Arc welding is one of the most important areas of application for industrial robots [11]. In most manufacturing welding situations, uncertainties in dimensions of the part, geometry of the joint, and the welding process itself require the use of sensors for maintaining weld quality. Several systems use a vision system to measure the geometry of the puddle of melted metal, as shown in Figure P6.3. This system uses a constant rate of feeding the wire to be melted.
(a) Calculate the maximum value for K for the system that will result in a stable system.
(b) For half of the maximum value of K found in part (a), determine the roots of the characteristic equation.
(c) Estimate the overshoot of the system of part (b) when it is subjected to a step input.
Figure P6.3
Welder control.

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Controller Arc Wire-melting process Desired Error diameter Puddle diameter (0.5ss 1) Vision system Measured diameter 0.005s1