Control Systems

Preface, Chapter 1 Introduction 1.1 Introduction 1.2 Basic Steps to Design a Control System 1.3 Mathematical Representation Chapter 2 Matrices 2.1 Introduction 2.2 Definition of Matrix 2.3 Square Matrix 2.4 Column Matrix or Vector 2.5 Row Matrix or Vector 2.6 Diagonal Matrix 2.7 Identity Matrix 2.8 NullMatrix 2.9 Symmetrie Matrix 2.10 Determinant of Matrix 7 2.11 Matrix Algebra 2.12 Transpose of a Matrix 2.13 Adjoint of a Matrix 2.14 Inverse of a Matrix 2.15 Rank of a Matrix 2.16 Trace of a Matrix 2.17 Derivative of a Matrix 2.18 Exponential of a Matrix Chapter 3 Laplace Transform 3.1 lntroduction 3.2 Definition of Laplace Transform 3.3 Laplace Theorems 3.4 Laplace Transform Theorems 3.5 Important Laplace Transform Pairs 3.6 Inverse Laplace Transform 3.7 Partial-Fraction Expansion Method 3.8 Convolution Integral 3.9 Solution of Differential Equations 3.10 Conclusion Chapter 4 MATLAB Basics 4.1 Introduction 4.2 MATLAB Environment 4.3 MATLAB Features 4.4 Vectors 4.5 Matrices 4.6 Eigenvalues and Eigenvectors 4.7 Transfer Functions 4.8 Polynomials 4.9 Partial Fractions 4.10 Symbolic Math Commands Chapter 5 Control System: Basic Theory 5.1 Introduction 5.2 Definition 5.3 Classification 5.4 General Classification 5.5 Elements of a Feedback Control System 5.6 Representation of Control Systems 5.7 Mason's Gain Formula 5.8 Conclusion Chapter 6 State-Space Concepts and Analysis of State-Equations 6.1 Introduction 6.2 Basicerms 6.3 Trajectories in State Space 6.4 Nonlinearities and Linearisation6.5 State Equation 6.6 State Equation: Homogenaus and Non-Homogenaus Parts 6.7 Solution ofNon-Homogeneous State Equations 6.8 Solution of Non-Homogenaus Time-Invariant Matrix Differential Equation 6.9 Solution ofHomogenous Time-lnvariant Matrix Differential Equation 6.10 State-Transition Matrix 6.11 Properties of State Transition Matrix 6.12 Computation of State Transition Matrix 6.13 Laplace Transform Solution of State-Equations (Frequency-Domain Analysis) 6.14 Transfer Function Matrix 6.15 Representation of State-Equation Solution in Terms of lj>(t) 6.16 Characteristic Equation 6.17 MATLAB Chapter 7 State-Space Modelling 7.1 lntroduction 7.2 State-Variable Diagram 7.3 State Models: Signal Flow Graphs 7.4 State Models-Various Forms 7.5 Similarity Transformations 7.6 Other Useful Transformation 7.7 Decomposition of Transfer Function 7.8 MATLAB Chapter 8 Controllability and Observability 8.1 lntroduction 8.2 Cantrollability and Observability 8.3 Definition 8.4 Cantrollability Tests 8.5 Rank of a Matrix 8.6 Observability Tests 8.7 Output Cantrollability 8.8 Pole-zero Cancellation in Transfer Function 8.9 Duality Theorem/Principle/Property 8.10 Design 8.11 Ackermann's Formula 8.12 MATLAB Summary 314 Problems and Solutions, Review Exercise, References, Index.