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4
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tre
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582 PERFORMANCE, STABILI-f'Y, DYNAMICS, AND CONTROL
_ Dutch RollApproximation
--- Complete Fifl.h-Ordcr System
t18
Fig. 6 23 Urut-step response (lateral-direchonal) of the general aviation airplane:
angle of yaw.
where
ASm = (mi'- btC:.B) (Ixllzl _"I2zl) (6.242)
B8ut = (-C}.p) (Ixllzl - Ix2zl) _ (Trll - biC).B)(lx Cnrbi + IziCipbi
+ Ixz] Ctrbt + Ixzi Cnpbi) - bi C).p(CiBb} Izl + Cn/Jbi Ixzl)
+ (mi - bi Cyr)(CIBbllxzl + IxICnBbl) (6.243)
C8 = bjz(mi - bi C),B)(Cip Cnr - qr C,,p) + bi Cyp(lxi Cnr + Izl Clp
+ Ixzl Clr + Ixzl Cnp) - Cy*bi(Cip Izl + Cnp I,zl)
+bi C).p (C,BC"rb~- - Cip Izl - Ixzl C"p - Cu C"Bb~)
+ (mi - bi Cyr) (Cip Ixzl + CiBCnpb<- - qp C~b2i + Ixl Cnp)
(6.244)
[Z
T
-o.5
-1-5
-2.5
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 583
Roil Subsidence Approximation
- Complete Fifth-Order System
.I.I.I.
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┃ -- -: - - - --- -- - - ┃
┃~..... li ┃
┃'~'};l{j ┃
┣━━━━━━━━━━━━━━━┫
┃ ┃
┣━━━━━━━━━━━━━━━┫
┃ ┃
┣━━━━━━━━━━━━━━━┫
┃ -...I.II..\- ┃
┗━━━━━━━━━━━━━━━┛
o 0.5
2 2.5 3 3.5 4
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