STABILITY
The stability of a system can be demonstrated by a mechanical system consisting of a ball and pointed rod. If the system is placed either exactly right side up or exactly upside down it will remain in the same position indefinitely. However, if any outside influence - a push, vibration, or a slight air current - disturbs it. it may react in one of two ways. If it returns to the original position, we say the system is stable. Otherwise it is unstable.
STABLE UNSTABLE
Other systems - mechanical, electrical, or other types - also can demonstrate stability and instability. We describe the stability of a system by its response to a step input. A step input is a sudden change of input value from one level to another. In the above system, the step input is the push off of vertical. In an automobile cruise control a command to change the speed from 40 mph to 65 mph would be an example of a step input.
When a step input is applied to a system, there can be three types of response:
1)
The system output may move to the new value and remain there. This can happen with
or without overshooting the desired value. This type of system is stable.
How fast the output settles to its final value is determined by the damping
of the system
2)
The system may overshoot the desired value, drop below the desired value in an undershoot,
return above to another overshoot, etc. If the over- and under- shoots are always
the same level, we say the system oscillates.
3)
The system may behave as in 2) above, but the size of the over- and under- shoots may
progressively increase. This type of system is unstable and if not
stopped by some other factor will tear itself apart.