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Control Systems Engineering

Book Description

Control Systems Engineering caters to the requirements of an interdisciplinary course on Control Systems at the under- graduate level. Featuring a balanced coverage of time response and frequency response analyses, the book provides an in-depth review of key topics such as components, modelling techniques and reduction techniques, well-augmented by clear illustrations.

Table of Contents

  1. Cover
  2. Title Page
  3. Contents
  4. Preface
  5. About the Author
  6. 1 Control System Modeling
    1. 1.1 Introduction
      1. 1.2 Classification of Control System
      2. 1.2.1 Open-Loop Control System
      3. 1.2.2 Closed-Loop Control System
    2. 1.3 Comparison of Open-Loop and Closed-Loop Control Systems
    3. 1.4 Differential Equations and Transfer Functions
      1. 1.4.1 Transfer Function Representation
      2. 1.4.2 Features and Advantages of Transfer Function Representation
      3. 1.4.3 Disadvantages of Transfer Function Representation
      4. 1.4.4 Transfer Function of an Open-Loop System
      5. 1.4.5 Transfer Function of a Closed-Loop System
      6. 1.4.6 Comparison of Positive Feedback and Negative Feedback Systems
    4. 1.5 Mathematical Modeling
      1. 1.5.1 Mathematical Equations for Problem Solving
    5. 1.6 Modeling of Electrical Systems
    6. 1.7 Modeling of Mechanical Systems
      1. 1.7.1 Translational Mechanical System
      2. 1.7.2 A Simple Translational Mechanical System
      3. 1.7.3 Rotational Mechanical System
      4. 1.7.4 A Simple Rotational Mechanical System
    7. 1.8 Introduction to Analogous System
      1. 1.8.1 Advantages of Electrical Analogous System
      2. 1.8.2 Force–Voltage Analogy
      3. 1.8.3 Force–Current Analogy
      4. 1.8.4 Torque–Voltage Analogy
      5. 1.8.5 Torque–Current Analogy
    8. Review Questions
  7. 2 Physical Systems and Components
    1. 2.1 Introduction
    2. 2.2 Electromechanical System
    3. 2.3 Hydraulic System
      1. 2.3.1 Advantages of Hydraulic System
      2. 2.3.2 Disadvantages of Hydraulic System
      3. 2.3.3 Applications of Hydraulic System
      4. 2.3.4 Devices Used in Hydraulic System
    4. 2.4 Pneumatic Systems
      1. 2.4.1 Gas Flow Resistance and Pneumatic Capacitance
      2. 2.4.2 Advantages of Pneumatic System
      3. 2.4.3 Disadvantages of Pneumatic System
      4. 2.4.4 Applications of Pneumatic System
      5. 2.4.5 Devices Used in Pneumatic System
      6. 2.4.6 Comparison between Hydraulic and Pneumatic Systems
    5. 2.5 Thermal Systems
      1. 2.5.1 Thermal Resistance and Thermal Capacitance
    6. 2.6 Liquid-Level System
      1. 2.6.1 Elements of Liquid-Level System
    7. 2.7 Introduction to Control System Components
    8. 2.8 Controllers
      1. 2.8.1 Controller Output as a Percentage Value
      2. 2.8.2 Measured Value as a Percentage Value
      3. 2.8.3 Set Point as a Percentage Value
      4. 2.8.4 Error as a Percentage Value
      5. 2.8.5 Types of Controllers
    9. 2.9 Electronic Controllers
      1. 2.9.1 ON–OFF Controller
      2. 2.9.2 Proportional Controller
      3. 2.9.3 Integral Controller
      4. 2.9.4 Derivative Controller
      5. 2.9.5 Proportional Integral Controller
      6. 2.9.6 Proportional Derivative Controller
      7. 2.9.7 Proportional Integral Derivative Controller
    10. 2.10 Potentiometers
      1. 2.10.1 Characteristics of Potentiometers
      2. 2.10.2 Power-Handling Capacity
      3. 2.10.3 Applications of Potentiometer
    11. 2.11 Synchros
      1. 2.11.1 Synchro Transmitter
      2. 2.11.2 Synchro Control Transformer
      3. 2.11.3 Synchro Error Detector
    12. 2.12 Servomotors
      1. 2.12.1 Classification of Servomotor
      2. 2.12.2 Features of Servomotor
      3. 2.12.3 DC Servomotor
      4. 2.12.4 AC Servomotor
      5. 2.12.5 Comparison between AC Servomotor and DC Servomotor
    13. 2.13 Tachogenerators
      1. 2.13.1 DC Tachogenerator
      2. 2.13.2 AC Tachogenerator
    14. 2.14 Stepper Motor
      1. 2.14.1 Permanent Magnet Stepper Motor
      2. 2.14.2 Variable Reluctance Stepper Motor
      3. 2.14.3 Hybrid Stepper Motor
      4. 2.14.4 Operation of Stepper Motor
      5. 2.14.5 Advantages of Stepper Motor
      6. 2.14.6 Applications of Stepper Motor
    15. 2.15 Gear Trains
      1. 2.15.1 Single Gear Train
      2. 2.15.2 Multiple Gear Trains
    16. Review Questions
  8. 3 Block Diagram Reduction Techniques
    1. 3.1 Introduction to Block Diagram
    2. 3.2 Open-Loop and Closed-Loop Systems Using Block Diagram
      1. 3.2.1 Advantages of Block Diagram Representation
      2. 3.2.2 Disadvantages of Block Diagram Representation
    3. 3.3 Block Diagram Representation of Electrical System
    4. 3.4 Block Diagram Reduction
      1. 3.4.1 Need for Block Diagram Reduction
      2. 3.4.2 Block Diagram Algebra
      3. 3.4.3 Rules for Block Diagram Reduction
      4. 3.4.4 Block Diagram Reduction for Complex Systems
    5. Review Questions
  9. 4 Signal Flow Graph
    1. 4.1 Introduction
      1. 4.1.1 Signal Flow Graph Terminologies
      2. 4.1.2 Properties of SFG
      3. 4.1.3 SFG Algebra
      4. 4.1.4 Mason’s Gain Formula for SFG
      5. 4.1.5 Signal Flow Graph From Differential Equation
      6. 4.1.6 Comparison between SFG and Block Diagram
    2. Review Questions
  10. 5 Time Response Analysis
    1. 5.1 Introduction
    2. 5.2 Time Response of the Control System
      1. 5.2.1 Transient Response
      2. 5.2.2 Steady-State Response
    3. 5.3 Standard Test Signals
      1. 5.3.1 Impulse Signal
      2. 5.3.2 Step Signal
      3. 5.3.3 Ramp Signal
      4. 5.3.4 Parabolic Signal
    4. 5.4 Poles, Zeros and System Response
      1. 5.4.1 Poles and Zeros of a Transfer Function
      2. 5.4.2 Stability of the System
    5. 5.5 Type and Order of the System
      1. 5.5.1 Type of the System
      2. 5.5.2 ORDER of the System
    6. 5.6 First-Order System
      1. 5.6.1 Performance Parameters of First-Order System
      2. 5.6.2 Time Response of a First-Order System
    7. 5.7 Second-Order System
      1. 5.7.1 Classification of Second-Order System
      2. 5.7.2 Performance Parameters of Second-Order System
      3. 5.7.3 Time Response of the Second-Order System
      4. 5.7.4 Time-Domain Specifications for an Underdamped Second-Order System
    8. 5.8 Steady-State Error
      1. 5.8.1 Characteristic of Steady-State Error
      2. 5.8.2 Determination of Steady-State Error
      3. 5.8.3 Steady-State Error in Terms of G(s)
      4. 5.8.4 Steady-State Error in Terms of T(s)
      5. 5.8.5 Static Error Constants and System Type
      6. 5.8.6 Generalized or Dynamic Error Coefficients
    9. 5.9 Effect of Adding Poles and Zeros in the Second-Order System
      1. 5.9.1 Effect of Adding Poles
      2. 5.9.2 Effect of Adding Zeros
    10. 5.10 Response with P, PI and PID Controllers
      1. 5.10.1 Proportional Derivative Control
      2. 5.10.2 Proportional Integral Control
      3. 5.10.3 Proportional Plus Integral Plus Derivative Control (PID Control)
    11. 5.11 Performance Indices
    12. Review Questions
  11. 6 Stability and Routh–Hurwitz Criterion
    1. 6.1 Introduction
    2. 6.2 Concept of Stability
    3. 6.3 Stability of Linear Time-Invariant System
      1. 6.3.1 Stability Based on Natural Response of the System, c(t)natural
      2. 6.3.2 Stability Based on the Total Response of the System, c(t)6.3
    4. 6.4 Mathematical Condition for the Stability of the System
    5. 6.5 Transfer Function of the System, G(s)
      1. 6.5.1 Effects of Location of Poles on Stability
    6. 6.6 Zero-Input Stability or Asymptotic Stability
      1. 6.6.1 Importance of Asymptotic Stability
    7. 6.7 Relative Stability
    8. 6.8 Methods for Determining the Stability of the System
    9. 6.9 Routh–Hurwitz Criterion
      1. 6.9.1 Minimum-Phase System
      2. 6.9.2 Non-Minimum-Phase System
    10. 6.10 Hurwitz Criterion
      1. 6.10.1 Hurwitz Matrix Formation
      2. 6.10.2 Disadvantages of Hurwitz Method
    11. 6.11 Routh’s Stability Criterion
      1. 6.11.1 Necessary Condition for the Stability of the System
      2. 6.11.2 Special Cases of Routh’s Criterion
      3. 6.11.3 Applications of Routh’s Criterion
      4. 6.11.4 Advantages of Routh’s Criterion
      5. 6.11.5 Limitations of Routh’s Criterion
    12. Review Questions
  12. 7 Root Locus Technique
    1. 7.1 Introduction
    2. 7.2 Advantages of Root Locus Technique
    3. 7.3 Categories of Root Locus
      1. 7.3.1 Variation of Loop Gain with the Root Locus
    4. 7.4 Basic Properties of Root Loci
      1. 7.4.1 Conditions Required for Constructing the Root Loci
      2. 7.4.2 Usage of the Conditions
      3. 7.4.3 Analytical Expression of the Conditions
      4. 7.4.4 Determination of Variable Parameter K
      5. 7.4.5 Minimum and Non-Minimum Phase Systems
    5. 7.5 Manual Construction of Root Loci
      1. 7.5.1 Properties / Guidelines for Constructing the Root Loci
      2. 7.5.2 Flow Chart for Constructing the Root Locus for a System
    6. 7.6 Root Loci for different Pole-Zero Configurations
    7. 7.7 Effect of Adding Poles and Zeros in the System
      1. 7.7.1 Addition of Poles to the Loop Transfer Function, G(s)H(s)
      2. 7.7.2 Effect of Addition of Poles
      3. 7.7.3 Addition of Zero to the Loop Transfer Function
      4. 7.7.4 Effect of Addition of Zeros
    8. 7.8 Time Response from Root Locus
    9. 7.9 Gain Margin and Phase Margin of the System
      1. 7.9.1 Gain Margin of the System
      2. 7.9.2 Phase Margin of the System
    10. 7.10 Root Locus for K < 0 Inverse Root Locus or Complementary Root Loci
      1. 7.10.1 Steps in Constructing the Inverse Root Loci Manually
    11. 7.11 Pole-Zero Cancellation Rules
    12. 7.12 Root Contours (Multi-Variable System)
    13. Review Questions
  13. 8 Frequency Response Analysis
    1. 8.1 Introduction
      1. 8.1.1 Advantages of Frequency Response Analysis
      2. 8.1.2 Disadvantages of Frequency Response Analysis
    2. 8.2 Importance of Sinusoidal Waves for Frequency Response Analysis
    3. 8.3 Basics of Frequency Response Analysis
    4. 8.4 Frequency Response Analysis of Open-Loop and Closed-Loop Systems
      1. 8.4.1 Open-Loop System
      2. 8.4.2 Closed-Loop System
      3. 8.4.3 Closed-Loop System with Poles and Zeros
    5. 8.5 Frequency Response Representation
      1. 8.5.1 Determination of Frequency Response
    6. 8.6 Frequency Domain Specifications
    7. 8.7 Frequency and Time Domain Interrelations
      1. 8.7.1 Frequency Domain Specifications
    8. 8.8 Effect of Addition of a Pole to the Open-Loop Transfer ­Function of the System
    9. 8.9 Effect of Addition of a Zero to the Open-Loop Transfer ­Function of the System
    10. 8.10 Graphical Representation of Frequency Response
    11. 8.11 Introduction to Bode Plot
      1. 8.11.1 Reasons for Using Logarithmic Scale
      2. 8.11.2 Advantages of Bode Plot
      3. 8.11.3 Disadvantages of Bode Plot
    12. 8.12 Determination of Frequency Domain Specifications from Bode Plot
    13. 8.13 Stability of the System
      1. 8.13.1 Based on Crossover Frequencies
      2. 8.13.2 Based on Gain Margin and Phase Margin
    14. 8.14 Construction of Bode Plot
      1. 8.14.1 Effect of Damping Ratio x
    15. 8.15 Constructing the Bode Plot for a Given System
      1. 8.15.1 Construction of Magnitude Plot
      2. 8.15.2 Construction of Phase Plot
    16. 8.16 Flow Chart for Plotting Bode Plot
    17. 8.17 Procedure for Determining the Gain K from the ­Desired Frequency Domain Specifications
    18. 8.18 Maximum Value of Gain
    19. 8.19 Procedure for Determining Transfer Function from Bode Plot
    20. 8.20 Bode Plot for Minimum and Non-Minimum Phase Systems
    21. Review Questions
  14. 9 Polar and Nyquist Plots
    1. 9.1 Introduction to Polar Plot
    2. 9.2 Starting and Ending of Polar Plot
    3. 9.3 Construction of Polar Plot
    4. 9.4 Determination of Frequency Domain Specification from Polar Plot
      1. 9.4.1 Gain Crossover Frequency w gc
      2. 9.4.2 Phase Crossover Frequency w pc
      3. 9.4.3 Gain Margin gm9.11
      4. 9.4.4 Phase Margin pm
    5. 9.5 Procedure for Constructing Polar Plot
    6. 9.6 Typical Sketches of Polar Plot on an Ordinary Graph and Polar Graph
    7. 9.7 Stability Analysis using Polar Plot
      1. 9.7.1 Based on Crossover Frequencies
      2. 9.7.2 Based on Gain Margin and Phase Margin
      3. 9.7.3 Based on the Location of Phase Crossover Point
    8. 9.8 Determining the Gain K from the Desired Frequency Domain Specifications
      1. 9.8.1 When the Desired Gain Margin of the System is Specified
      2. 9.8.2 When the Desired Phase Margin of the System is Specified
    9. 9.9 Introduction to Nyquist Stability Criterion
    10. 9.10 Advantages of Nyquist Plot
    11. 9.11 Basic Requirements for Nyquist Stability Criterion
    12. 9.12 Encircled and Enclosed
      1. 9.12.1 Encircled
      2. 9.12.2 Enclosed
    13. 9.13 Number of Encirclements or Enclosures
    14. 9.14 Mapping of s-Plane into Characteristic Equation Plane
    15. 9.15 Principle of Argument
    16. 9.16 Nyquist Stability Criterion
    17. 9.17 Nyquist Path
    18. 9.18 Relation Between G(s) H(s)-Plane and F(s)-Plane
    19. 9.19 Nyquist Stability Criterion Based on the Encirclements of −1+ j 0
    20. 9.20 Stability Analysis of the System
    21. 9.21 Procedure for Determining the Number of Encirclements
      1. 9.21.1 Flow chart for Determining the Number of Encirclements Made by the Contour in G(s)H(s)-Plane
    22. 9.22 General Procedures for Determining the Stability of the System Based on Nyquist Stability Criterion
      1. 9.22.1 Flow chart for Determining the Stability of the System Based on Nyquist Stability Criterion
    23. Review Questions
  15. 10 Constant M- and N-Circles and Nichols Chart
    1. 10.1 Introduction
    2. 10.2 Closed-Loop Response from Open-Loop Response
    3. 10.3 Constant M-Circles
      1. 10.3.1 Applications of Constant M-Circles
      2. 10.3.2 Resonant Peak Mr and Resonant Frequency wr from Constant M-Circles
      3. 10.3.3 Variation of Gain K with Mr and wr 10.6
      4. 10.3.4 Bandwidth of the System
      5. 10.3.5 Stability of the System
      6. 10.3.6 Determination of Gain K Corresponding to the Desired Resonant Peak (Mr)desired
      7. 10.3.7 Magnitude Plot of the System from Constant M-Circles
    4. 10.4 Constant N-Circles
      1. 10.4.1 Phase Plot of the System from Constant N-Circles
    5. 10.5 Nichols Chart
      1. 10.5.1 Reason for the Usage of Nichols Chart
      2. 10.5.2 Advantages of Nichols Chart
      3. 10.5.3 Transformation of Constant M- and N-Circles into Nichols Chart
      4. 10.5.4 Determination of Frequency Domain Specifications from Nichols Chart
      5. 10.5.5 Determination of Gain K for a Desired Frequency Domain Specifications
    6. Review Questions
  16. 11 Compensators
    1. 11.1 Introduction
    2. 11.2 Compensators
      1. 11.2.1 Series or Cascade Compensation
      2. 11.2.2 Feedback or Parallel Compensation
      3. 11.2.3 Load or Series-Parallel Compensation
      4. 11.2.4 State Feedback Compensation
      5. 11.2.5 Forward Compensation with Series Compensation
      6. 11.2.6 Feed-forward Compensation
      7. 11.2.7 Effects of Addition of Poles
      8. 11.2.8 Effects of Addition of Zeros
      9. 11.2.9 Choice of Compensators
    3. 11.3 Lag Compensator
      1. 11.3.1 Determination of Maximum Phase Angle fm
      2. 11.3.2 Electrical Representation of the Lag Compensator
      3. 11.3.3 Effects of Lag Compensator
      4. 11.3.4 Design of Lag Compensator
      5. 11.3.5 Design of Lag Compensator Using Bode Plot
      6. 11.3.6 Design of Lag Compensator Using Root Locus Technique
    4. 11.4 Lead Compensator
      1. 11.4.1 Determination of Maximum Phase Angle fm
      2. 11.4.2 Electrical Representation of the Lead Compensator
      3. 11.4.3 Effects of Lead Compensator
      4. 11.4.4 Limitations of Lead Compensator
      5. 11.4.5 Design of Lead Compensator
      6. 11.4.6 Design of Lead Compensator Using Bode Plot
      7. 11.4.7 Design of Lead Compensator Using Root Locus Technique
    5. 11.5 Lag–Lead Compensator
      1. 11.5.1 Electrical Representation of the Lag–Lead Compensator
      2. 11.5.2 Effects of Lag–Lead Compensator
      3. 11.5.3 Design of Lag–Lead Compensator
      4. 11.5.4 Design of Lag–Lead Compensator Using Bode Plot
      5. 11.5.5 Design of Lag–Lead Compensator Using Root Locus Technique
    6. Review Questions
  17. 12 Physiological Control Systems
    1. 12.1 Introduction
    2. 12.2 Physiological Control Systems
    3. 12.3 Properties of Physiological Control Systems
      1. 12.3.1 Target of the Homeostasis
      2. 12.3.2 Imbalance in the Homeostasis
      3. 12.3.3 Homeostasis Control Mechanisms
    4. 12.4 Block Diagram of the Physiological Control System
      1. 12.4.1 Types of Control Mechanism
    5. 12.5 Differences Between Engineering and Physiological Control Systems
    6. 12.6 System Elements
      1. 12.6.1 Resistance
      2. 12.6.2 Capacitance
      3. 12.6.3 Inductance
    7. 12.7 Properties Related to Elements
    8. 12.8 Linear Models of Physiological Systems: Two ­Examples
      1. 12.8.1 Lung Mechanism
      2. 12.8.2 Skeletal Muscle
    9. 12.9 Simulation—Matlab and Simulink Examples
    10. Review Questions
  18. 13 State-Variable Analysis
    1. 13.1 Introduction
      1. 13.1.1 Advantages of State-Variable Analysis
    2. 13.2 State-Space Representation of Continuous-Time LTI Systems
    3. 13.3 Block Diagram and SFG Representation of a Continuous State-Space Model
    4. 13.4 State-Space Representation
    5. 13.5 State-Space Representation of Differential Equations in Physical Variable Form
      1. 13.5.1 Advantages of Physical Variable Representation
      2. 13.5.2 Disadvantages of Physical Variable Representation
    6. 13.6 State-Space Model Representation for Electric Circuits
    7. 13.7 State-Space Model Representation for Mechanical System
      1. 13.7.1 State-Space Model Representation of Translational / Rotational Mechanical System
    8. 13.8 State-Space Model Representation of Electromechanical ­System
      1. 13.8.1 Armature-Controlled DC Motor
      2. 13.8.2 Field-Controlled DC Motor
    9. 13.9 State-Space Representation of a System Governed by Differential Equations
    10. 13.10 State-Space Representation of Transfer Function in Phase Variable Forms
      1. 13.10.1 Method 113.22
      2. 13.10.2 Method 213.23
      3. 13.10.3 Method 313.25
      4. 13.10.4 Advantages of Phase-Variable Representation
      5. 13.10.5 Disadvantages of the Phase-Variable Representation
    11. 13.11 State-Space Representation of Transfer Function in Canonical Forms
      1. 13.11.1 Controllable Canonical Form
      2. 13.11.2 Observable Canonical Form
      3. 13.11.3 Diagonal Canonical Form
      4. 13.11.4 Jordan Canonical Form
    12. 13.12 Transfer Function from State-Space Model
    13. 13.13 Solution of State Equation for Continuous Time Systems
      1. 13.13.1 Solution of Homogenous-Type State Equation
      2. 13.13.2 Solution of Non-Homogenous Type State Equation
      3. 13.13.3 State Transition Matrix
      4. 13.13.4 Properties of State Transition Matrix
    14. 13.14 Controllability and Observability
      1. 13.14.1 Criteria for Controllability
      2. 13.14.2 Criteria for Observability
    15. 13.15 State-Space Representation of Discrete-Time LTI Systems
      1. 13.15.1 Block Diagram and SFG of Discrete State-Space Model
    16. 13.16 Solutions of State Equations for Discrete-Time LTI Systems
      1. 13.16.1 System Function H(z)
    17. 13.17 Representation of Discrete LTI System
    18. 13.18 Sampling
      1. 13.18.1 Sampling Theorem
      2. 13.18.2 High Speed Sample-and-Hold Circuit
    19. Review Questions
  19. 14 MATLAB Programs
    1. 14.1 Introduction
    2. 14.2 MATLAB in Control Systems
      1. 14.2.1 Laplace Transform
      2. 14.2.2 Inverse Laplace Transform
      3. 14.2.3 Partial Fraction Expansion
      4. 14.2.4 Transfer Function Representation
      5. 14.2.5 Zeros and Poles of a Transfer Function
      6. 14.2.6 Pole-Zero Map of a Transfer Function
      7. 14.2.7 State-Space Representation of a Dynamic System
      8. 14.2.8 Phase Variable Canonical Form
      9. 14.2.9 Transfer Function to State-Space Conversion
      10. 14.2.10 State-Space to Transfer Function Conversion
      11. 14.2.11 Series/Cascade, Parallel and Feedback Connections
      12. 14.2.12 Time Response of Control System
      13. 14.2.13 Performance Indices from the Response of a System
      14. 14.2.14 Steady State Error from the Transfer Function of a System
      15. 14.2.15 Routh–Hurwitz Criterion
      16. 14.2.16 Root Locus Technique
      17. 14.2.17 Bode Plot
      18. 14.2.18 Nyquist Plot
      19. 14.2.19 Design of Compensators Using Matlab