Size: px
Start display at page:

Transcription

3 Part B 1. Design a phase lag network for a system having G(s) = K/s(1+0.2s) 2 to have a phase margin of The open loop transfer function of a certain unity feedback control system is given by G(s) = K/s (s+1). It is desired to have the velocity error constant K v =10,and the phase margin to be atleast 60 0.Design a phase lag series compensator. 3. Consider a unity feedback control system with an open loop transfer function is G(s) = K/s (s+2) 2.Design a suitable lead compensator so that phase margin is atleast 50 0 and velocity error constant is 20s The open loop transfer function of a certain unity feedback control system is given by G(s) = K/s (0.1s+1)(0.2s+1).It is desired to have the phase margin atleast Design a suitable phase lead series compensator. 5. Consider a unity feedback control system with an open loop transfer function is G(s) = K/s (2s+1)(0.5s+1).Design a suitable lag-lead compensator to meet the following specifications. (i) Kv = 30 (ii) phase margin Consider a unity feedback control system with an open loop transfer function is G(s) = K/s (s+2) 2.Design a suitable lead compensator so that phase margin is atleast 50 0 and velocity error constant is 20s The open loop transfer function of a certain unity feedback control system is given by G(s) = K/s (0.1s+1)(0.2s+1).It is desired to have the phase margin atleast Design a suitable phase lead series compensator. 8. Consider a unity feedback control system with an open loop transfer function is G(s) = K/s (2s+1)(0.5s+1).Design a suitable lag-lead compensator to meet the following specifications. (i) Kv = 30 (ii) phase margin 50 9.Use Routh stability criterion to determine the no.of roots in the left half plane, the right half plane and on imaginary axis for the given characteristic equation: (i) S 5 +4S 4 +8S 3 +8S 2 +7S+4 =0 (ii) S 7 +5S 6 +9S 5 +9S 4 +4S 3 +20S S +36 =0 10.The open loop transfer function of certain unity feedback system are given below. In each case,discuss the stability of the closed loop system as a function of K > 0. Determine the values of K which will causesustained oscillations in the closed loop system.what are the corresponding oscillating frequencies? K (i) (ii) K (S+1) (S+2)(S+4)(S 2 +6S+25) S(S-1)(S2+4S+16) 6. By use of Nyquist stability criterion determine whether the closed loop system having the following open loop transfer functions are stable or not. If not,how many closed loop poles lie in the right half of the S-plane?

4 (i) 180 G(s)H(s) = (S+1)(S+2)(S+5) 1+4S (ii) G(s)H(s) = (S 2 (1+S)(1+2S) 11. Sketch the Nyquist plot for a feed back system with open loop transfer function K(S+10) 2 G(s)H(s) = S 3 Find the range of values of K for which the system is stable. 12. Consider a unity feedback system with open loop transfer function G(s) = 1/S(S+1).Design a P D controller so that the phase margin of the system is 30 0 at a frequency of 2 rad/sec. 13. A unity feedback system has an open loop transfer function as G(s) = 50/(S+3)(S+1). Design a PI controller so that the phase margin of the system is 35 0 at a frequency of 1.2 rad/sec. 14. Consider a unity feedback system with open loop transfer function G(s) = 20/(S+2)(S+4)(S+0.5). Design a PID controller so that the phase margin of the system is 30 0 at a frequency of 2 rad/sec and the steady state error for unit ramp input is 0.1 Unit III- DESIGN IN DISCRETE DOMAIN Part A 1. Define optimal control with example 2. Why do we use state variable technique for optimal control analysis? 3. Define tracking problem 4. State minimum time problem 5. Define minimum control effort problem 6. Define state regulator problem 7. State optimal control problem 8. Give the performance index of output regulator problem 9. What are the main theoretical approaches for optimal control? 10. What is the fundamental theorem of calculus of variation? 11. Write down the Euler Lagrange s equation. 12. What is meant by transversality condition? 13. Give the boundary value relationship used for minimization of functional when a. When t1 is free and x(t1) is fixed

5 b. When t1 and x(t1) both are free. 14. What is the necessary and sufficient condition for optimal control u to minimize the Hamiltonian function? 15. State Pontryagin s minimum principle 16. Give the control and state variable inequality constraints 17. Distinguish the terms Hamiltonian function and Hamiltonian matrix 18. State the Hamiltonian-Jacobi equation 19. Write down the expression for optimal control using Riccati equation. 20. Give the performance index of regulator problem and solution of Matrix Riccati equation. Part B 1. The characteristic Equation of a sampled data control system is given below. Check the stability of the system using Jury s stability test. (i) Z Z Z Z = 0 (ii) Z Z Z 0.04 = 0 2.The digital process of a unity feedback system is described by the transfer unction K (z ) Gh 0 G(z) = ; T = 1s (z-1)(z-0.368) Sketch the root locus plot for 0 K and from there obtain the value of K that results in marginal stability. Also find the frequency of oscillations. 3. Given K (z ) Gh 0 G(z) = ; T = 1s ( z 1 ) 2 Sketch the root locus plot for 0 K. Using the information in the root locus plot, determine the range of values of K for which the closed loop system is stable. 4 (i)for a system with the following Z-transfer function, find the normalized steady state error between input and output, for a step input 20 Z 2 D(z) = Z Z + 1 (ii)write a short note on direct discrete design 5 (i) Let G(s) = 2/(s+2). Discuss the effect of discretizing G(s) for control purpose using ZOH and sampling the output at every 0.02 sec and 0.05 sec. Briefly explain the properties of Root Loci in Z-plane

6 Unit IV- DISCRETE STATE VARIABLE DESIGN Part-A 1. What is pole placement by state feedback? 2. How control system design is carried in state space? 3. What is the necessary condition to be satisfied for designing state feedback? 4. Draw the block diagram of the system with feedback. 5. What is the control law used in state variable feedback? 6. Write down the Ackermann s formula used to find the state feedback gain matrix k. 7. What do you mean by pole placement by output feedback? 8. Give the control law used in output feedback. 9. What is the need for output feedback. 10. Write short notes on dynamic programming. 11. Give the problem statement of dynamic programming. 12. Give the schematics of state transition for discrete time system used in dynamic programming. 13. State the advantages of using dynamic programming approach for solving optimal control problem. 14. What are the principles on which dynamic programming is based on? 15. Give the minimum cost of Jth stage process using dynamic programming. 16. Give the necessary and sufficient condition to determine optimal control by dynamic programming. 17. State the disadvantages of using dynamic programming approach for solving optimal control problem. 18. Give a short note on principle of casuality. 19. Give a short note on principle of invariant embedded. 20. Give a short note on principle of optimality. Part-B 1. Given the state equations of a linear system is dx(t)/dt = A x(t) + B u(t) With u(t) = u(kt)= constant for kt t< ( k+1)t.the system is discretized,resulting in the following discrete-data state equations : x( k+1)t = Φ(T) x(kt) + θ(t) u(kt) Find the matrices Φ(T) and θ(t). A = B = 2. A discrete data control system is described by the state equation : x( k+1) = A x(k) + B u(k) A= B = Determine the controllability of the system. 3.A linear controlled process of a discrete data control system is described by the following state equations: dx(t)/dt = A x(t) + B u(t) where A = B = u(t) = u(kt) for kt t< ( k+1)t. Determine the values of the sampling period T that makes the system uncontrollable.

7 4. Given the discrete data control system x( k+1) = A x(k) + B u(k) c(k) = D x(k) Where A = A = B = D = [ 1-1] the control is realized through the state feedback u(k) = -G x(k) = -[ g 1 g 2 ] x(k) where g 1 and g 2 are real constants. Determine the value of g 1 and g 2 that must be avoided for the system to be completely observable. 5. The dynamic equations of a digital process are given as x( k+1) = A x(k) + B u(k) c(k) = D x(k) Where A = B = D = [ 1 1] the state feedback control is u(k) = -G x(k) where G = [g 1 g 2 ]. Design a full order observer so that x(k) is observed from c(k) 6. Consider a digital control system x( k+1)t = A x(kt) + B u(kt) where A = B =. The state feedback control is described by u(kt) = -K x(kt) where K = [k 1 k 2 ].Find the values of k 1 and k 2 so that the roots of the characteristic equation of the closed loop system are at 0.5 and Find the controller gain for the discrete system described by A = and B = ] to place the closed loop system poles at Z= 0.8 ± j 0.25 using direct pole placement. 8.(i) Let A = B = Find the state feed back gain matrix such that the eigen values of A- BG are at 0 and 0.3 (ii) Write notes on full order Observer. 9 Given the state equations of a linear system is dx(t)/dt = A x(t) + B u(t) With u(t) = u(kt)= constant for kt t< ( k+1)t.the system is discretized,resulting in the following discrete-data state equations : x( k+1)t = Φ(T) x(kt) + θ(t) u(kt) Find the matrices Φ(T) and θ(t). A = B = 10. Investigate the controllability and observability of the following system: (i) x(k+1) = x(k) + u(k) y(k) = x(k) (ii) x(k+1) = x(k) + u(k) y(k) = x(k) Unit-V- LQR AND LQG DESIGN Part-A 1. What is the need for observer? 2. Write a note on full order observer. 3. Write a note on reduced order observer. 4. Give the modified state and output equation of a system with Luenberger observer.

8 5. What are the criteria involved in selecting Luenberger gain matrix L? 6. Give the limitation of Luenberger observer. 7. State separation principle 8. Explain Bucy filter. 9. State any two rules used for assessing an acceptable estimate. 10. Write down the PDF function for jointly Gaussian Variable. 11. Write a note on Weiner filter 12. Give the design procedure for LQR controller 13. Write down the Ackermann s formula for finding the observer gain matrix. 14. What do you mean by whit noise? 15. Draw the structure of optimal estimator. 16. Draw the system representation including input distribution and measurement noise. 17. Give the expression of Kalman gain. 18. Draw the block diagram of Discrete Kalman Filter. Part-B 11. Derive the necessary and sufficient condition to be satisfied along the optimal trajectory using Hamiltonian formulation starting from the results of calculus variation approach for a state tracking problem of a linear time invariant system. 12. Derive the matrix Riccati equation and state the necessary and sufficient condtion for optimal solution. 13. (a) Derive the optimal control policy for the following optimal control problem = -2x + u min J = ½ (b) Write notes on kalman filter. 14. Find the optimal control law for the system = x + u with the performance index J = (x u u 2 2 ) dt 15. Determine the optimal control law for the system = x + u y = x such that the following performance index is minimized J = (y y u 2 ) dt

### R10. IV B.Tech II Semester Regular Examinations, April/May DIGITAL CONTROL SYSTEMS JNTUK

Set No. 1 1 a) Explain about the shifting and scaling operator. b) Discuss briefly about the linear time invariant and causal systems. 2 a) Write the mapping points between S-Plane and Z-plane. b) Find

### R a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies.

SET - 1 II B. Tech II Semester Supplementary Examinations Dec 01 1. a) Compare open loop and closed loop control systems. b) Clearly bring out, from basics, Force-current and Force-Voltage analogies..

### KINGS 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

### (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.

### VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur

VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year

### DEPARTMENT 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

NADAR SARASWATHI COLLEGE OF ENGINEERING AND TECHNOLOGY Vadapudupatti, Theni-625531 Question Bank for the Units I to V SE05 BR05 SU02 5 th Semester B.E. / B.Tech. Electrical & Electronics engineering IC6501

EC6405 - CONTROL SYSTEM ENGINEERING Questions and Answers Unit - I Control System Modeling Two marks 1. What is control system? A system consists of a number of components connected together to perform

### INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad ELECTRICAL AND ELECTRONICS ENGINEERING TUTORIAL QUESTION BANK

Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad -500 043 ELECTRICAL AND ELECTRONICS ENGINEERING TUTORIAL QUESTION BAN : CONTROL SYSTEMS : A50 : III B. Tech

### Contents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42

Contents Preface.............................................. xiii 1. Introduction......................................... 1 1.1 Continuous and Discrete Control Systems................. 4 1.2 Open-Loop

### INSTITUTE 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

### Controls Problems for Qualifying Exam - Spring 2014

Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function

### VALLIAMMAI 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

### 6.1 Sketch the z-domain root locus and find the critical gain for the following systems K., the closed-loop characteristic equation is K + z 0.

6. Sketch the z-domain root locus and find the critical gain for the following systems K (i) Gz () z 4. (ii) Gz K () ( z+ 9. )( z 9. ) (iii) Gz () Kz ( z. )( z ) (iv) Gz () Kz ( + 9. ) ( z. )( z 8. ) (i)

### Control Systems Lab - SC4070 Control techniques

Control Systems Lab - SC4070 Control techniques Dr. Manuel Mazo Jr. Delft Center for Systems and Control (TU Delft) m.mazo@tudelft.nl Tel.:015-2788131 TU Delft, February 16, 2015 (slides modified from

### R10 JNTUWORLD B 1 M 1 K 2 M 2. f(t) Figure 1

Code No: R06 R0 SET - II B. Tech II Semester Regular Examinations April/May 03 CONTROL SYSTEMS (Com. to EEE, ECE, EIE, ECC, AE) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry

### SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015

FACULTY OF ENGINEERING AND SCIENCE SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 Lecturer: Michael Ruderman Problem 1: Frequency-domain analysis and control design (15 pt) Given is a

### Digital Control Systems

Digital Control Systems Lecture Summary #4 This summary discussed some graphical methods their use to determine the stability the stability margins of closed loop systems. A. Nyquist criterion Nyquist

### Root Locus Methods. The root locus procedure

Root Locus Methods Design of a position control system using the root locus method Design of a phase lag compensator using the root locus method The root locus procedure To determine the value of the gain

### Control Systems. University Questions

University Questions UNIT-1 1. Distinguish between open loop and closed loop control system. Describe two examples for each. (10 Marks), Jan 2009, June 12, Dec 11,July 08, July 2009, Dec 2010 2. Write

### EC 8391-CONTROL SYSTEMS ENGINEERING. Questions and Answers PART-A. Unit - I Systems Components And Their Representation

EC 8391-CONTROL SYSTEMS ENGINEERING Questions and Answers PART-A Unit - I Systems Components And Their Representation 1. What is control system? A system consists of a number of components connected together

### INTRODUCTION 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 linear-time-invariant

### Dynamic Compensation using root locus method

CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 9 Dynamic Compensation using root locus method [] (Final00)For the system shown in the

### Test 2 SOLUTIONS. ENGI 5821: Control Systems I. March 15, 2010

Test 2 SOLUTIONS ENGI 5821: Control Systems I March 15, 2010 Total marks: 20 Name: Student #: Answer each question in the space provided or on the back of a page with an indication of where to find the

### EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING

EC 2255 - CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING 1. What is meant by a system? It is an arrangement of physical components related in such a manner as to form an entire unit. 2. List the two types

### EECS C128/ ME C134 Final Wed. Dec. 15, am. Closed book. Two pages of formula sheets. No calculators.

Name: SID: EECS C28/ ME C34 Final Wed. Dec. 5, 2 8- am Closed book. Two pages of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score 2 2 6 3 4 4 5 6 6 7 8 2 Total

### CHAPTER 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

### ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques

CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques [] For the following system, Design a compensator such

### EECS C128/ ME C134 Final Thu. May 14, pm. Closed book. One page, 2 sides of formula sheets. No calculators.

Name: SID: EECS C28/ ME C34 Final Thu. May 4, 25 5-8 pm Closed book. One page, 2 sides of formula sheets. No calculators. There are 8 problems worth points total. Problem Points Score 4 2 4 3 6 4 8 5 3

### Time 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

### 1 Chapter 9: Design via Root Locus

1 Figure 9.1 a. Sample root locus, showing possible design point via gain adjustment (A) and desired design point that cannot be met via simple gain adjustment (B); b. responses from poles at A and B 2

### Overview of the Seminar Topic

Overview of the Seminar Topic Simo Särkkä Laboratory of Computational Engineering Helsinki University of Technology September 17, 2007 Contents 1 What is Control Theory? 2 History

### 100 (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

### IC6501 CONTROL SYSTEMS

DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical

### X 2 3. Derive state transition matrix and its properties [10M] 4. (a) Derive a state space representation of the following system [5M] 1

QUESTION BANK 6 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code :SYSTEM THEORY(6EE75) Year &Sem: I-M.Tech& I-Sem UNIT-I

### PID controllers. Laith Batarseh. PID controllers

Next Previous 24-Jan-15 Chapter six Laith Batarseh Home End The controller choice is an important step in the control process because this element is responsible of reducing the error (e ss ), rise time

### Step input, ramp input, parabolic input and impulse input signals. 2. What is the initial slope of a step response of a first order system?

IC6501 CONTROL SYSTEM UNIT-II TIME RESPONSE PART-A 1. What are the standard test signals employed for time domain studies?(or) List the standard test signals used in analysis of control systems? (April

### Homework 7 - Solutions

Homework 7 - Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the

### 1 An Overview and Brief History of Feedback Control 1. 2 Dynamic Models 23. Contents. Preface. xiii

Contents 1 An Overview and Brief History of Feedback Control 1 A Perspective on Feedback Control 1 Chapter Overview 2 1.1 A Simple Feedback System 3 1.2 A First Analysis of Feedback 6 1.3 Feedback System

### Discrete Systems. Step response and pole locations. Mark Cannon. Hilary Term Lecture

Discrete Systems Mark Cannon Hilary Term 22 - Lecture 4 Step response and pole locations 4 - Review Definition of -transform: U() = Z{u k } = u k k k= Discrete transfer function: Y () U() = G() = Z{g k},

### 10ES-43 CONTROL SYSTEMS ( ECE A B&C Section) % of Portions covered Reference Cumulative Chapter. Topic to be covered. Part A

10ES-43 CONTROL SYSTEMS ( ECE A B&C Section) Faculty : Shreyus G & Prashanth V Chapter Title/ Class # Reference Literature Topic to be covered Part A No of Hours:52 % of Portions covered Reference Cumulative

### MATH4406 (Control Theory) Unit 1: Introduction Prepared by Yoni Nazarathy, July 21, 2012

MATH4406 (Control Theory) Unit 1: Introduction Prepared by Yoni Nazarathy, July 21, 2012 Unit Outline Introduction to the course: Course goals, assessment, etc... What is Control Theory A bit of jargon,

### CYBER EXPLORATION LABORATORY EXPERIMENTS

CYBER EXPLORATION LABORATORY EXPERIMENTS 1 2 Cyber Exploration oratory Experiments Chapter 2 Experiment 1 Objectives To learn to use MATLAB to: (1) generate polynomial, (2) manipulate polynomials, (3)

### MAS107 Control Theory Exam Solutions 2008

MAS07 CONTROL THEORY. HOVLAND: EXAM SOLUTION 2008 MAS07 Control Theory Exam Solutions 2008 Geir Hovland, Mechatronics Group, Grimstad, Norway June 30, 2008 C. Repeat question B, but plot the phase curve

### ECE317 : 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

### Here represents the impulse (or delta) function. is an diagonal matrix of intensities, and is an diagonal matrix of intensities.

19 KALMAN FILTER 19.1 Introduction In the previous section, we derived the linear quadratic regulator as an optimal solution for the fullstate feedback control problem. The inherent assumption was that

### D(s) G(s) A control system design definition

R E Compensation D(s) U Plant G(s) Y Figure 7. A control system design definition x x x 2 x 2 U 2 s s 7 2 Y Figure 7.2 A block diagram representing Eq. (7.) in control form z U 2 s z Y 4 z 2 s z 2 3 Figure

### Lecture 11. Frequency Response in Discrete Time Control Systems

EE42 - Discrete Time Systems Spring 28 Lecturer: Asst. Prof. M. Mert Ankarali Lecture.. Frequency Response in Discrete Time Control Systems Let s assume u[k], y[k], and G(z) represents the input, output,

### EI6801 Computer Control of Processes Dept. of EIE and ICE

Unit I DISCRETE STATE-VARIABLE TECHNIQUE State equation of discrete data system with sample and hold State transition equation Methods of computing the state transition matrix Decomposition of discrete

### Outline. Classical Control. Lecture 5

Outline Outline Outline 1 What is 2 Outline What is Why use? Sketching a 1 What is Why use? Sketching a 2 Gain Controller Lead Compensation Lag Compensation What is Properties of a General System Why use?

### Performance 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 Steady-state Error and Type 0, Type

### Subject: Optimal Control Assignment-1 (Related to Lecture notes 1-10)

Subject: Optimal Control Assignment- (Related to Lecture notes -). Design a oil mug, shown in fig., to hold as much oil possible. The height and radius of the mug should not be more than 6cm. The mug must

### EE C128 / ME C134 Fall 2014 HW 6.2 Solutions. HW 6.2 Solutions

EE C28 / ME C34 Fall 24 HW 6.2 Solutions. PI Controller For the system G = K (s+)(s+3)(s+8) HW 6.2 Solutions in negative feedback operating at a damping ratio of., we are going to design a PI controller

### Alireza Mousavi Brunel University

Alireza Mousavi Brunel University 1 » Control Process» Control Systems Design & Analysis 2 Open-Loop Control: Is normally a simple switch on and switch off process, for example a light in a room is switched

### FATIMA 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

### Chapter 7. Digital Control Systems

Chapter 7 Digital Control Systems 1 1 Introduction In this chapter, we introduce analysis and design of stability, steady-state error, and transient response for computer-controlled systems. Transfer functions,

### Systems Analysis and Control

Systems Analysis and Control Matthew M. Peet Arizona State University Lecture 21: Stability Margins and Closing the Loop Overview In this Lecture, you will learn: Closing the Loop Effect on Bode Plot Effect

### DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD

206 Spring Semester ELEC733 Digital Control System LECTURE 7: DESIGN USING TRANSFORMATION TECHNIQUE CLASSICAL METHOD For a unit ramp input Tz Ez ( ) 2 ( z ) D( z) G( z) Tz e( ) lim( z) z 2 ( z ) D( z)

### Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: Student ID number... Signature...

Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: 29..23 Given and family names......................solutions...................... Student ID number..........................

### DIGITAL CONTROLLER DESIGN

ECE4540/5540: Digital Control Systems 5 DIGITAL CONTROLLER DESIGN 5.: Direct digital design: Steady-state accuracy We have spent quite a bit of time discussing digital hybrid system analysis, and some

### UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) IN BIOMEDICAL ENGINEERING SEMESTER 1 EXAMINATION 2017/2018 ADVANCED BIOMECHATRONIC SYSTEMS

ENG0016 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) IN BIOMEDICAL ENGINEERING SEMESTER 1 EXAMINATION 2017/2018 ADVANCED BIOMECHATRONIC SYSTEMS MODULE NO: BME6003 Date: Friday 19 January 2018

### Linear State Feedback Controller Design

Assignment For EE5101 - Linear Systems Sem I AY2010/2011 Linear State Feedback Controller Design Phang Swee King A0033585A Email: king@nus.edu.sg NGS/ECE Dept. Faculty of Engineering National University

### Feedback Control of Linear SISO systems. Process Dynamics and Control

Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals

### Control Systems Engineering ( Chapter 8. Root Locus Techniques ) Prof. Kwang-Chun Ho Tel: Fax:

Control Systems Engineering ( Chapter 8. Root Locus Techniques ) Prof. Kwang-Chun Ho kwangho@hansung.ac.kr Tel: 02-760-4253 Fax:02-760-4435 Introduction In this lesson, you will learn the following : The

### ECEN 605 LINEAR SYSTEMS. Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability 1/27

1/27 ECEN 605 LINEAR SYSTEMS Lecture 20 Characteristics of Feedback Control Systems II Feedback and Stability Feedback System Consider the feedback system u + G ol (s) y Figure 1: A unity feedback system

### CHAPTER 7 STEADY-STATE RESPONSE ANALYSES

CHAPTER 7 STEADY-STATE 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

### Distributed Real-Time Control Systems

Distributed Real-Time 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

### CONTROL SYSTEMS ENGINEERING Sixth Edition International Student Version

CONTROL SYSTEMS ENGINEERING Sixth Edition International Student Version Norman S. Nise California State Polytechnic University, Pomona John Wiley fir Sons, Inc. Contents PREFACE, vii 1. INTRODUCTION, 1

### CONTROL OF DIGITAL SYSTEMS

AUTOMATIC CONTROL AND SYSTEM THEORY CONTROL OF DIGITAL SYSTEMS Gianluca Palli Dipartimento di Ingegneria dell Energia Elettrica e dell Informazione (DEI) Università di Bologna Email: gianluca.palli@unibo.it

### Index. 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,

### Topic # Feedback Control

Topic #5 6.3 Feedback Control State-Space Systems Full-state Feedback Control How do we change the poles of the state-space system? Or,evenifwecanchangethepolelocations. Where do we put the poles? Linear

### ECE 486 Control Systems

ECE 486 Control Systems Spring 208 Midterm #2 Information Issued: April 5, 208 Updated: April 8, 208 ˆ This document is an info sheet about the second exam of ECE 486, Spring 208. ˆ Please read the following

### Outline. Classical Control. Lecture 1

Outline Outline Outline 1 Introduction 2 Prerequisites Block diagram for system modeling Modeling Mechanical Electrical Outline Introduction Background Basic Systems Models/Transfers functions 1 Introduction

### Digital Control Engineering Analysis and Design

Digital Control Engineering Analysis and Design M. Sami Fadali Antonio Visioli AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is

### Transient 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

### Feedback Control of Dynamic Systems

THIRD EDITION Feedback Control of Dynamic Systems Gene F. Franklin Stanford University J. David Powell Stanford University Abbas Emami-Naeini Integrated Systems, Inc. TT Addison-Wesley Publishing Company

### a. Closed-loop system; b. equivalent transfer function Then the CLTF () T is s the poles of () T are s from a contribution of a

Root Locus Simple definition Locus of points on the s- plane that represents the poles of a system as one or more parameter vary. RL and its relation to poles of a closed loop system RL and its relation

### ME 475/591 Control Systems Final Exam Fall '99

ME 475/591 Control Systems Final Exam Fall '99 Closed book closed notes portion of exam. Answer 5 of the 6 questions below (20 points total) 1) What is a phase margin? Under ideal circumstances, what does

### EE C128 / ME C134 Final Exam Fall 2014

EE C128 / ME C134 Final Exam Fall 2014 December 19, 2014 Your PRINTED FULL NAME Your STUDENT ID NUMBER Number of additional sheets 1. No computers, no tablets, no connected device (phone etc.) 2. Pocket

### Course Summary. The course cannot be summarized in one lecture.

Course Summary Unit 1: Introduction Unit 2: Modeling in the Frequency Domain Unit 3: Time Response Unit 4: Block Diagram Reduction Unit 5: Stability Unit 6: Steady-State Error Unit 7: Root Locus Techniques

### MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 Problem Set #4 Posted: Thursday, Mar. 7, 13 Due: Thursday, Mar. 14, 13 1. Sketch the Root

### ECE317 : Feedback and Control

ECE317 : Feedback and Control Lecture : Routh-Hurwitz stability criterion Examples Dr. Richard Tymerski Dept. of Electrical and Computer Engineering Portland State University 1 Course roadmap Modeling

### 7.4 STEP BY STEP PROCEDURE TO DRAW THE ROOT LOCUS DIAGRAM

ROOT LOCUS TECHNIQUE. Values of on the root loci The value of at any point s on the root loci is determined from the following equation G( s) H( s) Product of lengths of vectors from poles of G( s)h( s)

### Übersetzungshilfe / 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 -

### OPTIMAL CONTROL AND ESTIMATION

OPTIMAL CONTROL AND ESTIMATION Robert F. Stengel Department of Mechanical and Aerospace Engineering Princeton University, Princeton, New Jersey DOVER PUBLICATIONS, INC. New York CONTENTS 1. INTRODUCTION

### 1 x(k +1)=(Φ LH) x(k) = T 1 x 2 (k) x1 (0) 1 T x 2(0) T x 1 (0) x 2 (0) x(1) = x(2) = x(3) =

567 This is often referred to as Þnite settling time or deadbeat design because the dynamics will settle in a Þnite number of sample periods. This estimator always drives the error to zero in time 2T or

### Solution for Mechanical Measurement & Control

Solution for Mechanical Measurement & Control December-2015 Index Q.1) a). 2-3 b).3-4 c). 5 d). 6 Q.2) a). 7 b). 7 to 9 c). 10-11 Q.3) a). 11-12 b). 12-13 c). 13 Q.4) a). 14-15 b). 15 (N.A.) Q.5) a). 15

### (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

### Learn2Control Laboratory

Learn2Control Laboratory Version 3.2 Summer Term 2014 1 This Script is for use in the scope of the Process Control lab. It is in no way claimed to be in any scientific way complete or unique. Errors should

### CONTROL * ~ SYSTEMS ENGINEERING

CONTROL * ~ SYSTEMS ENGINEERING H Fourth Edition NormanS. Nise California State Polytechnic University, Pomona JOHN WILEY& SONS, INC. Contents 1. Introduction 1 1.1 Introduction, 2 1.2 A History of Control

### Unit 8: Part 2: PD, PID, and Feedback Compensation

Ideal Derivative Compensation (PD) Lead Compensation PID Controller Design Feedback Compensation Physical Realization of Compensation Unit 8: Part 2: PD, PID, and Feedback Compensation Engineering 5821:

### EEE 184 Project: Option 1

EEE 184 Project: Option 1 Date: November 16th 2012 Due: December 3rd 2012 Work Alone, show your work, and comment your results. Comments, clarity, and organization are important. Same wrong result or same

### The output voltage is given by,

71 The output voltage is given by, = (3.1) The inductor and capacitor values of the Boost converter are derived by having the same assumption as that of the Buck converter. Now the critical value of the

### 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 s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics

### Subject: 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:

### CONTROL SYSTEMS LECTURE NOTES B.TECH (II YEAR II SEM) ( ) Prepared by: Mrs.P.ANITHA, Associate Professor Mr.V.KIRAN KUMAR, Assistant Professor

LECTURE NOTES B.TECH (II YEAR II SEM) (2017-18) Prepared by: Mrs.P.ANITHA, Associate Professor Mr.V.KIRAN KUMAR, Assistant Professor Department of Electronics and Communication Engineering MALLA REDDY

### Chapter 2. Classical Control System Design. Dutch Institute of Systems and Control

Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steady-state Steady-state errors errors Type Type k k systems systems Integral Integral

### Exam. 135 minutes + 15 minutes reading time

Exam January 23, 27 Control Systems I (5-59-L) 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