
The closed-loop control system is unstable if u
T
(t) ¼L
1
{U
T
(s)} is ever in phase with e(t)
and its ampl itude is greater than one. When this occurs, the error signal propagates around the loop
and increases in magnitude while doing so. Conversely, when e(t) and u
T
(t) are in phase and
ju
T
(t)j¼ju
T
(t)j< 1, a stable system results. Finally, a marginally stable system exists when e(t)
and u
T
(t) are in phase and ju
T
(t)j¼ju
T
(t)j¼1.
Since the negative sign in u
T
(t) is equivalent to 1808 phase shift, u
T
(t) will be in phase with
e(t) whenever u
T
(t) lags e(t)by1808, that is, there is a combined total of 1808 phase lag in the
open-loop system. The