hw3_f08 - Homework Set #3: MAE 4720/7720 Modern Control...

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Homework Set #3: MAE 4720/7720 – Modern Control Fall 2008 Due October 7, 2008 Problem 1: Consider again the motion of an unpowered (gliding) reusable launch vehicle (RLV) first introduced in HW#1. The vehicle parameters are Vehicle mass m = 4000 slugs Wing reference area S = 1600 ft 2 Zero-lift drag coefficient C D 0 = 0.036 Induced-drag coefficient K = 0.22 Atmospheric density model parameters: ρ SL = 0.002377 slugs/ft 3 β = 30,500 ft The (instantaneous) trajectory state we wish to linearize the system about is: Velocity V * = 480 ft/s Flight-path angle γ * = -10 deg Down-range distance x * = -63,500 ft Altitude h * = 10,000 ft Note that we can compute the required (reference) lift coefficient * L C from the governing equation of motion for flight-path angle ( ) and the requirement that the reference flight- path angle * is constant. a) Is this system controllable? Justify your answer. b)
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hw3_f08 - Homework Set #3: MAE 4720/7720 Modern Control...

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