Category: Science & Engineering

QuadCopter Dynamics and Controls: Ramp-Up Reading…

QuadCopter Dynamics and Controls: Ramp-Up Reading…

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 …

+ Read More

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 …

+ Read More

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 …

+ Read More

Propeller Blade, “Lift”

Propeller Blade, “Lift”

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 …

+ Read More

Quadrotor Dynamic Model: Propeller Gyroscopic Effect.

Quadrotor Dynamic Model: Propeller Gyroscopic Effect.

The equations below are 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 …

+ Read More

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. We covered gyroscopic effect of the total air-frame in the, “equations of motion” post a few weeks ago. Next we looked at the torque induced by the gyroscopic …

+ Read More

Linear Quadratic Control with Reference Input

Linear Quadratic Control with Reference Input

The last post was our introduction to the Linear Quadratic Regulator (LQR). We saw there that as we started with initial conditions or introduced a disturbance the LQR will drive the states to zero. In the simulations we saw the graphic of the copter converge on the zero state: zero roll, pitch, yaw, and respective …

+ Read More

Maximum Thrust vs. Battery Voltage

Maximum Thrust vs. Battery Voltage

In a previous post we got the Ardupilot simulator stable running the linear-quadratic attitude controller, but we had a hack in-place for normalizing our body torque commands from Newton-meters to -1 to +1 for input to the Ardupilot motor sub-system. Purpose This post uses a test stand to measure maximum available thrust over a range …

+ Read More

Gyroscope History: Lead Computing Gunsights

Gyroscope History: Lead Computing Gunsights

In this post we’ll dissect and simulate basic concepts embodied in early gyro instrumentation applications in combat gun sights. We’ll build a deeper understanding of gyro mechanics through this application of their first principle: output torque resulting from precession. We’ll learn some interesting history too. The basic problem to solve is this: when we fire …

+ Read More

Motor-Prop Model Validation

Motor-Prop Model Validation

In a recent post we used the Tyto 1520 test stand to get at a maximum thrust available from our motor-prop system. We want that maximum thrust so we can normalize our LQ controller command output for the Ardupilot motor command as outlined here. The Tyto 1520 offers great value for under $200. While we …

+ Read More