On the Nature of Natural Control

Abstract

This paper examines families of structural control systems and reveals inherent properties that provide the essential motivation behind the theory of Natural Control. It is determined that the associated fuel consumed by the controls is near minimal when the natural frequencies are identical to the controlled modal frequencies, and when the natural modes of vibration are identical to the controlled modes of vibration. Also, by casting the objective to suppress vibration in the form of an exponential stability condition, it is found that vibration is most efficiently suppressed when the modal damping rates are identical to a designer chosen decay rate. The use of a limited number of control forces over distributed control is characterized by a change in fuel consumed by the controls and by a deterioration in the dynamic performance reflected by changes in the modal damping rates. The Natural Control of a space truss demonstrates the results.

Light impulsive damping of spacecraft exhibiting normal mode behavior

“…The preservation of the natural modes of vibration is a property of fuel optimal control. 6 The natural modes of vibration are preserved only if the control force does not recouple the associated modal equations of motion. Thus, the preservation of the natural modes of vibration is verified by substituting Eq.…”