Feedback Loops

Feedback loops are often used in modeling systems in biology, economics, mechanics, electronics, and computer operating systems.

A feedback loop samples the output of a process. Computations are done on those samples. These computations are called the feedback gain.  The resulting feedback is called the feedback signal.  This feedback signal is combined with new input. This is symbolized by the summation sign (the capital Greek letter sigma, which you used in algebra).

When the feedback acts to magnify the changes made by the process, the feedback loop is called a positive feedback loop.  This is indicated by the use of the plus sign in the diagram above.  In a mechanical system, this feedback might be a lever, and the feedback gain might be controlled by the position of the fulcrum of the lever.  In a sound system, the feedback gain might be an amplifier.  If you ever called a radio talk show host and left your radio on, you had a positive feedback loop.  Your voice was sampled at the radio station and transmitted.  Your radio amplified the voice which reentered the telephone.  You soon had a screech, and the radio announcer asked you to turn your radio off (interrupting the feedback loop) while you completed the phone call. In a computer operating system, the feedback gain can be a decision to increase the number of jobs in the Ready queue to increase utilization of the CPU.

When the feedback acts to dampen or reduce the changes made by the process, the feedback loop is called a negative feedback loop.  This is indicated by the use of a minus sign in the diagram above.  In a mechanical system, this feedback might be a sheet of rubber between two objects.  The rubber dampens vibration.  In a sound system, the feedback gain might be a noise canceller.  This is used by the phone company to eliminate echo.  In a computer operating system, the feedback gain can be a decision to decrease the number of jobs in the Ready queue to decrease paging device thrashing.

In the simplest of systems, the summation is a simple addition or subtraction of a single feedback signal and only a plus sign or a minus sign is used (not both).  The computation in the feedback loop consists of a simple multiplication by a positive constant.  The plus sign is used when this feedback is added to the new input, and you have a positive feedback loop. The minus sign is used when this feedback is subtracted, and you have a negative feedback loop.

In more complex systems, there can be multiple feedback signals that are combined with multiple input signals in a more complicated way.  The simple plus or minus sign does not adequately identify the operation.  Only the capital sigma is used.