The force exerted by a reciprocating actuator is estimated as a weighted
sum of three quantities: a reaction-mass acceleration, a baseplate
acceleration, and a relative acceleration of the reaction-mass relative
to the baseplate. In one embodiment, acceleration sensors measure the
reaction-mass acceleration and the baseplate acceleration; and a
displacement transducer measures a relative displacement of the
reaction-mass relative to the baseplate. A double-differentiator
generates the value of the relative acceleration from the second
derivative of the relative displacement. In the sum, the relative
acceleration is weighted by factor representative of the ratio of the
difference between the masses of the reaction-mass and the baseplate to
the sum of the masses of the reaction-mass and the baseplate.