Table of Contents

Table of Contents

The interactive examples are organized in four main chapters: Mathematical Examples, Time-domain Examples, Frequency-domain Examples and State-space Examples.

  • 1. Mathematical Examples

  • 1.1 Complex Numbers

  • 1.1.1 Complex Numbers in Cartesian Form

  • 1.1.2 Complex Numbers in Polar Form

  • 1.1.2 Powers of Complex Numbers

  • 1.2 Derivatives of Polynomials

  • 1.3 Integrals of Polynomials

  • 1.4 Matrix Operations

  • 1.5 Functions and Their Graphs

  • 1.6 Fast-Fourier Transform (FFT)

  • 1.7 Laplace Transform

  • 2. Time-domain Examples

  • 2.1 Water Level Control System

  • 2.2 Antenna Azimuth Position Control System

  • 2.3 Mechanical and Electrical Systems

  • 2.4 Differential Equations

  • 2.5 Linearization

  • 2.5.1 Linearization of a Function

  • 2.5.2 Linearization of a Simple Pendulum

  • 2.6 Poles, Zeros – Basics

  • 2.7 Pole/Zero Placement

  • 2.8 Partial Fraction Decomposition

  • 2.9 First- and Second-Order Systems - Basics

  • 2.10 Time Response of the First-Order Systems

  • 2.11 Dominant Pole Approximation

  • 2.12 Loading Problem

  • 2.13 Routh and Hurwitz Stability Criterion

  • 2.14 PID Controller

  • 2.14.1 Time Response

  • 2.14.2 Closed-Loop System

  • 2.15 Steady-state Error

  • 2.16 Root Locus

  • 3. Frequency-domain Examples

  • 3.1 Transfer Functions

  • 3.2 Bode Diagram

  • 3.3 Nyquist Diagram

  • 3.4 Negative Feedback systems

  • 3.5 Gain and Phase Margin

  • 3.6 PID Controller – Basics

  • 3.6.1 Tuning a PID controller

  • 3.6.2 PID Control of First-Order Systems

  • 3.6.3 PID Control of First-Order Systems with Integrator

  • 3.6.4 PID Control of First-Order Systems with Time Delay

  • 3.6.5 PID Control of Second-Order Undamped and Critically Damped Systems

  • 3.6.6 PID Control of Second-Order Underdamped Systems

  • 3.6.7 PID Control of Second-Order Overdamped Systems

  • 3.6.8 PID Disturbance Rejection

  • 3.6.9 Discrete PID Control of Continuous First-Order Systems

  • 3.6.10 Discrete PID Control of Continuous Second-Order Systems

  • 3.7 PID Controller Design

  • 3.7.1 Operational Amplifier – P Controller

  • 3.7.2 Operational Amplifier – PI Controller

  • 3.7.3 Operational Amplifier – PD Controller

  • 3.7.4 Operational Amplifier – PID Controller

  • 3.8 Real-world Systems

  • 3.8.1 Mass-Spring-Damper

  • 3.8.2 Ball and Beam

  • 3.8.3 DC Motor

  • 3.8.4 Ball screw Positioner

  • 3.8.5 Pendulum on a Cart

  • 4. State-space Examples

  • 4.1 Solution of Differential Equations in Matrix Form

  • 4.2 Modal Analysis

  • 4.3 Diagonal Matrices

  • 4.3.1 Convergent Modes Only

  • 4.3.2 Divergent Modes

  • 4.4 Jordan Form

  • 4.4.1 Jordan Form with Real Eigenvalues

  • 4.4.2 Jordan Form with Complex Eigenvalues

  • 4.5 Transition From Differential Equation to State Space Form

  • 4.6 Modal Analysis of the Mass-Spring-Damper System

  • 4.7 Car Speed Dynamics

  • 4.7.1 Modal Analysis of Car Speed Dynamics

  • 4.8 Lunar Lander Lateral Position Dynamics

  • 4.8.1 Modal Analysis of Lunar Lander

  • 4.9 Equilibrium Points

  • 4.9.1 Example 1

  • 4.9.2 Example 2

  • 4.9.3 Example 3

  • 4.10 Internal Stability

  • 4.10.1 Example 1

  • 4.10.2 Example 2

  • 4.10.3 Example 3

  • 4.10.4 Example 4

  • 4.11 Observability

  • 4.12 Controllability

  • 4.13 State Space Formulation and Transfer Function

  • 4.14 Internal and External Stability

  • 4.15 Asymptotic Observer

  • 4.16 Luenberger Observer with Dynamic Requirements

  • 4.17 Observer for the Mass-Spring-Damper System

  • 4.18 Observer for Unobservable Plants

  • 4.19 State Feedback Control

  • 4.19.1 State Feedback Control - Performance

  • 4.19.2 State Feedback Control - Tracking Specifications

  • 4.19.3 State Feedback Control for Mass-Spring-Damper System

  • 4.20 Regulator Design

  • 4.20.1 Regulator for Mass-Spring-Damper System

  • 4.21 Real-world Examples

  • 4.21.1 Satellite Orbit Control

  • 4.21.2 Quadrotor Longitudinal Velocity Control

  • 4.21.3 Lunar Lander Horizontal Position Control

  • 4.21.4 Crane Load Position Control

  • 4.21.5 Robotic Arm with Flexible Joint Control

  • 4.21.6 Rotary Actuator Position Control

  • 4.21.7 Missile Attitude Control

  • 4.21.8 Hard Disk Head Control

  • 4.21.9 Car Cruise Control

  • 4.21.10 Aircraft Taxi Trajectory Control

  • 4.21.11 Quadrotor Lateral Position Control

  • 4.21.12 Pneumatic Position Control

  • 4.21.13 Autonomous Underwater Vehicle (AUV) Velocity Control

  • 4.21.14 Autonomous Underwater Vehicle (AUV) Heading Control

  • 4.21.15 Autonomous Underwater Vehicle (AUV) Depth Control