Today, we will talk about open-loop control systems.
For this, we’re going to visit your house and see if we can find everyday examples.
Let’s start with the kitchen.
One of the devices you use daily is your toaster.
You place a slice of bread in it, then set its timer, and when it’s done, your toast pops out.
The bread’s color has changed based on the timer setting you chose.
Here, the toaster with the bread is an open-loop system that takes an input, time,
and gives an output, bread color.
Now suppose that you’re using the toaster for the first time.
You don’t know what setting the timer should be at to get your desired bread color.
In this case, you can do a couple of experiments.
You can input different timer settings, and wait until your output settles to a value,
then mark your findings on this plot.
Putting a slice of bread in the toaster
and setting the timer to a level of 2 gives you, let’s say, light brown bread.
In the next experiment,
for an input of level 4, you get medium brown.
And in the last one,
your input is 6, and you get a dark brown color.
If you now fit a curve through these points,
this represents the model of the toaster with the bread at steady state.
Remember that you want to find the time setting for your desired bread color.
To find this mathematically,
let’s equate the input to u and the output to y.
In the experiments,
for different values of u, you found the corresponding values of y.
So you can write y as a function of u.
But now you want to do the opposite.
Given the desired value of y, you want to calculate the value of u.
In mathematical terms,
this corresponds to taking the inverse of the function.
Therefore, to calculate the time you need for your desired bread color,
you take the inverse of it.
See, open-loop control is really easy.
Let’s jump to another room and see if we can find an open-loop system there.
Oh, this is little Timmy who wants to take a warm shower,
but he’s not tall enough to turn the shower handle
So, he asks for your help.
In this open-loop system,
the handle position is the input and water temperature is the output.
To help little Timmy, you turn the handle to different positions,
and based on this the water temperature changes.
Open-loop control seems to work perfectly.
All you need is to do a couple of experiments
and, once you have an idea of the model of your system,
you can easily find the input needed to get a desired output.
But are there any situations where open-loop control may fail?
Reconsider the toaster example.
Through trial and error,
you found that setting the timer to three gives you your desired bread color.
But what happens when you use a different type of bread, like a bagel?
You may end up having a burnt bagel
because the time settings you found by trial and error were for a slice of bread.
Let’s also look at the mathematical interpretation of this.
Through experiments you found the function f that determines the relationship between time and color.
But now that you use a different type of bread,
this relationship is not represented by f anymore, but another function, g.
Therefore, if you use the inverse of f,
you’re not going to get your desired color,
because the input needed to get the desired output is now calculated by taking the inverse of g.
This shows that open-loop control fails if you have variations in your system.
Now let’s go back to the shower example.
You positioned the handle such that little Timmy gets a nice warm shower,
but what happens when someone runs the dishwasher?
Water gets freezing cold.
The reason is that when the dishwasher is running,
the hot water supply is used up and therefore less hot water is available for the shower.
So, the water temperature drops.
This is another shortcoming of open-loop control.
Unexpected environmental changes acting on the system affect the output.
Let’s summarize what we’ve seen in this video.
Open-loop control is easy and conceptually simple.
Through experiments, you find the model of your system.
If there are no variations or unexpected events,
you know what input to give to the system to get a desired output.
However, when there are variations in the system or unexpected events,
open-loop control is unreliable.
So, the question is: how do we handle the shortcomings of open-loop control?
We’ll answer this question in the next video, where we’ll discuss feedback control.