Wide-Beam Sensors for Controlling Dual-Delay Systems

An important class of dual delay feedback systems of open-loop transfer-function G (s)=k exp (Xs)/ {1-exp(Ws)} is shown to be unstable if ration X/W is noninteger. By means of z-transform techniques it is shown that, by using a feedback transducer that senses over a substantial distance either side its central axis, closed-loop stability may be restored. Such transducers, here termed "wide-beam sensors", include transmission, backscatter and natural radiation types as well as electromechanical conveyor-belt weighers etc. The paper demonstrates that designing transducers for very narrow beams mat not be desirable from the overall system viewpoint.