Interactive examples
Interactive examples
The interactive examples are organized in four section
- 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
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- 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
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- 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
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- 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
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