# Negative feedback

Negative feedback is a type of feedback, during which a system responds so as to reverse the direction of change. Since this process tends to keep things constant, it is stabilizing and attempts to maintain homeostasis. When a change of variable occurs within a stable negative feedback control system, the system will attempt to establish equilibrium. Negative feedback is also used in amplification systems to stabilise and improve their amplification characteristics (see eg Operational amplifiers).

A simple and practical example is a room thermostat (and indeed any thermostat). When the temperature in a heated room reaches a certain upper limit the room heating is switched off so that the temperature begins to fall. When the temperature drops to a lower limit, the heating is switched on again. Provided the limits are close to each other a steady room temperature is maintained. The same applies, but in reverse of course, to a cooling system, as in air conditioning, or a refrigerator or freezer.

Open systems (ecological, biological, social) contain many types of regulatory circuits, among which are positive and negative feedback systems. 'Positive' and 'negative' do not refer to desirability, but rather to the sign of the multiplier in the mathematical feedback equation. The negative feedback loop tends to bring a process to equilibrium, while the positive feedback loop tends to accelerate it away from equilibrium.

Following is a list of negative feedback systems:

• Circulatory control
• Erythrocyte concentration
 Contents

## In gaming

In games, negative feedback is a critical and heavily exploited mechanism for stabilizing the resources in a game. It has a number of uses:

• To maintain a consistent level of challenge and excitement. For example, AI opponents often adjust their skill level towards that of the player, challenging both novice and expert players alike. Racing games similarly offer advantages to those falling behind.
• To stretch out a game that would otherwise finish too quickly. For example, in Settlers of Catan, if a player has close to the winning number of points, other players will not trade with them, making it difficult and expensive to attain the final points needed to win. This gives other players time to catch up.
• To magnify late advantages while eliminating early ones, creating more exciting end games. In the Catan example, a player who has less points but more resources can get more in trade than one who used their resources earlier to attain more points, enabling the player who is behind to catch up. This makes it more likely that two or more players will simultaneously be very close to winning.

Negative feedback loops can also cause problems when they arise in a game accidentally. For example, a player might feel like they have no real control in a racing game if the opponent is always right behind them, or a game may become too long or become impossible for any of the players to win.

## in Amplifiers

Consider a voltage amplifier (other systems are similar).

In normal use we have Vout = A Vin, where the amplification A may in general be a function of both frequency and voltage.

Now devise a feedback loop so that a fraction -B of the output is added to the input. (for an 'operational amplifier' two resistors suffice -see Operational amplifier)

Then the input to the amplifier is now V'in, where

V'in = Vin - B. Vout

and so

Vout = A Vin'

Thus A'= Vout/Vin = A/(1+AB) and A' -> 1/B when A is large.

The effective amplification A' is then set by the characteristics of the feedback constant B, thus making linearising and stabilising the amplification characteristics straightforward.

Note also that if there are conditions where BA=-1, the amplifier has infinite amplification - it has become an oscillator, and the system is unstable.

The stability characterisitics of the gain feedback product (BA) are often displayed and investigated on a Nyquist plot (a polar plot of the gain/phase shift as a parametric function of frequency).

## Sources

• Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0262240459. Chapter 18: Games as Cybernetic Systems.

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy