How to calculate a pid controller

Control by PID1

is a control method often used for servos.

Don't you know what a bondage is? Well, it's a system, capable of reaching and

maintain a setpoint thanks to the measurements it performs.

Imagine, for example, in a car on the highway. You want to drive at 130Km / h

without having to press the accelerator. Your car's cruise control should

by itself maintain this speed. When approaching a slope the system "notices" that for

the same power at the level of the motor, it no longer reaches the 130 km / h setpoint and will add a

little acceleration. Yes but by how much? And how long will it take for the system to

stabilize around the setpoint?

That's the whole servo problem and PID control is one way to solve it!

PID is the most widely used regulator in industry. The idea of this control body is to

intentionally modify the value of the error which remains between the setpoint and the measurement

performed.

For example in the case of a position control the error would be: ε = c (p) - s (p)

In the case of proportional control, the error is virtually amplified by a certain gain

constant that should be determined according to the system.

Setpoint (t) = Kp.ε (t)

What in Laplace gives:

Setpoint (p) = Kp.ε (p)

Explanation:

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