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┃ ┃ ┃ ┃ . ┃ ┃ ┃ l ┃ ┃
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234
5 6 7 8 9 10
t, s .
~g. 6.22 Unit-step response Oateral-directional) of the general a~niation airplane:
yaw rate~
where
Ap.& = Cy8. (Ixllzl - Ix2zl)
(6.237)
Bp.81 = -bi CyBr.(lxl Cnr + Clp Izl + Clr Ixzl + Cnplxzl)
+ bi C),p(lzl CL& + Cn8o Ixz I) - (Fr?l - bi Cyr)(Cl8a Ixzl + Cn8a Ixl)
(6.238)
Cp.8, = b?jCy8a(Clp C,,r - Ctr Cnp) + Cy4(CI8, Izl + Cn8a IxzJ)
- bf C).P (CL8,Cnr - Cn8a C,r) + bi (mi - bi Cyr)(Cn8" C,p - C,Sa Cnp)
(6.239)
Dp.b" = -bi Cy+ (q8,Cnr - Cn8a Clr) (6.240)
Expanding the determinant Aiar, we get a fifth-order polynomial in s, which is of
theYform"F '
Alar = A8 S5 + B8 S4 + CBr"S3 + D8iuS2 + E8rus (6.241)
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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