CLCML

The proportional-Integral-Derivative controller widely used in closed-loop control systems. Additionally to current error, it uses error derivative and past errors.

$u(t)=K_{p}e(t) + K_i \int_{0}^{t} e(\tau)d\tau + K_{D}\frac{d}{dt}e(t)$

u(t) - the output of the controller, e(t) - is an error

$K_{p}, K_{i} , K_{D}$ are constants for proportional, integral and differential parts subsequenly.

Constants act as filters and their choice depends on a set goal. The proportional filter serves as an all-pass; integral term filters low frequencies and differential term compensate high frequencies.

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