A manufacturer uses an adhesive to form a seam along the edge of the material, as shown in Figure AP13.2. It is critical that the glue be applied evenly to avoid flaws; however, the speed at which the material passes beneath the dispensing head is not constant. The glue needs to be dispensed at a rate proportional to the varying speed of the material. The controller adjusts the valve that dispenses the glue [12].
The system can be represented by the block diagram shown in Figure P13.15, where Gp(s) = 5/10.04s + 12 with a zero-order hold G0(s). Use a controller
that represents an integral controller. Determine G(z) D(z) for T = 40 ms, and plot the root locus. Select an appropriate gain K and plot the step response.
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