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I would like to know more about PID. The math behind it, the calculations, the parameters, everything in detail. We know we can change the PID values on Mission Planner by observing the flight. That is what a customer does. But from a developer point of view I would like to know everything about drone PID.

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The forums are retiring in 2021 and are now closed for new topics and comments.

That is an almost endless rabbit hole, it would take many years of university studies to learn it (not even necessarily to understand it!) But if you are strong willed about it, here are a few youtube resources I came across that explain stuff in a more practical way (not so much academic stuff however)

To understand the math, you need to have a strong background in high level calculus, differential equations, and physics or whatever field of science and engineering you would like to apply PID control too. (It appears in just about everything! from aerodynamics to mechanics to electronics!)

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To model the behavior of a drone, you would need to know physics very well, be able to deal with complicated geometry, vectors, forces, torque, etc. Then you would need to also be competitive in aerodynamic properties of the propellers, and understand how they produce thrust as a function of RPM and/or torque, how the ESCs convert a PWM signal from a flight controller into a "power level" for the motor, because you want to know how the output signals of the flight controller relate to the quadcopters position with respect to time. That is where the differential equations come in, and control system theory. That is further complicated by the fact there are delays in the accelerometer data and gyroscopic data feedback mechanisms (generally manifesting as a limited updating rate as flight controllers tend to use discrete digital feedback.)

Hello. I have completed Mechanical engineering and I have a decent amount of knowledge in physics, calculus, aerodynamics etc. However I haven't studied much about electronics, control systems or PIDs. I just started reading about PIDs a week ago. I read a few pages and saw some videos and they have explained it very well. But I would definitely like to learn more, especially about the math calculations behind how PIDs work. I read about all the parts of the drone before I started building one (motors, propellers, ESCs etc). Therefore I think it would be worth giving a shot in reading about PIDs in depth. If you could share some information or links it would be great. Thanks a lot.

competent* not competitive lol

P = proportional

I = integral

D = derivative

All that PID does is describe how one control surface responds to a directive...

It has nothing to do with density altitude drone mass, speed and desired changes to flight path...

Depends on how you define it though...
Some drone manufacturers use "PID" for everything to make an otherwise low end product appear much better and fancier.
I've even them with PID supported controllers.
Far down in the tiny fineprint you could read that it was nothing more than "shock absorbers" in the stick axis so fast movements caused a higher resistance.

I guess it helps know the topics when you want to build a drone from scratch to get the right results in Google LOL

To know "everything" about PID requires a degree in control engineering. How long have you got ?

Google is your friend - more than enough info on drone programming if you try to look for it.

+1 too big a subject to cover in a few words.