Contents

• 1. Vector Space

  Objectives, Introduction, Linear Vector Space, Vectors: Linearly Dependent and Linearly Independent, Linear Combinations, Basis Vectors, and Dimensionality, Basis Extension Theorem, Theorem, Theorem, Domain and Range, Linearity, Time Invariance, Causality, Relaxedness, Review Questions

  2. State Variable Analysis

  Objectives, Introduction, Concept of State Variable Approach, Comparison of Conventional Control Theory and Modern Control Theory, State Concepts, State Model for Linear Systems, Matrix, Definition, Algebra of Matrices, Minors and Cofactors, Adjoint of a Square Matrix, Inverse of a Matrix, Rank of a Matrix, Representation of Physical System by Differential Equation, Electrical System, Mechanical System, Analogous Systems, Review Questions

  3. State Models

  Objectives, Introduction, State Space Representation using Physical Variables, State Space Representation using Phase Variables, State Space Representation using Differential Equation, State Space Representation using Transfer function, Development of State Model into Controllable Canonical Form or First Companion form, Development of State Model in Observable Canonical Form (Using Block Diagram) , Development of Signal Flow Graph from Given Transfer Function,

  State Space Representation using Canonical Form, Jordan Canonical Form,

  Derivation of Transfer Function from State Model, Diagonal Matrix,Similarity Transformation, Review Questions

  4. Eigen Values, Vectors and Solution of State Equation

  Objectives, Eigen Values and Eigen Vectors, Eigen values or Characteristic Roots,  Eigen Vectors or Characteristic Vectors, Diagonalization, Laplace Transfer Method for Solving State Equations, Properties of State–Transition Matrix, Brief Idea of State Variable Analysis in Discrete Time Domain, Concepts of Controllability and Observability, Pole Placement by State Feedback, Ackermann’s Formula, Review Questions

  5. Digital Control Systems

  Objectives, Introduction, Spectrum Analysis of Sampling Process, Signal Reconstruction, Difference Equations, The Z-transform, Z and S Domain Relationship, Properties of Z-Transform, The Z Transfer Function (Pulse Transfer Function), Pulse Transfer Function of Cascaded-Elements, Pulse Transfer Function of closed-loop, Control Systems, The Inverse Z-Transform,  Review Questions

  6. Stability and Controller

  Objectives, Introduction, Modeling of Sample-hold Circuit,  Steady State Accuracy (Error), Stability Analysis in Z-plane, Jury Stability Test, Hurwitz Criterion, Routh Stability Criterion, Necessary Condition for a System to be Stable,   Sufficient Condition, Limitations, Bilinear Transformation, Singular Cases in Bilinear Transformation, Digital PID Controller, Adaptive Controller, Review Questions

  P.Papers