A laser beam can be used to weld, drill, etch, cut. And mark metals, as shown In Figure P5.3(a) [14]. Assume we have a work requirement for an accurate laser to mark a parabolic path with a closed-loop control system, as shown in Figure P5.3(b). Calculate the necessary gain to result in a steady-state error of 5 mm for r(t) = t2 cm.

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Mirror Laser cavity Focusing lens Nozzle assembly Beam Workpiece FIGURE P5.3 Laser beam control.