U.S. patent number RE33,937 [Application Number 07/464,298] was granted by the patent office on 1992-05-26 for active vibration isolation system.
This patent grant is currently assigned to Barry Wright Corporation. Invention is credited to Dale W. Schubert.
United States Patent |
RE33,937 |
Schubert |
May 26, 1992 |
**Please see images for:
( Certificate of Correction ) ** |
Active vibration isolation system
Abstract
An active force actuated vibration isolation system uses a
velocity sensor in the form of a velocity-sensitive geophone to
sense payload velocity and modifies the geophone signal to control
the force applied to oppose the vibration. The modified signal
effectively reduces the inherent resonant frequency of the geophone
and avoids instability.
Inventors: |
Schubert; Dale W. (Sudbury,
MA) |
Assignee: |
Barry Wright Corporation
(Newton Lower Falls, MA)
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Family
ID: |
24876422 |
Appl.
No.: |
07/464,298 |
Filed: |
January 12, 1990 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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716026 |
Mar 26, 1985 |
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Reissue of: |
43630 |
Apr 28, 1987 |
04796873 |
Jan 10, 1989 |
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Current U.S.
Class: |
267/136; 248/550;
267/64.16; 318/460 |
Current CPC
Class: |
G05D
19/02 (20130101); B64C 27/001 (20130101); F16F
7/1011 (20130101); F16F 9/049 (20130101); F16F
15/02 (20130101); G01V 1/184 (20130101); B60G
2202/152 (20130101); B60G 2202/412 (20130101); B60G
2202/42 (20130101); B60G 2400/10 (20130101); B60G
2400/51222 (20130101); B60G 2400/60 (20130101); B60G
2500/20 (20130101); B60G 2600/26 (20130101); B60G
2800/012 (20130101); B60G 2800/014 (20130101); B64C
2027/004 (20130101); B60G 2202/16 (20130101) |
Current International
Class: |
B64C
27/00 (20060101); F16F 7/10 (20060101); F16F
15/02 (20060101); G05D 19/00 (20060101); G01V
1/18 (20060101); G05D 19/02 (20060101); G01V
1/16 (20060101); F16M 001/00 (); F16M 013/00 ();
B60G 017/00 () |
Field of
Search: |
;188/1.11,180,378,298
;267/136,137,140.1,140.5,122,124,65.15,64.16,64.25
;248/542,550,562,636,638 ;280/707 ;91/361 ;92/97 ;244/17.13,17.27
;73/430,649,654 ;318/114,460 ;364/426.01,431.07,421,422
;367/185,187 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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0117173 |
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Oct 1978 |
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JP |
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1087208 |
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Oct 1967 |
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GB |
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Other References
"Active Vibration Isolation of Human Subjects from Severe Dynamics
Environments", Calcaterra & Schubert, Amer. Society of Mech.
Engr. N.Y., N.Y., Mar. 30, 1969. .
"Active Vibration & Shock Isolation", Ruzicka, SAE
Transactions, vol. 77, Society of Automative Engineers, Inc. 1969.
.
"Servo-Controlled Pneumatic Isolators--Their Properties &
Applications," Kunica, paper presented at the Nov. 7-11 meeting of
the Amer. Society of Mech. Engineers, Chicago, Ill., Nov. 1965.
.
Transactions of the ASME Journal of Mech. Design, "Fail-Safe
Vibration Control Using Active Force Generators", 81-DET085, Guntur
and Sunkar, Nov. 1981. .
Transactions of the ASME Journal of Engineering for Industry,
"Theoretical & Experimental Investigation of Electrohydraulic
Vibration Isolation Sys.", Paper #69-Vibr. 40, Schubert &
Ruzicka, Mar. 1969. .
NASA Contractor Report "Study of Active Vibration Isolation Systems
for Severe Ground Transportation Environments", Calcaterra,
Cavanaugh and Schubert, NASA Wash. D.C., Nov. 1969. .
"Research on Active Vibration Isolation Techniques for Aircraft
Protection", Calcaterra & Schubert, AMR-L-TR-67-138, Aerospace
Medical Research Lab, Dec. 1966. .
"Active Vibration Isolation of Aerial Cameras", PEPI paper
presented at the Institute of Environmental Sciences 14th Ann.
Tech. meeting St. Louis, Mo. Mar. 30, 1968..
|
Primary Examiner: Oberleitner; Robert J.
Attorney, Agent or Firm: Pandiscio & Pandiscio
Parent Case Text
This application is a continuation application of U.S. application
Ser. No. 06/716,026, filed Mar. 26, 1985 now abandoned.
Claims
I claim:
1. A vibration isolation system comprising:
a payload mass;
a support;
a passive isolation system for supporting said payload mass on said
support;
a velocity transducer for sensing vibrational movement of said
payload mass .[.relative to said support.]. and for producing a
velocity transducer output signal that varies as a function of the
velocity of said payload mass as it undergoes vibrational motion
.[.relative to said support.].;
control circuit means responsive to said velocity transducer output
signal for modifying said velocity transducer output signal so that
the effective resonant frequency of said velocity transducer is
substantially lower than the resonant frequency of said passive
isolation system;
a force transducer for applying a force to said payload mass in
response to an input signal; and
signal applying means for applying said modified velocity
transducer output signal as said input signal to said force
transducer so as to cause said force transducer to apply a force to
said payload mass in a direction opposite to the direction of
movement of said mass as it vibrates.
2. A vibration isolation system according to claim 1 wherein said
control circuit means modifies said velocity transducer output
signal so that the effective resonant frequency of said velocity
transducer is lower than the resonant frequency of said passive
isolation system by at least one decade.
3. A vibration isolation system according to claim 1 wherein said
control circuit means and said signal applying means form a
feedback loop having a feedback gain of substantially zero at
dc.
4. A vibration isolation system according to claim 3 wherein said
feedback loop has a relatively small feedback gain at frequencies
above 200 Hz.
5. A vibration isolation system according to claim 1 wherein said
control circuit means and said signal applying means form a
negative feedback loop between said velocity transducer and said
force transducer, and said loop is characterized by a gain of
substantially zero at dc and at frequencies above about 200 Hz.
6. A vibration isolation system according to claim 1 wherein said
control circuit means comprises at least two series-connected
lag-lead stages for controlling signal gain and phase as a function
of frequency.
7. A vibration isolation system according to claim 6 wherein each
lag-lead stage comprises an operational amplifier having first and
second input terminals and an output terminal, a lag-lead feedback
network coupling its output terminal to its first input terminal,
and further including means for applying the output signal of said
velocity transducer to the second input terminal of the operational
amplifier of the first in series of said lag-lead stages; and
further wherein said signal applying means is arranged to couple
the output signal appearing on the output terminal of the
operational amplifier of the last in series of said lag-lead stages
to input terminal of said force transducer.
8. A vibration isolation system according to claim 7 wherein said
control circuit means comprises three of said lag-lead stages.
9. A vibration isolation system according to claim 1 wherein said
velocity transducer is a geophone.
10. A vibration isolation system according to claim 9 wherein said
geophone comprises a case, a proof mass suspended in said case, and
means for sensing the velocity of said proof mass relative to said
case and for producing said velocity transducer output signal, and
further including means for applying said velocity transducer
output signal to said control circuit means, and a resistor
connected between said last-mentioned means and ground for damping
said velocity transducer output signal, said resistor having a
value such that the overall fraction of critical damping is
unity.
11. A vibration isolation system according to claim 1 wherein said
force transducer is an electromagnetic device and comprises a
speaker magnet voice coil assembly having a first magnetic
structure defining an annular air gap and a second coil-supporting
structure mounted in said air gap so as to permit substantially
frictionless relative motion between said first and second
structures in response to said modified velocity transducer output
signal.
12. A vibration isolation system comprising:
a payload;
a support;
a passive isolation system for supporting said payload on said
support;
a geophone disposed so as to sense vibrational movement of said
payload .[.relative to said support.]., said geophone comprising a
case, a proof mass suspended within the case, and means for
measuring the relative velocity of the proof mass relative to the
case and for producing an output signal that is proportional to
said relative velocity by the expression S(X-Z), where S is the
Laplace operator, X is the displacement of the case relative to
said support, and Z is the displacement of the proof mass as the
payload undergoes vibrational movement;
circuit means coupled to said geophone for modifying said geophone
output signal so that it is more nearly proportional to the actual
velocity shown by the expression SX of said case and payload;
a force transducer for applying a force to said payload in response
to an input signal; and
means for applying said modified geophone output signal as an input
signal to said force transducer so as to cause said force
transducer to apply a force to said payload in a direction in
opposition to the direction of movement of said payload as it
vibrates.
13. A vibration isolation system according to claim 12 wherein said
circuit means modifies said geophone output signal so that the
effective resonant frequency of said geophone is lower than the
resonant frequency of said passive isolation system by at least one
decade.
14. A vibration isolation system comprising:
a payload mass;
a support;
a passive isolation system supporting said payload mass on said
support;
a geophone for sensing vibrational movement of said payload mass
.[.relative to said support.]. and for producing an output signal
in response to said movement, said geophone comprising a case
adapted to vibrate with said payload mass, a proof mass suspended
in said case so as to be capable of displacement relative to said
case as said case undergoes vibrational movement, and means for
measuring said relative displacement and providing in response
thereto a geophone output signal that is represented approximately
by the following equation using Laplacian notation: ##EQU11## where
E.sub.v (s) represents the geophone transfer function, .beta.=gain
in units of volts per inch per second, S=the Laplace operator, X is
the displacement of the geophone case, Z is the displacement of the
proof mass, S(X-Z) is the relative velocity of the proof mass
relative to the geophone case, .xi..sub.g is the geophone fraction
of critical damping, and w.sub.g is the proof mass resonant
frequency;
control circuit means responsive to said geophone output signal for
modifying said geophone output signal so that the effective
resonant frequency of said geophone is lower than the resonant
frequency of said passive isolation system by at least one
decade;
a force transducer for applying a force to said payload mass in
response to an input signal; and
means for applying said modified geophone output signal as an input
signal to said force transducer so as to cause said force
transducer to apply a force to said payload mass in a direction in
opposition to the direction of movement of said payload mass as it
vibrates.
15. A vibration isolation system according to claim 14 wherein said
control circuit means has a transfer function which is
approximately as follows: ##EQU12## where: g(s) is the transfer
function of said control circuit means,
w.sub.g is the geophone resonant frequency,
S is the Laplace operator and
T.sub.g is a time constant= ##EQU13##
16. A vibration isolation system according to claim 15 wherein said
circuit means modifies said geophone output signal so that the
effective resonant frequency of said geophone is lower than the
resonant frequency of said passive isolation system by at least one
decade.
17. A vibration isolation system according to claim 15 wherein said
circuit means comprises a plurality of leg-lead amplifier stages
adapted to provide substantially zero gain at dc and high gain
greater than unity at the frequencies of said vibrational motion
except that the gain is substantially less than unity for all
frequencies at open loop phase angles of .+-.180 degrees.
18. A vibration isolation system comprising:
a payload mass;
a support means supporting said payload mass so that said payload
mass is subject to vibrational motion and will respond to
application of a force opposing said vibrational motion, said
support means comprising a passive isolation system;
a geophone for sensing vibrational movement of said mass
.[.relative to said support.]. and for producing a transducer
output signal that varies as a function of the velocity of said
payload mass as it undergoes vibrational motion .[.relative to said
support.].;
circuit means responsive to said geophone output signal for
modifying said geophone output signal;
an electromagnetic force transducer for applying a force to said
payload mass in response to an input signal; and
means for applying said modified geophone output signal as an input
signal to said force transducer so as to cause said force
transducer to apply a force to said payload mass in a direction in
opposition to the direction of movement of said payload mass as it
vibrates;
said circuit means being adapted to modify the output signal of
said geophone so as to as to provide a compensated geophone
transfer function represented as follows: ##EQU14## where: F(s) is
the geophone transfer function, g(s) is the transfer function of
said circuit means, T.sub.g is the geophone time constant, and S is
the Laplace operator.
19. An active vibration isolation system comprising:
a payload mass supported so as to be subject to vibrational motion
and to respond to application of a force opposing said vibrational
motion;
a geophone for producing a velocity signal in response to
vibrational motion of said payload mass;
an electrically operated force transducer for applying a force to
said payload mass in response to an input signal;
circuit means responsive to said velocity signal for producing a
control signal that provides a compensated geophone transfer
function as follows: ##EQU15## where F(s) is the transfer function
of the geophone, g(s) is the transfer function of the circuit
means, T.sub.g = is the time constant for the geophone, and S is
the Laplace operator; and
means for applying said control signal as an input signal to said
force transducer.
20. A system according to claim 19 wherein said payload mass is
supported by a passive vibration isolation means.
21. A system according to claim 20 wherein said circuit means
modifies said velocity signal so as to lower the effective resonant
frequency of said geophone to approximately a decade below the
resonant frequency of said passive vibration isolation means.
22. A system according to claim 19 wherein said circuit means
modifies said velocity signal so that effectively the response of
said geophone is equivalent to that of a geophone having a resonant
frequency about 10 times lower than the resonant frequency of said
first-mentioned geophone.
23. An active vibration control system for a payload that is
supported relative to a supporting structure and is subject to
undesirable vibration in a plurality of degrees of freedom
comprising:
a plurality of geophones mounted on said payload, each of said
geophones being oriented to sense a velocity component of said
payload in a predetermined one of several degrees of freedom and
adapted to produce a geophone electrical output signal that varies
as a function of the velocity component in said predetermined one
degree of freedom;
a plurality of force actuators each operable in response to an
individual input signal for applying a force to said payload in
opposition to vibrational motion of said payload in one of said
degrees of freedom;
a plurality of channel circuit means each adapted to produce a
channel electrical output signal in response to an input
signal;
a plurality of means for applying said geophone output signals as
input signals to said channel circuit means; and
means for applying said channel output signals to said force
actuators;
said channel circuit means being adapted to modify said geophone
output signals so that each of said channel circuit means output
signals provides a compensated geophone transfer function that is
represented approximately as follows: ##EQU16## where F(s) is the
transfer function of one of said geophones, g(s) is the transfer
function of the channel circuit means to which the output signal of
said one geophone is applied, T.sub.g = is the time constant for
said one geophone, and S is the Laplace operator.
24. A system according to claim 23 wherein each of said channel
circuit means effectively lowers the natural resonant frequency of
one of said geophones to approximately a decade below the natural
resonant frequency of said passive vibration isolation means.
25. A system according to claim 23 wherein each of said channel
circuit means modifies the output signal of one of said geophones
so that it is equivalent to the signal produced by a geophone
having a resonant frequency approximately ten time less than the
actual resonant frequent of said one geophone.
26. A system according to claim 23 wherein each of said channel
circuit means comprises a plurality of lag-lead amplifier stages
for controlling gain and phase as a function of frequency.
27. A system according to claim 23 wherein said payload is
supported on said base by a plurality of passive vibration
isolation systems so that said payload has said several degrees of
freedom.
28. A system according to claim 27 wherein said channel circuit
means effectively lower the natural resonant frequency of said
geophones to approximately a decade below the natural resonant
frequency of said passive vibration isolation means.
29. A system according to claim 23 wherein said force transducers
are electromagnetic devices. .Iadd.
30. A vibration isolation system according to claim 1 wherein said
force transducer is an electrically-controlled pneumatic device.
.Iaddend. .Iadd.
31. A vibration isolation system according to claim 12 wherein said
force transducer is an electrically-controlled pneumatic device.
.Iaddend. .Iadd.32. A vibration isolation system according to claim
19 wherein said force transducer is an electrically-controlled
pneumatic device. .Iaddend. .Iadd.33. A vibration isolation system
according to claim 23 wherein said force actuators are
electrically-controlled pneumatic devices. .Iaddend.
.Iadd.34. An active vibration isolation system comprising:
a payload mass;
a piston attached to said payload mass;
first pneumatic means, connected to said piston and having a first
pressure chamber, for urging said piston in a first direction in
accordance with an increase in fluid pressure in said first
pressure chamber and for permitting said piston to move in a second
opposite direction in accordance with a decrease in fluid pressure
in said first pressure chamber;
second pneumatic means, connected to said piston and having a
second pressure chamber, for urging said piston in said second
opposite direction in accordance with an increase in fluid pressure
in said second pressure chamber and for permitting said piston to
move in said first direction in accordance with a decrease in fluid
pressure in said second pressure chamber;
pressure sensor means for measuring the fluid pressures in said
first and second pressure chambers and for providing a differential
pressure signal which is representative of the difference in
pressure between said first pressure chamber and said second
pressure chamber;
a velocity transducer for sensing vibrational movement of said
payload mass and for providing an electrical velocity signal that
varies as a function of the velocity of said payload mass as it
undergoes vibrational motion;
control circuit means for generating an electrical flow command
signal that varies as a function of said differential pressure
signal and said velocity signal; and
pneumatic control means for adding fluid to, or exhausting fluid
from, said first and second pressure chambers so as to vary the
fluid pressures in said first and second pressure chambers in
response to said flow control signal so as to cause said first and
second pneumatic means to cause said piston to move in a direction
opposite to the direction of movement of
said mass as it vibrates. .Iaddend. .Iadd.35. A system according to
claim 34 wherein each of said first and second pneumatic means
comprises a flexible diaphragm that is coupled to said piston so as
to apply forces to said piston in accordance with the fluid
pressures in said first and
second pressure chambers. .Iaddend. .Iadd.36. A system according to
claim 34 further including a support, a passive isolation system
for supporting said payload mass on said support, and electronic
means for modifying said velocity signal so that the effective
resonant frequency of said velocity transducer is substantially
lower than the resonant frequency of said passive isolation system,
and said control circuit means comprises a differential summing
device for comparing said modified velocity signal and said
differential pressure signal and producing an output error signal
that varies in accordance with the difference between said modified
velocity signal and said differential pressure signal, and means
for deriving said flow command signal from said output error
signal. .Iaddend. .Iadd.37. A system according to claim 34 wherein
said velocity transducer
is a geophone. .Iaddend. .Iadd.38. A system according to claim 37
wherein said electronic means modifies said velocity signal so that
the effective resonant frequency of said velocity transducer is
lower than the resonant frequency of said passive isolation system
by at least one decade. .Iaddend. .Iadd.39. A system according to
claim 36 wherein said electronic means modifies said velocity
signal so that the effective resonant frequency of said velocity
transducer is lower than the resonant frequency of said passive
isolation system by approximately one decade. .Iaddend. .Iadd.40. A
system according to claim 34 wherein said pneumatic control means
comprises a servovalve for adding fluid to or exhausting fluid from
said first and second chambers whereby to vary the fluid pressures
in said chambers, said servovalve being adapted to add fluid to one
chamber while exhausting fluid from the other chamber in accordance
with changes in said flow command signal, with said servovalve
being arranged so as to vary the fluid pressures in said chambers
responsively to said flow command signal so as to urge said piston
to move in a direction opposite to the direction of movement of
said pay load mass as it vibrates. .Iaddend. .Iadd.41. A system
according to claim 40 wherein said fluid is air. .Iaddend.
.Iadd. A system according to claim 40 wherein said first and second
pneumatic means comprise first and second flexible diaphragms
respectively that are coupled to opposite ends of said piston, each
of said diaphragms being arranged to apply a force to said piston
with the magnitude of the forces applied by said first and second
diaphragms varying in accordance with the fluid pressures in said
first and second chambers respectively. .Iaddend. .Iadd.43. An
active vibration isolation system comprising:
a payload mass;
a support;
passive isolation means for supporting said payload mass on said
support;
a piston connected to said payload mass so that a force applied to
said piston will be transmitted to said payload mass;
a velocity transducer for sensing vibrational movement of said
payload mass and for providing a velocity signal that varies as a
function of the velocity of said payload mass as it undergoes
vibrational motion;
means for modifying said velocity signal so as to provide a
modified velocity signal such that the effective resonant frequency
of said velocity transducer is substantially lower than the
resonant frequency of said passive isolation means;
first pneumatic means for applying a first force to said piston,
said first pneumatic means comprising a first pressure chamber and
a first displaceable means coupled to said first chamber so as to
be moveable responsively to changes in the fluid pressure in said
first chamber, with said first displaceable means (a) moving in a
direction to increase the volume of said first chamber when a fluid
under pressure is injected into said first chamber and (b) moving
in a direction to decrease the volume of said first chamber when a
fluid under pressure is exhausted from said first chamber;
second pneumatic means for applying a second force to said piston,
said second pneumatic means comprising a second pressure chamber
and a second displaceable means coupled to said second chamber so
as to be moveable responsively to changes in the fluid pressure in
said second chamber, with said second displaceable means (a) moving
in a direction to increase the volume of said second chamber when a
fluid under pressure is injected into said second chamber and (b)
moving in a direction to decrease the volume of said second chamber
when a fluid under pressure is exhausted from said second
chamber;
said first and second displaceable means being disposed in
force-coupling relation with said piston, with said first and
second pneumatic means being disposed so that said second force is
applied to said piston in opposition to said first force, whereby
said first and second displaceable means can urge said piston to
move in a first or second direction so as to apply a directional
force to said payload mass; and
pneumatic control means comprising electrically operable valve
means operable responsively to a flow command input signal for (a)
injecting a fluid under pressure into said first chamber when said
flow command signal undergoes a change in a first selected
direction and exhausting fluid under pressure from said first
chamber when said flow command signal undergoes a change in a
second selected direction opposite to said first selected
direction, and (b) exhausting a fluid under pressure from said
second chamber when said flow command signal undergoes a change in
said first selected direction and injecting fluid under pressure
into said second chamber when said flow command signal undergoes a
change in said second selected direction;
pressure sensor means for measuring the fluid pressures in said
first and second pressure chambers and for providing a differential
pressure signal which is representative of the difference between
the fluid pressure in said first pressure chamber and the fluid
pressure in said second pressure chamber;
electrical circuit means for generating a flow command signal that
varies as a function of said differential pressure signal and said
modified velocity signal; and
means for applying said flow command signal as the input to said
valve means so as to cause said valve means to inject fluid into
one and exhaust fluid from the other of said first and second
chambers according to changes in said flow command signal, whereby
said first and second pneumatic means cooperate to urge said piston
to move in a direction opposite to the direction of movement of
said mass as it vibrates. .Iaddend.
Description
BACKGROUND OF THE INVENTION
This invention relates to vibration control and isolation systems
and is related generally to applicant's prior U.S. Pat. No.
3,701,499 which discloses a variety of vibration control and
isolation systems employing acceleration sensors and feedback loops
containing signal components derived from acceleration and other
quantities.
The systems described in applicant's prior patent suggest various
electronic compensation circuits for feedback signals and also the
possibility of employing velocity sensors. No system is shown or
suggested which employs velocity sensor derived signals which are
modified electronically to provide a vibration isolation system
that reduces transmitted or induced vibrations by a large factor
for all frequencies above an extremely low frequency, approaching
zero, with stability assured for all frequencies.
The combination of passive and active vibration control systems has
been analyzed in a paper by a Guntur and Sankar entitled "Fail-Safe
Vibration Control Using Active Force Generators" published by the
American Society of Mechanical Engineers in the transactions,
Journal of Mechanical Design, Paper No. 81-DET-85. The generalized
form of a combined active and passive system is illustrated in FIG.
3 of this article and the transmissability characteristic of a
velocity analog force feedback system is shown in FIG. 4 for
various values of gain. The description is with reference to the
theoretical "Sky-hook" damper without reference to the sensor for
derivation of the velocity signal or the requirements for
maintaining stability throughout the frequency range of
operation.
SUMMARY OF THE INVENTION
The present invention provides for a vibration isolating system
that operates in response to a velocity sensor providing a signal
representative of velocity to an electronic circuit which is
adapted to provide extremely high gain over all frequencies above
the very low frequencies near zero frequency with provision to
avoid instability at all frequencies by reducing the gain value to
substantially less than unity at phase angles of .+-.180.degree..
The system operates in the preferred form relative to a passive
vibration isolation system thereby minimizing the requirements for
substantial force application components and the attendant bulk and
expense of power amplifiers for their actuation. The system
isolates the payload from the residual vibration that is
transmitted by a conventional passive system with a consequent
absolute vibration value far below that which is applied to the
system by transmission of base motion or applied inertial
forces.
The present invention provides a velocity feedback force actuated
vibration isolation control system characterized by vibration
transmission attenuation (i.e., vibration isolation) at
substantially all frequencies and the absence of any substantial
resonance response which results from the achievement of a high
degree of stability at all frequencies such that base vibration
transmission to the payload and oscillatory response to impulse
loading are reduced by an order of magnitude or better relative to
a passive isolation system of the same resonant frequency. The term
"passive isolation system" as used herein refers to a conventional
system designed specifically to remove seismic vibrations including
industrial environment induced vibrations.
The principal object of the present invention is to provide a
stable force feedback vibration isolation system using velocity
sensing.
A further object is to provide velocity sensing in combination with
signal processing in a vibration isolation system to provide
reduced amplitude and lower resonant frequency of a payload due to
transmitted or inertial excitations relative to passive systems
while maintaining a high degree of stability over the required
frequency range.
Another object is to provide an active system which combines
passive and velocity force feedback components, and which exhibits
both a reduced oscillatory amplitude and associated decay or
setting by an order of magnitude relative to the passive system
alone, in response to a steady state and/or transient
excitation.
The above and other features of the invention including various
novel details of construction and combination of parts will now be
described with reference to the accompanying drawings, and pointed
out in the claims. It will be understood that the particular
vibration control system embodying the invention is shown and
described by way of illustration only and not as a limitation. The
principles and features of this invention may be employed in varied
and numerous embodiments without departing from the scope of the
invention.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic representation of a combined passive and
velocity feedback force actuated vibration isolation system.
FIG. 2 is a partial schematic of a signal feedback circuit used in
the system of FIG. 1.
FIG. 3 is a schematic diagram of a complete feedback circuit for
the system of FIG. 1.
FIG. 4 is a representation of a mass supported for motion with six
degrees of freedom with corresponding active force application for
vibration control.
FIG. 5 is a top plan view of a platform having six degrees of
freedom stabilized in accordance with the invention.
FIG. 6 is a elevation view partly in section of FIG. 6.
FIG. 7 is a transmissivity curve showing the passive resonant
response and the response obtained with the active system of this
invention in the embodiment of FIG. 6.
FIG. 8 is a response curve for an impact loading of the pay load in
the system of FIG. 5.
FIG. 9 is a sectional view showing the arrangements of parts in an
electromagnetic force transducer.
FIG. 10 is a schematic diagram of the application of the invention
to a pneumatic force servo system.
DETAILED DESCRIPTION
Referring to FIG. 1 a single degree of freedom velocity feedback
force actuated vibration isolation control system will be
described. In accordance with conventional representation for
vibration isolation analyses the system shown in FIG. 1 has a
payload mass M, 11, supported with reference to a support structure
12 by a resilient spring 13 having a spring constant K and a
viscous damper 14 having a damper coefficient C. The system is
subject to disturbances which include: (a) base motion transmitted
typically through support structure 12 to the payload mass 11, and
(b) external forces applied directly to the payload mass 11.
Also shown in FIG. 1 is a position feedback system which is
generally responsive with slow response to the changes in the
position of support 12 designated by quantity U and positions of
the payload 11 designated by the quantity X, all in the vertical
direction, which is the assumed direction of the degree of freedom
involved, such that the output of a position servo 15 maintains
spring 13 at approximately a predetermined compression level. For
example, the system as thus far described could represent a work
table isolated by passive isolation means 13-14 and maintained at a
working level that is adjusted for changes in gross weight or the
like.
In accordance with the present invention the payload mass 11
supported by support system 15 and passively damped by elements 13
and 14 is further isolated from vibrations whether they occur due
to vibration transmitted from the support surface 12 or from impact
or inertial forces that operate directly on the payload mass 11.
This further insolation is achieved by a velocity feedback, circuit
stabilized to provide a counteracting force application applied to
the payload mass 11 without the instability associated with
oscillation, i.e., a realizable system.
The basic system of the invention comprises a velocity sensor 21
for developing an electrical signal representing an approximation
of the velocity of payload mass 11 in the direction of the degree
of freedom of motion. The velocity signal is applied through an
electronic circuit 22 providing the necessary transfer function for
controlling a force application unit 23 which applies a force
F.sub.v to the payload mass M. The feedback from sensor 21 through
circuit 22 to force generating unit 23 is negative such that the
application of the force F.sub.v tends to cancel the velocity
components which produces the output signal from transducer 21.
The selection of the velocity sensor 21 can be made from various
known devices such as displacement, velocity and acceleration
sensors per se where the displacement measuring transducer would
require that the measured quantity be differentiated to obtain
velocity and the accelerometer would require integration to obtain
the velocity quantity. Both of the sensors requiring this extra
processing step have other limitations in terms of sensitivity and
threshold response. In accordance with the invention the preferred
form of transducer 21 is a unit known as the velocity sensor
geophone.
Velocity sensitive geophones measure the relative velocity between
the unit base or case of the sensor and a suspended mass called the
proof mass. The sensor consists of a coil of wire containing many
terms of very fine wire suspended on very linear and compliant
springs within a magnetic field provided by a core and permanent
magnet assembly. The motion to be measured is the velocity of the
payload 11.
It was discovered however, that the electro-magnetic sensor
actually measures the relative velocity of the proof mass relative
to the case. The relative motion of the proof mass and case are
determined by the dynamics of the suspended mass.
The geophone output voltage E, is proportional to the relative
velocity. As will be readily understood by one skilled in this art,
the sensor's electrical voltage response can be approximated
mathematically, using Laplacian Notation, as follows: ##EQU1##
where .beta..perspectiveto.gain in units of volts per inch per
second and is derived by the geophone calibration.
S.perspectiveto.Laplace Operator
X.perspectiveto.displacement of geophone case.
Z=displacement of proof mass.
S(X-Z).perspectiveto.relative velocity of proof mass to geophone
case
.xi..sub.g .perspectiveto.Geophone fraction of critical
damping.
W.sub.g .perspectiveto.proof mass resonant frequency
The geophone output response vector magnitude and associated phase
angle are related to the actual velocity of the geophone case which
is to be measured, SX. Converting Equation (I) to the frequency
plane, the actual geophone output can be stated for our purposes as
(where SX represents X in the time domain) ##EQU2## where
w.perspectiveto.frequency
X.perspectiveto.velocity to be measured
Equation (II) yields the output's vector magnitude and Equation
(III) yields the associated phase angle.
The above frequency response equations indicate that the geophone
response output signal can peak at the resonant frequency, w.sub.g,
if the fraction of critical damping is small. The fraction of
critical damping is controlled by the magnitude of viscous damping.
The viscous damping provided for the control of the output response
at the resonant frequency comes from two sources. First, the proof
mass coil suspension has some natural and inherent viscous damping
caused by eddy currents flowing as the coil moves in the magnetic
field. The inherent damping is not small and typically gives rise
to a fraction of critical damping of about 0.3. Additional damping
is easily added by placing a resistor across the output of the
geophone. The presence of the damping resistor causes current to
flow through the coil of wire as voltages are induced by coil
movement in the magnetic field. The magnitude of this additional
damping can be quite large. Preferably, the damping resistor is
such that the overall function of critical damping is unity, or
.xi..sub.g =1.0. With this unity value the output voltage will not
show a resonant peak and will exhibit a smooth curve transition
into the operation region above the frequency w=w.sub.g. In
addition, for .xi..sub.b =1.0 the transfer function given in
Equation (I) may be factored into two poles as shown below:
##EQU3##
Importantly, the geophone output response modeled by this transfer
function of Equation (IV) is not, as one can easily see, equal to
the product of the gain and the measured velocity of the case. This
product is further multiplied by the bracketed term to yield a more
accurate and usable approximation of the actual geophone output.
This transfer function, in its factored form, can be used to design
an electrical processing network whose output can be fed back to
provide active vibration isolation. Such a network will be
described below.
Commercially available geophones include a wide variety of units
with a wide range of signal capability, frequency response and
cost. Typically the lowest frequency models are the most expensive.
For applications in accordance with the invention it is desirable
to have both small size and relatively low cost. Geophones for
sensing velocity are commercially available which have response
characteristics as described mathematically in Equation (IV). One
suitable geophone is the model HS-1 manufactured by Geo Space
Corporation, Houston, Tex.
The other transducer required for force actuator systems is the
force generating unit 23 shown in FIG. 1. One practical form of
this actuator is a modified high-fidelity loud speaker assembly
chosen for its characteristics and availability to operate from a
control system circuit using conventional integrated circuit
elements. With these requirements in mind as assembly such as that
illustrated in FIG. 9 was used. FIG. 9 shows a conventional speaker
magnet voice coil assembly comprising a steel core 91, a permanent
ferrite magnet 92 and an annular steel yoke 93 providing with the
upright extension of core 91 an air gap 94. Mounted for movement
within the air gap 94 is a non-metallic cylinder 95 on which a
multiturn coil 96 is wound. The construction should provide:
(1) force output that is proportional to an input current
(2) substantially frictionless motion in all axes of movement.
(3) little added spring stiffness to the spring rates provided by
the passive vibration isolation system.
An integrated circuit power amplifier can meet the linear response
requirement, number (1) above. These integrated circuit power
amplifiers are small and inexpensive and very desirable to use when
possible as final power output stages of a control system's
electronic circuitry. For power level above twelve watts, or two
amps output current, discrete power amplifiers must be made up from
individual power transistors which greatly adds complexity and cost
to the electrical control system circuitry.
Requirement No. 2 is quite important, since friction force levels
can act as force noise sources leading to a higher payload output
response level. Perhaps this can be best understood by way of
example. Consider, using a 100-pound payload and an actuator for
force generation having a friction force of say only 1/100 of one
pound, could not control vibration acceleration response levels at
the system output below the acceleration level in G units of
A.sub.g =F/W=0.01/100 or 10.sup.-4 g units. However, the desired
response level of the isolated payload is one Micro-G or less. To
obtain a vibration level of less than one Micro-G, the force
actuator friction level must be less than 1.times.10.sup.-6 pounds
per 100 pounds of payload weight that the actuator acts upon. Thus
the friction requirement for the force actuator is extreme,
essentially the actuator must be frictionless.
The most effective manner to produce a substantially frictionless
force transducer is to use a magnet and coil assembly from a
high-quality loud speaker with a wider than normal gap for the coil
to move within. One example, which worked acceptably was magnet
used with a 10-inch high fidelity woofer loud speaker. One skilled
in the art should understand that a commercially processed loud
speaker may have to be adapted for use in accordance with the
present invention. For example, the existing gap width might have
to be increased.
After magnetization a voice coil was placed in the field to obtain
a calibration scale factor for the force actuator. The calibration
scale factor is an important design parameter yielding the overall
loop gain and maximum force capabilities for the actuator.
Typically, such actuators are capable of providing two pounds of
force per ampere of input current.
In the assembly of a velocity feedback, force actuated vibration
isolation control system either the magnet or the coil may be
rigidly attached to the payload with the remaining component
rigidly attached to the isolation system base or cabinet
structure.
Having discussed the sensing and actuating means, it is now timely
to discuss the operation of the vibration isolation system.
Critical to desired operation is a realizable system. This term,
commonly used in servo-mechanical analysis, denotes the condition
wherein the system is stable. To determine system stability, it is
necessary to analyze and modify the system open loop transfer
function.
In accordance with the present invention the stability of the
velocity signal feedback loop is assured by selection of the
transfer function G of the network 22 connecting the geophone 21 to
the force transducer 23. Stability in such systems can be analyzed
by opening the loop and determining the output voltage E.sub.o in
response to a given input voltage E.sub.in as shown in FIG. 1, the
ratio of which being called the open loop transfer function. The
switch 24 is shown in FIG. 1 for purposes of this analyses and is
not ordinarily required in an actual system.
If the network 22 has a transfer function which merely represents a
high gain amplifier, instability results. Such instability is
generally associated with excessive gain and .+-.180.degree. phase
shift at some frequency of operation. The velocity sensed by the
velocity sensor 21 will include the amplified vibration due to the
resonance point of the passive vibration of the isolation system
13-14 and this frequency generally is near the resonant frequency
of the geophone 21 itself. Finding the proper transfer function for
the network 22 requires compensating for this effect.
Analyzing the phase and gain relationships shows that the
amplification and phase shift at resonance of the passive vibration
isolation system occurs at a frequency slightly lower than the
geophone natural frequency. The geophone is very highly damped, as
is explained above, with .xi.=1.0, and thus has no resonance
amplification. If the geophone resonant frequency could be placed
well below, say by a decade, the passive system resonance then the
stability state will be vastly different. With a geophone resonance
one decade or so lower in frequency than the passive system
resonance, the open loop transfer function goes through nearly
180.degree. of phase lag prior to the frequencies at which gains
greater than unity exist, thereby allowing the open loop transfer
function to pass through the .+-.180.degree. phase point with a
gain substantially less than one. Typically, the gain at said point
has been maintained at approximately 0.3.
For a low resonance frequency of the geophone relative to the
passive system resonance, much more gain may be applied and still
have a stable system. In general, the higher the velocity feedback
gain, the higher the degree of vibration isolation. The highest
possible gain is sought that will still yield a stable and well
behaved active vibration isolation control system.
The process of closing the loop and obtaining a higher gain is
called stabilization. To do this requires acting on the geophone
electrical signal by linear or non-linear electrical networks as
will now be described.
With reference again to FIG. 1, the transfer function of the
geophone, F(s), may be factored as shown below for the condition of
critical damping .xi..sub.g =1.0 ##EQU4##
Let the term w.sub.g or the geophone resonant frequency be
expressed as a time period called a time constant such that
##EQU5##
Placing this term into the geophone transfer function and
rearranging terms gives the expression: ##EQU6##
A modified transfer function may be obtained by feeding the
geophone electrical signal through an electronic network such as
shown in FIG. 2. This network is two leg-lead networks using, for
purposes of example, two operational amplifiers 25, 26 with
feedback networks comprised of the two resistors R.sub.F and
R.sub.g and the capacitor C.
The transfer function g(s)=E.sub.out /E.sub.in for the circuit in
FIG. 2 will now be determined.
In this circuit R.sub.f, R.sub.g, and C may be chosen such that the
value of R.sub.p C (where R.sub.p is the parallel resistance of
both the feedback, R.sub.f, and ground "R.sub.g resistors) is equal
to the geophone time constant Y.sub.g. In addition, the value of
R.sub.f is selected such that R.sub.f C has a value ten times
greater than R.sub.p C. With these values, the transfer function
for the electronic compensator circuit 22 can be approximated as:
##EQU7##
Now placing the above transfer function G(s) in series with
function shown below: ##EQU8## which simplifies by pole, zero
cancellation to: ##EQU9##
The compensated response of the geophone is now exactly equivalent
to that of a geophone having a resonant frequency that is ten times
lower than the actual value. With the addition of the geophone
compensator, the phase shift of the feedback signal takes place
prior to the resonant frequency and motion amplification of the
passive system, thus the entire control system now has low gain
when the phase angle is close to .+-.180.degree., and high gain
where the phase angle is close to 0.degree.. The low gain, for
example, has been maintained at less than 0.35 and the high gain at
greater than 10.
The feedback circuit as analyzed for FIG. 2 was applied to the
velocity force feedback system of FIG. 1 with further modifications
as now will be described with reference to FIG. 3.
In FIG. 3 the geophone 21 and the force actuator 23 are identified
as the elements previously described in FIG. 1. The coil of the
geophone 21 is connected across a damping resistor 31 as previously
described. The damped output of the geophone 21 is one input to an
operational amplifier 32 the output of which is applied to a
potentiometer the top of which supplies the other input of
operational amplifier 32 thereby controlling the gain of the
velocity signal. The output of the gain control operational
amplifier 32 is applied through a first-leg network 33 to a first
lag-lead circuit 35 corresponding to circuit 25 of FIG. 2. The
output of amplifier 35 is applied to a first lead network 34 which
supplies an input to an operational amplifier 36 corresponding to
amplifier 26 of FIG. 2. The output of amplifier 35 is passed
through a second lead network 37 to a third lag-lead circuit 38
(similar to 35 and 36) the output of which passes through a second
lag network 39. The output signal from network 39 is applied as the
input to a power amplifier 40 which in turns drives the coil of the
force transducer 23.
As can be seen in FIG. 3, the preferred feedback circuit includes
three phase rotation elements. While the addition of geophone
compensation shown in FIG. 2, provides for much more velocity
feedback gain, it was experimentally found that the addition of a
third lag-lead compensation stage 38 in FIG. 3 allows even more
gain to be applied. Importantly, the additional phase rotation
element maintains the overall control system resonance
transmissibility to even smaller values, about 1.10 (as shown in
FIG. 7), compared to the two element circuit.
The loop gain used in the control system is adjustable by means of
potentiometer 42 and can be set such that the gain at a phase shift
of .+-.180.degree., called the gain margin, is 0.35, and the phase
shift at unity gain called the phase margin, is .+-.45.degree. from
.+-.180.degree.. For this condition the basic system stability
state is excellent. At high frequencies where minor resonances in
some part of the entire system can cause gain amplification and
near unstable conditions the lag networks 33 and 39 in the feedback
loop lower the loop gain above 200 cycles per second. In addition
the high DC gain associated with the lag-lead networks, which
causes large DC offset voltages due to errors in the DC operating
level of the operational amplifiers is avoided by the two lead
networks 34 and 37 placed in series in the feedback loop to block
DC and very low frequency signals.
Six Degree of Freedom System
Referring to FIG. 4 a mass used as a platform 41 for vibration
isolation has six degrees of freedom. These six degrees of freedom
are shown in FIG. 4 as motion corresponding to vertical, roll,
pitch, horizontal long axis, horizontal short axis, and yaw. All
possible motions of the mass can be described by motions in these
six degrees of freedom through translation along and rotation about
the three mutually perpendicular axes.
Achievement of low vibration level for the platform 41 using an
active vibration isolation system requires active vibration
isolation controlling all six degrees of freedom. This may be done
by using three independent translatory control systems and three
independent rotational control systems. However, rotational control
systems are hard to implement mechanically both from a sensor and
actuator point of view. Thus, translatory control systems only are
used to obtain the same goal of control of all six degrees of
freedom. In FIG. 4 typical points of application for six linear
force actuations, 1, 2, 3, 4, 5 and 6 are shown. Each force
actuation results from an actuator and sensor combination and
corresponds to a channel. In FIG. 4 channels 1 and 2 control part
of the vertical axis, and all of the pitch axis. Channels 1, 2 and
3 control all of the vertical axis and all of the roll axis.
Channel 4 controls all of the horizontal long axis and channels 5
and 6 combined control all of the horizontal short axis and all of
the yaw axis.
Ideally, motions in any one axis are completely independent of
other motions in other axes, such for example if a displacement
occurs on the vertical axes 1, 2, 3 combined, no other motions or
rotations occur on any other axis. This independence of degrees of
freedom however, is nearly impossible to achieve in a real world
system. In an actual system constructed, the three vertical
channels are nearly independent in that a combined motion of
channels 1, 2 and 3 generate almost pure vertical translation with
little horizontal or rotational motion. Control of pitch and roll
is also quite good, in that the combined motions of channels 1, 2
and 3 to generate a pitch or roll motion only will generate little
motion in yaw or the two horizontal directions. However, motion
generated by the actuators on channels 4, 5 and 6 generate axis
coupling in that motion of channel 4 generates some pitch and
motion by either channel 5 or 6 generates some roll as well as yaw
motion. The location of the force actuators in the horizontal plane
was selected to act at points on the payload mass that minimized
the coupling effect.
Another form of coupling is caused by gravity and exists only on
the horizontal channels. When a horizontal HS-1 geophone is exactly
level with respect to gravity, there is no gravitational force
acting in the horizontal direction. If, however, a roll or pitch
motion takes place an acceleration component occurs in the nearly
horizontal plane of the geophone sensitive axis.
For small angles of rotation A of the geophone sensitive axis, the
sine of the angle A is nearly equal to the angle A itself or A=sin
A. Thus the output of the geophone is dependent on the velocity
motion sensed in its own plane plus some signals generated by
gravity when rotations of a horizontal plane occur. In equation
form, the actual geophone output, neglecting the geophone output
dynamics becomes: ##EQU10## This coupling effect causes stability
problems for the horizontal channels because control motions of a
vertical channel couple to horizontal sensors, when pitch or roll
occurs, and causes false signals. Thus an interaction between
vertical and horizontal channels exists due only to gravity, but
which nevertheless must be dealt with. The solution chosen was to
limit the low frequency response of the horizontal channels 4, 5
and 6 by the use of higher frequency DC blocking lead networks,
43,44 of FIG. 3, having a higher resonant frequency, as well as a
lower overall loop gain, as compared to the vertical channels, as
will be understood by those skilled in the art.
Referring now to FIGS. 5 and 6 the plan and elevation views of an
embodiment of the invention with six degrees of freedom is shown.
The payload is a table work surface 61 supported in a frame 62 by
four passive but height regulated vibration isolation elements 63
located generally near the corners of the work table 61.
Six velocity sensing geophones 64, 65, 66, 67, 68 and 69 are
mounted on the table 61 with their axes of motion sensing aligned
to sense the individual components of the six degrees of
freedom.
Mounted between the frame 62 and the table 61 are a plurality of
force actuators of the type described with reference to FIG. 9.
Thus as shown in FIG. 5 there are two actuators 71 and 72
positioned to control the short axis Y translation and yaw. There
are four vertical force actuators 73, 74, 75 and 76 for controlling
vertical motion and pitch and roll and there is an actuator 77
positioned to control long axis Y translation. It will be noted
that their are seven force actuators in FIGS. 5 and 6, one more
than that described with reference to FIG. 4. This merely
represents allocating the signal response from the third channel
motion between the two actuators 73 and 75 instead of the pivot
motion indicated in FIG. 4. Thus actuators 73 and 75 operate
jointly on the same signal which is modified relative to the
signals described with the circuit of FIG. 5 in a manner which will
be apparent to those skilled in the art.
Referring to FIG. 7 the transmissivity curve of the embodiment of
the invention shown in FIG. 6 as measured is shown in curve 81 with
a comparison curve 82 representing the transmissivity curve of the
passive isolation system alone. As will be noted the curve 82
exhibits a natural resonance at approximately three Hz where the
transmitted motion is actually amplified by a factor of almost 10.
It is this phenomenon universal with passive systems which the
present invention so effectively avoids. As seen in the curve 81,
the resonance of the system has been reduced in frequency by
approximately a factor of 10 occuring somewhere near 0.4 Hz and its
amplitude is greatly reduced being approximately 1.1. Thereafter
the attentuation provided by the active force velocity feedback
system of the invention reduces the percent transmission well below
1.0 and in fact it is approximately 0.1 at the frequency of
resonance of the passive system alone. The curve 81 represents the
response with the passive and active systems both present and hence
is the actual result achieved by the invention. As noted curve, 81
continues to reduce the percent transmission until it merges with
the isolation provided by the passive system alone as indicated in
curve 82 somewhere in the region of 30 Hz.
Referring to FIG. 8 a typical example of the results achieved with
the embodiment of the invention described in FIG. 6 is shown. The
top curve 83 shown in FIG. 8 represents the response of the
combined passive and active system of the invention to a 1.5
inch-pound impact load such as drop of a rubber ball on a 50 pound
payload of FIG. 5, the curve 84 shown in FIG. 8 represents the
response of the passive system alone to the same impact loading.
Note that the initial deflection is approximately the same for
curves 83 and 84 but that the recovery time with the active system
operating as indicated in curve 83 is much shorter and of
substantially lower amplitude than the oscillatory deflection shown
in curve 84. As can be seen from curve 83, a vibration isolation
system made in accordance with the present invention exhibits a
fast settling time resulting from the large damping forces
generated by the feedback. The increased system damping not only
results in superior vibration isolation compared with typical
passive systems, but also greatly reduces the system payload
response motions resulting from external forces applies to the
payload.
Alternative Embodiment
Whenever a payload is of such character that it requires a force of
more than approximately 2 pounds to counteract externally applied
forces, the use of electromagnetic force transducers such as
described with reference to FIG. 9 become expensive and ultimately
impractical. Other types of force actuation means can be
substituted without departing from the scope of the invention. In
FIG. 10 a pneumatic system is shown wherein a payload 101 is
supported from a piston 102 which is freely suspended from
diaphragms 103 in an upper and lower pressure cylinders 104,
105.
The pressure within the cylinders 104, 105 operates on the equal
upper and lower area surfaces of the piston 102 to apply the motion
of the piston 102 to the payload 101. This pressure is controlled
by a flow control servovalve 106 which applies differential
pressure to the piston 102 to move same.
The flow control servovalve 106 is controlled by a servo system
comprising a force command signal input at line 107 corresponding
to the final velocity sensor signal which is compared in a
differential summing device 108 with a signal representing the
differential pressure in the cylinders 104 and 105 obtained from a
differential pressure transducer 109. Any deviation in position
called for by the velocity signal on line 107 relative to the
position established by the differential pressure sensed by unit
109 results in an error signal output which is applied to a
transfer function device .[.111.]. .Iadd.110 .Iaddend.and pneumatic
amplifier .[.112.]. .Iadd.111 .Iaddend.to control the servovalve
106. The system of FIG. 10 thus applies force from the piston 102
to the payload 101 in accordance with the requirements of the
velocity signal on line 107 to achieve the results described in the
present invention where higher values of force are required.
While the invention has been described by reference to specific
embodiments, it will be apparent to those skilled in the art that
the invention can be applied to a wide variety of vibration
isolation and control systems.
* * * * *