A Quadcopter study looked like a fun challenge. It’s a busy area of interest, so there are papers and materials to use as a guide.

In the process, we’ll revisit optimal control, estimation, classical and state-space design techniques, system linearization methods and other topics. This is a good problem for a deep-dive due to the many degrees-of-freedom and multiple inputs and multiple outputs.

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 …

QuadCopter DC Motor(BLDC) + Propeller Dynamics

## QuadCopter DC Motor(BLDC) + Propeller Dynamics

I decided to start on the inner loops. By this I mean the control loops for each propeller drive system. A Brushless DC Motor (BLDC) is standard for hobby-sized quadrotors, so let’s assume the motor type. I haven’t sized anything yet: propellers or motors, but I can get the dynamic model figured out and put …

Quadrotor: 4 props to stabilize the platform

## Quadrotor: 4 props to stabilize the platform

In a recent post I shared a mathematical model for the combination brushless DC motor (BLDC), gearbox, and propeller model. A small quadrotor motor might not have a gearbox. It might have the propeller mounted directly to the shaft of a small hobby motor. A gearbox helps match the motor to the load: the propeller. …

Revisit the Motor-Propeller Model

## Revisit the Motor-Propeller Model

It was fun to mess with the motor-propeller differential equation and linearization in my earlier 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 …

In  the last post I was able to clarify the load torque of the propeller applied through the gearbox to the motor shaft. I haven’t yet covered the main point of the propeller: LIFT! A propeller blade is just a spinning wing at each cross-sectional location. The propeller force described in the NASA diagram in an …

Quadcoptor Platform Equations of Motion: Dynamic Model

## Quadcoptor Platform Equations of Motion: Dynamic Model

It’s been over one month since I last posted. Back then I took a journey into fluid mechanics to offer a glimpse into how propellers work. I was motivated to do this as I was previously working-out the electric motor and propeller dynamics when I started to recall my mechanics studies. It’s a good time …

Quadrotor Dynamic Model: Propeller Gyroscopic Effect.

## Quadrotor Dynamic Model: Propeller Gyroscopic Effect.

I copied the equations below from the last post, where we see we matched our Bouabdallah paper‘s equations for rotational motion. We know some propeller input is going to be a part of the applied torque. There is going to be a set of equations for linear motion too, but let’s clarify what is going on …

Finalizing Equations Of Motion: Thrust Inputs from Propellers

## Finalizing Equations Of Motion: Thrust Inputs from Propellers

This post explains how we determine propeller thrust and drag factors for our quadcopter project. The last couple posts have been working-out the sum-of-torques on our quad-copter. The first, “unforced” model considers the gyroscopic effect of the total air-frame. That was the first, “equations of motion” post a few weeks ago. Next we looked at …

Quadrotor: Simplifications for, “Classical” Controller Design

## Quadrotor: Simplifications for, “Classical” Controller Design

The last few posts covered each of three dynamic details separately: Gyroscopic effect of the rigid body (the entire quadcopter). Gyroscopic effect of the spinning propellers. Propeller thrust and drag effects. We’re going to use all of this information as we look at controlling the flight of a quadcopter, but first we’re going to make …