{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

s11_ps10_spring04

s11_ps10_spring04 - Unied Engineering II Spring 2004...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Unified Engineering II Spring 2004 Problem S11 (Signals and Systems) Consider an aircraft flying 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 ζω n s + ω 2 n ) where the natural frequency of the phugoid mode is g ω n = 2 (2) v 0 the damping ratio is 1 ζ = (3) 2( L 0 /D 0 ) 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 ζω n s + ω 2 n ) is the normalized transfer function, corresponding to normalized input 2 g u ( t ) = δT 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. 2. Suppose we try to control the altitude through a feedback loop, as shown below G(s) + u(t) e(t) r(t) h(t) k
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
That is, the control input u ( t ) (normalized throttle) is a gain k times the error, e ( t ), which is the difference between the altitude
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}