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

The high frequency attenuation is expressed by the relation of equation
(19) . The cross-over frequency is defined by the intersection of
the low and high frequency asymptotes.
Phase shift is represented by straight lines on semilogarithmic
coordinates in figure 7. The slope of the low frequency line is defined
by the slope of the first order system (equation (14)) at jd = 45O. The
slope of the high frequency line is defined by the slope of the second order
system (equation (20)) at $ = 90'. The low frequency phase shift line
passes through # = 45' at the low frequency band break frequency ( fl) .
The high frequency phase shift line is oriented by the cross-over frequency.
In figure 7 the cross-over frequency is shown to occur after
the low frequency phase shift line has reached the 90° limit. The orientation
of the high frequency phase shift line for other relative
locations of the cross-over frequency is shown in connection with the
experimental responses.
Experimental responses. - Figure 8 shows the experimentally and analytically
determined effect on the frequency response of the hydraulic
servomotor of the parameters: load inertia and input amplitude.
Figure 8(a) shows the effect of load inertia on the amplitude attenuation
and on the phase shift. An increase in load inertia results in a
reduction in the frequency at which the attenuation becomes rapid. In
the analytical expression developed in this paper (summarized in fig. 7)
this effect is evident in the increased value of E' with increasing
load inertia and the consequent reduction in the values of f2 and f3.
Figure 8(b) shows the effect of input amplitude on the frequency
response. The increase in input amplitude is seen to have an effect similar
to that of increasing load inertia. This effect is made evident in
the analysis by equation (17).
In both amplitude and phase shift the agreement between the measured
responses and the analytical straight line approximations is in general
well within the experimental accuracy. The slopes of the attenuation and
phase data clearly demonstrate the first order characteristics of the
response in the low frequency band the the second-order characteristics
of.the response in the high frequency band. The transition from first
to second order characteristics at the calculated break frequency is
quite pronojmced.
APPLICATION TO DESIGlV
Design Relations
From equatiol23 (3) and (8) the following expressions for the piston
area and the product of the feedback ratio and port xidth of a straight
line servomotor can be derived: