book

Control Systems Engineering

Name: Control Systems Engineering
Author: S. Salivahanan
ISBN: 9789332558267

by S. Salivahanan

April 2015

Intermediate to advanced

1056 pages

24h 40m

English

Pearson Education India

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Cover
Title Page
Contents
Preface
About the Author
1 Control System Modeling
1.1 Introduction1.2 Classification of Control System1.2.1 Open-Loop Control System1.2.2 Closed-Loop Control System1.3 Comparison of Open-Loop and Closed-Loop Control Systems1.4 Differential Equations and Transfer Functions1.4.1 Transfer Function Representation1.4.2 Features and Advantages of Transfer Function Representation1.4.3 Disadvantages of Transfer Function Representation1.4.4 Transfer Function of an Open-Loop System1.4.5 Transfer Function of a Closed-Loop System1.4.6 Comparison of Positive Feedback and Negative Feedback Systems1.5 Mathematical Modeling1.5.1 Mathematical Equations for Problem Solving1.6 Modeling of Electrical Systems1.7 Modeling of Mechanical Systems1.7.1 Translational Mechanical System1.7.2 A Simple Translational Mechanical System1.7.3 Rotational Mechanical System1.7.4 A Simple Rotational Mechanical System1.8 Introduction to Analogous System1.8.1 Advantages of Electrical Analogous System1.8.2 Force–Voltage Analogy1.8.3 Force–Current Analogy1.8.4 Torque–Voltage Analogy1.8.5 Torque–Current AnalogyReview Questions
2 Physical Systems and Components
2.1 Introduction2.2 Electromechanical System2.3 Hydraulic System2.3.1 Advantages of Hydraulic System2.3.2 Disadvantages of Hydraulic System2.3.3 Applications of Hydraulic System2.3.4 Devices Used in Hydraulic System2.4 Pneumatic Systems2.4.1 Gas Flow Resistance and Pneumatic Capacitance2.4.2 Advantages of Pneumatic System2.4.3 Disadvantages of Pneumatic System2.4.4 Applications of Pneumatic System2.4.5 Devices Used in Pneumatic System2.4.6 Comparison between Hydraulic and Pneumatic Systems2.5 Thermal Systems2.5.1 Thermal Resistance and Thermal Capacitance2.6 Liquid-Level System2.6.1 Elements of Liquid-Level System2.7 Introduction to Control System Components2.8 Controllers2.8.1 Controller Output as a Percentage Value2.8.2 Measured Value as a Percentage Value2.8.3 Set Point as a Percentage Value2.8.4 Error as a Percentage Value2.8.5 Types of Controllers2.9 Electronic Controllers2.9.1 ON–OFF Controller2.9.2 Proportional Controller2.9.3 Integral Controller2.9.4 Derivative Controller2.9.5 Proportional Integral Controller2.9.6 Proportional Derivative Controller2.9.7 Proportional Integral Derivative Controller2.10 Potentiometers2.10.1 Characteristics of Potentiometers2.10.2 Power-Handling Capacity2.10.3 Applications of Potentiometer2.11 Synchros2.11.1 Synchro Transmitter2.11.2 Synchro Control Transformer2.11.3 Synchro Error Detector2.12 Servomotors2.12.1 Classification of Servomotor2.12.2 Features of Servomotor2.12.3 DC Servomotor2.12.4 AC Servomotor2.12.5 Comparison between AC Servomotor and DC Servomotor2.13 Tachogenerators2.13.1 DC Tachogenerator2.13.2 AC Tachogenerator2.14 Stepper Motor2.14.1 Permanent Magnet Stepper Motor2.14.2 Variable Reluctance Stepper Motor2.14.3 Hybrid Stepper Motor2.14.4 Operation of Stepper Motor2.14.5 Advantages of Stepper Motor2.14.6 Applications of Stepper Motor2.15 Gear Trains2.15.1 Single Gear Train2.15.2 Multiple Gear TrainsReview Questions
3 Block Diagram Reduction Techniques
3.1 Introduction to Block Diagram3.2 Open-Loop and Closed-Loop Systems Using Block Diagram3.2.1 Advantages of Block Diagram Representation3.2.2 Disadvantages of Block Diagram Representation3.3 Block Diagram Representation of Electrical System3.4 Block Diagram Reduction3.4.1 Need for Block Diagram Reduction3.4.2 Block Diagram Algebra3.4.3 Rules for Block Diagram Reduction3.4.4 Block Diagram Reduction for Complex SystemsReview Questions
4 Signal Flow Graph
4.1 Introduction4.1.1 Signal Flow Graph Terminologies4.1.2 Properties of SFG4.1.3 SFG Algebra4.1.4 Mason’s Gain Formula for SFG4.1.5 Signal Flow Graph From Differential Equation4.1.6 Comparison between SFG and Block DiagramReview Questions
5 Time Response Analysis
5.1 Introduction5.2 Time Response of the Control System5.2.1 Transient Response5.2.2 Steady-State Response5.3 Standard Test Signals5.3.1 Impulse Signal5.3.2 Step Signal5.3.3 Ramp Signal5.3.4 Parabolic Signal5.4 Poles, Zeros and System Response5.4.1 Poles and Zeros of a Transfer Function5.4.2 Stability of the System5.5 Type and Order of the System5.5.1 Type of the System5.5.2 ORDER of the System5.6 First-Order System5.6.1 Performance Parameters of First-Order System5.6.2 Time Response of a First-Order System5.7 Second-Order System5.7.1 Classification of Second-Order System5.7.2 Performance Parameters of Second-Order System5.7.3 Time Response of the Second-Order System5.7.4 Time-Domain Specifications for an Underdamped Second-Order System5.8 Steady-State Error5.8.1 Characteristic of Steady-State Error5.8.2 Determination of Steady-State Error5.8.3 Steady-State Error in Terms of G(s)5.8.4 Steady-State Error in Terms of T(s)5.8.5 Static Error Constants and System Type5.8.6 Generalized or Dynamic Error Coefficients5.9 Effect of Adding Poles and Zeros in the Second-Order System5.9.1 Effect of Adding Poles5.9.2 Effect of Adding Zeros5.10 Response with P, PI and PID Controllers5.10.1 Proportional Derivative Control5.10.2 Proportional Integral Control5.10.3 Proportional Plus Integral Plus Derivative Control (PID Control)5.11 Performance IndicesReview Questions

6 Stability and Routh–Hurwitz Criterion
6.1 Introduction6.2 Concept of Stability6.3 Stability of Linear Time-Invariant System6.3.1 Stability Based on Natural Response of the System, c(t)natural6.3.2 Stability Based on the Total Response of the System, c(t)6.36.4 Mathematical Condition for the Stability of the System6.5 Transfer Function of the System, G(s)6.5.1 Effects of Location of Poles on Stability6.6 Zero-Input Stability or Asymptotic Stability6.6.1 Importance of Asymptotic Stability6.7 Relative Stability6.8 Methods for Determining the Stability of the System6.9 Routh–Hurwitz Criterion6.9.1 Minimum-Phase System6.9.2 Non-Minimum-Phase System6.10 Hurwitz Criterion6.10.1 Hurwitz Matrix Formation6.10.2 Disadvantages of Hurwitz Method6.11 Routh’s Stability Criterion6.11.1 Necessary Condition for the Stability of the System6.11.2 Special Cases of Routh’s Criterion6.11.3 Applications of Routh’s Criterion6.11.4 Advantages of Routh’s Criterion6.11.5 Limitations of Routh’s CriterionReview Questions
7 Root Locus Technique
7.1 Introduction7.2 Advantages of Root Locus Technique7.3 Categories of Root Locus7.3.1 Variation of Loop Gain with the Root Locus7.4 Basic Properties of Root Loci7.4.1 Conditions Required for Constructing the Root Loci7.4.2 Usage of the Conditions7.4.3 Analytical Expression of the Conditions7.4.4 Determination of Variable Parameter K7.4.5 Minimum and Non-Minimum Phase Systems7.5 Manual Construction of Root Loci7.5.1 Properties / Guidelines for Constructing the Root Loci7.5.2 Flow Chart for Constructing the Root Locus for a System7.6 Root Loci for different Pole-Zero Configurations7.7 Effect of Adding Poles and Zeros in the System7.7.1 Addition of Poles to the Loop Transfer Function, G(s)H(s)7.7.2 Effect of Addition of Poles7.7.3 Addition of Zero to the Loop Transfer Function7.7.4 Effect of Addition of Zeros7.8 Time Response from Root Locus7.9 Gain Margin and Phase Margin of the System7.9.1 Gain Margin of the System7.9.2 Phase Margin of the System7.10 Root Locus for K < 0 Inverse Root Locus or Complementary Root Loci7.10.1 Steps in Constructing the Inverse Root Loci Manually7.11 Pole-Zero Cancellation Rules7.12 Root Contours (Multi-Variable System)Review Questions
8 Frequency Response Analysis
8.1 Introduction8.1.1 Advantages of Frequency Response Analysis8.1.2 Disadvantages of Frequency Response Analysis8.2 Importance of Sinusoidal Waves for Frequency Response Analysis8.3 Basics of Frequency Response Analysis8.4 Frequency Response Analysis of Open-Loop and Closed-Loop Systems8.4.1 Open-Loop System8.4.2 Closed-Loop System8.4.3 Closed-Loop System with Poles and Zeros8.5 Frequency Response Representation8.5.1 Determination of Frequency Response8.6 Frequency Domain Specifications8.7 Frequency and Time Domain Interrelations8.7.1 Frequency Domain Specifications8.8 Effect of Addition of a Pole to the Open-Loop Transfer Function of the System8.9 Effect of Addition of a Zero to the Open-Loop Transfer Function of the System8.10 Graphical Representation of Frequency Response8.11 Introduction to Bode Plot8.11.1 Reasons for Using Logarithmic Scale8.11.2 Advantages of Bode Plot8.11.3 Disadvantages of Bode Plot8.12 Determination of Frequency Domain Specifications from Bode Plot8.13 Stability of the System8.13.1 Based on Crossover Frequencies8.13.2 Based on Gain Margin and Phase Margin8.14 Construction of Bode Plot8.14.1 Effect of Damping Ratio x8.15 Constructing the Bode Plot for a Given System8.15.1 Construction of Magnitude Plot8.15.2 Construction of Phase Plot8.16 Flow Chart for Plotting Bode Plot8.17 Procedure for Determining the Gain K from the Desired Frequency Domain Specifications8.18 Maximum Value of Gain8.19 Procedure for Determining Transfer Function from Bode Plot8.20 Bode Plot for Minimum and Non-Minimum Phase SystemsReview Questions
9 Polar and Nyquist Plots
9.1 Introduction to Polar Plot9.2 Starting and Ending of Polar Plot9.3 Construction of Polar Plot9.4 Determination of Frequency Domain Specification from Polar Plot9.4.1 Gain Crossover Frequency w gc 9.4.2 Phase Crossover Frequency w pc9.4.3 Gain Margin gm9.119.4.4 Phase Margin pm9.5 Procedure for Constructing Polar Plot9.6 Typical Sketches of Polar Plot on an Ordinary Graph and Polar Graph9.7 Stability Analysis using Polar Plot9.7.1 Based on Crossover Frequencies9.7.2 Based on Gain Margin and Phase Margin9.7.3 Based on the Location of Phase Crossover Point9.8 Determining the Gain K from the Desired Frequency Domain Specifications9.8.1 When the Desired Gain Margin of the System is Specified9.8.2 When the Desired Phase Margin of the System is Specified9.9 Introduction to Nyquist Stability Criterion9.10 Advantages of Nyquist Plot9.11 Basic Requirements for Nyquist Stability Criterion9.12 Encircled and Enclosed9.12.1 Encircled9.12.2 Enclosed9.13 Number of Encirclements or Enclosures9.14 Mapping of s-Plane into Characteristic Equation Plane9.15 Principle of Argument9.16 Nyquist Stability Criterion9.17 Nyquist Path9.18 Relation Between G(s) H(s)-Plane and F(s)-Plane9.19 Nyquist Stability Criterion Based on the Encirclements of −1+ j 09.20 Stability Analysis of the System9.21 Procedure for Determining the Number of Encirclements9.21.1 Flow chart for Determining the Number of Encirclements Made by the Contour in G(s)H(s)-Plane9.22 General Procedures for Determining the Stability of the System Based on Nyquist Stability Criterion9.22.1 Flow chart for Determining the Stability of the System Based on Nyquist Stability CriterionReview Questions
10 Constant M- and N-Circles and Nichols Chart
10.1 Introduction10.2 Closed-Loop Response from Open-Loop Response10.3 Constant M-Circles10.3.1 Applications of Constant M-Circles10.3.2 Resonant Peak Mr and Resonant Frequency wr from Constant M-Circles10.3.3 Variation of Gain K with Mr and wr 10.610.3.4 Bandwidth of the System10.3.5 Stability of the System10.3.6 Determination of Gain K Corresponding to the Desired Resonant Peak (Mr)desired10.3.7 Magnitude Plot of the System from Constant M-Circles10.4 Constant N-Circles10.4.1 Phase Plot of the System from Constant N-Circles10.5 Nichols Chart10.5.1 Reason for the Usage of Nichols Chart10.5.2 Advantages of Nichols Chart10.5.3 Transformation of Constant M- and N-Circles into Nichols Chart10.5.4 Determination of Frequency Domain Specifications from Nichols Chart10.5.5 Determination of Gain K for a Desired Frequency Domain SpecificationsReview Questions
11 Compensators
11.1 Introduction11.2 Compensators11.2.1 Series or Cascade Compensation11.2.2 Feedback or Parallel Compensation11.2.3 Load or Series-Parallel Compensation11.2.4 State Feedback Compensation11.2.5 Forward Compensation with Series Compensation11.2.6 Feed-forward Compensation11.2.7 Effects of Addition of Poles11.2.8 Effects of Addition of Zeros11.2.9 Choice of Compensators11.3 Lag Compensator11.3.1 Determination of Maximum Phase Angle fm11.3.2 Electrical Representation of the Lag Compensator11.3.3 Effects of Lag Compensator11.3.4 Design of Lag Compensator11.3.5 Design of Lag Compensator Using Bode Plot11.3.6 Design of Lag Compensator Using Root Locus Technique11.4 Lead Compensator11.4.1 Determination of Maximum Phase Angle fm11.4.2 Electrical Representation of the Lead Compensator11.4.3 Effects of Lead Compensator11.4.4 Limitations of Lead Compensator11.4.5 Design of Lead Compensator11.4.6 Design of Lead Compensator Using Bode Plot11.4.7 Design of Lead Compensator Using Root Locus Technique11.5 Lag–Lead Compensator11.5.1 Electrical Representation of the Lag–Lead Compensator11.5.2 Effects of Lag–Lead Compensator11.5.3 Design of Lag–Lead Compensator11.5.4 Design of Lag–Lead Compensator Using Bode Plot11.5.5 Design of Lag–Lead Compensator Using Root Locus TechniqueReview Questions
12 Physiological Control Systems
12.1 Introduction12.2 Physiological Control Systems12.3 Properties of Physiological Control Systems12.3.1 Target of the Homeostasis12.3.2 Imbalance in the Homeostasis12.3.3 Homeostasis Control Mechanisms12.4 Block Diagram of the Physiological Control System12.4.1 Types of Control Mechanism12.5 Differences Between Engineering and Physiological Control Systems12.6 System Elements12.6.1 Resistance12.6.2 Capacitance12.6.3 Inductance12.7 Properties Related to Elements12.8 Linear Models of Physiological Systems: Two Examples 12.8.1 Lung Mechanism 12.8.2 Skeletal Muscle12.9 Simulation—Matlab and Simulink ExamplesReview Questions
13 State-Variable Analysis
13.1 Introduction13.1.1 Advantages of State-Variable Analysis13.2 State-Space Representation of Continuous-Time LTI Systems13.3 Block Diagram and SFG Representation of a Continuous State-Space Model13.4 State-Space Representation13.5 State-Space Representation of Differential Equations in Physical Variable Form 13.5.1 Advantages of Physical Variable Representation 13.5.2 Disadvantages of Physical Variable Representation13.6 State-Space Model Representation for Electric Circuits13.7 State-Space Model Representation for Mechanical System 13.7.1 State-Space Model Representation of Translational / Rotational Mechanical System13.8 State-Space Model Representation of Electromechanical System 13.8.1 Armature-Controlled DC Motor 13.8.2 Field-Controlled DC Motor13.9 State-Space Representation of a System Governed by Differential Equations13.10 State-Space Representation of Transfer Function in Phase Variable Forms 13.10.1 Method 113.22 13.10.2 Method 213.23 13.10.3 Method 313.25 13.10.4 Advantages of Phase-Variable Representation 13.10.5 Disadvantages of the Phase-Variable Representation13.11 State-Space Representation of Transfer Function in Canonical Forms 13.11.1 Controllable Canonical Form 13.11.2 Observable Canonical Form 13.11.3 Diagonal Canonical Form 13.11.4 Jordan Canonical Form13.12 Transfer Function from State-Space Model13.13 Solution of State Equation for Continuous Time Systems 13.13.1 Solution of Homogenous-Type State Equation 13.13.2 Solution of Non-Homogenous Type State Equation 13.13.3 State Transition Matrix 13.13.4 Properties of State Transition Matrix13.14 Controllability and Observability13.14.1 Criteria for Controllability13.14.2 Criteria for Observability13.15 State-Space Representation of Discrete-Time LTI Systems13.15.1 Block Diagram and SFG of Discrete State-Space Model13.16 Solutions of State Equations for Discrete-Time LTI Systems13.16.1 System Function H(z)13.17 Representation of Discrete LTI System13.18 Sampling13.18.1 Sampling Theorem13.18.2 High Speed Sample-and-Hold CircuitReview Questions
14 MATLAB Programs
14.1 Introduction14.2 MATLAB in Control Systems14.2.1 Laplace Transform14.2.2 Inverse Laplace Transform14.2.3 Partial Fraction Expansion14.2.4 Transfer Function Representation14.2.5 Zeros and Poles of a Transfer Function14.2.6 Pole-Zero Map of a Transfer Function14.2.7 State-Space Representation of a Dynamic System14.2.8 Phase Variable Canonical Form14.2.9 Transfer Function to State-Space Conversion14.2.10 State-Space to Transfer Function Conversion14.2.11 Series/Cascade, Parallel and Feedback Connections14.2.12 Time Response of Control System14.2.13 Performance Indices from the Response of a System14.2.14 Steady State Error from the Transfer Function of a System14.2.15 Routh–Hurwitz Criterion14.2.16 Root Locus Technique14.2.17 Bode Plot14.2.18 Nyquist Plot14.2.19 Design of Compensators Using Matlab

Content preview from Control Systems Engineering

7 ROOT LOCUS TECHNIQUE

7.1 Introduction

The closed-loop poles or the roots of the characteristic equation of the system determines the absolute and relative stability of linear control systems. Investigating the trajectories of the roots of the characteristic equation is an important study in linear control systems. Root loci introduced by W. R. Evans in 1946 are the trajectories of the roots of the characteristic equation or the graphical representation of the closed-loop poles when certain system parameter varies. In addition, it is a powerful method of analysis and design for stability and transient response.

The location of closed-loop poles in the control system depends on the variable loop gain in the system. Hence, it is necessary ...

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