Optimum lead-controller synthesis in feedback-control systems

The phase lead network, shown in figure 1, had demonstrated its ability to improve the relative stability of linear feedback amplifiers long before it was adopted as one of the principal stabilizing networks by those interested in the newer field of servomechanisms. Its wide acceptance was based upon its simple form when dealing with d.c. signals and its ability to produce rate-type signal components without mechanical devices. When used as a synthesis tool in connection with the Nyquist plot (1)¿ of the loop-transfer characteristics, it allows considerable freedom in shaping the contour to conform to generally acceptable standards of performance to the limited extent with which they can be interpreted on this Nyquist plot. The major drawback of the phase-lead network is its attenuation of the signal components, an attenuation which may be readily appreciated if this network is viewed as a resistance voltage divider under static (d.c.) conditions. This sacrifice is all the more objectionable in applications where higher-frequency noise components are present and the need to maintain the signal-to-noise ratio has virtually eliminated this useful tool from systems whose inputs contain large noise components. A system controlled by a radar signal provides just such a situation.