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Rewrite this in the following form:
                     k+ 2k+ 2k
           G(s)-.-\     -        (5.275)
            l -+b+~+b
y(s)
= r(s~                        (5.276)
or
     y(s)(l+b +b +b)=f(s)(k+ k+ k)     (5.277)
Then,
                            y(s) = 1 [-b,y(s) + kf (s) + 1 ([-(s)kai - b2y(s)]
                                                      s
                                     +1 [ka2-(s) - b3y(s)l)]                                               (5.278)
                      s
Let
                                     SX3(S) = ka2r(s) - b3y(s)                         (5.279)
                                                    SX2(S) - kair (s) - bzy(s) + X3(S)                                (5.280)
                                               SX1(S) - -bi y(s) + X2(S) + kr (s)                             (5.281)
so that
                                              y(s) = xi(s)                                 (5.282)
Talang the inverse Laplace transforms, we obtain the desired dual phase-variable
  b::-",l[x:l+[::lkr,t) (5.283,
and
                                            y(t) = xi(t)                                (5,284)
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426              PERFORMAhICE, STABILrfY, DYNAMICS, AND CONTROL
a)
-o
nl
\-
~
a
 c -0
o
                c)
Fig.436    C,r,CU,and C~ for the aircraft ofExample 4.10.
      For supersonic speeds, no general method of calculation is available. However,
a crude e~timate of the vertical tailis obtained using Eq. (4.618) with a,, evaluated
　
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