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mercial airplanes during the cruise fiight when the airplane is in the cruise mode.
Usually, with such a system, the airplane is manually operated during the climb
and descent portions of the flight. Once the aircraft has reached the desirect cruise
altitude, the altitude-hold autopilot is engaged. The autopilot will then maintain
that altitude, making whatever corrections necessary when updrafts or downdrafts
tend to cause the aircraft to gain or lose altitude.
Some autopilots have the feature that enables the pilot to enter a given flight
altitude in advance. In this case, the autopilot flies the aircraft, making it climb
or descend to attain the desired altitude. On reaching that altitude, the autopilot
Fig. 6.46 Block diagram of the outerloop of the pitch displacement autopiIoL
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 617
Real A,os
Fig. 6.47 Root-Iocus of the outer loop of the pitch displacement autopilot for the
business jeL
Ilg. 6.48 . Unit-step response of the pitch displacement autopilot for the business jet.
618 PERFORMANCE, STABiLITY, DYNAMICS, AND CONTROL
a) Scbematic diagram
Jng.6.49 Altitude-holdautopiIoL
h
automatically levels the aircraft and, afterwards, it will maintain that altitude until
told to do otherwise.
The schematic diagram ofa typical altitude-hold autopilotis shown in Fig. 6.49a.
The corresponding block diagram is shown in Fig. 6.49b. Wc have a lag compen-
sator in the forward path, which is required to retain stability on closing the outer
loop. The transfer fuPnction of the lag compensator is assumed as
Gc = k(s : ~).8)
(6.374)
The transfer function for the altitude-to-elevator input can be obtained as fol-
lows:
h = Uo siny
y -.O -a
(6.375)
(6.376)
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL 619
where Uo is the fiight velocity and y is the fiight path angle. Then,
sh(s) = Uoy(s)
h(s) Uoy(s)
Z 8e~S~ = A8e~S~
(6.377)
(6.378)
Uo[O(s) - a(s)]
= ABe(S) (6.379)
To illustrate the design procedure, let us consider the general aviation airplane
once again and design an altitude-hold autopilot for it. Using Eqs. (6.163) and
(6.164), we get
h(s) = Uo (-biS2 +(di - b2)S + (d2 - b3)) (6.380)
A8.(s~ = . a~s3 + a -S2 + a3S
where bi - -0.0273, b2 - -2.0366, b3 - O, ai -0.1695, a2 -.0.8494, a3 -
2.1851, di - -2.0112, and d2 - -3.9018.
At first, let us assume that there is no pitch rate feedback. The corresponding
root-locus of the altitude-hold autopilot with only altitude feedback is shown in
Fig. 6.50. We observe that, as soon as the outer loop is closed, the system becomes
unstable for any positive value of the gain k3. Therefore, we need to add the inner
loop with pitch rate feedback as shown in Fig. 6.51. The transfer function Gq is
Fig. 6.50 Root-Iocus of altitude-hold autopilot for the general aviation airplane.
.:l!
620 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
given by
Fig. 6.51 Inner loop ofthe altitude hold autopiIoL
dis + d2 (6.381)
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