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

second, at least to the proper order of magnitude. Thus, if we attempt
to rid ourselves of the trouble with the relative or absolute instability
of the hydraulic system by cutting down the bandwidth, we soon reach a
point where the time of response of this part of the overall system becomes
undesirably long. In one sense, this is indeed an unfortunate circumstance,
since the bandwidth of this part of the system can simply be reduced by
cutting down the gain, the bandwidth being r0ughJ.y proportional to the gain
over the range of frequencies of interest to us.
The second alternative for eliminating the undesirable effects of
coupling between two highl~ underdamged system--the flutter system and
the hydraulic system--involves stabildnation of the hydrado system wNle
maintaining the hi& gain essential for fast response. The diagram of
figure 5 indicates the difficulties involved here. As it now stands, the
hydraulic system is charact eristied by a transfer function-the Laplace
transform of the ratio of the output over the input-with three polesone
at the origin, and the other two a conjugate complex pair very close
to the jw-axis. If we use the root-locus method of analysis we can see
at once the effect of closing the loop with varying amounts of gain. In
particular, we study what happens to the poles of the closed-loop transfer
function of the hydraulic system as the gain is increased. For very low
values of gain, the poles of the closed-loop system function are identical
with those of the open-loop transfer function. As the gain is increased,
the poles of the closed-loop system function move toward infinity, the
location of all the zeros of the open-loop function. The particular paths
taken by these poles as the gain is varied are shown in Fig. 6: one moves
out from the ori- along the negative-real axis, the other two move away
from the conjugate cornex pair of poles over into the right-half plane.
For a relatively low value of gain, these poles have crossed into the righthalf
plane, indicating that the closed-loop system is unstable.
How CM such a system be stabillzed? There are a variety of nays, im
terms of the pole-zero loci, and then a number of ways in which these desired
changes may be instrumented. We consider only one general method in any
detail. The furdamental difficulty is the proximity of the conjugate poles
to the jW ds. This arises because of the very sharp resonance betwem
the compressibility of the ofl and the mechanical and aerodynamical load.
This resonance can be msde less sharp, and also incidentally moved to a lower
frequency, if the compressibility of the oil can be effectively isolated from
the load--in other words, if at the same time the expanding oil is giving the
piston an extra push, there exists an alternate network which is absorbing
this extra effective flow. One possible system for doing this is shown in
fig. 7.
Hare in Fig. 7 both the hydrauuc-mechanical system and the equivalent '
electrical network are shown. In the equivalent circuit, the load corresponds
to the series resonant circuit made up of LC, Rc, and Cc, repressnting
respectively the mass, damping, and compUance of the aerodynamical and
mechanical load. The oil compressibility is represented by the parallcondenser
C. The resonance phenomena, speaking in electrical terms, ie