Wide-beam sensors for controlling dual-delay systems

A class of dual delay feedback systems of open loop transfer function G(s) = k exp(-Xs)/l - exp(-Ws) is shown to be unstable if ratio 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 of its central axis, closed-loop stability may be restored. Such transducers, termed widebeam sensors, include transmission, backscatter and natural radiation types as well as electromechanical conveyor belt weighers. Designing transducers for very narrow beams may not be desirable from the overall system viewpoint.