P. Dantowitz et al., PHASE-SHIFTER - A NONLINEAR CIRCUIT FOR DIRECT MEASUREMENT OF PHASE MARGIN IN FEEDBACK-CONTROL SYSTEMS, IEEE transactions on instrumentation and measurement, 43(4), 1994, pp. 630-636
A novel nonlinear circuit called a ''Phase Shifter'' is introduced whi
ch accurately measures the phase margin of a linear system operating i
n a feedback control loop. The measurement is made by inserting the ph
ase shifter in the control loop, causing it to undergo self-sustained
oscillations (limit cycle) of relatively low amplitude. It is shown th
at sustained oscillations occur at the gain crossover frequency, and t
he phase margin is equal to the phase lag of the inserted circuit. A c
omplete analysis of the amplitude and frequency of oscillation, which
employs the classical sinusoidal-input describing function, is also gi
ven and the stability of the limit cycle and its neighborhood, using t
he theory of integral manifolds, is included.