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Unformatted text preview: EE 428 PROBLEM SET 3 DUE: 28 Sep 2007 Reading assignment: Ch 3 sections 3.6 through 3.8 and section 4.1. Problem 10 (25 points) The landing of an airplane consists of three phases. First, the airplane is guided by radio direction-finding equipment toward the airport with approximately the correct heading. Within a few miles of the airport, radio contact is made with the radio beam of the i nstrument l anding s ystem (ILS). The pilot follows this beam to guide the airplane along a glide-path angle γ of approximately − 3 ◦ toward the runway. Finally, at an altitude h(t) of approximately 100 ft, the ﬂare-out phase of the landing begins. During this final phase of the landing, the ILS radio beam is no longer effective (because of electromagnetic disturbances), nor is the − 3 ◦ glide-path angle desirable from the viewpoint of safety and comfort. Therefore, the pilot must guide the airplane along the desired ﬂare path by making visual contact with the ground. The objective of this problem is to develop a state-space model and all-integrator block-diagram of the airplane for the final phase of the landing (the last 100 ft of the airplane’s descent). The airplane is guided to the proper location by air traﬃc control. The altitude h(t) and rate of ascent dh/dt at the beginning of this ﬂare-out phase range from 80 to 120 ft and from -16 to -24 ft/sec, respectively. The airplane is waved-off for values outside this range. Finally, only the longitudinal motion (that is, the motion in a vertical plane) is of interest in the final landing phase. Lateral motion of the airplane is required primarily to point the airplane down the runway, and is accomplished prior to the final ﬂare-out phase of the landing. The first step in the development of the state-space model and design of the landing control system is the formulation of the equations of motion of the airplane. The coordinates and angles of the airplane are depicted in Figure 1 and the symbols are defined in Table 1. The formulation of the equations of motion begins with a consideration of the aerodynamic forces and moments and the application of the fundamental laws of mechanics. The assumption that the deviation from the equilibrium ﬂight condition is small is then utilized to linearize the resulting equations. Because of the landing geometry, the glide-path angle γ is suﬃciently small so that the small- angle approximations sin γ ≈ γ and cos γ ≈ 1 can be made. Finally, the assumption is made that the velocity V of the airplane is maintained essentially constant during the landing by utilizing throttle control. Thus, the longitudinal motion of the aircraft is controlled entirely by the elevator deﬂection δ (t)....
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- Fall '07
- 1 kg, 1 sec, Gu Hx