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Ap(s) __ 0.0076s (6.282)
A8a~s~-. 76~:;~7tf
Ayr(s) -- ._0.00'76s _0.002 (6.283)
A8a~s~-6. 76.6~~76.
A[3(s) __ 0.0024S2+0.16s . (6.284)
A8r~S~-6. .76~.6~~76.
Arjr(s)=. _0.1582s-0.0294 (6.285)
A78r(S)=6. 76-.t~7f16.
For the spiral approximation,
Ap(s)_ 0.0021s2+0.0016s
~8(s~= ood0: -J:0-4S
Ap(s) _ 0.0097s
A8o~s~=-.6~fT.T. ~04S
Ap(s)_ = 1.8204 x l0~4 SZ +8.6321 x 10-4S
A8r~S- ~7~7~=G-
Ayj(s) . 0.0061
~ ))=-6. -7. To4S
A8 (s '
(6.286)
(6.287)
(6.288)
(6.289)
We note that
p(s) = s A~(s) (6,290)
r (s) = sAp(s) (6.291)
n zurplane and the final
Usmg the above transfer functions of the g~tatralt~fesatioof the lateral_directional
va}ue theorem (see Chapter 5), the steady-st Ls a step input can be obtained.
variables Ap, A4, and p for a grven input such as :
However, this is left as an exercise to the reader.
6.3.4 Lateral.Oirectional Frequency Response
~elateral_directionalfrequency responrseol:tsouaileron and rudderinputs is ofinter-
est oecause the pilotinput to these two contrrol surfaces can be considered as a signal
with a frequency content.The bandwidth ofthe human pilotis about 4rad/s (Ref. 3).
Therefore, it is reasonable to expect that a human pilot can control any lateral-
directional flight path variable using aileron/rudder mputs within this range of f. r3eV'
quency. The autopilots ha've much higher bandwidths, up to 20-25 rad/s (Ref. 3).
As an example of the lateral_directional frequency response, we have presented
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