Report of the Second Piloted Aircraft Flight Control System - Acgsc.org

eutione, the aerodynamics and the contrdl stiok dynamicre If the phugoid
motion and very low frequency behavior is neglected, the a-cr
behaver essmtially as a sewnd-order rgrstem, with a tranefer f'unction
of the form ahom in SQ. 1. The relative damping ratio assoaicrted wlth
the conJugete pole8 here ir in our arample about 0.4. At'high apwds,
this relative damping ratio could be axpected to go or low as 0.1 or lesr.
Additional phaae lag is introduced in the uontrol stick dynamics, the
medwiaal vtan frm the control otick to the input to the hydraulic
~grrt-. The ~grutm wr ere oonaidaring here ir ahom in Fig. 3 atxi ha8
en rppmxbate tranafer funotion af the form: -
The overall open-loop systsm th& has a transfer function proportional
to the product of these two individual functions.
K
Sfs+8.Z)(sZ+ 7:l.s tC3)
The corresponding pole configuration for the open-loop wstem is of the
fom shown in Pigo 10.
We now consider what happens as we close the loop and bring up the loop
gain from a very low value. The poles of the closed-loop transfer function
move in the maaner shown in Fig. U. For relatively low values of loop gain,
the closed-loop system is unstable. How can this ~syotem be stabillzed? In
particular, haw can the system be stabilized at a value of loop gain vrNch
is mfficie~lrtly high to insure that we have adequate control characteristics?
The first and mgot obvious method is to introduce a device to cut the qotem
off, at least part way, at very low frequenciee-a device which the electronic
engineer wuuld term integral control. Such a device necessarily tends, as
we saw earlier, huuever, to decrease the speed of response of the system. We
have felt that the primary Job of any stabilization that is introduced should
be to force the airplane to respond more rapidly than the aerodynamical
uoefficients would ordinarily allow. Certainly, at least, thq stabilization
system should not make the system more sluggish.
Considering this pole configuration, one possibility is irmnediately
evident. We might attempt to move the pole due to the stick dynamics, wr
at-8.2, so far out into the l&-half plane that the system essentially
reduces to a third-order rither than a f ourth-order system. This can be
readily accomplished as shoun in Fig. U simply by an increase in the value
of the damping.coeffic5mt fp. There are two difficulties that arise at
once however, with such a scheme of partial stabilization. Flrst, the force
-
required of the pilot to move the stick at a constant velocity, when he is
moving essentially against this damper, increases intolerably. Secondly,
the time lag betwleen the stick and the output of the hydraulic ~ s t e ~
increases proportional to this damping coefficient. In particular, this
time lag, assuming the hydraulic system acts instantaneously, is given tgr
the ratio of the damping coefficient, fp, to the spring constant of the
push-rod, k, as is shown in appendix A. Thus, about the beet we can do