Consider the system whose transfer function is given by: 1()(21)(3)Gsss=++. (a)Use the root-locus design methodology to design a lead compensator that will provide a closed-loop damping ζ =0.4and a natural frequency ωn=9 rad/sec. The general transfer function for lead compensation is given by(b)Use MATLAB to plot the root locus of the feed-forward transfer function, D(s)*G(s), and verify if the closed loop system pole is located on a root locus for the calculated value of K

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.