# Control Systems/Common Nonlinearities

There are some nonlinearities that happen so frequently in physical
systems that they are called \"Common nonlinearities\". These common
nonlinearities include Hysteresis, Backlash, and Dead-zone.

## Hysteresis

Continuing with the example of a household thermostat, let\'s say that
your thermostat is set at 70 degrees (Fahrenheit). The furnace turns on,
and the house heats up to 70 degrees, and then the thermostat dutifully
turns the furnace off again. However, there is still a large amount of
residual heat left in the ducts, and the hot air from the vents on the
ground may not all have risen up to the level of the thermostat. This
means that after the furnace turns off, the house may continue to get
hotter, maybe even to uncomfortable levels.

So the furnace turns off, the house heats up to 80 degrees, and then the
air conditioner turns on. The temperature of the house cools down to 70
degrees again, and the A/C turns back off. However, the house continues
to cool down, and then it gets too cold, and the furnace needs to turn
back on.

As we can see from this example, a bang-bang controller, if poorly
designed, can cause big problems, and it can waste lots of energy. To
avoid this, we implement the idea of **Hysteresis**, which is a set of
threshold values that allow for overflow outputs. Implementing
hysteresis, our furnace now turns off when we get to 65 degrees, and the
house slowly warms up to 75 degrees, and doesn\'t turn on the A/C unit.
This is a far preferable solution.

## Backlash

•Backlash refers to the angle that the output shaft of a gearhead can
rotate without the input shaft moving. Backlash arises due to tolerance
in manufacturing; the gear teeth need some play to avoid jamming when
they mesh. An inexpensive gearhead may have backlash of a degree or
more, while more expensive precision gearheads have nearly zero
backlash. Backlash typically increases with the number of gear stages.
Some gear types, notably harmonic drive gears (see Section 26.1.2), are
specifically designed for near-zero backlash, usually by using flexible
elements.

E.g.: Mechanical gear.

## Dead-Zone

A dead-zone is a kind of non linearity in which the system doesn\'t
respond to the given input until the input reaches a particular level or
it can refer to a condition in which output becomes zero when the input
crosses certain limiting value.

## Inverse Nonlinearities

### Inverse Backlash

### Inverse Dead-Zone

