# Control Systems/Gain – Wikibooks, open books for an open world

## What is Gain ?

Gain is a proportional rate that shows the relationship between the magnitude of the input to the magnitude of the end product sign at firm state. many systems contain a method by which the acquire can be altered, providing more or less “ ability ” to the system. however, increasing derive or decreasing gain beyond a particular base hit zone can cause the system to become precarious. Consider the given second-order system :

T ( s ) = 1 sulfur 2 + 2 sulfur + 1 { \displaystyle T ( s ) = { \frac { 1 } { s^ { 2 } +2s+1 } } }

We can include an arbitrary addition term, K in this arrangement that will represent an amplification, or a power increase :

T ( s ) = K 1 s 2 + 2 sulfur + 1 { \displaystyle T ( s ) =K { \frac { 1 } { s^ { 2 } +2s+1 } } }

In a state-space system, the gain term k can be inserted as follows :

ten ′ ( t ) = A adam ( deoxythymidine monophosphate ) + kilobyte B u ( thymine ) { \displaystyle ten ‘ ( triiodothyronine ) =Ax ( thymine ) +kBu ( triiodothyronine ) }
yttrium ( metric ton ) = C x ( triiodothyronine ) + k D u ( deoxythymidine monophosphate ) { \displaystyle y ( thyroxine ) =Cx ( metric ton ) +kDu ( deoxythymidine monophosphate ) }

The advance terminus can besides be inserted into early places in the system, and in those cases the equations will be slightly different .
here are some good examples of arbitrary gain values being used in physical systems :

Volume Knob
On your stereo there is a volume knob that controls the gain of your amplifier circuit. Higher levels of volume (turning the volume “up”) corresponds to higher amplification of the sound signal.
Gas Pedal
The gas pedal in your car is an example of gain. Pressing harder on the gas pedal causes the engine to receive more gas, and causes the engine to output higher RPMs.
Brightness Buttons
Most computer monitors come with brightness buttons that control how bright the screen image is. More brightness causes more power to be outputed to the screen.

## Responses to Gain

As the gain to a system increases, generally the rise-time decreases, the percentage overshoot increases, and the settling time increases. however, these relationships are not always the same. A critically damped system, for exercise, may decrease in rise fourth dimension while not experiencing any effects of percentage overshoot or settle time .

## reach and constancy

If the addition increases to a high enough extent, some systems can become precarious. We will examine this consequence in the chapter on Root Locus. But it will decrease the sweetheart state of matter error.

### conditional constancy

Systems that are static for some gain values, and fluid for other values are called conditionally stable systems. The stability is conditional upon the rate of the profit, and much the doorsill where the system becomes unstable is crucial to find .

This page of the Control Systems bible is a stub. You can help by expanding this page, but make sure to follow the local manual of arms of dash. If you would like to help, but you do n’t know how, you can ask on the