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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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