Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

The closed-loop control system is unstable if u

T

(t) ¼L

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

ju

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 ju

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)by1808, that is, there is a combined total of 1808 phase lag in the

open-loop system. The