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

where %, , %+ , fi , and A r' are perturbed qwtiti@r, aad
st* 'd &* are steady-state values.
Slmpllfication of equation (17) may be obtained conaidespecific
operating .,conditionso For eutample, since perturbatioarr are. beconsidered
about a steady-state cyllnder pres8u.m diifemntirl, the tom
d4 */df must be disregazdedo PPrthernore, it is a recognisd
fact that hydreullc servos generally are nearest instability at, or nwr,
the no-load conditiono* This zero laad condition closely correqadr to
a faired surfaces position, wherein the VO~UIB~B of oil on either ride of
the piston are very nearly equal. The effective oilrolme bar beem
previously defined as
4ra j
&+G
and since A = -A -
then
d
rldk dr( 6-c/;
5+G
so if 9 c, then fIr'=o ,
or
a constant bc I*
The approdmate linearized expression for perturbed fla thw
obtained under the foregoing conditions is
The physical representation of the oil within the cyllnder as a
spring is developed as follows:
Consider, first, an open ended cylinder that bas bean subJectad to
force d F and ccmpressed a Uear displacement A A , as shown b,
Pigo 50
* The effective damping tern, Cp , approaches eem as 4 , ud
hmce the cylinder had, dtninishee, See page 8.