Stabilization of carrier-frequency servomechanisms. I. Gain-phase margin diagrams of controller characteristics

Abstract

In this first part a method of analysis of linear carrier-frequency systems is indicated, and applied in particular to electrical servomechanisms using a two-phase alternating-current control motor. The performance of such a servo, as regards stability and fidelity of the output as a copy of the input, depends on the action of a controller-demodulator unit including the motor. A calculation of the steady-state effect of a linear transfer characteristic on the suppressed-carrier modulated error signal makes possible application of the Nyquist stability criterion. The method does not require symmetry of the characteristics about the carrier frequency; if such symmetry is present the system is similar to an ordinary or d-c. servo. Thus a band-rejection network tuned to the carrier frequency has an approximate proportional plus derivative action on the envelope of the error signal, resulting in an “anti-hunt” or stabilizing effect similar to that due to a translated band-rejection characteristic (center at zero-frequency) in a corresponding d-c. servo. A procedure is given for construction of transformed Nyquist diagrams, or gain-phase margin diagrams. The effect of the correctly tuned band-rejection network, as well as the effects of bandwidth, of the network being tuned off the carrier frequency, of increasing gain or velocity constant k ν, and of the use of phase-shifting networks, are clearly shown by a series of such diagrams.