Open-Loop Control Systems | Understanding Control Systems, Part 1

Summary

This video script explores open-loop control systems using everyday examples like toasters and showers. It explains how these systems work with a set input to achieve a desired output, such as adjusting the toaster's timer for different bread colors. However, the script also highlights the limitations of open-loop control, such as its failure when system variations occur, like using a different type of bread or when the hot water supply is affected by the dishwasher. The video concludes by posing the question of how to overcome these shortcomings, setting the stage for the next video on feedback control.

Takeaways

• 🍞 **Toaster Example**: An open-loop control system is demonstrated by a toaster, where the input (timer setting) affects the output (bread color).
• ⏱️ **Trial and Error**: Finding the right setting for desired output involves trial and error, establishing a model by plotting input-output relationships.
• 📈 **Modeling**: The toaster's behavior is modeled by plotting the relationship between timer settings and bread color, then fitting a curve to these points.
• 🔄 **Inverse Function**: To achieve a desired output, one must calculate the input by taking the inverse of the established function.
• 🚿 **Shower Handle**: Another open-loop system is adjusting a shower handle to achieve a desired water temperature.
• 🔧 **System Variations**: Open-loop systems can fail when there are variations, such as using a different type of bread in the toaster, which changes the input-output relationship.
• 🌡️ **Environmental Changes**: Unforeseen changes, like running a dishwasher, can affect the output of an open-loop system by altering available resources.
• ⚠️ **Reliability Issues**: Open-loop control is unreliable when faced with system variations or unexpected events, as it lacks feedback to adjust to these changes.
• 🔄 **Feedback Control**: The shortcomings of open-loop control will be addressed in the next video, which will discuss feedback control systems.
• 📚 **Conceptual Simplicity**: Open-loop control is easy to understand and implement, but it requires a clear model of the system to be effective.

Q & A

What is an open-loop control system?

An open-loop control system is one that takes an input and produces an output without any feedback mechanism to adjust the output based on the result. It simply follows a predetermined path or setting.

How is a toaster an example of an open-loop system?

A toaster is an example of an open-loop system because it takes an input (the timer setting) and produces an output (the color of the toasted bread) without adjusting the process based on the actual color of the bread.

What is the significance of the timer setting in the context of the toaster example?

The timer setting in the toaster example is significant because it represents the input that determines the output (bread color). It's how the user controls the toasting process without feedback.

Why might someone need to experiment with the toaster's timer setting?

Someone might need to experiment with the toaster's timer setting to find the optimal time to achieve their desired bread color, especially if they are using the toaster for the first time or with a different type of bread.

How does the color of the toasted bread relate to the open-loop control system?

The color of the toasted bread is the output of the open-loop control system, which is determined by the input (timer setting). It represents the result of the control action without any feedback loop.

What is the mathematical concept demonstrated by the toaster example?

The toaster example demonstrates the mathematical concept of function and its inverse. The function represents the relationship between the input (timer setting) and the output (bread color), and finding the inverse allows one to determine the input needed for a desired output.

Why might open-loop control fail in the context of the toaster example?

Open-loop control might fail in the toaster example because it does not account for variations such as different types of bread. The settings found by trial and error for one type of bread may not work for another, leading to an incorrect output.

How does the shower example illustrate an open-loop system?

The shower example illustrates an open-loop system where the handle position is the input and the water temperature is the output. The user adjusts the handle without feedback from the water temperature to achieve the desired warmth.

What is a potential issue with open-loop control in the shower example?

A potential issue with open-loop control in the shower example is that unexpected environmental changes, such as someone running the dishwasher, can affect the output (water temperature) without the system adjusting for it.

What are the limitations of open-loop control systems as discussed in the script?

The limitations of open-loop control systems include their inability to adjust for variations in the system or unexpected events, making them unreliable in such situations. This is because they lack a feedback mechanism to correct the output based on the actual results.

What is the main takeaway from the discussion on open-loop control systems?

The main takeaway is that while open-loop control systems are easy to understand and implement, they are not robust to system variations or external disturbances, which can lead to unreliable control outcomes.

Outlines

00:00

🍞 Open-Loop Control Systems Explained

This paragraph introduces the concept of open-loop control systems using everyday examples found in a house. The toaster is used as a primary example to explain how an input (time setting) affects the output (bread color). The process of experimentation to determine the relationship between input and output is described, leading to the creation of a model represented by a curve. The concept of taking the inverse of this function to achieve a desired output is also discussed. The paragraph highlights the simplicity of open-loop control but also points out its limitations when faced with system variations, such as using a different type of bread, which would require a new model. The example of a shower handle being adjusted to achieve a desired water temperature further illustrates open-loop control, but also introduces the issue of external factors like running a dishwasher affecting the system's performance.

05:01

🔄 Limitations of Open-Loop Control

The second paragraph delves into the limitations of open-loop control systems. It emphasizes that while these systems are easy to understand and work well under stable conditions, they can be unreliable when faced with variations or unexpected events. The paragraph uses the previous examples to illustrate this point, such as the change in bread type affecting the toaster's output and the dishwasher's impact on the shower's water temperature. The summary concludes by posing a question about how to overcome these shortcomings, setting up the discussion for the next video which will cover feedback control systems.

Keywords

💡Open-loop control system

An open-loop control system is one where the control action is independent of the system's output. In the video, this concept is introduced using the example of a toaster, where the user sets a timer without feedback from the actual toasting process. The toaster operates based on a predetermined input (time setting) and produces an output (toast color) without any adjustments during the process. This system is straightforward but lacks the ability to compensate for changes in the system or environment.

💡Input

In control systems, input refers to the variable that is set or adjusted by the user to influence the system's behavior. In the context of the video, the input is exemplified by the timer setting on the toaster or the position of the shower handle. These inputs are the user's way of interacting with the system to achieve a desired outcome, such as toasting bread to a specific color or adjusting the water temperature for a shower.

💡Output

Output in a control system is the result or response that the system produces in reaction to the input. The video uses the color of the toasted bread and the temperature of the shower water as examples of outputs. These are the tangible results that the user observes, which indicate whether the system is performing as expected based on the input provided.

💡Steady state

A steady state in a system refers to a condition where the output remains constant over time, despite possible variations in the input. The video script mentions fitting a curve through experimental points to represent the model of the toaster at steady state, which means that for a given input (timer setting), the output (bread color) stabilizes at a predictable value.

💡Model

A model in the context of control systems is a representation or abstraction of the system that helps in understanding and predicting its behavior. The video describes creating a model by plotting the relationship between the timer setting (input) and the resulting bread color (output) from the toaster experiments. This model is used to predict the input needed to achieve a specific output.

💡Inverse function

An inverse function is a mathematical concept where the roles of the input and output are reversed. In the video, the concept is used to explain how, given a desired output (toast color), one can calculate the required input (timer setting) by taking the inverse of the function that relates timer settings to toast colors. This is a way to solve for the input when the desired output is known.

💡Variations

Variations refer to changes or differences in the system's components or conditions that can affect its performance. The video script illustrates this with the example of toasting a bagel instead of bread, where the previously determined settings for bread would not yield the desired result for the bagel due to its different properties. Variations highlight the limitations of open-loop control systems in handling unpredicted changes.

💡Unexpected events

Unexpected events are occurrences that are not anticipated and can disrupt the system's performance. In the video, the example of someone running the dishwasher while little Timmy is taking a shower demonstrates how such an event can alter the system's output (water temperature) due to changes in the availability of hot water. This scenario shows the vulnerability of open-loop systems to external influences.

💡Feedback control

Feedback control is a control system strategy that involves using the system's output to adjust the input, thereby compensating for variations and maintaining the desired output. Although not explicitly detailed in the video script, the mention of feedback control at the end suggests that it is a solution to the limitations of open-loop systems discussed throughout the video.

💡Experiments

Experiments in this context refer to the process of testing and observing the system's behavior under different conditions to gather data. The video describes conducting experiments with the toaster to determine the relationship between timer settings and toast color. These experiments are crucial for developing a model and understanding how to manipulate the input to achieve a specific output.

Highlights

Introduction to open-loop control systems using everyday examples.

Toaster as an open-loop system with time as input and bread color as output.

Experimentation process to determine the relationship between timer settings and bread color.

Plotting the results of experiments to model the toaster's behavior.

Using the inverse function to calculate the desired timer setting for a specific bread color.

Exploring open-loop systems in the bathroom with the shower handle and water temperature.

Demonstration of how open-loop control works with the shower handle example.

Discussing the limitations of open-loop control when using different types of bread in the toaster.

Mathematical interpretation of system variations affecting open-loop control.

The impact of unexpected environmental changes on open-loop control, exemplified by the dishwasher.

Summary of open-loop control's ease and simplicity under ideal conditions.

Highlighting the unreliability of open-loop control in the presence of system variations or unexpected events.

Teasing the solution to open-loop control's shortcomings in the next video on feedback control.

Transcripts

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.