 5 Servo Motor) Different performance specifications for all 4 DC motors supplied
More informationVälkomna till TSRT15 Reglerteknik Föreläsning 8
Välkomna till TSRT15 Reglerteknik Föreläsning 8 Summary of lecture 7 More Bode plot computations Lead-lag design Unstable zeros - frequency plane interpretation Summary of last lecture 2 W(s) H(s) R(s)
More informationChapter 8. Constant Current Sources
Chapter 8 Methods of Analysis Constant Current Sources Maintains same current in branch of circuit Doesn t matter how components are connected external to the source Direction of current source indicates
More informationUnit 8 Combination Circuits
Unit 8 Combination Circuits Objectives: Define a combination circuit. List the rules for parallel circuits. List the rules for series circuits. Solve for combination circuit values. Characteristics There
More informationStudent Exploration: Quadratics in Factored Form
Name: Date: Student Exploration: Quadratics in Factored Form Vocabulary: factored form of a quadratic function, linear factor, parabola, polynomial, quadratic function, root of an equation, vertex of a
More informationMotor Control. Suppose we wish to use a microprocessor to control a motor - (or to control the load attached to the motor!) Power supply.
Motor Control Suppose we wish to use a microprocessor to control a motor - (or to control the load attached to the motor!) Operator Input CPU digital? D/A, PWM analog voltage Power supply Amplifier linear,
More informationEquipment and materials from stockroom:! DC Permanent-magnet Motor (If you can, get the same motor you used last time.)! Dual Power Amp!
University of Utah Electrical & Computer Engineering Department ECE 3510 Lab 5b Position Control Using a Proportional - Integral - Differential (PID) Controller Note: Bring the lab-2 handout to use as
More informationFrequency Response Analysis and Design Tutorial
1 of 13 1/11/2011 5:43 PM Frequency Response Analysis and Design Tutorial I. Bode plots [ Gain and phase margin Bandwidth frequency Closed loop response ] II. The Nyquist diagram [ Closed loop stability
More informationIMC based Smith Predictor Design with PI+CI Structure: Control of Delayed MIMO Systems
MATEC Web of Conferences42, ( 26) DOI:.5/ matecconf/ 26 42 C Owned by the authors, published by EDP Sciences, 26 IMC based Smith Predictor Design with PI+CI Structure: Control of Delayed MIMO Systems Ali
More informationLecture 5 Introduction to control
Lecture 5 Introduction to control Feedback control is a way of automatically adjusting a variable to a desired value despite possible external influence or variations. Eg: Heating your house. No feedback
More informationEE 482 : CONTROL SYSTEMS Lab Manual
University of Bahrain College of Engineering Dept. of Electrical and Electronics Engineering EE 482 : CONTROL SYSTEMS Lab Manual Dr. Ebrahim Al-Gallaf Assistance Professor of Intelligent Control and Robotics
More information3. Voltage and Current laws
1 3. Voltage and Current laws 3.1 Node, Branches, and loops A branch represents a single element such as a voltage source or a resistor A node is the point of the connection between two or more elements
More informationUnofficial Comment Form Project Geomagnetic Disturbance Mitigation
Project 2013-03 Geomagnetic Disturbance Mitigation Please DO NOT use this form for submitting comments. Please use the electronic form to submit comments on the Standard. The electronic comment form must
More informationCantonment, Dhaka-1216, BANGLADESH
International Conference on Mechanical, Industrial and Energy Engineering 2014 26-27 December, 2014, Khulna, BANGLADESH ICMIEE-PI-140153 Electro-Mechanical Modeling of Separately Excited DC Motor & Performance
More informationAn Overview of Linear Systems
An Overview of Linear Systems The content from this course was hosted on TechOnline.com from 999-4. TechOnline.com is now targeting commercial clients, so the content, (without animation and voice) is
More informationLesson number one. Operational Amplifier Basics
What About Lesson number one Operational Amplifier Basics As well as resistors and capacitors, Operational Amplifiers, or Op-amps as they are more commonly called, are one of the basic building blocks
More informationExam 2 Review Sheet. r(t) = x(t), y(t), z(t)
Exam 2 Review Sheet Joseph Breen Particle Motion Recall that a parametric curve given by: r(t) = x(t), y(t), z(t) can be interpreted as the position of a particle. Then the derivative represents the particle
More informationCHAPTER 4. Techniques of Circuit Analysis
CHAPTER 4 Techniques of Circuit Analysis 4.1 Terminology Planar circuits those circuits that can be drawn on a plane with no crossing branches. Figure 4.1 (a) A planar circuit. (b) The same circuit redrawn
More informationThe diodes keep the output waveform from getting too large.
Wien Bridge Oscillat CIRCUIT: The Wien bridge oscillat, see Fig., consists of two voltage dividers. It oscillates (approximately) sinusoidally at the frequency that produces the same voltage out of both
More informationPosition Control of DC Motor by Compensating Strategies
Position Control of DC Motor by Compensating Strategies S Prem Kumar 1 J V Pavan Chand 1 B Pangedaiah 1 1. Assistant professor of Laki Reddy Balireddy College Of Engineering, Mylavaram Abstract - As the
More informationIEEE Power & Energy Society
IEEE Power & Energy Society IEEE Tutorial Course Power System Stabilization Via Excitation Control 9TP5 Copyright IEEE 9 978--444-569-5 IEEE TUTORIAL COURSE POWER SYSTEM STABILIZATION VIA EXCITATION CONTROL
More informationSkills Practice Skills Practice for Lesson 4.1
Skills Practice Skills Practice for Lesson.1 Name Date Squares and More Using Patterns to Generate Algebraic Functions Vocabulary Match each word with its corresponding definition. 1. linear function a.
More informationThe University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #2
The University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #2 Date: November 18, 2010 Course: EE 313 Evans Name: Last, First The exam is scheduled to last 75 minutes. Open books
More informationDEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING & TECHNOLOGY EEE 402 : CONTROL SYSTEMS SESSIONAL
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING BANGLADESH UNIVERSITY OF ENGINEERING & TECHNOLOGY EEE 402 : CONTROL SYSTEMS SESSIONAL Experiment No. 1(a) : Modeling of physical systems and study of
More informationReview of Filter Types
ECE 440 FILTERS Review of Filters Filters are systems with amplitude and phase response that depends on frequency. Filters named by amplitude attenuation with relation to a transition or cutoff frequency.
More informationHomework Assignment 07
Homework Assignment 07 Question 1 (Short Takes). 2 points each unless otherwise noted. 1. A single-pole op-amp has an open-loop low-frequency gain of A = 10 5 and an open loop, 3-dB frequency of 4 Hz.
More informationRoot Locus Design. by Martin Hagan revised by Trevor Eckert 1 OBJECTIVE
TAKE HOME LABS OKLAHOMA STATE UNIVERSITY Root Locus Design by Martin Hagan revised by Trevor Eckert 1 OBJECTIVE The objective of this experiment is to design a feedback control system for a motor positioning
More informationIntroduction to Digital Control
Introduction to Digital Control Control systems are an integral part of modern society. Control systems exist in many systems of engineering, sciences, and in human body. Control means to regulate, direct,
More informationLECTURE THREE SIGNAL FLOW GRAPH
3rd Yearomputer ommunication EngineeringU ontrol Theor LETUE THEE SIGNAL FLOW GAPH 3.1 Introduction The block diagram reduction technique is tedious and time consuming. Signal flow method gives an alternative
More informationModeling Amplifiers as Analog Filters Increases SPICE Simulation Speed
Modeling Amplifiers as Analog Filters Increases SPICE Simulation Speed By David Karpaty Introduction Simulation models for amplifiers are typically implemented with resistors, capacitors, transistors,
More informationReview guide for midterm 2 in Math 233 March 30, 2009
Review guide for midterm 2 in Math 2 March, 29 Midterm 2 covers material that begins approximately with the definition of partial derivatives in Chapter 4. and ends approximately with methods for calculating
More informationMicroelectronic Circuits II. Ch 9 : Feedback
Microelectronic Circuits II Ch 9 : Feedback 9.9 Determining the Loop Gain 9.0 The Stability problem 9. Effect on Feedback on the Amplifier Poles 9.2 Stability study using Bode plots 9.3 Frequency Compensation
More informationRotary Motion Servo Plant: SRV02. Rotary Experiment #02: Position Control. SRV02 Position Control using QuaRC. Student Manual
Rotary Motion Servo Plant: SRV02 Rotary Experiment #02: Position Control SRV02 Position Control using QuaRC Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1 3. OVERVIEW OF FILES...2
More information