Control System. Contents


 Lenard Williams
 1 years ago
 Views:
Transcription
1 Contents Chapter Topic Page Chapter Chapter Chapter3 Chapter4 Introduction Transfer Function, Block Diagrams and Signal Flow Graphs Mathematical Modeling Control System 35 Time Response Analysis of No
2 India s No IES Academy Contents Chapter5 Chapter6 Chapter7 Chapter8 Chapter9 Frequency Analysis Stability Analysis of Control System Root Locus Technique Compensators Industrial Controllers Chapter0 Introduction to State Space Variable Page 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
3 India s No IES Academy Chapter Contents for this chapter Introduction. Introduction. Open Loop System 3. Mathematical Model for Openloop 4. ClosedLoop 5. Mathematical Model for ClosedLoop System 6. Comparison of Open Loop and Closed Loop 7. Laplace Transform 8. Basic Laplace Transform Theorem 9. Summary. Introduction Theory at a Glance (For IES, GATE, PSU & JTO) Control system is a combination of elements arranged in a planned manner. Where each element causes an effect to produce a desire output. Example of control systems. System for the control of position.. System for the control of velocity.. Open Loop System. No feedback in open loop system is used.. Control system (openloop) depends only on the accuracy of input calibration. Example of openloop control system. Traffic signal light. Electric lift 3. Automatic washing machine 3. Mathematical Model for Openloop C G R Page 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
4 India s No IES Academy Chapter Where, G gain of system C o/p of system R input Points:. Feedback system is not used for improving stability.. An openloop system may become unstable when we used negative feedback. 4. ClosedLoop In a closed loop control system the output has an effect on control action through a feedback. Example of closedloop system:. D.C. Motor speed control. Radar tracking system 3. Auto pilot system 5. Mathematical Model for ClosedLoop System C R G +GH * Here feedback is negative. This form is also called control canonical form From figure C(S) G(S) E(S) As a Forward path transfer function B(S) H(S) C(S) As a feedback transfer function The o/p of summing point E(S) [ R(S) B(S) ] ; C(S) R(S) B(S) ; G(S) C(S) R(S) C(S) H(S) ; G(S) C(S) R(S) G(S) G(S) C(S) H(S) ; C(S) [ +G(S) H(S) ] R(S) G(S) Page3 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
5 India s No IES Academy Chapter C(S) G(S) R(S) +G(S) H(S) 6. Comparison of Open Loop and Closed Loop Open Loop System. The accuracy of an open loop system depends on the calibration of the i/p. Closed Loop System. As the error between the reference input and the output is continuously measuredthrough feedback.. The open loop system is more stable.. The closed loop system is less stable. 3. It is less accurate. 3. It is more accurate. 4. It is cheap and less complex. 4. It is expensive and more complex circuit. 5. Effect of Noise and disturbance is more in open loop control system. 7. Laplace Transform Laplace transformation is very great tool in control system. The mathematical expression for laplace transforms LF(t) st F(S) F(t) e dt 0 5. Effect of Noise and disturbance is less in closed loop control system. F(S) The term laplace transform of F(t) is used for the letter LF(t). 8. Basic Laplace Transform Theorem Basic theorems of laplace transform are given below Theorem : Multiplication by a constant Let k be a constant and F(S) be the laplace transform of F(t), then [ Kf(t) ] Theorem : Sum and difference KF(S) Let F(S) and F(S) be the laplace transform of f ( t ) f ( t) ( ) ( ) ±, then f t ± f t F(S)± F (S) Page4 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
6 India s No IES Academy Chapter Theorem 3: Differentiation df(t) i. L SF(S)F(0) dt [ ] df(t) ii. L S F(S)F(0)f (0) dt df(0) where, F (0) dt In general, for higher order derivatives or F(t) n d F() t L sfs n s f O s f f dt n n n () ( n ) ( ) ( ) (0) (0) Where, F (0) denotes the i th order derivative of f(t) with respect to t, Theorem 4: Integration i. L F(t) + S F(S) F (0) ii. L F(t) + + S S S S F(S) F (0) F (0) Theorem 5: Shift in time The laplace transform of F(t) delayed by time T is equal to the laplace transform F(t) multiplied by e ST that is ST L [ F(t T)u s(t T) ] e F(S) Where US(t T) denotes the unit step function that is shifted in time to the right by T. Theorem 6: Complex shifting The laplace transform of F(t) multiplied by transform F(S), with S replaced by ( S ± α ) L e αt Theorem 7: Initialvalue theorem If the laplace transform of F(t) is F(S), then t 0 αt e, where α is a constant is equal to the laplace that is F(t) F(S±α) lim F( t) lim SF( S ) S Page5 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
7 India s No IES Academy Chapter Theorem 8: Final value theorem lim F( t) lim SLF( t) t S 0 lim F( t) lim SF( S) t S 0 Point to be Remember If the denominator of SF(S) has any root having real part as zero or positive, then final value theorem is not valid. [GATE 007] USEFUL TRANSFORM (LAPLACE) PAIR F(t) F(S) LF(t) δ(t) unit impulse 3 U(t) S 4 U(t T) st e S 5 t S t S n t n s + at e at e at te at te 3 n s+ a s a ( s+ a) ( s a) 3 h αt n+ te n/ ( s+ a ) Page6 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
8 India s No IES Academy Chapter ω 4 sinωt s +ω αt 5 e cosωt αt 6 e sinωt 7 sin hα t 8 cos hα t s + α ( ) s + α + ω ω ( ) s + α + ω α s α s s α 9. Summary. Open loop control system no feedback used.. In closed loop control system we used feedback. 3. Open loop system is more stable. 4. Closed loop system is more accurate. 5. Final value theorem can not used if denominators of SF(S) have real part as a zero or positive. Page7 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
9 India s No IES Academy Chapter ASKED OBJECTIVE QUESTIONS (GATE, IES) Basic Laplace Transform Theorem GATE. If the Laplace Transform of a signal y(t) is Y() s, ss ( ) then its final value is: [GATE007] (a)  (b) 0 (c) 0 (d) Unbounded t GATE. The unit impulse response of a system is f () t e, t 0 [GATE006] For this system, the steadystate value of the output for unit step input is equal to (a)  (b) 0 (c) (d) ClosedLoop IES. When a human being tries to approach an object, his brain acts as (a) An error measuring device (b) A controller [IES999] (c) An actuator (d) An amplifier IES. Assertion (A): Feedback control systems offer more accurate control over openloop systems. [IES000] Reason (R): The feedback path establishes a link for input and output comparison and subsequent error correction. (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true but R is NOT the correct explanation of A (c) A is true but R is false (d) A is false but R is true IES3. Consider the following statements: [IES000]. The effect of feedback is to reduce the system error. Feedback increases the gain of the system in one frequency range but decreases in another 3. Feedback can cause a system that is originally stable to become unstable Which of these statements are correct? (a), and 3 (b) and (c) and 3 (d) and 3 IES4. Consider the following statements which respect to feedback control systems: [IES006] Page8 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
10 India s No IES Academy Chapter. Accuracy cannot be obtained by adjusting loop gain.. Feedback decreases overall gain. 3. Introduction of noise due to sensor reduces overall accuracy. 4. Introduction of feedback may lead to the possibility of instability of closed loop system. Which of the statements given above are correct? (a),, 3 and 4 (b) Only, and 4 (c) Only and 3 (d) Only, 3 and 4 IES5. A negativefeedback closedloop system is supplied to an input of 5V. The system has a forward gain of and a feedback gain of a. What is the output voltage? [IES009] (a).0 V (b).5 V (c).0 V (d).5 V Basic Laplace Transform Theorem ω IES6. Consider the function F(s) where F(s) is the Laplace transform s + ω of f(t). What is the steadystate value of f(t)? [IES009] (a) Zero (b) One (c) Two (d) A value between  and + IES7. The transfer function of a lineartimeinvariant system is given as. What is the steadystate value of the unitimpulse response? ( s + ) [IES009] (a) Zero (b) One (c) Two (d) Infinite Page9 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
11 India s No IES Academy Chapter Answers with Explanation (Objective) GATE. Ans. (d) Y() s SS ( + ) Final value of Y(s) LT ( Y( s)) LT LT + ( + ) SS S S Yt () e t ut () final value t GATE. Ans. (c) Unit impulse response of a system is f() t e t t 0 f() s S + O/P for unit step I/P S + S SS ( + ) ( Cs ( )) lim S t s 0 SS ( + ) IES. Ans. (b) IES. Ans. (a) IES3. Ans. (d) Feedback is applied to reduce the system error. Consider the example. Cs ( ) Gs ( ) Rs GsHs ( ) ( ) ( ) s + s s+ Thus, we see that the closed loop system is unstable while the open loop system is stable. IES4. Ans. (d) Page0 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
12 India s No IES Academy Chapter IES5. Ans. (d) Output voltage Vin A AB 5x.5V + + ( xx ) IES6. Ans. (d) This is the Laplace transform of sin t. So, f(t) sin t Steadystate value of f(t) is undetermined because poles of F(s) are not in LHS of splane. Therefore, steadystate value will vary between  and +. IES7. Ans. (a) Steady state value lims 0 s 0 s+ ( ) Page 5, st Floor, Jia Sarai, Near IIT. New Delhi6 Ph: ,
Dr 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 splane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationAN INTRODUCTION TO THE CONTROL THEORY
OpenLoop controller An OpenLoop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, nonlinear dynamics and parameter
More informationENGIN 211, Engineering Math. Laplace Transforms
ENGIN 211, Engineering Math Laplace Transforms 1 Why Laplace Transform? Laplace transform converts a function in the time domain to its frequency domain. It is a powerful, systematic method in solving
More informationIntroduction & Laplace Transforms Lectures 1 & 2
Introduction & Lectures 1 & 2, Professor Department of Electrical and Computer Engineering Colorado State University Fall 2016 Control System Definition of a Control System Group of components that collectively
More information(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:
1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.
More informationUnit 2: Modeling in the Frequency Domain Part 2: The Laplace Transform. The Laplace Transform. The need for Laplace
Unit : Modeling in the Frequency Domain Part : Engineering 81: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 1, 010 1 Pair Table Unit, Part : Unit,
More informationPerformance of Feedback Control Systems
Performance of Feedback Control Systems Design of a PID Controller Transient Response of a Closed Loop System Damping Coefficient, Natural frequency, Settling time and Steadystate Error and Type 0, Type
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) splane Time response p =0 s p =0,p 2 =0 s 2 t p =
More informationAlireza Mousavi Brunel University
Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 OpenLoop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched
More informationLTI Systems (Continuous & Discrete)  Basics
LTI Systems (Continuous & Discrete)  Basics 1. A system with an input x(t) and output y(t) is described by the relation: y(t) = t. x(t). This system is (a) linear and timeinvariant (b) linear and timevarying
More information20.6. Transfer Functions. Introduction. Prerequisites. Learning Outcomes
Transfer Functions 2.6 Introduction In this Section we introduce the concept of a transfer function and then use this to obtain a Laplace transform model of a linear engineering system. (A linear engineering
More informationLinear Control Systems Solution to Assignment #1
Linear Control Systems Solution to Assignment # Instructor: H. Karimi Issued: Mehr 0, 389 Due: Mehr 8, 389 Solution to Exercise. a) Using the superposition property of linear systems we can compute the
More informationAPPLICATIONS FOR ROBOTICS
Version: 1 CONTROL APPLICATIONS FOR ROBOTICS TEX d: Feb. 17, 214 PREVIEW We show that the transfer function and conditions of stability for linear systems can be studied using Laplace transforms. Table
More informationCHAPTER 7 STEADYSTATE RESPONSE ANALYSES
CHAPTER 7 STEADYSTATE RESPONSE ANALYSES 1. Introduction The steady state error is a measure of system accuracy. These errors arise from the nature of the inputs, system type and from nonlinearities of
More informationPID Control. Objectives
PID Control Objectives The objective of this lab is to study basic design issues for proportionalintegralderivative control laws. Emphasis is placed on transient responses and steadystate errors. The
More informationf(t)e st dt. (4.1) Note that the integral defining the Laplace transform converges for s s 0 provided f(t) Ke s 0t for some constant K.
4 Laplace transforms 4. Definition and basic properties The Laplace transform is a useful tool for solving differential equations, in particular initial value problems. It also provides an example of integral
More informationLecture 12. AO Control Theory
Lecture 12 AO Control Theory Claire Max with many thanks to Don Gavel and Don Wiberg UC Santa Cruz February 18, 2016 Page 1 What are control systems? Control is the process of making a system variable
More informationME 304 CONTROL SYSTEMS Spring 2016 MIDTERM EXAMINATION II
ME 30 CONTROL SYSTEMS Spring 06 Course Instructors Dr. Tuna Balkan, Dr. Kıvanç Azgın, Dr. Ali Emre Turgut, Dr. Yiğit Yazıcıoğlu MIDTERM EXAMINATION II May, 06 Time Allowed: 00 minutes Closed Notes and
More informationExam. 135 minutes + 15 minutes reading time
Exam January 23, 27 Control Systems I (559L) Prof. Emilio Frazzoli Exam Exam Duration: 35 minutes + 5 minutes reading time Number of Problems: 45 Number of Points: 53 Permitted aids: Important: 4 pages
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 informationAnalysis and Design of Control Systems in the Time Domain
Chapter 6 Analysis and Design of Control Systems in the Time Domain 6. Concepts of feedback control Given a system, we can classify it as an open loop or a closed loop depends on the usage of the feedback.
More informationAn Introduction to Control Systems
An Introduction to Control Systems Signals and Systems: 3C1 Control Systems Handout 1 Dr. David Corrigan Electronic and Electrical Engineering corrigad@tcd.ie November 21, 2012 Recall the concept of a
More informationIntroduction to Feedback Control
Introduction to Feedback Control Control System Design Why Control? OpenLoop vs ClosedLoop (Feedback) Why Use Feedback Control? ClosedLoop Control System Structure Elements of a Feedback Control System
More informationLaplace Transforms. Chapter 3. Pierre Simon Laplace Born: 23 March 1749 in BeaumontenAuge, Normandy, France Died: 5 March 1827 in Paris, France
Pierre Simon Laplace Born: 23 March 1749 in BeaumontenAuge, Normandy, France Died: 5 March 1827 in Paris, France Laplace Transforms Dr. M. A. A. Shoukat Choudhury 1 Laplace Transforms Important analytical
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : CONTROL SYSTEMS BRANCH : ECE YEAR : II SEMESTER: IV 1. What is control system? 2. Define open
More informationROOT LOCUS. Consider the system. Root locus presents the poles of the closedloop system when the gain K changes from 0 to. H(s) H ( s) = ( s)
C1 ROOT LOCUS Consider the system R(s) E(s) C(s) + K G(s)  H(s) C(s) R(s) = K G(s) 1 + K G(s) H(s) Root locus presents the poles of the closedloop system when the gain K changes from 0 to 1+ K G ( s)
More informatione st f (t) dt = e st tf(t) dt = L {t f(t)} s
Additional operational properties How to find the Laplace transform of a function f (t) that is multiplied by a monomial t n, the transform of a special type of integral, and the transform of a periodic
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 informationINTRODUCTION TO DIGITAL CONTROL
ECE4540/5540: Digital Control Systems INTRODUCTION TO DIGITAL CONTROL.: Introduction In ECE450/ECE550 Feedback Control Systems, welearnedhow to make an analog controller D(s) to control a lineartimeinvariant
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : CONTROL SYSTEMS STAFF NAME: Mr. P.NARASIMMAN BRANCH : ECE Mr.K.R.VENKATESAN YEAR : II SEMESTER
More informationDEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK SUBJECT CODE & NAME: CONTROL SYSTEMS YEAR / SEM: II / IV UNIT I SYSTEMS AND THEIR REPRESENTATION PARTA [2
More informationFEEDBACK CONTROL SYSTEMS
FEEDBAC CONTROL SYSTEMS. Control System Design. Open and ClosedLoop Control Systems 3. Why ClosedLoop Control? 4. Case Study  Speed Control of a DC Motor 5. SteadyState Errors in Unity Feedback Control
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 informationGATE : , Copyright reserved. Web:www.thegateacademy.com
GATE2016 Index 1. Question Paper Analysis 2. Question Paper & Answer keys : 080617 66 222, info@thegateacademy.com Copyright reserved. Web:www.thegateacademy.com ANALYSIS OF GATE 2016 Electrical Engineering
More informationNADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni
NADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni625531 Question Bank for the Units I to V SE05 BR05 SU02 5 th Semester B.E. / B.Tech. Electrical & Electronics engineering IC6501
More informationDr. Ian R. Manchester
Dr Ian R. Manchester Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the splane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus
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 information100 (s + 10) (s + 100) e 0.5s. s 100 (s + 10) (s + 100). G(s) =
1 AME 3315; Spring 215; Midterm 2 Review (not graded) Problems: 9.3 9.8 9.9 9.12 except parts 5 and 6. 9.13 except parts 4 and 5 9.28 9.34 You are given the transfer function: G(s) = 1) Plot the bode plot
More informationFundamental of Control Systems Steady State Error Lecturer: Dr. Wahidin Wahab M.Sc. Aries Subiantoro, ST. MSc.
Fundamental of Control Systems Steady State Error Lecturer: Dr. Wahidin Wahab M.Sc. Aries Subiantoro, ST. MSc. Electrical Engineering Department University of Indonesia 2 Steady State Error How well can
More informationLecture 7: Laplace Transform and Its Applications Dr.Ing. Sudchai Boonto
DrIng 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 informationAnalysis of SISO Control Loops
Chapter 5 Analysis of SISO Control Loops Topics to be covered For a given controller and plant connected in feedback we ask and answer the following questions: Is the loop stable? What are the sensitivities
More informationELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques
CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 LeadLag Compensation Techniques [] For the following system, Design a compensator such
More informationME 132, Dynamic Systems and Feedback. Class Notes. Spring Instructor: Prof. A Packard
ME 132, Dynamic Systems and Feedback Class Notes by Andrew Packard, Kameshwar Poolla & Roberto Horowitz Spring 2005 Instructor: Prof. A Packard Department of Mechanical Engineering University of California
More informationLaplace Transform Analysis of Signals and Systems
Laplace Transform Analysis of Signals and Systems Transfer Functions Transfer functions of CT systems can be found from analysis of Differential Equations Block Diagrams Circuit Diagrams 5/10/04 M. J.
More informationSchool of Mechanical Engineering Purdue University. ME375 Feedback Control  1
Introduction to Feedback Control Control System Design Why Control? OpenLoop vs ClosedLoop (Feedback) Why Use Feedback Control? ClosedLoop Control System Structure Elements of a Feedback Control System
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #24 Wednesday, March 10, 2004 Dr. Ian C. Bruce Room: CRL229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Remedies We next turn to the question
More informationI Laplace transform. I Transfer function. I Conversion between systems in time, frequencydomain, and transfer
EE C128 / ME C134 Feedback Control Systems Lecture Chapter 2 Modeling in the Frequency Domain Alexandre Bayen Department of Electrical Engineering & Computer Science University of California Berkeley Lecture
More information10 Transfer Matrix Models
MIT EECS 6.241 (FALL 26) LECTURE NOTES BY A. MEGRETSKI 1 Transfer Matrix Models So far, transfer matrices were introduced for finite order state space LTI models, in which case they serve as an important
More informationÜbersetzungshilfe / Translation aid (English) To be returned at the end of the exam!
Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 3.. 24 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid 
More informationSolution for Mechanical Measurement & Control
Solution for Mechanical Measurement & Control December2015 Index Q.1) a). 23 b).34 c). 5 d). 6 Q.2) a). 7 b). 7 to 9 c). 1011 Q.3) a). 1112 b). 1213 c). 13 Q.4) a). 1415 b). 15 (N.A.) Q.5) a). 15
More informationUsing MATLB for stability analysis in Controls engineering Cyrus Hagigat Ph.D., PE College of Engineering University of Toledo, Toledo, Ohio
Using MATLB for stability analysis in Controls engineering Cyrus Hagigat Ph.D., PE College of Engineering University of Toledo, Toledo, Ohio Abstract Analyses of control systems require solution of differential
More informationGATE : , Copyright reserved. Web:www.thegateacademy.com
Index. Question Paper Analysis 2. Question Paper & Answer keys : 08067 66 222, info@thegateacademy.com Copyright reserved. Web:www.thegateacademy.com ANALYSIS OF GATE 206 Electrical Engineering CN Mathematics
More informationDynamic System Response. Dynamic System Response K. Craig 1
Dynamic System Response Dynamic System Response K. Craig 1 Dynamic System Response LTI Behavior vs. NonLTI Behavior Solution of Linear, ConstantCoefficient, Ordinary Differential Equations Classical
More informationChapter 6: The Laplace Transform. ChihWei Liu
Chapter 6: The Laplace Transform ChihWei Liu Outline Introduction The Laplace Transform The Unilateral Laplace Transform Properties of the Unilateral Laplace Transform Inversion of the Unilateral Laplace
More informationVALLIAMMAI ENGINEERING COLLEGE
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK V SEMESTER IC650 CONTROL SYSTEMS Regulation 203 Academic Year 207 8 Prepared
More informationEEE 184: Introduction to feedback systems
EEE 84: Introduction to feedback systems Summary 6 8 8 x 7 7 6 Level() 6 5 4 4 5 5 time(s) 4 6 8 Time (seconds) Fig.. Illustration of BIBO stability: stable system (the input is a unit step) Fig.. step)
More informationStudy Material. CONTROL SYSTEM ENGINEERING (As per SCTE&VT,Odisha new syllabus) 4th Semester Electronics & Telecom Engineering
Study Material CONTROL SYSTEM ENGINEERING (As per SCTE&VT,Odisha new syllabus) 4th Semester Electronics & Telecom Engineering By Sri Asit Kumar Acharya, Lecturer ETC, Govt. Polytechnic Dhenkanal & Sri
More informationSystems Engineering/Process Control L4
1 / 24 Systems Engineering/Process Control L4 Inputoutput models Laplace transform Transfer functions Block diagram algebra Reading: Systems Engineering and Process Control: 4.1 4.4 2 / 24 Laplace transform
More informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 2 Laplace Transform I 1/52
1/52 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 2 Laplace Transform I Linear Time Invariant Systems A general LTI system may be described by the linear constant coefficient differential equation: a n d n
More informationModeling and Control Overview
Modeling and Control Overview D R. T A R E K A. T U T U N J I A D V A N C E D C O N T R O L S Y S T E M S M E C H A T R O N I C S E N G I N E E R I N G D E P A R T M E N T P H I L A D E L P H I A U N I
More informationProfessor Fearing EE C128 / ME C134 Problem Set 7 Solution Fall 2010 Jansen Sheng and Wenjie Chen, UC Berkeley
Professor Fearing EE C8 / ME C34 Problem Set 7 Solution Fall Jansen Sheng and Wenjie Chen, UC Berkeley. 35 pts Lag compensation. For open loop plant Gs ss+5s+8 a Find compensator gain Ds k such that the
More informationGoodwin, Graebe, Salgado, Prentice Hall Chapter 11. Chapter 11. Dealing with Constraints
Chapter 11 Dealing with Constraints Topics to be covered An ubiquitous problem in control is that all real actuators have limited authority. This implies that they are constrained in amplitude and/or rate
More information2.004 Dynamics and Control II Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8 I * * Massachusetts
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 information(an improper integral)
Chapter 7 Laplace Transforms 7.1 Introduction: A Mixing Problem 7.2 Definition of the Laplace Transform Def 7.1. Let f(t) be a function on [, ). The Laplace transform of f is the function F (s) defined
More information6.302 Feedback Systems Recitation 16: Compensation Prof. Joel L. Dawson
Bode Obstacle Course is one technique for doing compensation, or designing a feedback system to make the closedloop behavior what we want it to be. To review:  G c (s) G(s) H(s) you are here! plant For
More informationESE319 Introduction to Microelectronics. Feedback Basics
Feedback Basics Stability Feedback concept Feedback in emitter follower Onepole feedback and root locus Frequency dependent feedback and root locus Gain and phase margins Conditions for closed loop stability
More informationMath 216 Second Midterm 20 March, 2017
Math 216 Second Midterm 20 March, 2017 This sample exam is provided to serve as one component of your studying for this exam in this course. Please note that it is not guaranteed to cover the material
More informationSolutions to SkillAssessment Exercises
Solutions to SkillAssessment Exercises To Accompany Control Systems Engineering 4 th Edition By Norman S. Nise John Wiley & Sons Copyright 2004 by John Wiley & Sons, Inc. All rights reserved. No part
More informationModule 02 Control Systems Preliminaries, Intro to State Space
Module 02 Control Systems Preliminaries, Intro to State Space Ahmad F. Taha EE 5143: Linear Systems and Control Email: ahmad.taha@utsa.edu Webpage: http://engineering.utsa.edu/ taha August 28, 2017 Ahmad
More informationRoot Locus. Motivation Sketching Root Locus Examples. School of Mechanical Engineering Purdue University. ME375 Root Locus  1
Root Locus Motivation Sketching Root Locus Examples ME375 Root Locus  1 Servo Table Example DC Motor Position Control The block diagram for position control of the servo table is given by: D 0.09 Position
More informationLecture 1: Feedback Control Loop
Lecture : Feedback Control Loop Loop Transfer function The standard feedback control system structure is depicted in Figure. This represend(t) n(t) r(t) e(t) u(t) v(t) η(t) y(t) F (s) C(s) P (s) Figure
More informationDefinition of the Laplace transform. 0 x(t)e st dt
Definition of the Laplace transform Bilateral Laplace Transform: X(s) = x(t)e st dt Unilateral (or onesided) Laplace Transform: X(s) = 0 x(t)e st dt ECE352 1 Definition of the Laplace transform (cont.)
More informationEssence of the Root Locus Technique
Essence of the Root Locus Technique In this chapter we study a method for finding locations of system poles. The method is presented for a very general setup, namely for the case when the closedloop
More informationGATE 2009 Electronics and Communication Engineering
GATE 2009 Electronics and Communication Engineering Question 1 Question 20 carry one mark each. 1. The order of the differential equation + + y =e (A) 1 (B) 2 (C) 3 (D) 4 is 2. The Fourier series of a
More informationLecture 9. Welcome back! Coming week labs: Today: Lab 16 System Identification (2 sessions)
232 Welcome back! Coming week labs: Lecture 9 Lab 16 System Identification (2 sessions) Today: Review of Lab 15 System identification (ala ME4232) Time domain Frequency domain 1 Future Labs To develop
More informationMATHEMATICAL MODELS AND BLOCK DIAGRAMS. Partial fraction expansions. Difference equation of system. secondorder differential equation
MATHEMATICAL MODELS AND BLOCK DIAGRAMS Matrices differential equations and Solution of secondorder differential equation Partial fraction expansions Determinant, inverse and eigenvalues of a matrix Solution
More informationDistributed RealTime Control Systems
Distributed RealTime Control Systems Chapter 9 Discrete PID Control 1 Computer Control 2 Approximation of Continuous Time Controllers Design Strategy: Design a continuous time controller C c (s) and then
More informationChapter 3 : Linear Differential Eqn. Chapter 3 : Linear Differential Eqn.
1.0 Introduction Linear differential equations is all about to find the total solution y(t), where : y(t) = homogeneous solution [ y h (t) ] + particular solution y p (t) General form of differential equation
More informationLecture 17 Date:
Lecture 17 Date: 27.10.2016 Feedback and Properties, Types of Feedback Amplifier Stability Gain and Phase Margin Modification Elements of Feedback System: (a) The feed forward amplifier [H(s)] ; (b) A
More informationECE 380: Control Systems
ECE 380: Control Systems Course Notes: Winter 2014 Prof. Shreyas Sundaram Department of Electrical and Computer Engineering University of Waterloo ii Acknowledgments Parts of these course notes are loosely
More informationAutomatique. A. Hably 1. Commande d un robot mobile. Automatique. A.Hably. Digital implementation
A. Hably 1 1 Gipsalab, GrenobleINP ahmad.hably@grenobleinp.fr Commande d un robot mobile (Gipsalab (DA)) ASI 1 / 25 Outline 1 2 (Gipsalab (DA)) ASI 2 / 25 of controllers Signals must be sampled and
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21211 1 / 39 Feedback
More informationFrequency Response of Linear Time Invariant Systems
ME 328, Spring 203, Prof. Rajamani, University of Minnesota Frequency Response of Linear Time Invariant Systems Complex Numbers: Recall that every complex number has a magnitude and a phase. Example: z
More informationChapter 10 Feedback. PART C: Stability and Compensation
1 Chapter 10 Feedback PART C: Stability and Compensation Example: Noninverting Amplifier We are analyzing the two circuits (nmos diff pair or pmos diff pair) to realize this symbol: either of the circuits
More informationNotes for ECE320. Winter by R. Throne
Notes for ECE3 Winter 45 by R. Throne Contents Table of Laplace Transforms 5 Laplace Transform Review 6. Poles and Zeros.................................... 6. Proper and Strictly Proper Transfer Functions...................
More informationSingular Value Decomposition Analysis
Singular Value Decomposition Analysis Singular Value Decomposition Analysis Introduction Introduce a linear algebra tool: singular values of a matrix Motivation Why do we need singular values in MIMO control
More informationTransient response via gain adjustment. Consider a unity feedback system, where G(s) = 2. The closed loop transfer function is. s 2 + 2ζωs + ω 2 n
Design via frequency response Transient response via gain adjustment Consider a unity feedback system, where G(s) = ωn 2. The closed loop transfer function is s(s+2ζω n ) T(s) = ω 2 n s 2 + 2ζωs + ω 2
More informationControl System Design
ELEC ENG 4CL4: Control System Design Notes for Lecture #22 Dr. Ian C. Bruce Room: CRL229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca Friday, March 5, 24 More General Effects of Open Loop Poles
More informationInverted Pendulum. Objectives
Inverted Pendulum Objectives The objective of this lab is to experiment with the stabilization of an unstable system. The inverted pendulum problem is taken as an example and the animation program gives
More informationFREQUENCYRESPONSE DESIGN
ECE45/55: Feedback Control Systems. 9 FREQUENCYRESPONSE DESIGN 9.: PD and lead compensation networks The frequencyresponse methods we have seen so far largely tell us about stability and stability margins
More informationQ. 1 Q. 25 carry one mark each.
Q. Q. 5 carry one mark each. Q. Consider a system of linear equations: x y 3z =, x 3y 4z =, and x 4y 6 z = k. The value of k for which the system has infinitely many solutions is. Q. A function 3 = is
More informationECE137B Final Exam. There are 5 problems on this exam and you have 3 hours There are pages 119 in the exam: please make sure all are there.
ECE37B Final Exam There are 5 problems on this exam and you have 3 hours There are pages 9 in the exam: please make sure all are there. Do not open this exam until told to do so Show all work: Credit
More informationChapter 13 Digital Control
Chapter 13 Digital Control Chapter 12 was concerned with building models for systems acting under digital control. We next turn to the question of control itself. Topics to be covered include: why one
More informationThe requirements of a plant may be expressed in terms of (a) settling time (b) damping ratio (c) peak overshoot  in time domain
Compensators To improve the performance of a given plant or system G f(s) it may be necessary to use a compensator or controller G c(s). Compensator Plant G c (s) G f (s) The requirements of a plant may
More informationSolutions to Assignment 7
MTHE 237 Fall 215 Solutions to Assignment 7 Problem 1 Show that the Laplace transform of cos(αt) satisfies L{cosαt = s s 2 +α 2 L(cos αt) e st cos(αt)dt A s α e st sin(αt)dt e stsin(αt) α { e stsin(αt)
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 OpenLoop Process The study of dynamics was limited to openloop systems Observe process behavior as a result of specific input signals
More informationCDS 101/110a: Lecture 102 Control Systems Implementation
CDS 101/110a: Lecture 102 Control Systems Implementation Richard M. Murray 5 December 2012 Goals Provide an overview of the key principles, concepts and tools from control theory  Classical control 
More informationChapter 5 HW Solution
Chapter 5 HW Solution Review Questions. 1, 6. As usual, I think these are just a matter of text lookup. 1. Name the four components of a block diagram for a linear, timeinvariant system. Let s see, I
More informationAnalysis III for DBAUG, Fall 2017 Lecture 10
Analysis III for DBAUG, Fall 27 Lecture Lecturer: Alex Sisto (sisto@math.ethz.ch Convolution (Faltung We have already seen that the Laplace transform is not multiplicative, that is, L {f(tg(t} L {f(t}
More information