A roll-wrapping machine (RWM) receives, wraps, and labels large paper rolls produced in a paper mill [9, 16]. The RWM consists of several major stations: positioning station, waiting station, wrapping station, and so forth. We will focus on the positioning station. The positioning station is the first station that sees a paper roll. This station is responsible for receiving and weighing the roll, measuring its diameter and width, determining the desired wrap for the roll, positioning it for downstream processing, and finally ejecting it from the station.
Functionally, the RWM can be categorized as a complex operation because each functional step (e.g., measuring the width) involves a large number of field device actions and relies upon a number of accompanying sensors.
The control system for accurately positioning the width-measuring arm is shown. The negative pole p of the positioning arm is normally equal to 2, but it is subject to change because of loading and misalignment of the machine, (a) For p = 2, design a compensator so that the complex roots are s = -2 ± j2√3 .(b) Plot y(t) for a step input R(s) = 1/s. (c) Plot y(t) for a disturbance Td(s) = 1/s, with R(s) = 0. (d) Repeat parts (b) and (c) when p changes to 1 and Gc(s) remains as designed in part (a). Compare the results for the two values of the negative pole p.