In one mode of operation, the autopilot of a jet transport is used to control altitude. For the purpose of designing the altitude portion of the autopilot loop, only the long-period airplane dynamics are important. Assume that the linearized relationship between altitude and elevator angle for the long-period dynamics is
𝐺(𝑠) =
𝐻(𝑠) 𝛿(𝑠)
=
250 𝑠(𝑠 + 5)(𝑠 + 50)
ft/sec deg The autopilot receives from the altimeter an electrical signal proportional to altitude. This signal is compared with a command signal (proportional to the altitude selected by the pilot), and the difference provides an error signal. The error signal is processed through compensation, and the result is used to command the elevator actuators. A block diagram of this system is shown in figure below. You have been given the task of analysing the frequency response and stability of this system. Begin by considering a proportional control law D(s) = K.
1. Draw a Bode plot of the open-loop system for D(s) = K = 1
2. Find the approximate gain and phase margins of this system