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

Figure 2 shows an oscillographlc record of the response of a servomotor
to a step input under a relatively heavy inertia load. The traces
shown are: position responee, timing mark, downstream, cylinder pressure,
and upstream cylinder pressure. The characteristic acceleration phase
and dead heat deceleration phase are quite' clearly demonstrated. It will
be noted that the downstream cylinder pressure exceeds the supply pressure
in the deceleration phaee and at the same time the upstream cylinder
pressure is driven to zero (cavitation occurs).
Linear equation for approximation of the acceleration phase of the
responee. - It is indicated by the measured reeqonee of hydrdlic servomotors
under inertia loads that the acceleration phase may be approximated
by a linear second order systein. The general form of a second order differential
equation with constant coefficient may be written
At m load the servomotor responds as a first brder system. Equation
(4) should therefore reduce to equation (1) for the inertialess
case. meref ore :
At the start of the transient (t = + o), the upstream cylinder
pressure Is equal to the supply pressure and the domtream cylinder
pressure ia kual to the drain pressure . Hence when
Substituting these values in equation (4)
me differential equation that approximates the acceleration phaee is
then