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

  • State Space Formulation and Modal Analysis

    • Response of a system in state space form using the Lagrange Equation

    • Modal Analysis

    • Modal analysis for diagonal matrices

    • Modal Analysis and Jordan Form

  • System Dynamics in State Space

    • Spring-Mass-Damper system - response to inputs and initial conditions

    • Modal analysis of the spring damper system

  • Equilibrium Points

    • Equlibrium Points as a function of input and dynamic matrix eigenvalues

    • Systems with single or infinite equilibrium points and eigenvectors

    • Relations between dynamic matrix structure and equilibrium points

  • Stability

    • Stability and dynamic matrix eigenvalues

    • Convergent and divergent modes and stability

    • Convergent and divergent modes and initial conditions

  • Structural Properties

    • Observability

    • Controllability

    • Pole-zero cancellations

    • Internal and external stability

  • Asymptotic observers

    • Observer design in general

    • Observer desin with performance specifications

    • Observer design and desired closed loop dynamics

    • Observer desin for the mass-spring-damper system

    • Observers for non-observable plants

  • Pole placement

    • Pole placement in general

    • Pole placement with performance specifications

    • Pole placement for the mass-spring-damper system

    • Pole placement with observer feedback

    • Pole placement for the mass-spring-damper systemusing an observer for state feeback

  • Practical design examples on real world applications

    • Lunar Lander altitude control

    • Lunar lander landing position control

    • Hydraulic Cylinder control

    • Control of Robotic Arm with flexible joint

    • Rotary actuator position control

    • Missile attitude control

    • Hard Disk Head control

    • Car cruise control

    • Quadrotor velocity control

    • Quadrotor position control

    • Quadrotor attitude control

    • Practical design examples on real world applications

    • AUV velocity control

    • AUV heading Control

    • AUV depth control