PID Motor Speed Control

Control systems

A speed loop around a DC motor with inertia $J$ , friction $b$ , and a driver that saturates at $\pm12\ \mathrm V$ . The controller sums $K_pe$ , $K_i\int e\,dt$ , and $K_d\dot e$ with conditional-integration anti-windup; each change re-simulates the full step response, including a load step halfway through.

Live circuit steady-state offset 12.2 %

Drag a value tag to change that part. Click a wire to clip a probe on.

Causal signal trace paused

Form the error The summing junction subtracts the measured speed from the setpoint; everything downstream reacts to this error.

t_{\mathrm{stage}}=\htmlData{math-slot=value}{\mathtt{0.00}}\,\mathrm{s}

Step 1 / 5 Form the error

Notebook: 9 parts and 11 wires, modelled as discrete PID + first-order DC motor with saturation

Recommended lab 16 of 18

Tune P, I, and D for a fast, offset-free step response without windup.

Builds on: Closed-Loop Buck Converter

Predict, then test

With only proportional control ( $K_i = K_d = 0$ ), the motor must overcome friction. Where does its speed settle?

Commit before the explanation appears. This is a prediction, not a quiz score.

Governing model

u = K_p e + K_i\!\int e\,dt + K_d\,\dfrac{de}{dt} \;\cdot\; J\dot\omega = K u - b\,\omega - \tau_L

Parts

setpoint $\omega_{set}$
parallel $K_p,\ K_i/s,\ K_d s$ paths
saturating driver
motor + tachometer

Limits of the model

$K_p: 0$ – $10$
$K_i: 0$ – $20$
$K_d: 0$ – $0.5$
driver limit $\pm12\ \mathrm V$

Diagnosis challenge The fault is hidden. Work it out from the changed outputs first.

Notebook: 9 parts and 11 wires, modelled as discrete PID + first-order DC motor with saturation

With only proportional control (Ki=Kd=0K_i = K_d = 0Ki​=Kd​=0), the motor must overcome friction. Where does its speed settle?

With only proportional control ( $K_i = K_d = 0$ ), the motor must overcome friction. Where does its speed settle?