### Author: mtimmons

What is a “quad-rotor”? Well you probably know it’s a thing with four rotors. We buy it as a, “drone” and we fly it with a remote control or via a phone app acting like one. I’ll probably bounce between the terms quad-rotor and quadcopter throughout. I mean the same thing. It is incredible what …

I started to sketch a quadrotor model myself and derive the equations of motion, but I lost confidence and figured it would be best to sample the literature first. Below is a list of papers I found online. Click the links to see the papers. All the papers are useful, but I found the, “PID …

Dynamics and Controls Study Materials

## Dynamics and Controls Study Materials

I’ve enjoyed great opportunities to both study and work on mechanics, electronics, real-time control systems and supporting software for automated machines: Agricultural machine control for the most part, and some neat control systems problems in communications, sensors,  and other areas. Dynamic Modelling One thing I really like about, modelling a dynamic system is you need …

QuadCopter DC Motor(BLDC) + Propeller Dynamics

## QuadCopter DC Motor(BLDC) + Propeller Dynamics

Ultimately we’ll buy Electronic Speed Controllers (ESCs) for our Quad motors. They take PWM in and produce drive voltages for brushless DC motors. Let’s jump in to understand the motor-propeller subsystem on a quadrotor. DC Motor Modelling You’ll find basic DC motor equations in any undergraduate dynamics textbook. I add the Bouabdallah model for the …

Open Forum

## Open Forum

If you have a problem to solve and you’re looking for ideas, or maybe you want to challenge me to start a blog series on a new problem that you think we should tackle, please comment here! I encourage any students with interests or questions about any engineering or science field to inquire here. I …

Quadrotor: 4 props to stabilize the platform

## Quadrotor: 4 props to stabilize the platform

In the last post we arrived at a mathematical model for the combination brushless DC motor (BLDC), gearbox, and propeller model. A small quadrotor motor will not have a gearbox. It will have the propeller mounted directly to the shaft of a small hobby motor. In larger craft a gearbox helps match the motor to …

Revisit the Motor-Propeller Model

## Revisit the Motor-Propeller Model

It’s been fun to mess with the motor-propeller differential equation and linearization in an post. However, when I got into looking-up some rough parameter estimates and performing dimensional analysis (seeing if the units worked-out right for me in the equations) I ran into some problems. I realized I was not only needing numbers, but I …

In  the last quadcopter post we clarified the load torque of the propeller applied through the gearbox to the motor shaft. We won’t even have a gearbox but the terms in the equation needed clarification. We haven’t yet covered the main point of the propeller: LIFT! A propeller blade is just a spinning wing at each …

Quadcoptor Platform Equations of Motion: Dynamic Model

## Quadcoptor Platform Equations of Motion: Dynamic Model

Here we’ll derive the equations of motion for copter attitude: it’s roll, pitch, and yaw or orientation in the sky relative to an observer on the ground. The X,Y,Z position of the craft relative to the same observer comprise the other degrees-of freedom. We’ll later see how thrust and attitude drive to the X,Y,Z position, …