Control Systems
Control Systems
ISBN 9789394828209
 Publication Date

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This fundamental textbook on control engineering is designed to bridge the gap and strike a balance between theory and practice. The book has its emphasis on conceptual clarity, ease-of- understanding and lucid presentation. A significant highlight of the book is Mat Lab examples and simulations, and solved problems from university examinations and competitive examinations.

  • Cover
  • Halftitle Page
  • Title Page
  • Copyright Page
  • Contents
  • Foreword
  • Preface
  • Acknowledgements
  • Chapter 1 Introduction to Control Systems
    • Introduction
    • 1.1 Basic Definitions and Terminologies
    • 1.2 Basic Elements of Control System
      • 1.2.1 Generic Control Loop Terminologies
    • 1.3 Open Loop and Closed Loop Systems
      • 1.3.1 Electronic Voltage Regulator—As a Closed Loop System
      • 1.3.2 Advantages and Disadvantages of Open Loop and Closed Loop Systems
      • 1.3.3 Comparison of Closed Loop and Open Loop Systems
    • 1.4 Transfer Functions
      • 1.4.1 Properties of Transfer Functions
      • 1.4.2 Representation of Transfer Functions
      • 1.4.3 Relative Degree of Transfer Functions and its Implications on Performance
      • 1.4.4 Classification of Transfer Functions Based on the Relative Degree
    • 1.5 Introduction to Modeling
      • 1.5.1 Types of Model
      • 1.5.2 Translational Mechanical Systems
      • 1.5.3 D’Alembertls Principle
      • 1.5.4 Procedure for Obtaining Transfer Function for Dynamical Systems
      • 1.5.5 Rotational Mechanical Systems
      • 1.5.6 Modeling of Electrical Systems
      • 1.5.7 Modeling of Electromechanical Systems
    • 1.6 Electrical Analogous of Mechanical Translation System
      • 1.6.1 Force-Voltage Analogy
      • 1.6.2 F-V Analogous Network
      • 1.6.3 F-V Analogous System
      • 1.6.4 Force-current Analogy
      • 1.6.5 Torque Current Analogous Circuit
    • Exercise
    • Short Questions and Answers
  • Chapter 2 Block Diagram Reduction and Signal Flow Graph
    • 2.1 Block Diagram Reduction
      • Introduction
      • Diagram Blocks
      • 2.1.1 Block Diagram of Physical Systems
        • Block Diagram Reduction
      • 2.1.2 Rules of Block Diagram Algebra
      • 2.1.3 Advantages and Disadvantages
        • Advantages
        • Disadvantages
    • 2.2 Signal flow graph
      • Introduction
      • 2.2.1 Definition of Signal Flow Graph
        • Signal Flow Graph Terminology
      • 2.2.2 Properties of Signal Flow Graph
      • 2.2.3 Signal Flow Graph Algebra
        • Procedure
    • 2.3 Block Diagram to Signal Flow Graph Conversion
      • Exercise
      • Short Questions and Answers
  • Chapter 3 Time Response Analysis
    • 3.1 Introduction to Timo Response Analysis
      • System Response
      • 3.1.1 Natural or Unforced Response of the System
      • 3.1.2 Test Signals and Need for Test Signals
        • Test Signals
      • 3.1.3 Need for Test Signals
      • 3.1.4 Transfer Function of Closed Loop System
      • 3.1.5 Poles & Zeros of Transfer Function
        • Note
      • 3.1.6 Order and Type of the System
        • Order of the System
      • 3.1.7 Type of the System
    • 3.2 First Order System Response
      • 3.2.1 Step Response Analysis of First Order System
      • 3.2.2 First Order System Performance Specifications
      • 3.2.3 Ramp Response Analysis of First Order System
      • 3.2.4 Impulse Response Analysis of First Order System
    • 3.3 Second Order System Response
      • 3.3.1 Generic Second Order Transfer Function
      • 3.3.2 Performance of Second Order System
      • 3.3.3 Damping Ratio and System Response
      • 3.3.4 Response of Second Order System for Step Input
      • 3.3.5 Response of Second Order System for Impulse Input
    • 3.4 Transient Response Specifications
    • 3.5 Response with P, PI and PID Controllers
      • 3.5.1 Proportional Mode
      • 3.5.2 Proportional Derivative Mode
      • 3.5.3 Derivative Mode
      • 3.5.4 Proportional Integral Mode
      • 3.5.5 Proportional Integral Derivative Mode
    • 3.6 Steady State Error
      • 3.6.1 Sources of Steady State Errors
      • 3.6.2 Evaluation of Steady State Error for a Given Input
    • 3.7 Static Error Constants
    • 3.8 Generalized Error Coefficient
    • 3.9 Computational Issues and Dynamic Error Coefficients
    • 3.10 Effects of Feedback
      • Introduction
      • The Feedback Principle
      • 3.10.1 Effect of Feedback on Noise
      • 3.10.2 Effect of Feedback on Stability
    • 3.11 Response of Higher Order Systems Using Time Response Analysis
    • Exercise
    • Short Questions and Answers
  • Chapter 4 Frequency Response Analysis
    • 4.1 Introduction to Frequency Response
      • 4.1.1 Complex Frequency Approach for Frequency Analysis
      • 4.1.2 Advantages and Disadvantages of Frequency Response Techniques
      • 4.1.3 Frequency Response Characteristics
      • 4.1.4 Frequency Response Specifications of Second Order Systems
      • 4.1.5 Correlation Between Second Order Frequency and Time Response
    • 4.2 Determination of Frequency Response
      • 4.2.1 Analytical Determination of Frequency Response
      • 4.2.2 Graphical Dt termination of Frequency Response
      • 4.2.3 Bode Diagram Approach for Frequency Response Estimation and Stability Determination
      • 4.2.4 Basic Terminologies in Bode Plot Plotting Bode Plots
      • 4.2.5 Determination of Gain Margin and Phase Margin from Bode Plot
        • Dead Time (or) Transportation Lag Block
      • 4.2.6 Frequency Response of Dead Time Block
    • 4.3 Polar Plots
      • 4.3.1 Procedure Determination of Gain Margin and Phase Margin of System from Polar Plot
    • 4.4 Nichols Chart
      • 4.4.1 Closed Loop Frequency Response From Nichols Chart
    • 4.5 M and N Circles (Relate Open Loop and Closed Loop Response)
    • 4.6 Obtaining the Minimum Phase Transfer Function from the Bode Magnitude Plot
    • 4.7 Non minimum Phase and All Pass Systems [jntu - 2007]
    • Exercise
    • Short Questions and Answers
  • Chapter 5 Stability Concepts
    • 5.1 Introduction to Stability
      • 5.1.1 Need for Stability
      • 5.1.2 Stability Definitions
    • 5.2 Routh Hurwitz (or) Algebraic Stability Criterion
      • 5.2.1 Hurwitz Statement
      • 5.2.2 Hurwitz Stability Criterion
      • 5.2.3 Routh Stability Criterion
      • 5.2.4 Relative Stability (Shifting the Origin)
      • 5.2.5 Disadvantages of Routh Stability Criterion
    • 5.3 Root Locus
      • Introduction
      • 5.3.1 Root Locus Detinition
      • 5.3.2 The Root Locus Concept
      • 5.3.3 Evans Conditions
      • 5.3.4 Rules for Construction of Root Locus
      • 5.3.5 Determination of Open Loop Gain for Specified Damping of Dominant Roots
      • 5.3.6 Step by Step Procedure to Draw Root Locus
    • 5.4 Nyquist Stability Criterion
      • 5.4.1 Basic Definitions
      • 5.4.2 Stability Analysis Using Nyquist Criterion
      • 5.4.3 Stability Analysis of Systems with Dead Time
      • 5.4.4 Relative stability Using the Nyquist Stability Criterion
    • Exercise
    • Short Questions and Answers
  • Chapter 6 Discrete Data Control Systems and State Space Methods
    • 6.1 Introduction
      • 6.1.1 Discrete and Continuous Signals
      • 6.1.2 Z-transforms
      • 6.1.3 Definition of Z-transform
      • 6.1.4 Region of Convergence and its Properties
      • 6.1.5 Properties of Z-transform
    • 6.2 Inverse Z-transform
    • 6.3 Basics of Discretization
      • 6.3.1 Reasons for Sampling
      • 6.3.2 Mathematical Model for Hold Operation
      • 6.3.3 Mathematical Model of Sample and Hold Operation
    • 6.4 Digital vs. Discrete Time Control Systems
      • 6.4.1 Advantages of Digital Control
      • 6.4.2 Sampling Theorem
    • 6.5 Open Loop and Closed Loop Sampled Data Control Systems
    • 6.6 State Space Analysis of Control Systems
      • 6.6.1 Advantages of State Space Formulation Against Transfer Function Approach
    • 6.7 State Space Representation
      • 6.7.1 Generic State Space Representation
      • 6.7.2 Basic Definitions
    • 6.8 State Space Representation of Physical Systems
      • 6.8.1 State Space Models from Transfer Functions
      • 6.8.2 Controller Canonical Form
      • 6.8.3 Observer Canonical Form
      • 6.8.4 Diagonal Form
    • 6.9 Transformation of State Space to Transfer Function
      • 6.9.1 Comments on State Space Realization from a Given Transfer Function
      • 6.9.2 Inverse of t he Matrix Using LU-Decomposition (Gauss-Seidel Method)
    • 6.10 Solution to State Equation
      • 6.10.1 Properties of Matrix Exponential
      • 6.10.2 Computation of Matrix Exponential
      • 6.10.3 Solution of State Equation with Input
    • 6.11 Eigenvalues, Eigenvectors and Jordan Canonical Form
      • 6.11.1 Left and Right Eigen Vector
    • 6.12 Similarity Transfoi mation
    • 6.13 Controllability and Observability
    • Exercise
    • Short Questions and Answers
  • Chapter 7 Control System Components
    • 7.1 Introduction to Control System Components
      • 7.1.1 Sensors
      • 7.1.2 Controllers
      • 7.1.3 Actuators
    • 7.2 Components of Control Systems
      • 7.2.1 Potentiometer
      • 7.2.2 Tacho Generator
      • 7.2.3 Operation of DC Tacho Generator
      • 7.2.4 Transfer Function of DC Tacho Generator
      • 7.2.5 Operation of AC Tacho generator
    • 7.3 Synchros
      • 7.3.1 Classification of Synchros
      • 7.3.2 Synchro Transmitter: (Synchro Generator)
      • 7.3.3 Synchro Control Transformer
      • 7.3.4 Synchro as Error Detector
    • 7.4 Actuators
      • 7.4.1 Stepper Motor
      • 7.4.2 Basic Configuration
      • 7.4.3 Modes of Operation of Stepper Motor
      • 7.4.4 Micro - Stepping Operation
      • 7.4.5 Dc Motors vs. Stepper Motors
    • 7.5 Servomotors
      • 7.5.1 Introduction
      • 7.5.2 DC Servo motors
      • 7.5.3 Armature Controlled DC Servomotor
      • 7.5.4 AC Servomotor
    • 7.6 Gyroscopes
      • 7.6.1 Basic Principle
      • 7.6.2 Application of Gyroscopes in Air Flights
    • 7.7 Controllers
      • 7.7.1 Need for Controller
      • 7.7.2 Digital Controllers
      • 7.7.3 Analog Controllers
      • 7.7.4 Integral Control
      • 7.7.5 Derivative Controllers (D)
      • 7.7.6 Composite Mode Controllers
      • 7.7.7 PID Controller
    • 7.8 Compensators
      • 7.8.1 Advantages and Disadvantages of Compensators
      • 7.8.2 Types of Compensation
      • 7.8.3 Types of Compensators
    • 7.9 Frequency and Time Domain Specification
    • 7.10 Analysis of Cascade Compensators
      • 7.10.1 Frequency Domain Interpretations
      • 7.10.2 Frequency at Which Maximum Phase Lead Occurs
      • 7.10.3 Realization of Lead Compensator
    • 7.11 Design Using Root Locus
    • 7.12 Lag Compensator
    • 7.13 Lag Lead Compensator
    • 7.14 Modulator and Demodulator (Signal Conditioning)
    • Exercise
    • Short Questions and Answers

Dr. S. Seshadhri is working with the industrial software systems division of the Indian Corporate Research Centre, ABB Global Industries and Services, Bangalore.He obtained his Ph.D. from National Institute of Technology, Trichy and masters from Anna University Chennai. Dr. B. Subathra is Associate Professor in Kalasalingam University, Srivilliputhur. She obtained her Ph.D. from National Institute of Technology, Trichy. She has more than 20 years of teaching experience. Her areas of interest are Process Control, Soft Computing and Intelligent Control.

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Description

This fundamental textbook on control engineering is designed to bridge the gap and strike a balance between theory and practice. The book has its emphasis on conceptual clarity, ease-of- understanding and lucid presentation. A significant highlight of the book is Mat Lab examples and simulations, and solved problems from university examinations and competitive examinations.

Table of contents
  • Cover
  • Halftitle Page
  • Title Page
  • Copyright Page
  • Contents
  • Foreword
  • Preface
  • Acknowledgements
  • Chapter 1 Introduction to Control Systems
    • Introduction
    • 1.1 Basic Definitions and Terminologies
    • 1.2 Basic Elements of Control System
      • 1.2.1 Generic Control Loop Terminologies
    • 1.3 Open Loop and Closed Loop Systems
      • 1.3.1 Electronic Voltage Regulator—As a Closed Loop System
      • 1.3.2 Advantages and Disadvantages of Open Loop and Closed Loop Systems
      • 1.3.3 Comparison of Closed Loop and Open Loop Systems
    • 1.4 Transfer Functions
      • 1.4.1 Properties of Transfer Functions
      • 1.4.2 Representation of Transfer Functions
      • 1.4.3 Relative Degree of Transfer Functions and its Implications on Performance
      • 1.4.4 Classification of Transfer Functions Based on the Relative Degree
    • 1.5 Introduction to Modeling
      • 1.5.1 Types of Model
      • 1.5.2 Translational Mechanical Systems
      • 1.5.3 D’Alembertls Principle
      • 1.5.4 Procedure for Obtaining Transfer Function for Dynamical Systems
      • 1.5.5 Rotational Mechanical Systems
      • 1.5.6 Modeling of Electrical Systems
      • 1.5.7 Modeling of Electromechanical Systems
    • 1.6 Electrical Analogous of Mechanical Translation System
      • 1.6.1 Force-Voltage Analogy
      • 1.6.2 F-V Analogous Network
      • 1.6.3 F-V Analogous System
      • 1.6.4 Force-current Analogy
      • 1.6.5 Torque Current Analogous Circuit
    • Exercise
    • Short Questions and Answers
  • Chapter 2 Block Diagram Reduction and Signal Flow Graph
    • 2.1 Block Diagram Reduction
      • Introduction
      • Diagram Blocks
      • 2.1.1 Block Diagram of Physical Systems
        • Block Diagram Reduction
      • 2.1.2 Rules of Block Diagram Algebra
      • 2.1.3 Advantages and Disadvantages
        • Advantages
        • Disadvantages
    • 2.2 Signal flow graph
      • Introduction
      • 2.2.1 Definition of Signal Flow Graph
        • Signal Flow Graph Terminology
      • 2.2.2 Properties of Signal Flow Graph
      • 2.2.3 Signal Flow Graph Algebra
        • Procedure
    • 2.3 Block Diagram to Signal Flow Graph Conversion
      • Exercise
      • Short Questions and Answers
  • Chapter 3 Time Response Analysis
    • 3.1 Introduction to Timo Response Analysis
      • System Response
      • 3.1.1 Natural or Unforced Response of the System
      • 3.1.2 Test Signals and Need for Test Signals
        • Test Signals
      • 3.1.3 Need for Test Signals
      • 3.1.4 Transfer Function of Closed Loop System
      • 3.1.5 Poles & Zeros of Transfer Function
        • Note
      • 3.1.6 Order and Type of the System
        • Order of the System
      • 3.1.7 Type of the System
    • 3.2 First Order System Response
      • 3.2.1 Step Response Analysis of First Order System
      • 3.2.2 First Order System Performance Specifications
      • 3.2.3 Ramp Response Analysis of First Order System
      • 3.2.4 Impulse Response Analysis of First Order System
    • 3.3 Second Order System Response
      • 3.3.1 Generic Second Order Transfer Function
      • 3.3.2 Performance of Second Order System
      • 3.3.3 Damping Ratio and System Response
      • 3.3.4 Response of Second Order System for Step Input
      • 3.3.5 Response of Second Order System for Impulse Input
    • 3.4 Transient Response Specifications
    • 3.5 Response with P, PI and PID Controllers
      • 3.5.1 Proportional Mode
      • 3.5.2 Proportional Derivative Mode
      • 3.5.3 Derivative Mode
      • 3.5.4 Proportional Integral Mode
      • 3.5.5 Proportional Integral Derivative Mode
    • 3.6 Steady State Error
      • 3.6.1 Sources of Steady State Errors
      • 3.6.2 Evaluation of Steady State Error for a Given Input
    • 3.7 Static Error Constants
    • 3.8 Generalized Error Coefficient
    • 3.9 Computational Issues and Dynamic Error Coefficients
    • 3.10 Effects of Feedback
      • Introduction
      • The Feedback Principle
      • 3.10.1 Effect of Feedback on Noise
      • 3.10.2 Effect of Feedback on Stability
    • 3.11 Response of Higher Order Systems Using Time Response Analysis
    • Exercise
    • Short Questions and Answers
  • Chapter 4 Frequency Response Analysis
    • 4.1 Introduction to Frequency Response
      • 4.1.1 Complex Frequency Approach for Frequency Analysis
      • 4.1.2 Advantages and Disadvantages of Frequency Response Techniques
      • 4.1.3 Frequency Response Characteristics
      • 4.1.4 Frequency Response Specifications of Second Order Systems
      • 4.1.5 Correlation Between Second Order Frequency and Time Response
    • 4.2 Determination of Frequency Response
      • 4.2.1 Analytical Determination of Frequency Response
      • 4.2.2 Graphical Dt termination of Frequency Response
      • 4.2.3 Bode Diagram Approach for Frequency Response Estimation and Stability Determination
      • 4.2.4 Basic Terminologies in Bode Plot Plotting Bode Plots
      • 4.2.5 Determination of Gain Margin and Phase Margin from Bode Plot
        • Dead Time (or) Transportation Lag Block
      • 4.2.6 Frequency Response of Dead Time Block
    • 4.3 Polar Plots
      • 4.3.1 Procedure Determination of Gain Margin and Phase Margin of System from Polar Plot
    • 4.4 Nichols Chart
      • 4.4.1 Closed Loop Frequency Response From Nichols Chart
    • 4.5 M and N Circles (Relate Open Loop and Closed Loop Response)
    • 4.6 Obtaining the Minimum Phase Transfer Function from the Bode Magnitude Plot
    • 4.7 Non minimum Phase and All Pass Systems [jntu - 2007]
    • Exercise
    • Short Questions and Answers
  • Chapter 5 Stability Concepts
    • 5.1 Introduction to Stability
      • 5.1.1 Need for Stability
      • 5.1.2 Stability Definitions
    • 5.2 Routh Hurwitz (or) Algebraic Stability Criterion
      • 5.2.1 Hurwitz Statement
      • 5.2.2 Hurwitz Stability Criterion
      • 5.2.3 Routh Stability Criterion
      • 5.2.4 Relative Stability (Shifting the Origin)
      • 5.2.5 Disadvantages of Routh Stability Criterion
    • 5.3 Root Locus
      • Introduction
      • 5.3.1 Root Locus Detinition
      • 5.3.2 The Root Locus Concept
      • 5.3.3 Evans Conditions
      • 5.3.4 Rules for Construction of Root Locus
      • 5.3.5 Determination of Open Loop Gain for Specified Damping of Dominant Roots
      • 5.3.6 Step by Step Procedure to Draw Root Locus
    • 5.4 Nyquist Stability Criterion
      • 5.4.1 Basic Definitions
      • 5.4.2 Stability Analysis Using Nyquist Criterion
      • 5.4.3 Stability Analysis of Systems with Dead Time
      • 5.4.4 Relative stability Using the Nyquist Stability Criterion
    • Exercise
    • Short Questions and Answers
  • Chapter 6 Discrete Data Control Systems and State Space Methods
    • 6.1 Introduction
      • 6.1.1 Discrete and Continuous Signals
      • 6.1.2 Z-transforms
      • 6.1.3 Definition of Z-transform
      • 6.1.4 Region of Convergence and its Properties
      • 6.1.5 Properties of Z-transform
    • 6.2 Inverse Z-transform
    • 6.3 Basics of Discretization
      • 6.3.1 Reasons for Sampling
      • 6.3.2 Mathematical Model for Hold Operation
      • 6.3.3 Mathematical Model of Sample and Hold Operation
    • 6.4 Digital vs. Discrete Time Control Systems
      • 6.4.1 Advantages of Digital Control
      • 6.4.2 Sampling Theorem
    • 6.5 Open Loop and Closed Loop Sampled Data Control Systems
    • 6.6 State Space Analysis of Control Systems
      • 6.6.1 Advantages of State Space Formulation Against Transfer Function Approach
    • 6.7 State Space Representation
      • 6.7.1 Generic State Space Representation
      • 6.7.2 Basic Definitions
    • 6.8 State Space Representation of Physical Systems
      • 6.8.1 State Space Models from Transfer Functions
      • 6.8.2 Controller Canonical Form
      • 6.8.3 Observer Canonical Form
      • 6.8.4 Diagonal Form
    • 6.9 Transformation of State Space to Transfer Function
      • 6.9.1 Comments on State Space Realization from a Given Transfer Function
      • 6.9.2 Inverse of t he Matrix Using LU-Decomposition (Gauss-Seidel Method)
    • 6.10 Solution to State Equation
      • 6.10.1 Properties of Matrix Exponential
      • 6.10.2 Computation of Matrix Exponential
      • 6.10.3 Solution of State Equation with Input
    • 6.11 Eigenvalues, Eigenvectors and Jordan Canonical Form
      • 6.11.1 Left and Right Eigen Vector
    • 6.12 Similarity Transfoi mation
    • 6.13 Controllability and Observability
    • Exercise
    • Short Questions and Answers
  • Chapter 7 Control System Components
    • 7.1 Introduction to Control System Components
      • 7.1.1 Sensors
      • 7.1.2 Controllers
      • 7.1.3 Actuators
    • 7.2 Components of Control Systems
      • 7.2.1 Potentiometer
      • 7.2.2 Tacho Generator
      • 7.2.3 Operation of DC Tacho Generator
      • 7.2.4 Transfer Function of DC Tacho Generator
      • 7.2.5 Operation of AC Tacho generator
    • 7.3 Synchros
      • 7.3.1 Classification of Synchros
      • 7.3.2 Synchro Transmitter: (Synchro Generator)
      • 7.3.3 Synchro Control Transformer
      • 7.3.4 Synchro as Error Detector
    • 7.4 Actuators
      • 7.4.1 Stepper Motor
      • 7.4.2 Basic Configuration
      • 7.4.3 Modes of Operation of Stepper Motor
      • 7.4.4 Micro - Stepping Operation
      • 7.4.5 Dc Motors vs. Stepper Motors
    • 7.5 Servomotors
      • 7.5.1 Introduction
      • 7.5.2 DC Servo motors
      • 7.5.3 Armature Controlled DC Servomotor
      • 7.5.4 AC Servomotor
    • 7.6 Gyroscopes
      • 7.6.1 Basic Principle
      • 7.6.2 Application of Gyroscopes in Air Flights
    • 7.7 Controllers
      • 7.7.1 Need for Controller
      • 7.7.2 Digital Controllers
      • 7.7.3 Analog Controllers
      • 7.7.4 Integral Control
      • 7.7.5 Derivative Controllers (D)
      • 7.7.6 Composite Mode Controllers
      • 7.7.7 PID Controller
    • 7.8 Compensators
      • 7.8.1 Advantages and Disadvantages of Compensators
      • 7.8.2 Types of Compensation
      • 7.8.3 Types of Compensators
    • 7.9 Frequency and Time Domain Specification
    • 7.10 Analysis of Cascade Compensators
      • 7.10.1 Frequency Domain Interpretations
      • 7.10.2 Frequency at Which Maximum Phase Lead Occurs
      • 7.10.3 Realization of Lead Compensator
    • 7.11 Design Using Root Locus
    • 7.12 Lag Compensator
    • 7.13 Lag Lead Compensator
    • 7.14 Modulator and Demodulator (Signal Conditioning)
    • Exercise
    • Short Questions and Answers
Biographical note

Dr. S. Seshadhri is working with the industrial software systems division of the Indian Corporate Research Centre, ABB Global Industries and Services, Bangalore.He obtained his Ph.D. from National Institute of Technology, Trichy and masters from Anna University Chennai. Dr. B. Subathra is Associate Professor in Kalasalingam University, Srivilliputhur. She obtained her Ph.D. from National Institute of Technology, Trichy. She has more than 20 years of teaching experience. Her areas of interest are Process Control, Soft Computing and Intelligent Control.

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