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# GATE Electronics & Communication Vol-8- Control Systems

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PUBLISHED FOR GATE 2018

 Edition 8th Authors R K Kanodia & Ashish Murolia Publisher NODIA Pages 688 Binding Paper Back Language English

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SALIENT FEATURES

• Brief Theory

• Problem Solving Methodology

• Fundamental Concepts & Formulae Review

• Vast Question book with Full Solutions

• Multiple Choice Questions, Memory Based Questions and Numerical Types Questions

• Full width coverage of GATE Syllabus

• Well explained and error free solutions

CHAPTER 1 TRANSFER FUNCTIONS

1.1 INTRODUCTION

1.2 CONTROL SYSTEM

1.2.1 Classification of Control System

1.2.2 Mathematical Modelling of Control System

1.3 TRANSFER FUNCTION

1.4 FEEDBACK SYSTEM

1.4.1 Basic Formulation

1.4.2 Transfer Function for Multivariable System

1.4.3 Effects of Feedback on System Characteristics

1.5 BLOCK DIAGRAMS

1.5.1 Block Diagram Reduction

1.6 SIGNAL FLOW GRAPH

1.6.1 Representation of Signal Flow Graph

1.6.2 Basic Terminologies of SFG

1.6.3 Gain Formula for SFG (Masonâ€™s Rule)

EXERCISE 1.1

EXERCISE 1.2

EXERCISE 1.3

SOLUTIONS 1.1

SOLUTIONS 1.2

SOLUTIONS 1.3

CHAPTER 2 STABILITY

2.1 INTRODUCTION

2.2 LTI SYSTEM RESPONSES

2.3 STABILITY

2.3.1 Stability for LTI Systems Using Natural Respons

2.3.2 Zero-Input and Asymptotic Stability

2.3.3 Stability Using Total Response

2.4 DEPENDENCE OF STABILITY ON LOCATION OF POLES

2.5 METHODS OF DETERMINING STABILITY

2.5.1 Routh-Hurwitz Criterion

2.5.2 Nyquist Criterion

2.5.3 Bode Diagram

2.6 ROUTH-HURWITZ CRITERION

2.6.1 Routhâ€™s Tabulation

2.6.2 Location of Roots of Characteristic Equation using Routhâ€™s Table

2.6.3 Limitations of Routh-Hurwitz Criterion

EXERCISE 2.1

EXERCISE 2.2

EXERCISE 2.3

SOLUTIONS 2.1

SOLUTIONS 2.2

SOLUTIONS 2.3

CHAPTER 3 TIME RESPONSE

3.1 INTRODUCTION

3.2 TIME RESPONSE

3.3 FIRST ORDER SYSTEMS

3.3.1 Unit Impulse Response of First Order System

3.3.2 Unit Step Response of First Order System

3.3.3 Unit Ramp Response of First Order System

3.3.4 Unit-Parabolic Response of First Order System

3.4 SECOND ORDER SYSTEM

3.4.1 Unit Step Response of Second Order System

3.5.1 Steady State Error for Unity Feedback System

3.5.2 Steady State Error due to Disturbance

3.5.3 Steady State Error for Non-unity Feedback

3.6 EFFECT OF ADDING POLES AND ZEROS TO TRANSFER FUNCTIONS

3.7 DOMINANT POLES OF TRANSFER FUNCTION

3.8 SENSITIVITY

EXERCISE 3.1

EXERCISE 3.2

EXERCISE 3.3

SOLUTIONS 3.1

SOLUTIONS 3.2

SOLUTIONS 3.3

CHAPTER 4 ROOT LOCUS TECHNIQUE

4.1 INTRODUCTION

4.2 ROOT LOCUS

4.2.1 The Root-Locus Concept

4.2.2 Properties of Root Locus

4.3 RULES FOR SKETCHING ROOT LOCUS

4.4 EFFECT OF ADDITION OF POLES AND ZEROS TO G(S)H(S)

4.5 ROOT SENSITIVITY

EXERCISE 4.1

EXERCISE 4.2

EXERCISE 4.3

SOLUTIONS 4.1

SOLUTIONS 4.2

SOLUTIONS 4.3

CHAPTER 5 FREQUENCY DOMAIN ANALYSIS

5.1 INTRODUCTION

5.2 FREQUENCY RESPONSE

5.2.1 Correlation Between Time and Frequency Response

5.2.2 Frequency Domain Specifications

5.2.3 Effect of Adding a Pole or a Zero to Forward Path Transfer Function

5.3 POLAR PLOT

5.4 NYQUIST CRITERION

5.4.1 Principle of Argument

5.4.2 Nyquist Stability Criterion

5.4.3 Effect of Addition of Poles and Zeros to G^s hH^s h on Nyquist Plot

5.5 BODE PLOTS

5.5.1 Initial Part of Bode Plot

5.5.2 Slope Contribution of Poles and Zeros

5.5.3 Determination of Steady State Error Characteristics

5.6 ALL-PASS AND MINIMUM PHASE SYSTEM

5.6.1 Pole-Zero Pattern

5.6.2 Phase Angle Characteristic

5.7 SYSTEM WITH TIME DELAY (TRANSPORTATION LAG)

5.8 GAIN MARGIN AND PHASE MARGIN

5.8.1 Determination of Gain Margin and Phase Margin using Nyquist Plot

5.8.2 Determination of Gain Margin and Phase Margin using Bode Plot

5.8.3 Stability of a System

5.9 CONSTANT M-CIRCLES AND CONSTANT N-CIRCLES

5.9.1 M-Circles

5.9.2 N -Circles

5.10 NICHOLS CHARTS

EXERCISE 5.1

EXERCISE 5.2

EXERCISE 5.3

SOLUTIONS 5.1

SOLUTIONS 5.2

SOLUTIONS 5.3

CHAPTER 6 DESIGN OF CONTROL SYSTEMS

6.1 INTRODUCTION

6.2 SYSTEM CONFIGURATIONS

6.3 CONTROLLERS

6.3.1 Proportional Controller

6.3.2 Proportional-Derivative (PD) Controller

6.3.3 Proportional-Integral (PI) Controller

6.3.4 Derivative Feedback Control

6.3.5 Proportional-Integral-Derivative (PID) Controller

6.4 COMPENSATORS

6.4.2 Lag Compensator

EXERCISE 6.1

EXERCISE 6.2

EXERCISE 6.3

SOLUTIONS 6.1

SOLUTIONS 6.2

SOLUTIONS 6.3

CHAPTER 7 STATE VARIABLE ANALYSIS

7.1 INTRODUCTION

7.2 STATE VARIABLE SYSTEM

7.2.1 State Differential Equations

7.2.2 Block Diagram of State Space

7.2.3 Comparison between Transfer Function Approach and State Variable Approach

7.3 STATE-SPACE REPRESENTATION

7.3.1 State-Space Representation using Physical Variables

7.3.2 State-Space Representation Using Phase Variable

7.4 SOLUTION OF STATE EQUATION

7.4.1 Solution of Non-homogeneous State Equation

7.4.2 State Transition Matrix by Laplace Transform

7.5 TRANSFER FUNCTION FROM THE STATE MODEL

7.5.1 Characteristic Equation

7.5.2 Eigen Values

7.5.3 Eigen Vectors

7.5.4 Determination of Stability Using Eigen Values

7.6 SIMILARITY TRANSFORMATION

7.6.1 Diagonalizing a System Matrix

7.7 CONTROLLABILITY AND OBSERVABILITY

7.7.1 Controllability

7.7.2 Output Controllability

7.7.3 Observability

7.8 STATE FEEDBACK CONTROL SYSTEM

7.9 STEADY STATE ERROR IN STATE SPACE

7.9.1 Analysis Using Final Value Theorem

7.9.2 Analysis Using Input Substitution

EXERCISE 7.1

EXERCISE 7.2

EXERCISE 7.3

SOLUTIONS 7.1

SOLUTIONS 7.2

SOLUTIONS 7.3

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