In the interests of improving airborne insulation of panels and of controlling room reverberation, a technique is studied for establishing control of the transverse vibrations of a thin plate by the application of active energy feedback. A localized point control force is derived from the sensed motion of some point on the plate surface. The superposition principle is applied in the form of a mobility analysis which shows that open loop gain conditions cannot result in a specific motion, including that of complete damping, of any arbitrary point on the plate surface but can be effective for particular points and for control of resonant modal motions under conditions of light damping. With velocity sensing, the characteristics for stable operation under the convenient condition of constant gain depend on maintenance of like symmetry, in the sense of an identity of velocity magnitude and sign, in the relative motion of sensing and control-force points. Bandwidth limitations are avoidable only by closure of the loop between these points. Two varieties of control force generator are involved: namely, where the generator mass is rigidly mounted and again where a spring mounting on the plate provides a self-supporting role. This is the first of two companion papers on active control of plate vibrations. Systems in which an array of multiple control units is used will be described in the second paper.