Feedback control, from first principles

Foundation lesson · Study time: about 20 minutes. Prerequisite: subtraction and basic algebra. Aim: identify a setpoint, measurement, error, controller, and plant; then calculate a proportional command.

Follow the information around the loop

A controller needs a target and a measurement. For the negative-feedback convention used here, error equals target minus measured output: e = r − y. The plant is the process being controlled; the controller chooses its input. Measuring the resulting output closes the loop.

Proportional control uses u = Kp × e. The gain Kp sets how strongly a given error changes the command. A larger gain does not guarantee a better system: dynamics, delay, noise, and actuator limits matter. Feedback alone does not prove stability.

An original calculation: a simulated speed loop

Suppose a classroom simulation has a target speed of 900 revolutions per minute and a measurement of 840 revolutions per minute. The error is 60 revolutions per minute. Choose a proportional gain of 0.4 percentage points of command per revolution per minute. The calculated command is 24%. At a measured speed of 880 revolutions per minute, the same law gives 8%.

For this example, assume commands are limited to 0–100% and a positive command increases speed. A negative result is clipped to zero; this actuator cannot command reverse torque. The arithmetic describes a control law, not a prediction of the next speed. A plant model is needed for that prediction.

Check your understanding

At a measurement of 875 revolutions per minute, what command follows? Answer: (900 − 875) × 0.4 = 10%. Explain why a measured speed above the target would produce a zero command after clipping. Then identify which measurement delay you would need to model before judging the response.

When studying a simulated response, examine stability, overshoot, settling time, and any remaining error. Proportional action may leave a nonzero steady error; the outcome depends on the plant and operating conditions.

Editorial note

Written independently for IIMEEE with AI assistance. Technical statements and the worked example were checked against the references listed below. No external prose, code, diagrams, or tables have been reproduced. These introductory notes use simplified assumptions; they are not instructions for operating machinery or live electrical equipment.