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

The solution to equation (11) , is
iB
The term Ae is a vector quantity having an' amplitude A and
a phase angle fd. From equation (12)
High frequency amgUtude attenuation. - At no-load the piston velocity
is at all times proportional to the valve opening; therefore in the
response to a sinusoidal input at no-load the pilot valve area is zero
at the ends of the output travel (the velocity 'being zero). Under an
inertia load the piston velocity is not linearly proportional to the
pilot valve opening and hence in the response to a sinusoidal input the
valve area is not necessarily zero at the ends of the output travel. If
at high frequencies, the response of the servomotor is assumed to be
essentially sinuaoidal, the maximum acceleration can be considered to
occur at the Limits of the output travel and hence when the piston veloc-
ity ie zero. Under the condition of negligible mass of the hydraulic
fluid, the pressure difference across the piston at any instant when the
piston velocity is zero and the pilot valve area is greater than zero,
is the pressure difference acrose the servomotor. Above some frequency
the system may then be approximated by a Unear system wherein the preseure
difference across the piston varies sinurroidally with an amplitude
of (P,-P~) and with the frequency of the input. On the baeie of this
app~oximetion the acceleration of the piston is
Integrating equation (15) and introducing the condition that x
varies about zero and neglecting changes in sign