Data processing: measuring – calibrating – or testing – Testing system – For transfer function determination
Reexamination Certificate
1999-05-04
2002-04-23
Grimley, Arthur T. (Department: 2852)
Data processing: measuring, calibrating, or testing
Testing system
For transfer function determination
C702S109000, C324S076270, C318S632000
Reexamination Certificate
active
06377900
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to a measuring system for measuring a transfer function matrix of a system to be controlled in a multi-degree of freedom vibration test or vibration control on a test object excited by multiple number of vibrators of a vibration testing apparatus.
In general, in this multi-degree of freedom vibration control, transfer function matrix of a system to be controlled must be determined in advance of the test. The measurements of each element of the transfer function matrix can roughly be classified into the following groups.
{circle around (1)} Classification by excitation methods:
An individual excitation method: a method in which vibrators are each individually excited to measure a column elements of the transfer function matrix; and
A simultaneous excitation method: a method in which vibrators are all simultaneously excited to measure all the elements of the transfer function matrix at once.
{circle around (2)} Classification by excitation signals:
Random signals; and
Sine-wave signals.
Of these classifications, the simultaneous excitation method using the random signals and the individual excitation method using random signals or sine-wave signals have been used hitherto to measure the transfer function matrix, but the simultaneous excitation method using sine-wave signals has never been used.
When comparison is made among the measurements of the transfer function matrix by the known methods on measuring time and a matter of protection of the vibration testing apparatus, the following evaluation is given.
{circle around (1)} Measuring time:
The measurement of the transfer function matrix which is performed in advance of the actual test should preferably be made in minimal measuring time, in consideration of the influence over a test object and the operating time for the test. The individual excitation method in which vibrators are each individually excited to measure the transfer function matrix is lack of practical utility in that the more the vibrators increases, the more time it takes. When comparison on the measuring time for the transfer function matrix is made between the measurement using random signals and the measurement using sine-wave signals, the measurement using random signals generally needs a shorter measuring time.
{circle around (2)} The matter of protection of the vibration testing apparatus:
In the individual excitation method, no consideration can be taken of the influence on other vibrators caused by an operation of one vibrator, for the reason of which the vibration testing apparatus may possibly be damaged. On the other hand, in the simultaneous excitation method, the vibration signals of the vibrators can be adjusted to take consideration of the influences on the mutual vibrators so that possible damage to the vibration testing apparatus is to be avoided. For example, when a test object
53
is simultaneously excited by two vibrators
51
,
52
, as shown in
FIG. 8
, the excitation can be adjusted so that the angle &thgr; of the test object
53
not to exceed a predetermined angle limitation.
In consideration of the measuring time and the matter of protection of the vibration testing apparatus, the simultaneous excitation method using random signals can generally be said to be the best method of the known measuring methods and is widely in practical use.
A brief description is given here on the method of measuring the transfer function matrix by means of the simultaneous excitation using random signals.
As shown in
FIG. 9
, an input signal waveform vector to a system to be controlled (comprising of each signal for driving each vibrator) is denoted as {x} and an output signal waveform vector from the system to be controlled (comprising of each response signal at each control point) is denoted as {y}.
The relation among {X}, {Y} and H is expressed by the following equation (1):
H{X}={Y}
(1)
where {X} is an input signal spectral vector which is the converted input signal vector in the frequency-domain by use of FFT (Fast Fourier Transformation) or equivalent; {Y} is an output signal spectral vector; and H is a transfer function matrix of the system to be controlled.
When both sides of the equation (1) are multiplied by the transposed vector of the complex conjugate of the vector {X}, the following equation (2) is obtained.
H{X}{{overscore (X)}}
T
={Y}{{overscore (X)}}
T
(2)
The left side of the equation (2) is the auto-spectrum matrix of the input signal and the right side thereof is the cross-spectrum matrix between the input signal and the output signal. When these are expressed as S
xx
and S
xy
, the equation (2) can be rewritten as the following equation (3).
HS
xx
=S
xy
(4)
Thus, the transfer function matrix H can be expressed by the following equation (4).
H=S
xy
S
−1
xx
(4)
where S
−1
xx
is the inverse matrix of S
xx
.
In the equation (4), the existence of the inverse matrix S
−1
xx
is required to calculate the transfer function matrix H, and as such requires that S
xx
be a regular matrix.
Supposing that the components of the input signal vector are random signals having no correlation, averaging of S
xx
allows the components having no correlation other than diagonal components to approach zero in the averaged S
xx
, and thus the averaged S
xx
results in a diagonal matrix. Since a diagonal matrix is a regular matrix, the existence of the inverse matrix is ensured.
Likewise, averaging process of S
xy
allows the components having no correlation between the input signals and the output signals to approach zero in the averaged S
xy
, and thus influences from other input signals can be eliminated from the relation between the specific input signals and the response signals.
Thus, the measurement of the transfer function matrix by means of the simultaneous excitation using random signals can be obtained by applying random signals having no correlation to the vibrators to excite the vibrators two or more times, followed by averaging the results.
Incidentally, a sine-wave vibration test that sine-wave excitations are simultaneously applied from the vibrators is sometimes conducted as a multi-degree of freedom vibration test. In this sine-wave vibration test as well, the transfer function matrix of a system to be controlled had to be measured hitherto by using random signals excitation which is different in nature from those in the vibration state in the actual test, that is done by the sine-wave excitation. As a result of this, an adequate accuracy sometimes could not be obtained. This can often be revealed particularly in a system to be controlled such as employing hydraulic actuators having strong nonlinear characteristics.
In the vibration test that uses the information of the transfer function matrix of the system to be controlled, the controllability and thus the test performance is dependent on the accuracy of the measured transfer function matrix of the system to be controlled. Because of this, it is generally preferable for improvement of the test performance to measure the transfer function matrix in the same vibration condition as in the actual test. In view of this, when a multi-degree of freedom vibration test is conducted for the system to be controlled having a strong nonlinear characteristic, it is preferable that the transfer function matrix is measured by use of the same nature signal as in the test, i.e., sine-wave signal, in the same vibration condition as in the test, i.e., in the simultaneous vibration.
When the transfer function matrix is measured with multiple number of vibrators excited simultaneously, influences from other input signals must be eliminated for judgment of the effect on a response point from a specified vibrator. However, in the case of the excitation signals being sine-wave signals, it is difficult to do so, because sine-wav
Ueno Kazuyoshi
Yamauchi Yoshikado
Charioui Mohamed
Grimley Arthur T.
IMV Corporation
Nixon & Peabody LLP
Studebaker Donald R.
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