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Unformatted text preview: Unified Engineering II Spring 2004 Problem S11 (Signals and Systems) Consider an aircraft ying in cruise at 250 knots, so that v 0 = 129 m/s Assume that the aircraft has lift-to-drag ratio L 0 = 15 D 0 Then the transfer function from changes in thrust to changes in altitude is 2 g 1 G ( s ) = (1) mv 0 s ( s 2 + 2 n s + 2 n ) where the natural frequency of the phugoid mode is g n = 2 (2) v 0 the damping ratio is 1 = (3) 2( L /D ) and g = 9 . 82 m/s is the acceleration due to gravity. The transfer function can be 2 g normalized by the constant factor mv 0 , so that 1 G ( s ) = (4) s ( s 2 + 2 n s + 2 n ) is the normalized transfer function, corresponding to normalized input 2 g u ( t ) = T mv 0 1. Find and plot the impulse response corresponding to the transfer function G ( s ), using partial fraction expansion and inverse Laplace techniques. Hint: The poles of the system are complex, so you will have to do complex arithmetic....
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- Fall '05