Welding processes have been automated over the past decades. Weld quality features, such as final metallurgy and joint mechanics, typically are not measurable online for control. Therefore, some indirect way of controlling the weld quality is necessary. A comprehensive approach to in-process control of welding includes both geometric features of the bead (such as the cross-sectional features of width, depth, and height) and thermal characteristics (such as the heat affected zone width and cooling rate). The weld bead depth, which is the key geometric attribute of a major class of welds, is very difficult to measure directly, but a method to estimate the depth using temperature measurement has been developed [26]. A model of the weld control system is shown in Figure AP9.3.

(a) Determine the phase margin and gain margin for the system when K = 1. (b) Repeat part (a) when K = 1.5. (c) Determine the bandwidth of the system for K = 1 and K = 1.5 by using the Nichols chart. (d) Predict the settling time (with a 2% criterion) of a step response for K = 1 and K = 1.5.