Control Systems: An Introduction

✍ Scribed by D. Sundararajan

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 318
• Category: Library

✦ Synopsis

This textbook is designed for an introductory, one-semester course in Control Systems for undergraduates and graduates in various engineering departments, such as electrical, mechanical, aerospace, and civil. It is written to be concise, clear, and yet comprehensive to make it easier for the students to learn this important subject with high mathematical complexity. The author emphasizes the physical simulation of systems, making it easier for readers to understand system behavior. The popular MATLAB® software package is used for programming and simulation. Every new concept is explained with figures and examples for a clear understanding. The simple and clear style of presentation, along with comprehensive coverage, enables students to obtain a solid foundation in the subject and for use in practical applications.

✦ Table of Contents

Preface
Contents
Abbreviations
1 Introduction
1.1 Basics of Control Systems
1.2 Basic Signals
1.2.1 The Unit-Step Signal
1.2.2 The Unit-Impulse Signal
1.2.3 The Unit-Ramp Signal
1.2.4 The Unit-Parabolic Signal
1.3 Sinusoids
1.3.1 The Polar Form of Sinusoids
1.3.2 The Rectangular Form of Sinusoids
Sum of Sinusoids with the Same Frequency
1.3.3 The Complex Sinusoids
Real Causal Exponential Signal
Exponentially Varying Amplitude Sinusoids
1.4 System Modeling
1.5 Summary
Exercises
2 The Laplace Transform
2.1 Laplace Transform
2.1.1 Properties of the Laplace Transform
Linearity
2.1.2 Time-Shifting
2.1.3 Frequency-Shifting
2.1.4 Time-Differentiation
2.1.5 Integration
2.1.6 Time-Scaling
2.1.7 Convolution in Time
2.1.8 Multiplication by t
2.1.9 Initial Value
2.1.10 Final Value
2.2 Laplace Transform Solution of Differential Equations
2.2.1 The Transfer Function
2.2.2 Transfer Function of Feedback Systems
2.3 Finding the Inverse Laplace Transform
2.3.1 Inverse Laplace Transform by Partial-FractionExpansion
2.4 Characterization of a System by Its Poles and Zeros and System Stability
2.5 Routh–Hurwitz Stability Criterion
2.6 Summary
Exercises
3 Mathematical Modeling of Electrical Systems
3.1 Modeling of Electrical Circuits
3.1.1 Circuit Analysis
Basic Elements in Electrical Circuits
3.1.2 Series Circuits
3.1.3 Parallel Circuits
3.1.4 Examples of Circuit Analysis
3.2 Summary
Exercises
4 Mathematical Modeling of Mechanical Systems
4.1 Modeling Electrical Systems
4.2 Modeling Translational Mechanical Systems
4.2.1 Theoretical Analysis
4.3 Modeling Rotational Mechanical Systems
4.3.1 Simple Pendulum
4.3.2 A Mechanical Rotational System
4.3.3 Field Current Controlled DC Motor
4.3.4 Armature-Controlled DC Motor
4.4 Summary
Exercises
5 Block Diagrams and Signal-Flow Graphs
5.1 Block Diagrams
5.2 Signal-Flow Graphs
5.2.1 Mason's Gain Formula
Conversion of a Block Diagram to the Corresponding SFG
5.3 Summary
Exercises
6 Steady-State and Transient Responses
6.1 Transfer Function of Feedback Systems
6.2 Steady-State Errors in Control Systems
6.2.1 Type 0 System
6.2.2 Type 1 System
6.2.3 Type 2 System
Steady-State Errors of Nonunity Feedback Systems
6.3 Unit-Step Response and Transient Response Specifications
6.4 Linearization
6.5 Parameter Sensitivity
6.6 Summary
Exercises
7 Root Locus
7.1 Plotting the Root Locus
7.1.1 Negative Feedback Systems
Angle of a Line in the Complex Plane
Breakaway and Break-in Points
7.1.2 Nonminimum-Phase Systems
7.2 Control System Design by Root Locus Method
7.2.1 Proportional Compensator
7.2.2 Proportional-Integral Compensator
7.2.3 Lag Compensator
7.2.4 Proportional-Derivative Compensator
Higher-Order Systems
7.2.5 Lead Compensator
Alternate Design
7.2.6 Proportional-Integral-Derivative Compensator
7.2.7 Lead-Lag Compensator
7.3 Summary
Exercises
8 Design of Control Systems in Frequency Domain: Bode Plot
8.1 Bode Plot
8.1.1 Bode Plot of a Lag Compensator
8.1.2 Bode Plot of a Lead Compensator
Approximation of e-Ts
8.2 Design of Control Systems
8.2.1 Relation Between Time-Domain and Frequency-Domain Specifications
Relation Between Phase Margin and the Damping Ratio ζ
8.2.2 Lag Compensator
8.2.3 Lead Compensator
8.2.4 Lead–Lag Compensator
8.2.5 Proportional–Integral–Derivative Compensator
The First Method
Second Method
8.3 Summary
Exercises
9 Nyquist Plot
9.1 Nyquist Plot
9.1.1 Nyquist Plots of Simple Transfer Functions
The Constant
First-Order Zero
First-Order Pole
Poles and Zeros at the Origin
9.2 Stability Analysis from Bode and Nyquist Plots
9.2.1 Nyquist Stability Criterion
Closed-Loop Stability from the Nyquist Plot
9.2.2 Nonminimum-Phase Systems
9.2.3 Systems with Delay Units
9.2.4 Pade Approximation of e-Ts
9.3 Summary
Exercises
10 State-Space Analysis of Control Systems
10.1 The State-Space Model
10.2 Frequency-Domain Solution of the State Equation
10.3 Time-Domain Solution of the State Equation
10.4 Commonly Used Realizations of Systems
10.5 Linear Transformation of State Vectors and Diagonalization
10.6 Controllability
10.7 Observability
10.8 Summary
Exercises
11 Design of Control Systems in State Space
11.1 Design by Pole-Placement
11.1.1 Direct Comparison Method
11.1.2 Using Transformation Matrix
11.1.3 Using Ackermann's Formula
11.2 State Observers
11.2.1 Design of Regulator Systems with Observers
Transfer Function of the Observer-Based Controller
11.3 Design of Control Systems with Observers
11.3.1 Quadratic Optimal Regulator Systems
11.4 Digital Implementation of Continuous-Time Systems
11.4.1 The Bilinear Transformation
Frequency Warping
Application of the Bilinear Transformation
11.5 Summary
Exercises
Answers to Selected Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Bibliography
Index

✦ Subjects

Technology & Engineering, Automation, Science, System Theory, Electrical, Language Arts & Disciplines, Library & Information Science, General