PHASE-SHIFTER - A NONLINEAR CIRCUIT FOR DIRECT MEASUREMENT OF PHASE MARGIN IN FEEDBACK-CONTROL SYSTEMS

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.