Proportional–Integral–Derivative Control

Lesson notes

Overview

A PID controller blends present, accumulated and predicted error to steer a system to its target. This topic is rated advanced and is number 25 of 93 in Engineering. Deeper models, formal results and harder reasoning.

What you are seeing

The panel above shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

A PID controller computes a correction from the error between the set point and the measurement: the proportional term acts on the present error, the integral on the accumulated past error to remove steady offsets, and the derivative on the rate of change to anticipate the future and damp oscillations, u = Kp e + Ki ∫e + Kd de/dt. It is the most widely used controller in industry, from thermostats to cruise control and drones, and must be tuned.

Reading the relationship

The expression "u = Kp e + Ki ∫e + Kd de/dt" is a compact summary of the idea. It uses the symbols u, K, p, e, i, d; name what each one stands for before you start. Notice that it contains a ratio, so increasing the denominator makes the result smaller, and an integral, which accumulates a quantity over an interval. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.

Try this

Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.

Common pitfalls

Always ask what the safety margin is and which assumption would break the design first. Idealised models hide losses, noise and limits.

How it connects

It builds on “Wind Turbine Power”, the topic before it in Engineering. Once you are comfortable, continue with “Proportional Control Only”.

Why it matters

Engineers use this idea to design structures, machines and systems that are safe, efficient and reliable.