Control system eliminates or reduces flexibility effects on the manual and automatic control of large flexible vehicles. It extracts rigid-body and flexible-body motion and adapts well when a flexible-body frequency coincides or nearly coincides with the control mode frequency

Howard, J. C.

English

NASA Technical Reports Server

April 1967	 Brief 67-10081 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Rigid-Body Motion Extracted from Total Motion of a Flexible Body 
The problem: 
Devise a method to eliminate or reduce flexibility 
effects on the manual and automatic control of large 
flexible vehicles. The complexity of conventional con-
trol systems is greatly increased by the introduction of 
structural feed-back at frequencies close to the closed-
loop, rigid-body control mode frequency. 
The solution: 
A method that extracts rigid-body motion from 
combined rigid-body and flexible-body motion. The 
method is well adapted to situations where a flexible-
body frequency coincides with or differs only slightly 
from the control mode frequency. 
How it's done: 
The method involves the extraction of rigid-body 
motion from the total motion of a flexible body. The 
technique uses series expansion of the motion of the 
elastic system in terms of normal modes and gener-
alized coordinates. A normal mode of free vibration 
is the spatial function or shape that a vibrating beam 
assumes when it oscillates at one of its natural fre-
quencies. The generalized coordinates define the time 
variation of modal amplitude. Normal modes of free 
vibration of an elastic system can be derived from a 
knowledge of the mass distribution, flexural stiffness, 
and shear stiffness. By equating measured sensor out-
puts to the motion described by a series of normal 
modes and generalized coordinates, a system of equa-
tions is obtained which can be solved for the rigid-
body components of the motion. The number of sen-
sors equals the number of terms of the series, although 
only a few terms of the series will be needed to 
adequately solve for the rigid-body components. The
solution of this system of equations evolves in the 
form of a series of products of processing functions 
and sensor outputs. The processing functions operate 
on the sensor outputs in such a way that the sum of 
the processed outputs gives the rigid-body motion. 
Advantages of the proposed method are its simplicity 
and the absence of any need for computer capability. 
Separation and rejection of bending motion is ac-
complished even in situations where a bending fre-
quency coincides with the frequency of the closed-loop 
rigid-body mode. 
Note: 
Further information concerning this invention is 
presented in NASA TN D-3109, "A Frequency Inde-
pendent Technique for Extracting the Rigid-Body 
Motion from the Total Motion of a Large Flexible 
Launch Vehicle" by James C. Howard, November 
1965, available from the Clearinghouse for Federal 
Scientific and Technical Information, Springfield, Vir-
ginia 22151; price $3.00. Inquiries may also be di-
rected to:
Technology Utilization Officer 
Ames Research Center 
Moffett Field, California 94035 
Reference: B67-10081 
Patent status: 
This invention is owned by NASA, and a patent ap-

plication has been filed. Royalty-free, non-exclusive 
licenses for its commercial use will be granted by 
NASA. Inquiries concerning license rights should be 
made to NASA, Code GP, Washington, D.C. 20546.
Source: James C. Howard
(ARC-63) 
Category 05 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States	 will be free from privately owned rights.
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Rigid-body motion extracted from total motion of a flexible body

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