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 which accurately measures the phase margin of a linear system operating in a feedback control loop. The measurement is made by inserting the phase shifter in the control loop, causing it to undergo self-sustained oscillations (limit cycle) of relatively low amplitude. It is shown that sustained oscillations occur at the gain crossover frequency, and the phase margin is equal to the phase lag of the inserted circuit. A complete analysis of the amplitude and frequency of oscillation, which employs the classical sinusoidal-input describing function, is also given and the stability of the limit cycle and its neighborhood, using the theory of integral manifolds, is included