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The P, I and D Terms

A PID controller combines three effects that each solve a problem: the P term gives a fast response proportional to the error, the I term integrates the error over time and removes steady-state error, and the D term reacts to how fast the error is changing and damps overshoot. Good control is about balancing the three against each other.

C(s)=K_p+\dfrac{K_i}{s}+K_ds

ideal PID controller

Symbols

$K_p$	proportional gain
$K_i$	integral gain
$K_d$	derivative gain

Example

$K_p=3$ , $T_i=0.5$ s:

$K_i=K_p/T_i=3/0.5=6$ .

K_p

gives a faster response but more overshoot – add an I term instead to remove steady-state error.

Practise pID control for free →

← Second-Order System and Overshoot · Closed Loop →

Part of Control Engineering: PID control.