Digital Control Systems : Theoretical Problems and Simulation Tools

"The objective of this book is to provide a collection of solved problems on control systems, with an emphasis on practical problems. System functionality is described, the modeling process is explained, the problem solution is introduced, and the derived results are discussed. Each chapter ends with a discussion on applying MATLAB®, LabVIEW, and/or Comprehensive Control to the previously introduced concepts. The aim of the book is to help an average reader understand the concepts of control systems through problems and applications. The solutions are based directly on math formulas given in extensive tables throughout the text."-- Provided by publisher Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Authors -- 1. Introduction -- 1.1 Introduction -- 1.2 Description of Analog and Digital Control Systems -- 1.3 Advantages of Digital Control Systems and Applications -- 2. z-Transform -- 2.1 Introduction -- 2.2 From Laplace Transform to z-Transform -- 2.2.1 Comparison of s- and z-Planes in the Region of Convergence -- 2.3 z-Transform Properties -- 2.3.1 Time Shift -- 2.3.2 Linearity -- 2.3.3 Time Reverse -- 2.3.4 Convolution -- 2.3.5 Differentiation in z-Domain -- 2.3.6 Initial and Final Value Theorem -- 2.4 Inverse z-Transform -- 2.4.1 Division Method -- 2.4.2 Method of Partial Fraction Expansion -- 2.4.3 Method of Complex Integration -- 2.5 Formula Tables -- 2.6 Solved Exercises -- 3. Transfer Function -- 3.1 Introduction -- 3.2 Open-Loop Sampled-Data Control System -- 3.3 Closed-Loop Sampled-Data Control System -- 3.4 Signal Flow Graphs -- 3.5 Mason's Formula -- 3.6 Difference Equations -- 3.7 Formula Tables -- 3.8 Solved Exercises -- 4. Transfer Function Discretization -- 4.1 Introduction -- 4.2 Discretization Methods -- 4.2.1 Impulse-Invariance Method or z-Transform Method -- 4.2.2 Step-Invariance Method or z-Transform Method with Sample and Hold -- 4.2.3 Backward Difference Method -- 4.2.4 Forward Difference Method -- 4.2.5 Bilinear or Tustin Method -- 4.2.6 Frequency Prewarping Method -- 4.2.7 Matched Pole-Zero Method -- 4.3 Comparison of Discretization Methods -- 4.4 Formulas -- 4.5 Solved Exercises -- 5. State-Space Representation -- 5.1 Introduction -- 5.2 Discrete-Time State-Space Equations -- 5.2.1 Eigenvalues and Eigenvectors -- 5.3 Solution of State Equations -- 5.4 State-Space Representation -- 5.4.1 Direct Form -- 5.4.2 Canonical Form -- 5.4.3 Controllable Canonical Form