(idea) by Dilly Tue Sep 24 2002 at 14:37:42
In relation to the biological system, negative feedback has many positive features. To take a very simplified model:


                |---------|
  +             |    K    |
--->O---------->| ------  |------------------------->
I   ^           |  sT+1   |           |     O
   -|           |---------|           |
    |                                 |
    |---------------------------------|


Aside from being very accurate, the negative feedback system also has a very unintuitive feature. For example:

Our transfer function H = K/(sT+1), a simple low pass filter. The transfer function for the loop would be H = H/(1+H) which would if we subbed in the equations be:

{K/sT+1} / {1+K/(sT+1)}

which would simplify further to get

k/sT+1+k

The steady state gain (the gain at an unvarying input or s=0) would be come k/1+k.

Now, lets say in a normal person the gain of the filter is 9. Then the gain of the entire loop would be 9/1+9 which would be 0.9. Now lets say you had a lesion in your brain which killed off about 4 neurons in this simplified case. Your gain would drop to 5. However, the loop gain would be 5/1+5 which is 0.83. Therefore, a loss of 44% of the number of neurons involved in a pathway would only leave you with a loss of 7.8% of system gain. Very useful!

Of course this is all very simplified. There are indeed no biological system in which you have a negative feedback with a single low pass filter. But it does give you a nice example of how they help the body resist damage.


I like it!