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Geq = a~S3 +~a2 +~Oa~s2 +~a3 +~Oa2~Okldl s +~O~a3 k d2~
(6.382)
;((;=(U) -bls2+(dl-b2)s+d2-b) (6.383)
ls+d2
The lag-compensator pole (s = -8) is sufficiently away from the origin so that
it has very little effect on the short-period dynamics. The root-locus of the outer
loop is shown in Fig. 6.54. We obse:rve that we have to confine ourselves to ver)/
Iow values of the compensator gain k3 to keep the system stable. A higher value
of k3 will make the system unstable. The effect of the compensator is obvious. It
has pulled to the left the branches of the root-locus that originate from the two
poles at the orig:in and migrate to the right half of the plane. This provides a small
range of stable values for the complex conjugate poles. With k3 = 0.1425, we get
the closed- loop poles at -8.5822, -6.3151 -i: j5.0691, -0.2118 :+: 1.1378, -1.94,
and -1.6175. .
To verify the design, we simulate the response of the system to a unit-step ele-
vator input as shown in Fig. 6.55. The large overshoot is due to the low value
of the damping ratio. Except for this, the system performance is satisfactory.
u
x
<
o.
ai
E
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 621
Fig. 6.52 Root-Iocus of the inner loop of the altitude-hold autopilot for the general
aviation airplane.
Fig.6.53 Outerloop of the aMtude-hold autopilot
622 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
ReaIAxis
Fig. 6.54 Root-Iocus of the outer loop of the pitch displacement autopilot for the
general aviation airplane.
2
1.8
1.6
1.4
1.2
s
91
o
0.8
0.6
0.4
0.2
o
Stap R8sponse, A~Utude Hold Auto-Pltot, GA Nrplane
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动力机械和机身手册3(93)
