In recent years, many automatic control systems for guided vehicles in factories have been installed. One system uses a magnetic tape applied to the floor to guide the vehicle along the desired lane [10, 15]. Using transponder tags on the floor, the automatically guided vehicles can be tasked (for example, to speed up or slow down) at key locations. An example of a guided vehicle in a factory is shown in Figure P7.19(a). We have

and Ka is the amplifier gain. Sketch a root locus and determine a suitable gain Kn so that the damping ratio of the complex roots is 0.707.
Figure P7.19
(a) An automatically guided vehicle.
(b) Block diagram.

2+4s 100 G)2 6) Ca) Actuator and vehicle Controller R(s) Direction _- reference Ms) Direction of travel Kin