Each component of a servo system generates a phase lag as well as an amplitude gain.
sinusoidal input command (which can be used to determine the frequency response of a servo system), if the open-loop gain is greater than unity when the phase shift from input signal to feedback signal is 180, the system will be unstable.
This is because the feedback sine wave is in phase with the input sine wave.
causing the output oscillations to become larger and larger until something breaks or corrective action is taken.
Figure 17-14(b)and(c)
shows the transient response of a stable and an unstable respectively, servo system responding to a step input command.
17-14(a) shows the step input command, which is a constant input voltage applied at time t 0 to produce a desired output.
Observe that even though the stable system exhibits overshoot.
the output oscillation quickly dampens as it approaches the steady desired value.
The unstable system is one that depicts repeated undamped oscillations, and thus the desired steady-state output value is not achieved.