Understanding Control Systems, Part 2: Feedback Control Systems

From the series: Understanding Control Systems

Today we’ll talk about feedback control. Let's go to your kitchen and see how you can use feedback control to toast bread perfectly.

You put a slice of bread in the toaster, set its timer level, and then turn it on. Depending on how long you toast the bread, you can get different colors. But you don't want just any color, you want to start your morning with this crispy, yummy toast.

There are two reasons this might be hard: If it's your first time using the toaster, you don't know how long to toast the bread. Or, assuming you do know how long to toast it, next time you might open the fridge and find a bagel or frozen bagel. These are variations that you may face, but regardless of these variations, you would still want to make perfect toast. So what if, instead of toasting the bread based on a timer setting, you toast it based on its color. “But how?” You might wonder.

If you continuously monitor the color of the bread, you'll know when exactly to turn off the toaster. This is the basic idea behind a feedback control system. Let's try this on a slice of bread and a frozen bagel. You turn on the toaster and start monitoring your bread. When the toast reaches the color you want, you turn off the toaster. Notice that you didn’t have prior information on how long to toast the bread. Monitoring them allowed you to tell when they have reached your desired color and when to turn off the toaster.

We will now read your mind. Don't worry, it’s not to hack your accounts or anything, but just to reveal the complete feedback control structure. While you are monitoring the bread, you draw a plot in your mind. On the y-axis you have the bread color that you're watching, and on the x-axis you have the time. This is what you want. Then, you start toasting, and this is what you see. At each time instant, you compute an error between what you see and what you want. If this error is not zero, you keep toasting. When “what you see” overlaps with “what you want”, the error becomes zero. Your yummy toast is ready, so you turn off the toaster. If we now project what you think in your mind onto the closed-loop structure here, we get the complete feedback loop. This part represents the comparison you make between “what you see” and “what you want”. You compute the difference between monitored and desired bread color, and this gives you the error. Then, based on the error, you decide whether to keep the toaster on or turn it off.

Next, we will switch rooms to see another example of feedback control and how it compensates for unexpected events. After eating your yummy toast, you're ready to take a warm shower. Similar to the previous example, you have a desired water temperature. By trial and error, you find the right position for the shower handle. You're planning to use this handle position for future showers, as well. But what happens when someone runs the dishwasher the next time you’re taking a shower? In this situation, the hot water is used up, and therefore the shower gets freezing cold. Let’s go back to the time where the dishwasher isn’t running yet and see how feedback control can compensate for this unexpected event. The water temperature is at your desired value; someone runs the dishwasher. Through your skin you sense that the water temperature drops. The error is now greater than zero. To compensate, you turn the shower handle towards the hot side and, as the temperature increases to the desired value, the error gets smaller. And the smaller the error gets, the smaller adjustments you make to the shower handle. If you now want to fully automate this process, you can use a thermocouple that measures the water temperature and then, based on the error, a controller can adjust the shower handle.

To summarize, in this video we’ve seen how feedback control works, how it handles variations in the system, and how it compensates for unexpected events. For the next video, don’t forget to buckle up, because you will drive to a party. You’ll learn about the terminology of basic components of a feedback control system.

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Recorded: 22 Nov 2016