Lecture 32 : General procedure for dynamics equation forming and introduction to control
Figure 32.7 Response
Physical systems can't change position instantaneously. They require some time to change position. So it will take some time to attain the desired position. So our desired response & actual response will differ from each other. The graph of displacemant versus time will be as follows which is actual response of block. Block is at rest initially & finally it should be at rest.
See that slope of OA =+ve & increasing i.e. Velocity is increasing (acceleration).
slope of AB= + ve & constant.
Slope of BC = -ve & decreasing i.e. Velocity is decreasing (Retardation).
Transient Response:
Steady state error:
Now suppose the task of moving is done but if there is difference between final desired position & actual position. That difference-- is known as steady state error. This should be as minimum as possible.
Stability:
Discussion on Transient response & Steady state error is immaterial if the system is not stable. Then what is meant by Stability?
For that consider a standard spring-mass-damper system.
--
is known as steady state error. This should be as minimum as possible. 
