### Category: Dynamics & Controls

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 …

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 of posts have been working out the sum of torque on our quadcopter. A few weeks ago, we covered the gyroscopic effect of the total airframe in the “equations of motion” post. Next, we looked at the …

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 …

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 …

## 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 …