Control Systems Engineering 2e
Author(s): S Palani
Subject(s): Engineering
ISBN 9789394828179
 Published Date
  Pages 682

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Control Engineering is a multi disciplinary subject and finds widespread application in the guidance, navigation and control of missiles, aeroplanes and ships, as well as in the process control industry. This book presents clear theoretical concepts reinforced by worked out numerical examples. It includes topics on Nyquist Stability Criterion, Signal Flow Graph, Root Locus Technique and comprehensive coverage on Control System Components.

Cover
Halftitle Page
About the author
Title Page
Copyright Page
Contents
Preface
Chapter 1 Introduction
1.1 The History of Automatic Control
1.2 Control System Terminologies
1.3 System Representation
1.4 Regulator System
1.4.1 Example of Open Loop Regulator System
1.4.2 Example of Closed Loop Regulator System
1.5 Example of Servomechanism
1.6 Computer Control System
1.6.1 Temperature Control System Using P.C.
1.6.2 Pressure Control System Using P.C.
1.7 Comparison of Open Loop and Closed Loop Systems
1.7.1 Advantages of Open Loop Systems
1.7.2 Disadvantages of Open Loop Systems
1.7.3 Advantages of Closed Loop Systems
1.7.4 Disadvantages of Closed Loop Systems
1.8 System Classification
1.8.1 Open and Closed Loop Systems
1.8.2 Linearand Non-Iinear Systems
1.8.3 Time Invariant and Time Varying Systems
1.8.4 Continuousand Discrete Systems
1.8.5 Deterministic and Stochastic Systems
1.8.6 Lumped Parameter and Distributed Parameter Systems
1.8.7 SISO and MIMO Systems
1.8.8 System Classification Based on Components Used
Chapter Summary
Exercise
Chapter 2 Mathematical Modeling of Physical Systems
2.1 Introduction
2.1.1 Mathematical Modeling-Transfer Funcrion Model
2.2 Mechanical Systems
2.2.1 Mechanical Translational Systems
2.2.2 Rotational System
2.2.3 Dynamic Equations of Mechanical Translational System
2.2.4 The Step by Step Procedure
2.3 Lever and Gear Arrangements
2.4 Transfer Function Model for Electrical Network
2.5 Transfer Function of Separately Excited D.C. Generator
2.5.1 No Load Transfer Function
2.6 Transfer Function of Armature Controlled D.C. Motor
2.6.1 No Load Transfer Function
2.6.2 Transfer Function under Loaded Condition
2.7 Transfer Function of Field Controlled D.C. Motor
2.8 Armature Controlled and Field Controlled D.C. Motor-Comparison
Chapter Summary
Exercise
Chapter 3 Elecirical Analogue
3.1 Introduction
3.2 Force-Voltage Analogy
3.3 Force-Current Analogy
Chapter Summary
Exercise
Chapter 4 Block Diagram Reduction Technique and Signal Flow Graph
4.1 Introduction
4.2 Block Diagram Representation of a System
4.3 Basic Connections for Blocks
4.3.1 Cascade Connection
4.3.2 Parallel Connection
4.3.3 Feedback Connection
4.4 Block Diagram Algebra
4.5 Multiple Input System
4.6 Advantages and Disadvantages of Block Diagram Representation
4.6.1 Advantages
4.6.2 Disadvantages
4.7 Signal Flow Graphs
4.8 Definitions of Basic Terms for Signal Flow Graph
4.9 Basic Rules of Signal Flow Graph
4.10 Basic Conneorion for Signal Flow Graph
4.11 Gain Formula For Signal Flow Graph (Mason’s Rule)
4.12 Signal Flow Graph Conversion from Block Diagram
4.13 Application of Mason’s Gain Formula between Output Node and Non-input Nodes
Chapter Summary
Exercise
Chapter 5 Time Response of Feedback Control Systems
5.1 Introduction
5.2 Second Order System Model
5.3 Steady State Error for Step Input
5.4 Steady State Error for a Ramp Input of ωi Slope
5.5 To Summarise
5.6 Transient Response (or Time Response or Dynamic Response) of First and Second Order Systems
5.7 Test Signals
5.7.1 Impulse Signal
5.7.2 Step Signal
5.7.3 Ramp Signal
5.7.4 Acceleration Signal
5.8 Review of Partial Fraction Expansion
5.9 Laplace Transform Table
5.9.1 Initial Value Theorem
5.9.2 Final Value Theorem
5.9.3 Shift Theorem
5.10 Analytical Method of Determining the Residues
5.11 Graphical Method of Determining the Residues
5.12 Transient Response of a First Order System
5.13 Performance Characteristics of First Order System
5.13.1 Time Constant
5.13.2 Settling Time
5.13.3 Time Delay
5.14 Transient Response of a Second Order System
5.15 Step Response of a Second Order System
5.15.1 Underdamped Case ζ < 1
5.15.2 Critically Damped Case ζ = 1
5.15.3 Overdamped Case ζ > 1
5.16 Expression for the Overshoot Mp
5.17 Time Domain Specifications
5.17.1 Overslioot
5.17.2 Time Delay td
5.17.3 Time Constant T
5.17.4 Rise Time tr
5.17.5 Settling Time ts
5.17.6 The Period of Oscillation
5.17.7 The Number of Oscillations before Settling Time is Reached
5.18 Impulse Response of a Second Order System
5.19 Type and Order of Feedback System
5.19.1 Static Error Coefficients and Steady State Error
5.20 Steady State Error for Step Input
5.21 Steady State Error for Velocity Input
5.22 Steady State Error for Acceleration Input
5.23 The Generalized or Dynamic Error Coefficients
5.23.1 Alternative Method of Determining Dynamic Error Constants
5.24 Steady State Error due to Disturbances
5.25 Effects of Adding Poles and Zeros to a Second Order System
5.25.1 Addition of a Pole
5.25.2 Addition of a Zero
5.26 PID Controllers
5.27 PD Controller
5.28 PI Controller
5.29 Rate Feedback or Tachogenerator Feedback Control
5.30 Reset Controllers
5.31 On-Off or Two Position Controller
5.32 Effect of Pole Location on Transient Response
5.33 The Sensitivity
Chapter Summary
Exercise
Chapter 6 Frequency Domain Analysis of Control Systems
6.1 Introduction
6.2 Advantages of Frequency Response Method
6.3 Frequency Response Plots
6.3.1 Polar Plot
6.3.2 Bode Plot
6.3.3 Magnitude versus Phase Shift Plot
6.4 Step by Step Procedure to Draw Polar Plot
6.5 Sketching a Polar Plot
6.6 Minimum and Non-minimum Phase Transfer Functions
6.7 Minimum Phase Transfer Function
6.8 All Pass Transfer Function
6.9 Correlation between Transient and Frequency Response Methods
6.10 Bode Plot
6.11 Advantages of Bode Plot
6.12 General Rule to Draw a Bode Plot
6.13 Step By Step Procedure to Draw the Bode Magnitude Plot
6.14 Bode Plot for Closed Loop Second Order System
6.15 Determination of Transfer Function from Bode Magnitude Plot
6.16 Frequency Domain Specifications
6.16.1 Phase Margin and Gain Margin from Bode Plots
6.17 Obtaining Closed Loop Frequency Response from Open Loop Transfer Function—The Constant M and N Circles and Nichol’s Chart
6.17.1 The Constant M Circles
6.17.2 The Constant N Circles
6.17.3 The Nichol’s Chart
6.18 Gain Adjustment for the Desired Mr Using Constant M Circle
6.19 Determination of K for the Given Mr from the Nichol’s Chart
6.20 Forced Sinusoidal Response
Chapter Summary
Exercise
Chapter 7 Stability of Linear Control Systems
7.1 Introduction
7.2 Relative Stability
7.2.1 Zero Input Stability
7.2.2 Asymptotic Stability
7.2.3 Marginal Stability
7.3 Impulse Response Function
7.4 Stability Definition via Impulse Response Function
7.5 Characteristic Equation of Control System
7.6 Stability Condition
7.7 Routh’s Stability Criterion
7.8 Factorising the Polynomial Using Routh-Hurwitz Method
7.9 Determination of RHP, LHP and Imaginary Roots from Routh’s Test
7.10 Determination of Marginal Value of K from Routh Test
7.11 Determination of Roots to the Right and Left of any Vertical Line other than the Origin
7.12 Routh’s Test for System with Transportation Lag
7.13 Conformal Mappings and the Principle of Arguments
7.14 The Principle of Arguments
7.15 Nyquist Stability Criterion
7.15.1 Nyquist Criterion-Statement
7.15.2 Advancages of Nyquist Stability Criterion
7.16 Procedure to Count Nr
7.17 Step by Step Procedure of Applying Nyquist Criterion
7.18 Nyquist Test for Systems with Imaginary Axis Poles of G(s)
7.19 Determination of Stability from Bode Diagram
7.20 Poles of GH(s) on the jω Axis
7.21 Nyquist Test for System with Time Delay (Transportation Lag)
Chapter Summary
Exercise
Chapter 8 Root Locus Technique
8.1 Introduction
8.2 The Construction of the Root Loci
8.3 To Determine the Gain Margin and Phase Margin from Root Locus
8.4 Root Locus with Addition of Poles
8.5 Root Locus with Addition of a Zero
8.6 Root Locus for K < 0 (Inverse Root Locus)
Chapter Summary
Exercise
Chapter 9 Design of Control Systems in Time and Frequency Domains
9.1 Introduction
9.2 Cascade Compensators
9.2.1 Lead Compensator
9.2.2 Transfer Function of Lead Compensator
9.2.3 Design of Lead Compensator by Frequency Response Method
9.2.4 Design of Lead Compensator Based on Root Locus Technique
9.2.5 Design of Lag Compensator
9.2.6 Phase Lag Compensator Design by Frequency Response Method
9.2.7 Phase Lag Compensator Design Using Root Locus Technique
9.2.8 Design of Lag-Lead Compensator
9.2.9 Lag-Lead Compensator Design Using Frequency Response Method
9.2.10 Design of Lag-Lead Network by Root Locus Method
9.3 Design of Feedback Controller: Rate or Tachometer Feedback
9.4 Design of PID Controllers
9.4.1 PID Controller Design in the Frequency Domain
9.4.2 PID Controller Design by Root Locus Method
Chapter Summary
Exercise
Chapter 10 Control System Components
10.1 Introduction
10.2 Error Detectors
10.2.1 Synchros
10.2.2 Transmitter (Synchro Generator)
10.2.3 Synchro Control Transformer (C.T) (Receiver)
10.2.4 Transfer Function of the Synchro
10.2.5 A Position Control System Using a Pair of Synchros as Error Detector
10.2.6 Potentiometer
10.2.7 Servo System Using Potentiometer as Error Detector
10.3 Servomotors
10.3.1 Two Phase A.C. Servomotor
10.3.2 The Stepper Motor
10.3.3 Advantages of Stepper Motors
10.3.4 Disadvantages of Stepper Motors
10.3.5 Applications of Stepper Motors
10.3.6 Types of Stepper Motorr
10.3.7 Stepper Motor—The Preliminaries
10.3.8 Variable Reluctance Stepper Motor
10.3.9 Rotor Movement
10.3.10 Permanent Magnet Stepping Motor
10.3.11 Construction of a Two Stack Reluctance Type Stepper Motor
10.3.12 How the Rotor Moves?
10.4 Hydraulic Servomotor
10.5 Pneumatic Controllers—Advantages
10.6 Pneumatic’Proportional Controller-Flapper Valves
10.7 Gear Trains
10.8 Tachogenerators
10.8.1 D.C. Tachogenerator
10.8.2 A.C. Tachogenerator
Chapter Summary
Exercise
Index

S Palani is the Dean and Professor, Department of Electronics and Communication Engineering Sudharsan Engineering College, Pudukkottai. He has published more than 40 research papers in reputed national and international journals.

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