Control Systems: Theory and Applications

Cover
Preface
Acknowledgements
Contents
Chapter 1: Fundamentals of Control Systems
	1.1 Basic Definitions
	1.2 Classification of Control Systems
	1.3 Open-Loop and Closed-Loop Systems
		1.3.1 Open-loop System
		1.3.2 Closed-loop System
	1.4 Effects of Feedback
	1.5 Servomechanism
	1.6 Standard Test Signals
		1.6.1 Step Function
		1.6.2 Ramp Function
		1.6.3 Parabolic Function
	1.7 Impulse Function [δ(t)]
	Significant Points
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 2: Laplace Transform and Matrix Algebra
	2.1 Laplace Transform
	2.2 Inverse Laplace Transform
	2.3 Laplace Transform of Standard Input Signals
		2.3.1 Unit Step Function
		2.3.2 Ramp Function
		2.3.3 Parabolic Function
	2.4 Exponential Function
	2.5 Sine Wave
	2.6 Cosine Wave
	2.7 Hyperbolic Sine Wave
	2.8 Hyperbolic Cosine Wave
	2.9 Laplace Transform of a Derivative [dt(t)/dt]
	2.10 Laplace Transform of an Integral tn
	2.11 Laplace Transform of e~at sinhcot
	2.12 Laplace Transform of e Coswt
	2.13 Laplace Transform of e sinhwt
	2.14 Laplace Transform of e-wt coshwt
	2.15 Laplace Transform of (t)
	2.16 Initial Value and Final Value Theorems
	2.17 Displacement Theorem
	2.18 Convolution
	2.19 Partial Fraction Expansion of F(s)
	2.20 Matrix
		2.20.1 Equality of Two Matrices
		2.20.2 Vector
		2.20.3 Square Matrix
		2.20.4 Diagonal Matrix
		2.20.5 Identity Matrix or Unity Matrix
		2.20.6 Zero Matrix
		2.20.7 Determinant of a Matrix
		2.20.8 Singular Matrix
		2.20.9 Transpose
		2.20.10 Symmetric Matrix
		2.20.11 Conjugate Matrix
		2.20.12 Conjugate Transpose
		2.20.13 Hermitian Matrix
		2.20.14 Addition of Matrices
		2.20.15 Multiplication of a Matrix by a Scalar
		2.20.16 Multiplication of a Matrix by a Matrix
		2.20.17 Power of a Matrix
		2.20.18 Rank of a Matrix
		2.20.19 Minor of a Matrix
		2.20.20 Co-factor
		2.20.21 Adjoint Matrix
		2.20.22 Inverse of a Matrix
		2.20.23 More Properties of Matrices
	Significant Points
	Additional Solved Examples
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 3: Transfer Function
	3.1 Transfer Function
	3.2 Impulse Response and Transfer Function
	3.3 Properties of Transfer Function (TF)
	3.4 Advantages and Disadvantages of Transfer Function
	3.5 Poles and Zeros of a Transfer Function
		3.5.1 Representation of Pole and Zero on the s-plane
		3.5.2 Characteristic Equation
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 4: Control System Components
	4.1 Potentiometers
	4.2 Synchros
		4.2.1 Transmitter
		4.2.2 Synchro Receiver
		4.2.3 Differential Synchro
		4.2.4 Control Transformer
	4.3 Linear Transducers
	4.4 Tachometer
	4.5 Accelerometer
	4.6 Miscellaneous Transducers
		4.6.1 Strain Gauge
		4.6.2 Temperature Transducers
		4.6.3 Pressure Transducers
		4.6.4 Gyroscope
	4.7 Power Actuators
		4.7.1 DC Generator
		4.7.2 DC Motor
			4.7.2.1 Armature controlled dc motor
			4.7.2.2 Field controlled dc motor
	4.8 AC Servomotors
	4.9 Servomechanism
		4.9.1 Positional Servomechanism
		4.9.2 Rate Servomechanism
	4.10 Thermal Systems
		4.10.1 Thermal Resistance
		4.10.2 Thermal Capacitance
		4.10.3 A First-Order Thermal System
		4.10.4 Second-Order Thermal System
	4.11 Fluid Systems
		4.11.1 Flow and Level as System Variable
		4.11.2 First Order-Fluid Level System
		4.11.3 Second Order-Fluid Level System
	4.12 Chemical Systems
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 5: Mathematical Modelling of Physical Systems
	5.1 Modelling of Mechanical Systems
		5.1.1 Translational Motion
		5.1.2 Rotational Motion
	5.2 Modelling of Electrical Systems
		5.2.1 Resistor
		5.2.2 Inductor
		5.2.3 Capacitor
	5.3 Analogous Systems
		5.3.1 Force-Voltage Analogy
		5.3.2 Force-Current Analogy
	5.4 Representation by Nodal Method
	5.5 Gear Trains
	5.6 Chain Driver
	5.7 Lever
	Significant Points
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 6: Block Diagram
	6.1 Definition of Basic Elements of Block Diagram
	6.2 Cannonical Form of Closed Loop System
	6.3 Rules for Block Diagram Reduction
	6.4 Procedure for Reduction of Block Diagram
	6.5 Reducing to Unity Feedback Systems
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 7: Signal-Flow Graphs
	7.1 Basic Definitions in SFG
	7.2 Rules for Signal-Flow Graph
		7.2.1 Addition Rule
		7.2.2 Transmission Rule
		7.2.3 Multiplication Rule
	7.3 Properties of Signal-Flow Graph
	7.4 Mason\'s Gain Formula
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 8: Time Domain Analysis of Control Systems
	8.1 Classification of Time Responses
		8.1.1 Transient Response
		8.1.2 Steady State Response
	8.2 System Time Response
	8.3 Analysis of Steady-State Error
	8.4 Type of Input and Steady-State Error
		8.4.1 Step Input
		8.4.2 Ramp Input
		8.4.3 Parabolic Input
	8.5 Steady-State Error for Type 0 ,1 , and 2 Systems
		8.5.1 Error for Step Input
		8.5.2 Error for Ramp Input
		8.5.3. Error for Parabolic Input
	8.6 Advantages and Disadvantages of Static Error Coefficient Method
	8.7 Generalised Error Coefficient Method
	8.8 Analysis of First-Order System
		8.8.1 Unit Step Response
		8.8.2 Time Constant
		8.8.3 Poles of Closed-Loop Transfer Function
	8.9 Analysis of Second-Order System
	8.10 Effect of on Second-Order System
		8.10.1 Effect of £ on pole location
		8.10.2 Effect of £ on Nature of Response
	8.11 Derivation of Time Response Specifications
		8.11.1 Delay Time (T)
		8.11.2 Rise Time ( T)
		8.11.3 Peak Time (Tp)
		8.11.4 Peak Overshoot (M)
		8.11.5 Settling Time (Ts)
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 9: Feedback Characteristics of Control Systems
	9.1 Effect of Parameter Variation in an Open-Loop Control System
	9.2 Effect of Parameter Variation in a Closed-Loop System
	9.3 Sensitivity of a Control System
		9.4.1 Sensitivity T(s) with Respect to G(s)
		9.4.2 Sensitivity of T(s) with Respect to H(s)
	9.5 Effect of Feedback on Time Constant of a Control System
	9.6 Effect of Feedback on Overall Gain
	9.7 Effect of Feedback on Stability
	9.8 Effect of Feedback on Disturbance
		9.8.1 Disturbance in the Feedback Path
		9.8.2 Disturbance at the Output
	9.9 Introduction to Basic Control Action of Controllers
		9.9.1 Two-Position Controllers
		9.9.2 Proportional Controller (P)
		9.9.3 Integral Controller (I)
		9.9.4 Proportional Plus Derivative Controllers
		9.9.5 Proportional Integral Controllers (PI)
		9.9.6 Proportional Plus Integral Plus Derivative Controller (PID)
		9.9.7 Rate Feedback Controller
	9.10 Realisation of Controllers with Opamp
		9.10.1 Controller
		9.10.2 Controller
		9.10.3 PI Controller
		9.10.4 PD Controller
		9.10.5 PID Controller
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 10: Stability
	10.1 Effect of Location of Poles on Stability
	10.2 Routh-Hurwitz Criterion
		10.2.1 Hurwitz\'s Criterion
		10.2.2 Routh\'s Stability Criterion
	Significant Points
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 11: Root Locus Method
	11.1 Fundamentals of Root Locus
	11.2 Relation between Poles and Zeros of OLTF with Poles of CLTF
	11.3 Angle and Magnitude Condition
	11.4 General Methods for Construction of Root Locus
	11.5 Steps for Solving Problems on Root Locus
	11.6 Cancellation Poles of G(S) and Zeros of H(S)
	11.7 Value of Gain Margin
	11.8 Phase Margin
	11.9 Root Locus with Positive Feedback
	11.10 Root Contour
	11.11 Effects of Addition of Poles
	11.12 Effects of Addition of Zeros
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 12: Frequency Domain Analysis
	12.1 Frequency Response
	12.2 Methods in Frequency Response
	12.3 Definitions of Frequency Domain Specifications
	12.4 Correlation Between Time and Frequency Domain Specifications for a Second-Order System
	12.5 Advantages of Frequency Domain Analysis
	12.6 Disadvantages of Frequency Response Methods
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 13: Bode Plot
	13.1 Logarithmic Plot
		13.1.1 The Constant Term K
		13.1.2 Zeros at the Origin
		13.1.3 Poles of the Origin
		13.1.4 Simple Zero (1 + jωT)
		13.1.5 Simple Pole ( 1 + jωT)_1
		13.1.6 Quadratic Poles
		13.1.7 Quadratic Zeros
	13.2 Steps to Plot Bode Plot
	13.3 Resultant Curve
	13.4 Stability Consideration
		13.4.1 Phase Margin
		13.4.2 Gain Margin
		13.4.3 All Pass and Minimum Phase Functions
	13.5 Advantages of a Bode Plot
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 14: Polar Plot
	14.1 Polar Plot of Standard Functions
		14.1.1 G(s) = 1 / s
		14.1.2 G(s) = s
		14.1.3 G(s) = 1/(1 + sa )
		14.1.4 G(s) = 1 + sa
		14.1.5 G(jw) = 1
		14.1.6 G(jw) = 1 + 2$
		14-1-7 G (jw) = ejwa  (transport lag)
		14.1.8 G(j\'w)
		14.1.9 G(JW)=(1+jwa)(1+jwb)
		14.1.10 G(jw) =
		14.1.11 G(jw)
		14.1.12 G(jw)
		14.1.13 G(jw)
	Additional Solved Examples
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 15: Nyquist Plot
	15.1 Basic Definitions
	15.2 Nyquist Analysis
		15.2.1 Mapping Theorem and the Principle of Argument
		15.2.2 Application of Mapping Theorem to Stability
	15.3 Polar Plots of G(S) H(S) and Stability
	15.4 Nyquist Path
		15.4.1 Nyquist Stability Criterion
	15.5 Drawing of a Nyquist Stability Plot
	15.6 Relative Stability
		15.6.1 Gain Margin
		15.6.2 Phase Margin
	15.7 Closed Loop Frequency Response
		15.7.1 M Circles [Constant Magnitude Loci]
		15.7.2 N Circles [Constant Phase Loci]
	15.8 Nichol\'s Chart
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 16: Introduction to Compensators
	16.1 Types of Compensation
		16.1.1 Series Compensation
		16.1.2 Parallel Compensation
		16.1.3 Series-Parallel Compensation
	16.2 Compensating Network
		16.2.1 Lead Compensator
		16.2.2 Lag Compensator
		16.2.3 Lag-Lead Compensator
	16.3 Compensation Using Root Locus
	Significant Points
	Short Questions with Answers
	Exercises
		Questions For Practice
		Test Yourself
		Answers
Chapter 17: State Variable Approach
	17.1 Advantages and Disadvantages of Modern Control Theory
	17.2 Basic Concepts
	17.3 State Model
	17.4 Non-Uniqueness of State Model
	17.5 Different Representations of a State Model
		17.5.1 State Space Representation Using Phase Variables in Controllable Conical Form (CCF)
		17.5.2 Phase Variable CCF Form for NumeratorsTerms
		17.5.3 Phase Variable in Observable Controllable Form (OCF)
		17.5.4 Cascade Decomposition
		17.5.5 Parallel Decomposition
		17.5.6 Jordan\'s Cannonical Form
	17.6 Eigen Value
	17.7 Transfer Function Derivation From the State Mode
	17.8 Solution of the State Equation
		17.8.1 Solution of Homogeneous State Equation
		17.8.2 State Transition Matrix
		17.8.3 Properties of STM
		17.8.4 Solution of Non-homogeneous State Equation
	17.9 Controllability
	17.10 Observability
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 18: Digital Control Systems
	18.1 Z Transform
	18.2 Z Transform of Some Common Sequence
	18.3 Properties of Z Transform
	18.4 Inverse Z Transform
	18.5 Digital Discrete-Time Systems
	18.6 Discrete-Time Signals
	18.7 Causal Signals
	18.8 Linear Discrete-Time Systems
	18.9 Difference Equations
	18.10 Role of Z Transform in Linear Difference Equations
	18.11 Stability of a Discrete-Time System
	Significant Points
	Additional Solved Examples
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Chapter 19: Non-Linear Control Systems
	19.1 The State Space Approach
	19.2 Phase Plane Method
	19.3 Describing Function Analysis
		19.3.1 Dead-Zone Non-linearity
		19.3.2 Saturation Non-linearity
		19.3.3 On-off Non-linearity with Dead-Zone
		19.3.4 On-off Non-linearity
		19.3.5 Dead-Zone and Saturation
		19.3.6 On-off Non-linearity with Hysteresis
		19.3.7 Relay with Dead-Zone and Hysteresis
		19.3.8 Backlash
	19.4 Stability
		19.4.1 Liapunov\'s First Theorem
		19.4.2 Liapunov\'s Second Method
	Significant Points
	Short Questions with Answers
	Exercises
		Questions for Practice
		Test Yourself
		Answers
Appendix A: Fuzzy Logic
	A.1 Fuzzy Sets
	A.2 Fuzzy Set Operations
	A.3 Properties of Fuzzy Sets
	A.4 Fuzzy Relations
		A.4.1 Operations on Fuzzy Relations
	A.5 Fuzzy Tolerance and Equivalence Relation
	A.6 Features of the Membership Function
	A.7 Standard forms and Boundaries
	A.8 Fuzzification
	A.9 Defuzzification
	A.10 Control System Design Stages
	A.11 Assumptions in a Fuzzy Control System Design
	A.12 Fuzzy Rules
Appendix B: MATLAB 6.1
	B.1 Starting Matlab
	B.2 Variables
	B.3 Matrix
	B.4 Matrix Multiplication
	B.5 Inverse of the Matrix
	B.6 Transfer Function
	B.7 Control System
	B.8 Block Diagram Reduction Example
Index