Implement a PID Controller

MediumPython

Problem

Implement one discrete PID control step for a Symbotic robotic shuttle axis. The controller must compute a bounded actuator command while preserving controller state between calls.

Formal Specification

Implement pid_step(setpoint, measurement, dt, state, kp, ki, kd, output_min, output_max). Inputs are numeric values except state, which is a dictionary containing integral, previous_error, and initialized. dt is the elapsed time in seconds and is strictly positive. Return a two-element tuple: (output, updated_state), where output is clamped to the inclusive output range and updated_state has the same three fields.

Use these rules:

Compute error = setpoint - measurement.
Use zero derivative on the first call. Otherwise compute (error - previous_error) / dt.
Update the integral using integral + error * dt.
Apply anti-windup: if the unclamped output exceeds a limit and the current error would push it farther beyond that limit, retain the previous integral.
Store the current error for the next call.

Constraints

0 < dt <= 10
-10^6 <= setpoint, measurement <= 10^6
0 <= kp, ki, kd <= 10^4
output_min < output_max
Inputs are finite numbers
state contains integral, previous_error, and initialized

Function Signature

def pid_step(setpoint, measurement, dt, state, kp, ki, kd, output_min, output_max):

Implement one discrete PID control step for a Symbotic robotic shuttle axis. The controller must compute a bounded actuator command while preserving controller state between calls.

Formal Specification

Use these rules:

Compute error = setpoint - measurement.
Use zero derivative on the first call. Otherwise compute (error - previous_error) / dt.
Update the integral using integral + error * dt.
Apply anti-windup: if the unclamped output exceeds a limit and the current error would push it farther beyond that limit, retain the previous integral.
Store the current error for the next call.