Open Loop vs Closed Loop: Why Your Toaster Burns Bread and Cruise Control Doesn’t

Toasters, washing machines and cruise control: the difference between open-loop and closed-loop control, why feedback makes a system less sensitive to its own parts, and a graph of both handling the same disturbance.

Most toasters are honest about one thing: they have no idea what's happening to your bread.

You turn the dial, the coils glow for a fixed time, and then the toast pops up. If the bread was frozen, it comes out pale. If it was thin and dry, it comes out black. The toaster did exactly what it was told. It just never looked.

That's the difference we're going to pin down today, and it's the most important split in all of control engineering: open loop versus closed loop.

Open loop: follow the plan, don't check

An open-loop system works from a plan it decided on in advance. It never measures the result.

You'll find them everywhere once you start looking. A washing machine runs a set programme whether the clothes are clean or not. A traffic light changes on a timer even when the road is empty. A microwave heats for two minutes, and your leftover dal is lava at the edges and cold in the middle.

Open loop isn't a bad word. These systems are cheap, simple and can't go unstable, because there's no feedback to go wrong. When the plant is predictable and nothing disturbs it much, open loop is often the sensible choice.

Closed loop: measure, compare, correct

A closed-loop system adds a sensor and feeds the result back. Now the controller works on the error, which is the gap between what we want and what we're actually getting.

Cruise control is the classic example. You set 80 km/h. The car starts climbing a hill, slows to 78, and the controller sees a 2 km/h error and opens the throttle a little. Nobody told it about the hill in advance. It found out by measuring.

My favourite cheap example is the float valve in a water tank. The float rises with the water and slowly closes the inlet. It has no electronics and no software, and it's still a proper closed-loop controller.

Why feedback is worth the trouble

Here's the part that surprises most students when they first work it out on paper. Feedback doesn't just fix disturbances. It also makes the system far less sensitive to its own parts changing.

Say the plant has transfer function $G(s)$ and the controller $C(s)$. Open loop, the output is simply

so if $G$ drifts by 20%, perhaps because a heater element is ageing or a motor is warming up, the output drifts by 20% too.

Close the loop and the output becomes

Now look at how a change in $G$ reaches the output. Engineers call this the sensitivity:

With a loop gain of $CG = 9$, the same 20% drift in the plant moves the output by only about 2%. Push the loop gain to 49 and it drops to about half a percent.

Seeing it on a graph

Let's make it concrete. Take a simple plant, $G(s) = \dfrac{1}{s + 1}$, and give it a step input. At $t = 5$ s a disturbance hits, like a door opening in our heated room from the last post.

Two things jump out. The closed loop is much faster: it settles in well under a second, while the open loop takes about four. And when the disturbance arrives, the open-loop output simply sags by 40% and stays there. The closed loop barely flinches.

You might also have spotted that the closed-loop curve settles at 0.9, not 1. That's a real limitation of this simple proportional controller, called steady-state error, and fixing it is exactly what integral action is for. We'll get there in a later post.

So which one should you use?

Ask yourself two questions.

Is the plant predictable, with nothing much disturbing it? If so, open loop may be all you need. Does it matter a lot if the output is off? If so, measure it and close the loop.

Feedback does come at a price. You need a sensor, and a badly tuned loop can oscillate or even go unstable, which an open-loop system never does. Keeping feedback stable is the subject of a good chunk of this course.

A small exercise

Pick three machines in your home and sort them into open loop and closed loop. For the closed-loop ones, name the sensor. Here's a hint: an electric iron, a pressure cooker and a mobile phone's screen brightness are all more interesting than they look. Drop your answers in the comments and I'll go through them.