Effect of wide-beam sensors on control of 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 ratio X/W in noninteger. By means of z-transform techniques, it is shown that, by using a feedback transducer that senses over a substantial distance either side of 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 may not be desirable from the overall system viewpoint.