The spatial bandwidth of cross-directional control systems for web processes

Cross-directional control systems have been installed on a wide range of web processes, and many of these systems use an array of actuators to control cross-directional variations. This paper investigates the controllable bandwidth of these systems by using the concept of spatial frequencies to separate the controllable and uncontrollable components of a cross-directional disturbance. This leads to an expression for the spatial bandwidths of the whole array in terms of the spatial-frequency response of a single actuator. The analysis is closely related to Shannon's sampling theory, and a phenomenon similar to aliasing occurs when the spacing between the actuators is too large. A practical specification for the design of an array of actuators is given in terms of the spatial bandwidth of an individual actuator.