Posts

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 …

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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 …

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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 …

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Quadrotor Roll, Pitch and Yaw Axis Lead Compensation (PID)

Quadrotor Roll, Pitch and Yaw Axis Lead Compensation (PID)

In the last post I simplified the model to arrive at a transfer function representing the roll and pitch axes independently for our ‘+’ shaped quadrotor. The following video explains how we stabilize this inherently unstable system. The PDF that follows is produced from the Maple document I review in the video. This, “lead-compensator” design …

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Simulation Methods: Double Integrator Example

Simulation Methods: Double Integrator Example

In the last post I focused on placing the lead zero for the roll and pitch axes based on the limit imposed by a second double-pole our plant introduces via the motor-propeller, ‘A’ term. I neglected to calculate the proportional gain required for unity-gain crossover at the frequency of maximum phase margin. I also did …

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Book Recommendation: Amazing Life of Science, Leadership Through Two Wars, and Education Reform

Book Recommendation: Amazing Life of Science, Leadership Through Two Wars, and Education Reform

To steal a line from football, here at MTwallets it’s about more than just, “X’s and O’s”. By that I mean more than just fascinating engineering and science problems to share and solve. Reading is a passion here too. History and biography in particular, but also good fiction. I’ve been wanting to grab from my …

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Quadrotor Control: State-Space Model

Quadrotor Control: State-Space Model

I covered, “PID” (Proportional-Integral-Differential) or, “classical” controller designs for the quadrotor platform in a post last fall…time flies! We really only employ the P and the D elements. The, ‘D’ is the, “lead compensator”. The proportional gain P is the last step and you can see how this design technique is performed in that post. This is …

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Quadrotor Linear Quadratic Regulator (LQR)

Quadrotor Linear Quadratic Regulator (LQR)

Big gap since the last post where we finally got the state-space model laid down. It got us to the plant model derived by Bouabdallah and others in his paper that we’ve used as a guide from the start. The goal all along has been not only to analyze and design candidate controllers for a Quadrotor platform, but to …

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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 …

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