Phase shifter: a nonlinear circuit for direct measurement of phase margin in feedback control systems

A nonlinear circuit called phase shifter is introduced. It 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 that the phase margin is equal to the phase lag of the inserted circuit. A complete analysis of computing amplitude and frequency of oscillation which employs the classical sinusoidal-input describing function is also given, and the stability of limit cycle and its neighborhood using the theory of integral manifolds is included. >