pagoda.skeleton.pid

pagoda.skeleton.pid(kp=0.0, ki=0.0, kd=0.0, smooth=0.1)

Create a callable that implements a PID controller.

A PID controller returns a control signal \(u(t)\) given a history of error measurements \(e(0) \dots e(t)\), using proportional (P), integral (I), and derivative (D) terms, according to:

\[u(t) = kp * e(t) + ki * \int_{s=0}^t e(s) ds + kd * \frac{de(s)}{ds}(t)\]

The proportional term is just the current error, the integral term is the sum of all error measurements, and the derivative term is the instantaneous derivative of the error measurement.

Parameters:

kp : float

The weight associated with the proportional term of the PID controller.

ki : float

The weight associated with the integral term of the PID controller.

kd : float

The weight associated with the derivative term of the PID controller.

smooth : float in [0, 1]

Derivative values will be smoothed with this exponential average. A value of 1 never incorporates new derivative information, a value of 0.5 uses the mean of the historic and new information, and a value of 0 discards historic information (i.e., the derivative in this case will be unsmoothed). The default is 0.1.

Returns:

controller : callable (float, float) -> float

Returns a function that accepts an error measurement and a delta-time value since the previous measurement, and returns a control signal.