Feedback systems take one…

It’s late and I’ve wanted to write about feedback systems all day, but there was so much to do.

Anyway, feedback systems are pretty damn cool and understanding how they exist and shape our world seems like something that everyone should know about.

In essence, there are two general types of feedback systems: positive feedback systems (amplification) and negative feedback systems (self-correcting).    Positive feedback systems tend to be wildly unstable in that whenever they are disturbed, they get ever further “out of whack,” whereas negative feedback systems are generally good at re-establishing a stable state.

Note–positive and negative in this context do not mean good or bad, but instead refer specifically to the mathematical sign that is attached to the data that is fed back into the system.  To elaborate a bit more–let’s go back to the beginning.

Let’s say you have a system.  This system has an input and an output and it has sensors to measure these things.  A common example of such a system is found in many homes and that is the heating system that people have.  Such a system deals with the temperature within a household and theoretically, it should try to make the temperature behave the way that the homeowners want.  Now, imagine that people get home from work, and find that it is 60 degrees in their house and they want it to be 70.  Thus, they crank the thermostat to 70 and that sends a signal to turn on the furnace, which then begins to heat the air , and thus the temperature begins to rise.

Now, here is where the difference comes in between positive and negative feedback systems.  In a negative feedback system, which is what most heating systems are (which will become obvious in a bit), the sensor measures the change in temperature that exists versus the desired state (60′ is 10 degrees less than 70’==-10 deg) and it sends this signal to the furnace with a negative sign to tell the furnace what the temperature should be.  Thus, the furnace, which also knows it is 60, is told to add onto the temperature a – (-10), which turns into a +10 degrees.  Along the way, as the temperature rises–let’s say to 65, then the difference is only -5, so the furnace is told to crank it back a bit, since it only needs to raise the temperature a -(-5)=+5 degrees, and thus it heads towards 70 degrees with information all along that tells it to speed up or slow down as it approaches the desired state.

However, let’s say the heater does go on a bit long, and the temperature rises to 71 degrees.  Now the negative feedback system measures the temperature, finds a difference of +1 degree and then sends it back with a negative sign= -1 to the heater, which then knows that it should shut off because the temperature the feedback system is telling it to produce “-1” degree of heat, which equals cooling.

This is how negative feedback systems work.  They look at whatever “error” there is between the current state and the ideal state, and they feed it back to tell the system to move in the opposite direction from what it had been doing.  This  tends to eliminate the error.

Positive feedback systems do just the reverse.  Using our example, a “positive-feedback” heating system would, when you told it to go to 70′ from 60′, measure the temperature difference, which would still be -10 between actual and ideal state, and then it would send that signal to the furnace with a positive sign–meaning that it would tell the furnace to do whatever it could to change the temperature from what it currently was to the new temperature which would be -10 degrees hotter==10 degrees colder.  Thus, this system would actually tell your furnace to shut off when you asked it to heat.

Now.. let’s just say that your apartment was already at 70′ and the heater happened to heat it up to 71′.  A positive feedback system would measure this 1′ error and send that signal back to the furnace, telling it that it should heat more to reach a new state of 71′. As it is heating more, obviously the temperature is going to rise, and when it gets to 72′, the positive feedback system will measure the 2′ difference from the 70′ setting, and send this back to the furnace positively and it will then heat even more–and it will keep going until it is heating as much as it can and you are all sweltering.

This is the basic function of feedback systems.

Now, what is cool, is that there are tons of these systems all around you–both in the mechanical world–suspension systems, music systems, most dynamic moving systems–and in the natural world.  Understanding how such systems work is pretty crucial to understanding a lot of what goes on in the world.

For example–although over the long term, markets tend to function as negative feedback systems in aggregate–in short term panics, they can function much more like positive feedback systems which leads to the boom/bust cycles we’ve observed recently a bit too often.

In any case–more on this tomorrow..

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About Prof. Woland

I contain multitudes. Come meet us.
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One Response to Feedback systems take one…

  1. Pingback: Information, Filters, and Power | The Philosophy of NOM

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