Cover -- Preface -- Contents -- Chapter 1 Control Systems and the Task of a Control Engineer -- 1.0 Introduction to Control Engineering -- 1.1 The Concept of Feedback and Closed Loop Control -- 1.2 Open-Loop Versus Closed-Loop Systems -- 1.3 Feedforward Control -- 1.4 Feedback Control in Nature -- 1.5 A Glimpse of the areas where Feedback Control Systems have been Employed by Man -- 1.6 Classification of Systems -- 1.6.1 Linear System -- 1.6.2 Time-Invariant System -- 1.7 Task of Control Engineers -- 1.8 Alternative Ways to Accomplish a Control Task -- 1.9 A Closer Look to the Control Task -- 1.9.1 Mathematical Modeling -- 1.9.2 Performance Objectives and Design Constraints -- 1.9.3 Controller Design -- 1.9.4 Performance Evaluation -- Chapter 2 Mathematical Preliminaries -- 2.0 The Laplace Transform -- 2.1 Complex Variables and Complex Functions -- 2.1.1 Complex Function -- 2.2 Laplace Transformation -- 2.2.1 Laplace Transform and Its Existence -- 2.3 Laplace Transform of Common Functions -- 2.3.1 Laplace Table -- 2.4 Properties of Laplace Transform -- 2.5 Inverse Laplace Transformation -- 2.5.1 Partial-Fraction Expansion Method -- 2.5.2 Partial-Fraction Expansion when F(s) has only Distinct Poles -- 2.5.3 Partial-Fraction Expansion of F(s) with Repeated Poles -- 2.6 Concept of Transfer Function -- 2.7 Block Diagrams -- 2.7.1 Block Diagram Reduction -- 2.8 Signal Flow Graph Representation -- 2.8.1 Signal Flow Graphs -- 2.8.2 Properties of Signal Flow Graphs -- 2.8.3 Signal Flow Graph Algebra -- 2.8.4 Representation of Linear Systems by Signal Flow Graph -- 2.8.5 Mason's Gain Formula -- 2.9 Vectors and Matrices -- 2.9.1 Minors, Cofactors and Adjoint of a Matrix -- 2.10 Inversion of a Nonsingular Matrix -- 2.11 Eigen Values and Eigen Vectors -- 2.12 Similarity Transformation -- 2.12.1 Diagonalization of Matrices -- 2.12.2 Jordan Blocks.

2.13 Minimal Polynomial Function and Computation of Matrixfunction Using Sylvester's Interpolation -- MATLAB Scripts -- Review Exercise -- Problems -- Chapter 3 State Variable Representation and Solution of State Equations -- 3.1 Introduction -- 3.2 System Representation in State-Variable Form -- 3.3 Concepts of Controllability and Observability -- 3.4 Transfer Function from State-Variable Representation -- 3.4.1 Computation of Resolvent Matrix from Signal Flow Graph -- 3.5 State Variable Representation from Transfer Function -- 3.6 Solution of State Equation and State Transition Matrix -- 3.6.1 Properties of the State Transition Matrix -- Review Exercise -- Problems -- Chapter 4 Analysis of Linear Systems -- 4.1 Time-Domain Performance of Control Systems -- 4.2 Typical Test Inputs -- 4.2.1 The Step-Function Input -- 4.2.2 The Ramp-Function Input -- 4.2.3 The Impulse-Function Input -- 4.2.4 The Parabolic-Function Input -- 4.3 Transient State and Steady State Response of Analog Control System -- 4.4 Performance Specification of Linear Systems in Time-Domain -- 4.4.1 Transient Response Specifications -- 4.5 Transient Response of a Prototype Second-Order System -- 4.5.1 Locus of Roots for the Second Order Prototype System -- 4.5.1.1 Constant ωn Locus -- 4.5.1.2 Constant Damping Ratio Line -- 4.5.1.3 Constant Settling Time -- 4.5.2 Transient Response with Constant ωn and Variable δ -- 4.5.2.1 Step Input Response -- 4.6 Impulse Response of a Transfer Function -- 4.7 The Steady-State Error -- 4.7.1 Steady-State Error Caused by Nonlinear Elements -- 4.8 Steady-State Error of Linear Control Systems -- 4.8.1 The Type of Control Systems -- 4.8.2 Steady-State Error of a System with a Step-Function Input -- 4.8.3 Steady-State Error of a System with Ramp-Function Input -- 4.8.4 Steady-State Error of a System with Parabolic-Function Input.

4.9 Performance Indexes -- 4.9.1 Integral of Squared Error (ISE) -- 4.9.2 Integral of Time Multiplied Squared Error (ITSE) Criteria -- 4.9.3 Integral of Absolute Error (IAE) Criteria -- 4.9.4 Integral of Time Multiplied Absolute Error (ITAE) -- 4.9.5 Quadratic Performance Index -- 4.10 Frequency Domain Response -- 4.10.1 Frequency Response of Closed-Loop Systems -- 4.10.2 Frequency-Domain Specifications -- 4.11 Frequency Domain Parameters of Prototype Second-Order System -- 4.11.1 Peak Resonance and Resonant Frequency -- 4.11.2 Bandwidth -- 4.12 Bode Diagrams -- 4.12.1 Bode Plot -- 4.12.2 Principal Factors of Transfer Function -- 4.13 Procedure for Manual Plotting of Bode Diagram -- 4.14 Minimum Phase and Non-Minimum Phase Systems -- Matlab Scripts -- Review Exercise -- Problems -- Chapter 5 The Stability of Linear Control Systems -- 5.1 The Concept of Stability -- 5.2 The Routh-Hurwitz Stability Criterion -- 5.2.1 Relative Stability Analysis -- 5.2.2 Control System Analysis Using Routh's Stability Criterion -- 5.3 Stability by the Direct Method of Lyapunov -- 5.3.1 Introduction to the Direct Method of Lyapunov -- 5.3.2 System Representation -- 5.4 Stability by the Direct Method of Lyapunov -- 5.4.1 Definitions of Stability -- 5.4.2 Lyapunov Stability Theorems -- 5.5 Generation of Lyapunov Functions for Autonomous Systems -- 5.5.1 Generation of Lyapunov Functions for Linear Systems -- 5.6 Estimation of Settling Time Using Lyapunov Functions -- Matlab Scripts -- Review Exercise -- Problems -- Chapter 6 Frequency Domain Stability Analysis and Nyquist Criterion -- 6.1 Introduction -- 6.1.1 Poles and Zeros of Open Loop and Closed Loop Systems -- 6.1.2 Mapping Contour and the Principle of the Argument -- 6.2 The Nyquist Criterion -- 6.2.1 The Nyquist Path -- 6.2.2 The Nyquist Plot Using a Part of Nyquist Path.

6.3 Nyquist Plot of Transfer Function with Time Delay -- 6.4 Relative Stability: Gain Margin and Phase Margin -- 6.4.1 Analytical Expression for Phase Margin and Gain Margin of a Second Order Prototype -- 6.5 Gain-Phase Plot -- 6.5.1 Constant Amplitude (M) and Constant Phase (N) Circle -- 6.6 Nichols Plot -- 6.6.1 Linear System Response Using Graphical User Interface in MATLAB -- MATLAB Scripts -- Review Exercise -- Problems -- Chapter 7 Root Locus Technique -- 7.1 Correlation of System-Roots with Transient Response -- 7.2 The Root Locus Diagram-A Time Domain Design Tool -- 7.3 Root Locus Technique -- 7.3.1 Properties of Root Loci -- 7.4 Step by Step Procedure to Draw the Root Locus Diagram -- 7.5 Root Locus Design Using Graphical Interface in MATLAB -- 7.6 Root Locus Technique for Discrete Systems -- 7.7 Sensitivity of the Root Locus -- MATLAB Scripts -- Review Exercise -- Problems -- Chapter 8 Design of Compensators -- 8.1 Introduction -- 8.2 Approaches to System Design -- 8.2.1 Structure of the Compensated System -- 8.2.2 Cascade Compensation Networks -- 8.2.3 Design Concept for Lag or Lead Compensator in Frequency-Domain -- 8.2.4 Design Steps for Lag Compensator -- 8.2.5 Design Steps for Lead Compensator -- 8.2.6 Design Examples -- 8.3 Design of Compensator by Root Locus Technique -- 8.3.1 Design of Phase-lead Compensator using Root Locus Procedure -- 8.3.2 Design of Phase-lag Compensator using Root Locus Procedure -- 8.4 PID Controller -- 8.4.1 Ziegler-Nichols Rules for Tuning PID Controllers -- 8.4.2 First Method -- 8.4.3 Second Method -- 8.5 Design of Compensators for Discrete Systems -- 8.5.1 Design Steps for Lag Compensator -- 8.5.2 Design Steps for Lead Compensator -- MATLAB Scripts -- Review Exercise -- Problems -- Chapter 9 State Feedback Design -- 9.1 Pole Assignment Design and State Estimation -- 9.1.1 Ackerman's Formula.

9.1.2 Guidelines for Placement of Closed Loop System Poles -- 9.1.3 Linear Quadratic Regulator Problem -- 9.2 State Estimation -- 9.2.1 Sources of Error in State Estimation -- 9.2.2 Computation of the Observer Parameters -- 9.3 Equivalent Frequency-Domain Compensator -- 9.4 Combined Plant and Observer Dynamics of the Closed Loop System -- 9.5 Incorporation of a Reference Input -- 9.6 Reduced-Order Observer -- 9.7 Some Guidelines for Selecting Closed Loop Poles in Pole Assignment Design -- MATLAB Scripts -- Review Exercise -- Problems -- Chapter 10 Sampled Data Control System -- 10.0 Why We are Interested in Sampled Data Control System? -- 10.1 Advantage of Digital Control -- 10.2 Disadvantages -- 10.3 Representation of Sampled Process -- 10.4 The Z-Transform -- 10.4.1 The Residue Method -- 10.4.2 Some Useful Theorems -- 10.5 Inverse Z-Transforms -- 10.5.1 Partial Fraction Method -- 10.5.2 Residue Method -- 10.6 Block Diagram Algebra For Discrete Data System -- 10.7 Limitations of the Z-Transformation Method -- 10.8 Frequency Domain Analysis of Sampling Process -- 10.9 Data Reconstruction -- 10.9.1 Zero Order Hold -- 10.10 First Order Hold -- 10.11 Discrete State Equation -- 10.12 State Equations of Systems with Digital Components -- 10.13 The Solution of Discrete State Equations -- 10.13.1 The Recursive Method -- 10.14 Stability of Discrete Linear Systems -- 10.14.1 Jury's Stability Test -- 10.15 Steady State Error for Discrete System -- 10.16 State Feedback Design for Discrete Systems -- 10.16.1 Predictor Estimator -- 10.16.2 Current Estimator -- 10.16.3 Reduced-order Estimator for Discrete Systems -- 10.17 Provision for Reference Input -- MATLAB Scripts -- Review Exercise -- Problems -- Chapter 11 Optimal Control -- 11.1 Introduction -- 11.2 Optimal Control Problem -- 11.3 Performance Index -- 11.4 Calculus of Variations.

11.4.1 Functions and Functionals.