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┃.                 ┃            ┃          ┃           I         .                                                          ┃       l                  ┃
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t, s
Fig. 6.25  Unit-.step response (Iateral-directional) of the general aviation airplane:
roll angle.
where
    Art,  -. (mi  - bi CyB)(lxi Cn8" + Ixzl Cl8.) + C).8a (Ixzl Ci/)bi + Ixi CnBbi)
          (6.249)
B?/,  = -Cyp (Ixzl Cn8o + Ixzl q8.) + (ttll  - b] Cyh)(Cl8o Cnpbi  - Cn8" C,pbi)
         + Cypbi ( - Cn8,CtBbl + Cn:a CnBbi) + Lzi c. ip + qp Cnpb~
       - CnBCtpb~ + Ixl Cnp                                                        (6.250)
Cv, = -Cypbi (CI&,Cnp - Cn&; Clp) + bi Cyp (Cnp Cl8" - Cip Cn8,,)
           + C).* (-C"8"  + CiBbi  + Ct8" Cnpbi) + bi (Ctp Cnp  - Ctp Cnp)
Dp = Cv4(Cnp Ciaso - Cip Cnt,)
(6.251)
(6.252)
               AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL         585
The transfer function for the bank angle is given by
A4(s)
A8a~s~ =
(mis - bi C),Bs - C),p)   Cy8tr       mis - bi CyrS
    -(Cip + bi CWs)       Cl8a    - (qrbis + IxzIS2)
    -(Cnp + bi C,,ps)       Cn8a    - (CnrbiS - IzIS2)
Alar
           (6.253)
Let N4,&  denote the determinantin the nurnerator. Expanding, we get
                                     6.8" = A6S2 + B6s + C4                        (6.254)
where
          A4 = (mi  - bi Cyp) (I.zi Cn8   + Iz I CL8,) + Cy8"(Lzl C"Bbi  + Iz] CLBbi)
           (6.255)
          Bi = -C).p (Ixzi Cn8a + Izl Clb,) + (lTII  ~ bi CyB)(Cn8,,Clr - CLai Cnr)bi
                  - Cy8,, (CiBCnrb~- - Cip/zl  - Cnp Ixzl  - CnBCtrb~)                       .
               + (mi - bi C},r)(q8i Cnpbl - Cna Ctpbi)                                 (6.256)
                           C6 = (mi - bi C).r)(Cia:,Cnp - Cn&Ctp)                (6.257)
Substituting the mass and aerodynamic characteristics of the general aviation air-
plane, we get the transfer functions of the general aviation airplane as follows:
　
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