Consider the wind tunnel control system of Problem P7.31 for K = 326. Obtain the Bode diagram and show that the P.M. = 25° and that the G.M. = 10 dB. Also, show that the bandwidth of the closed-loop system is 6 rad/s.
Problem:
The development of high-speed aircraft and missiles requires information about aerodynamic parameters prevailing at very high speeds. Wind tunnels are used to test these parameters. These wind tunnels are constructed by compressing air to very high pressures and releasing it through a valve to create a wind. Since the air pressure drops as the air escapes, it is necessary to open the valve wider to maintain a constant wind speed. Thus, a control system is needed to adjust the valve to maintain a constant wind speed. The loop transfer function for a unity feedback system is
where p = 7.3 + 9.7831j. Sketch the root locus and show the location of the roots for K = 326 and K = 1350.