ROOT LOCUS METHOD FOR ACTIVE CONTROL OF FLEXIBLE SYSTEMS.

Precise attitude and shape control of flexible spacecraft requires active control of flexural vibrations. This paper is concerned with the root locus method applied to active vibration control systems for a certain class of flexible bodies. A general characteristic equation is derived for a feedback system to control flexural vibrations with arbitrary numbers of sensors and actuators. Then it is shown, for the first time, that the characteristic equation in determinantal form may be reduced to a mathematically tractable form. It is also shown that under the condition of colocation of sensors and actuators the characteristic equation assumes a form in which the significance of this condition can be readily appreciated. Finally, the paper presents a numerical study to illustrate a practical procedure applying the root locus method to flexural vibration control systems.