PID

Combines proportional, forward-Euler integral, and backward-difference derivative terms from an error input.

Behavior

i(0) = ic
i(n) = i(n-1) + dt * e(n-1)       for n > 0
d(n) = (e(n) - e(n-1)) / dt       with e(-1) = e_ic
u_out(n) = kp * e(n) + ki * i(n) + kd * d(n)

Ports

Direction	Name	Type
Input	e	T
Output	u_out	T

Parameters

Name	Type	Default	Meaning
T	type (default f64)	f64	Float scalar type
kp, ki, kd	T	1.0, 0.0, 0.0	Proportional, integral, and derivative gains
ic	T	0.0	Initial integral state
e_ic	T	0.0	Error sample before the first tick

T defaults to f64 and is a scalar float type. dt must be nonzero because the derivative term is always computed, even when kd = 0.

Example

With dt = 0.1, kp = 2, ki = 1, kd = 0, ic = e_ic = 0, and errors 1, 1, outputs are 2, 2.1.