Marty Daniel - Plaidcircuitry

Negative Feedback and Homeostasis*

Homeostasis a property of living organisms that maintains internal processes in a stable, constant condition. One way organisms keep stable or homeostatic is through negative feedback.

Negative Feedback

One good example of negative feedback is using a thermostat to control central air conditioning in a building.

digital thermostat

It's the summer time and it's hot outside. You set the thermostat for about 75°F. When the room gets warmer than 75°F the air conditioner turns on and cools the room. When the temperature falls below 75°F the air conditioner turns off.

Here is a diagram of how an air conditioning system works...

negative feedback loop

After completing the model below complete the post lab activity.

We will create our own model of this negative feedback system in a program called Vensim. Here are the steps.

Vensim Icons

Box Variable

Auxiliary/
Constant Variable

Arrow

Equation

Select

Rate

Pacman Delete

Control Panel

Input/ Output Object

Run

Open Vensim and accept whatever model settings it gives you.
Create a Box variable of the Actual Room Temperature.
Create a Rate pipe called Air Conditioning going into the Actual Room Temperature. You click and release where the pipe begins and then click and release where the pipe ends. Don't try to drag it.
Now you need to create 3 Auxiliary/Constant Variables:
1. Set Temperature (this is your ideal room temperature)
2. Difference Temperature (this is the difference between your Set temperature and the Actual Room Temperature)
3. Air Conditioning State (this is 1 if the AC is on and 0 if the AC is off)
Now you need to draw arrows from items to other items that affect them. Look at the diagram below to help you. Again you need to click and release and not drag.
1. The state of the air conditioner (whether it is on or off) determines how the air conditioner is cooling the room.
2. The temperature you have set as the ideal room temperature and the actual room temperature are used to figure the Difference between the Set and the Actual temperatures.
3. The Difference is then used to determine the Air conditioning state.
Now we need to put in equations that will drive the system.
1. Click on the equation tool and each item that needs an equation will be highlighted in black.
2. Now click on each item and and put in the correct equation.
  1. Set your ideal room temperature in Set temperature. I set mine at 75° Fahrenheit.
  2. Now set your Difference as Actual Room Temperature - Set Temperature.
  3. Now we will do the state of the Air Conditioner. By state I mean is it on or off. Vensim will not understand these terms but it will understand numbers. 1 will mean on and 0 will mean off. We will use an IF, THEN, ELSE statement to do this. Remember using that in our Excel games? Here is how we will format our statement for Vensim: IF THEN ELSE(Difference between Set and Actual>1, 1, 0) What is says is, "If the difference between the temperature I Set and the Actual temperature greater than 1° Fahrenheit then set to 1 (turn it on); if it's not greater than 1° Fahrenheit then set to 0 (turn it off).
  4. Now we'll do another IF, THEN, ELSE for the Air conditioning pipe. Here is the statement: IF THEN ELSE(Air Conditioning State, -0.25, +0.025). This means if the air conditioning state is on (1), then subtract -0.25 from the room temperature and if it is not on add 0.025.**
  5. Now we will set the actual room temperature. I set it to begin at 95° Fahrenheit and then to be modified by the Air Conditioning.
3. If you have done all your equations then none of them should be highlighted.
Now we will set up our first graph so that there is some place for our data to be displayed. To do this click on the Control Panel.
1. Now choose the "Graphs" tab at the top of the window.
2. Choose new...
3. You can graph any thing you want but for this exercise I choose to graph the room temperature and the AC.
  1. Start by Giving it a short name that is easy to understand.
  2. Next give the Graph a title
  3. Now you need to set the X and Y values. The X is Time and the Y is set below by clicking on the Sel button and choosing Actual room Temperature.
  4. Set the label to Temperature and the units to Temperature (Fahrenheit).
  5. Hide the legend. It is unnecessary because you are graphing only one value that is named in your graph title.
  6. Click OK.
Now place your graph on your workspace. Click on the Input/Output object and then click on your worksheet. Use the select tool to move and size the graph on your workspace.
Run your graph.
1. Click on the Run icon.
2. Unless this is your first time to run the model you will get a dialog box that tells you that your data set already exists and asks you if you want to overwrite it. The answer is yes.
3. If you've set everything up correctly then you school get the graph you see below.
Now set up a graph to see how the state of the Air Conditioner toggles off and on. Use the same methods you used above and the settings in the screenshot to guide you.

AC State Graph Setup

vensim ac diagram

**How did I come up with these numbers? I thought about my air conditioner at home and estimated how it cooled my house. I figured every minute the the system ran it would cool the room about a quarter of a degree (in the summer in Houston that is optimistic!) When the AC is off I was guessing that it would warm more slowly each minute due to insulation so I set it to warm ten times more slowly by moving the decimal place over one.

* You can read a paper about positive and negative feedback here.

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In the long history of humankind (and animal kind, too) those who learned to collaborate and improvise most effectively have prevailed

- Charles Darwin