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Let
            (6.183)
                              U = [~g:]                       (6.184)
so that
                                                   X - AX + BU                                     (6.185)
where
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL           567
A-
a12
a22
a32
a42
a52
B~
a13
a23
a33
a43
a53
a14
a24
a34
a~
a54
   ali- C).p       C).4
     mi-blCyB 012-- -
                                               '    m] - bi CyB
a13 = _Cypbi
 m-b~CB a14-.0 a,s=-( ;gB)
                        a21 - 0     a22 - o
                a23 -.1     a24 - 0     a25 -0
         a31  = Cip IzI + Cnp I;zl  + gibiaii          a32 = gi bl a12
        a33 = Crpbi I~i + C,,P)rlzlbl + €lbla13       034 = 0
                    a35 = ClrblIzl + CnrCzlbl + gibiais
               a41 - a42 - a43 - a44 - 0      a45 - 1
                                    asi  =  I/i Cnp  + /;zl Cip  + blg2al1
      a52 = g2bla2        a53 = bi (Cnp I:  + Ctp/;zl + €2a13)
             a54 - O         ass = bi (I;  Cnr + IrzlClr + g'2a15)
      Cy8u   b12- Cy8,
      bii - (mi -biC,.B)        = (m   biC~B).
                                b21 - O       b22 -. O
(6.186)
(6.187)
b31  = Cl8u lztj + Cnb" I;zl + gibibii          b32 = Cl8r/z I  + Cnbr /;zl  + €lbl b12
b41 - 0     b42 - O
     bsi = Cn8a K-i + Cl8a Czl + g2blbll        b52 = Cn& ~ + Cl8r C~zl + g2blb12
where
gl = Iz] CiB + -l;zi Cn~3
g2 = Ci CnB + /:-zl Clp

42';;]
568           PERFORMANCE, STABILI-fY, DYNAMICS, AND CONTROL
    For free response, U = 0 so that the above equation reduces to
                                              X -. AX                                   (6.188)
As said before, for nontrivial solution, the determinant of (AI - A) must be zero
                                                      IAI - Al -. 0                                      (6.189)
　
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