Note: Descriptions are shown in the official language in which they were submitted.
5~2
The invention relates to a vibration isolation
apparatus and method, and more particularly to a supportive or
suspension system adapted to be coupled between two elements or
structures for the reduction of transmitted mechanical excita-
tions therebetween.
The prior art and the invention will be described
in conjunction with the accompanying drawings, in which:
Fig. 1 is a schematic representation of a conven-
tional vibration isolation system using linear viscous damping;
Fig. 2 is a schematic representation of a conventional
vibration isolation system with a viscous damper connected as a
"sky hook'7 damper; and
Fig. 3 is a schematic representation of a vibration
isolation system with a variable damping coefficient viscous
damper, made in accordance with the present invention.
Consider a conventional single degree of freedom
vibration isolation system using linear viscous damping such as is
presented in Figure 1. The forces acting on the payload of mass
"M", designated by the numeral 2, which is isolated relative to a
foundation 3, are the spring force which is described as being
equal to the spring stiffness constant "K" times the compression
of spring 4 which is the isolator relative deflection, the dissipation
force which is the linear damping coefficient "C" times the rate of
compression of viscous damper 6 which is the relative velocity.
These two forces must be counteracted by the isolated payload
mass 2 inertial force which is the payload mass coefficient "M"
multiplied by the acceleration of the payload mass itself.
In the vibration isolation field it is well known
that damping in linear viscous systems controls the resonant
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characteristics of the entire vibration iso1ation system.
Adding damping lowers the detrimental effect of the
resonance amplification. However, as the damping is
increased resonance amplification does indeed go down
but the degree of high frequency vibration isolation is
lowered. In fact, if the fraction of critical damping
is set to unity to
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1~'7~ ,42
eliminate the effect of resonance ampllfication, most all vibration
isolation is lost. Even at very high frequencies above the resonant
frequency, the rate of vibration isolation only increases by six
decibel per octave.
Another well-known type of vibration isolation system is one in
which the resonant amplification is well controlled by viscous
damping but does so in a manner so as to preserve the vibration
isolation offered at high frequencies. This type of vibration
isolation system uses a linear viscous damper connected to the
isolated payload so as to act as a "sky hook"; the configuration of
this type of vibration isolator is presented ln Figure 2. In this
figure, the linear viscous damper 6 is connected to the isolated
payload 2 at one end and to a stationary location in space at the
other end, known as a "sky hook" 8.
; 15 It is the stationa~y connection which makes the passive "sky
hook" damped system impossible to construct. For in the world of
vibrations all masses that are accessible to the vibration isolation
system are also in motion and thus do not act as a true "sky hook".
Such a system can be approximated by using active vibration
isolation techniques taught in my earlier patent application of
which this is a contlnuation in part, But my earlier invention,
like other active vibration isolation systems, is limited in its
effectiveness in two areas. First, such systems are generally
stability limited and thus cannot be ~ust "slipped in place", so to
speak, without the necessary system stabilization circuits tailored
; to suit the individual application. Secondly, such systems
generally require power to operate and are limited in both force and
motion output by power requirement limitations imposed by an
individual design. j '
go Desirable is an active vibration isolation system having a
controlled damping coefficient such that its vibration isolation
characteristics can be tailored as desired. Preferably, the
characteristics can be ~ailored to approximate a "sky hook" damper.
; Vnderstanding of the present invention would be aided by a
brief mathematical analysis of the "sky hook" type vibration
; isolation system as presented in Figure 2. For this system, the
damping force is equal to the payload's absolute velocity times the
viscous damping coefficient of the damper.
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The equatlon of motion for the "sky hook" damped vibration
isolation system is presented in EQ (l);
~(d2X) = K(U-X) - C(dX) (1)
In EQ (1), "dX" and "d2X" are the velocity and acceleration,
respectively, of the payload mass ~, and "U" is the tlme-dependent
displacement of the foundation relative to which the payload is
isolated. (Throughout the specification, the time derlvative shall
be symbolized for convenience without the denominator, "dt" or
~dt2~)
One solution of this equation, for the case of steady state
slnusoidal vibration, is the transmissibility vector equation for
the "sky hook" damper vibration isolation system. In Laplace
Transformation notation, the solution is as follows:
X[S] ~W2n
____ = ________________-_ (2)
j 3 u~sl [S+2(zeta)SW n + W2 ]
~'
where "W2n" is equal to "K" divided by "~1", "zeta" is equal to "C"
divided by the magnitude of critical damping, and "S" is the Laplace
Operator. I
The damping term associated with the system's fraction oE
critical damping, "zeta", appears in the denominator of the equation
only. This is unlike the analogous solution for the system
~ presented in Figure 1 wherein the "zeta" term appears in both the
- numerator and denominator. This seemingly minor dlfference between
the well-known equation for the transmissibility vector for the
conventional isolation system and the equation for the "sky hook"
damped isolation system has, however, profound effects in the manner
in which viscous damping manifests itself in the overall vibration
isolation characteristics. In the "sky hook" damped system, as the
degree of damping is increased and the fraction of critical damping
"zeta" approaches large values above unity, the amplification due to
resonance disappears and vibration isolation starts at zero
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frequency with a peak transmissibility of unity occurring also at
zero frequency. More importantly, the increase in damping used to
elimlnate the system's resonance also adds vibration isolation for
all frequencies below the undamped resonant frequency.
For "sky-hook" type systems the effect of additional damping
for small fractions of critical damping is virtually the same as for
the conventionally damped vibration isolation system ln the manner
in which the amount of resonant amplification is reduced. However
as the fraction of critical damping is increased, exceeding a value
of approximately 0.2, it is observed that not only is the
amplification of vibration due to the system resonance decreased but
. at the same time there is no loss of vibration isolation
characteristics at frequencies above resonance. This effect
continues even for very large fractions of critical damping.
Desireable, therefore, would be a realizable vibration
isolation system which achieves or at least approximates the
advantageous vibration isolation of a "sky hook" damped system.
Therefore, it should be apparent that an ob~ect of the present
invention is to provide an active vibration isolation system
exhibiting improved stability and requiring less power than
conventional active systems.
A further ob;ect of the present invention is to provide a
realizable vibration isolation system which is characterized by a
transmissibility vector equation approximating that of a "sky hook"
damper system, having substantially no resonant amplification.
SUM~ Y OF THE INVENTION
These and other objects of the invention are achieved by a
parametrically controlled active vibration isolation system
comprising a first sensor for deriving a first velocity signal
representative of ehe velocity of a payload, a second sensor for
deriving a second veloc.ity signal representive of the velocity of a
base, a viscous damper disposed to support said payload with
reference to said base, means for modulating the damping coefficient
of said viscous damper in response to a command signal, feedback
means for deriving a feedback signal representative of the damping
coefficient, and electronic means for continuously generating the
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command signal in response to said flrst and second velocity signals
and said feedback signal, whereby the damping coefficient of said
vlscous damper is controlled by automatic feedback and can approxi-
mate that of a "sky hook" vibration isolstion system.
~ S According to the preferred embodiment of the lnvention, both of
; the velocity sensors are geophones, and the modulating means
includes electromechanical drive means responsive to the command
signal for regulating the flow o;E llydraulic fluid through a
; servovalve. The servovalve preferably includes a unidirectional or
-, 10 bidirectional valve spool which acts to constrict fluid flow through
a passage connecting an actuator with an accummulator. The actuator
is adapted and configured to hydraulically support a payload with
` reference to a base on which the accummulator rests or to which it
; is secured.
The vibration isolation system as described and claimed herein
is, in effect, an active system since sensors of motion and
actuation lmplementation devices are required. This damping
technique, however, does noe require actuation devices which
actively generate forces. ~1any of the disadvantages of more
conventional active systems are eliminated because this variable
damper generates damping forces passively, and uses active methods
only to change the instantaneous value of the damping coefficient, a
technique which requires less power.
The invention also embraces the method by which vibration
2S isolation is achieved by such a system.
. 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 accompanyfng drawings and
pointed out in the clai~s. 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.
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DETAILED DESCRIPTION OF THE PRE~ERRED EMBODlMENT
A Overview of Basic System and ~athematical Description Thereof
Figure 3 presents a parametrically controlled active vibration
isolation system 10 made in accordance with the present invention,
including two response sensors 12, 14 operatively coupled with a
payload 16 and foundation or base 18 to derive a signal
representative of the velocity of the payload 16 and of the base 18,
dX and dU, respectively. It is recognized and discussed in the
earlier application of which this is a continuation-in-part, that
the outputs from the two response sensors 12, 14 give only an
approximation of the velocity due to the physics of the velocity
sensors and so may be processed appropriately to yield a more valid
velocity signal.
It should be understood that vibratory excitations of the
payload 16 or of the base 18 are isolated by the system 10, i.e.,
their transmission is reduced or eliminated for at least a range of
fre~uencies thereof.
The system 10 further includes a variable damping coefficient
yiscous damper 20 controlled by a servo-controller 22. The output
signal from the serv^-controller 22, called herein a "com~and
signal", is used to modulate the damping coefficient in a manner
such that the instantaneous damping coefficient is described as
shown in EQ (3).
Damping Coefficient = C = Cl[ABS(A[dX/dV])J (3)
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1~ 71542
where "A" is the lnstantaneous area of the orifice of the viscious
damper, "Cl" is the damping 'coefficient when the orifice is fully
open, and "dV" ls the relative velocity of the payload 16 wlth
respect to the base 18 and i9 equal to "dU" minus "dX".
With the damping servo terms of the system established by EQ 3,
and assuming sensors 12, 14 are identical so as to have identical
transfer functions, a simplified differential equation of motion may
be written to describe the vibration lsolation system 10. Once
again using the conventional force summation procedure for the
- lO sprlng, damper and mass inertial forces, an engineer in the art
could derive EQ (4),
M~d2X] = K[U-X]-Cl(dV)(A8S[A(dX/dV)]) (4)
Carefully note that the relative velocity, "dV", appears in
both the numerator and denominator of the damping term expression,
~nd, if it were not for the fact that the synthesized damping
, coefficient term has no sign, the two terms would cancel exactly and
mathematically form a true "sky hook" damped' system. The damping
term synthesized, however, has no sign since the feedback is used
only to modulate the damping coefficient, "C". Realizing this, we
can rewrite the equation with the terms cancelled. Thè differential
equation of motion of EQ (4) simplifies to the form presented in
EQ (5).
'.
M[(dX2) = K[U-X] - ClA[ABS(dX)](DELTA) (5)
Here the term "DELTA" is equal to plus or minus one (I) and
represents the sign of the 'relative velocity. Compare EQ (5) with
the equation for motion given in EQ (l).
' The above mathematical description of the system is idealized
in some respects and interfacing with the real world must be
considered. The actual ratio of velocities as described above would
, 30 have an infinite value lf the voltage signal representing the
~; absolute payload velocity were finite and the voltage signal
representing the relative velocity were zero. This is a condition
~1' occurring twice each cycle with sinusoidal vibration and, thus, is a
commonly occurring event. The servo-controller 22 cannot output an
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infinite voltage. Thus, the command slgnal must be llmlted to have
some specified maximum value whlch wlll be called VMAx, generally,
for example, approxlmately 10 volts. The command slgnal, however,
may still have all values between -UMAx and +UMAx, including zero.
In a real system, however, when the command ls zero, there must
always be some resldual damping remaining. Thus, ln a realizable
system, the damping coefficient must have a mlnimum value which ls
hereinaftèr referred to as '~C0'~. Thls leads to a formulation of the
command signal for a reallzable system ln the form presented ln the
EQ (6):
Damping Coefficient ~ C = C0 ll.0 + A~ABS(dX/dV))] (6)
In an actual system, the term CO ls the damplng present when
the command signal is zero, while the maximum value of the damplng
coefficlent is equal to C0 [1.0+A(UMAX)].
Thus, an active vlbratlon isolation system 10 has been modeled
i, .
; which is characterized by a transmlssibility vector equatlon, EQ
(S), approxlmatlng that of a "sky hook" damper glven in EQ (1).
Details of the elements of such a system shall now be descrlbed.
; B Electromechanlcal Viscous Damper 20
.... .
1~As just described, the vibration isolation system 10 in
accordance with the present invention operates through the dynamic
modulation of the vlscous damplng coefflclent of an otherwlse linear
vibratlon lsolator. A preferred method of modulating the viscous
damping coefficient is shown in Fig. 3. The damper 20 includes a
servovalve 30 which acts as electro-mechanical variable orifice
~-25 means for metering the flow of the fluid used to provide the damping
pressure drops and resulting dissipatlon forces. This flqw control
is achiaved by regulated restriction of the flow path in response to
an electrical signal i~?ut to the servovalve 30, called herein the
"command signal".
The electro-mechanical servovalve 30 used in accordance with
the present invention establishes a predetermined flow area which in
turn sets the instantaneous coefficient of damping of the vibration
isolation system to a prescribed magnitude. The servovalve 30
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dlffers somewhat from conventional servovalves. Normally
servovalves are utilized for controlling of flow of fluid from a
hydraulic or pneumatic pump which then generally causes the motion
! of the control system actuation device. The servovalve 30 does not
control the flow from a pump, but rather establishes a predetermined
valve opening allowing fluid flow in either dlrection. This takes
place passively at whatever pressure conditions happen to occur at a
given instant.
Vibration isolation depends on the time dependent modulation of
the magnitude of the damping or dissipation force. The dissipation
force is generated passively by the vibration isolation system 10 as
relative velocities develop across a dissipation element. The
dissipation force is equal to the instantaneous linear viscous
- damping coefficient, "C", multiplied by the relative velocity, and
is the term to be acted upon and controlled in the present
invention. Electro-mechanical control over the damping coefficient
is achieved by the vibration isolation system 10 utilizing the
;, servovalve 30 as a dissipation element within an incompressible
~, fluid path to generate the damping or dissipation forces. The
servovalve 30 includes electromechanical means for controllably
varying the flow area therethrough and thereby modulating the
damping coefficient of the vicious danger. The servovalve 30
lncludes a movable valve spool 32 including a rod or neck 34
connected to a cylindrical spool head 36 at or near one end and at
the other to a drive shaft 38. The spool head 36 is of a disk-like
~r' ' shape, having an outer cylindrical surface or land 40, and planar
~j end walls 42 connected to the land perpendicularly so as to form a
substantially sharp edge therebetween. The spool 32 is arranged to
be slidingly driven within a transverse passage 44 having an inner
diameter which permits the spool head 36 to slide therein with a
close fit.
The damper 20 in addition to the servovalve 30 comprises a
support cylinder or receptacle 50 including two chambers 52, 54
having the servovalve 30 connecting them so as to provide regulated
, 35 fluidic communication therebetween. The upper chamber 52 is a load
bearing chamber, and, in combination with a payload support 56 forms
a hydraulic single acting actuator 58 which is filled with an
incompressible fluid of low and constant viscosity. The lower
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chamber 54 is a small hydraulic accumulator which acts to store
incompressible hydraulic fluid at substantially a constant pressure.
As stated above, the function of the servovalve 30 is to meter
the flow of hydraulic fluld according to a desired control function.
Movement of valve spool 32 opens or closes orifices 60, 62 within
the fluidic circuit as lt is driven by the mechanical output of
electro-mechanical means 64 to which lt is operatively connected.
Preferably the orifices 60, 62 are of identical size and
configuration and direct the fluid flow perpendicularly against the
cylindrical land 40 of the spool head 36.
The valve spool 32 can further include support heads 66, 68, in
which case the rod 34 extends to connect all three heads 36, 66, 68.
The support heads 66, 68 act to prevent cocking of the spool 32
within transverse passage 44 and are disposed in spaced arrangement
on either side of the head 36. Full opening of the orifices 60, 62
by the valve spool 32 must be scaled such that the minimum fraction
of critical damping of the vibration isolation system is established
under all antlcipated vibration isolation system eY.citation
velocities.
`: 20 The allowable direction of travel of the servovalve spool 32
determines whether the servovalve 30 is of the unidirectional or
bidirectional type. A valve spool 32 which displaces only in one
direction forms a dedicated unidirectional servovalve, while a valve
- spool which displaces in both directions forms a bidirectional
servovalve. The bidirectional servovalve, however, can behave the
same as the unidirectional servovalve if the controlling signal to
the valve commands only one direction of spool travel; thus the
bidirectional servovalve can behave as both servovalve types in so
far as the resulting vibration isolation system response is
concerned.
The valve spool 32 is actuated by the electromechanical drive
~` means 64 which is capable of applying a driving force to displace
the rod 34 within pass..ge 44 with reference to orifices 60, 62 in
response to the command signal from the servo-controller 22 Thus
the drive means 64 serves to vary the opening of the variable
orifice. Preferably, it comprises an electro-magnetic solenoid of a
design such as is commonly used to drive a conventional loud
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speaker, although other forms of motors could be used. The control-
` ling mechanical force applied to the valve spool 3Z causes it to
accelerate in the direction of the applied force. However, a
; feedback signal representative of the posltion of the spool head 36
- 5 relative to orifices 60, 62 i9 used by the servo controller 20 to
control the electro-mechanical drive means 64. The feedback signal
is, also representative of the damping coefficient of the viscous
damper 20 since it represents the instantaneous flow area. It is
preferably derived by means 70 such as a displacement transducer,
for example, a linear variable differential transducer ('ILVOT")
` sensor operatively associated with the valve spool 32.
The flow of fluid through the servovalve 30 is proportional to
two parameters; namely the pressure drop across the servoyalve 30,
and the flow area.
Let P1 represent the pressure within the actuator 58 measured,
for example in orifice 60, and let P2 represent the pressure within
the hydraulic accumulator 54, measured for example in orifice 62.
; Vibratory acceleration of the payload 16 causes an inertial
~ force to be applied to the support cylinder 50. For most cases it
; 20 can be safely assumed that the flow through the orifices 60, 62 is
governed by Eq (7).
Q = CdA[SQRT(2dP/V)] e AC(dY) (7)
~here "Cd" is the damping coefficient of the valve opening for the
fluid, "SQRT" is an abbreviation for square root of the following
function, "dP" is an incremental pressure due to vibration
.
accelerations of the payload 16, "D" is the density of the fluid,
and ''Ac'' is the load area of the supporting cylinder.
The other relating equation for this system is that of the
damping force itself. The damping force is defined as:
Damping Force = Fd = A (dP) = C(dY) (8)
The damping coefficient, "C", as controlled by the servo-
controller 22 is already defined in EQ (3).
Letting "R" be the system scaling constants, defined by EQ (9),
'':'
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R - SQRT[Ac D/(2CdCo)] (9)
and substituting in the above equations yields the required
servovalve's orifice area for regulated flow, given by EQ (10).
A = R(SQRT[ABS dUt(l + G(ABS(dX/dV)))]) (10)
where "G" is gain.
Thus, to achieve the desired ob~ectives of the invention, the
flow area must be controlled in accordance witli EQ (10). Generally
the flow area is proportional to the valve spool's displacement, If
this is the case, the valve stroke is likewise defined. Therefore,
the command signal can be used to control the displacement of the
valve spool 32 resulting in a corresponding change in the flow area
in accordance with EQ 10, so as to exhibit a transmissability vector
equation for the vibration lsolation system 10 approximating that of
a "sky hook" damper. The electronics of the servo-controller as
shall be described hereinbelow generates the command signal to
regulate the flow area in accordance with EQ (10).
A further description of the viscous damper 20 and its
operation shall now be provided.
The payload support 56 is securable to the payload 16 and
received in a first end of the support cylinder 50 for pis~on-like
movement therein in response to excitations in the direction
indicated by an arrow, designated by the letter "a" in Fig. 3, which
is parallel to the axis of the support cylinder. In the preferred
embodiment, the displacement of valve spool 32 is in a direction
perpendicular to direction "a".
As previously stated, the payload support 56 cooperates with
the upper chamber 52 of the support cylinder 50 so as to form
actuator 58. The actuator 58 is preferrably a roliing diaphragm
type hydraulic actuator which is suitable in instances wherein a low
-~ 30 resonant frequency is required. The use of a rolling diaphragm 80
to interconnect and seal the payload support 56 to the innsr wall of
the support cylinder 50 reduces the high coefficient of frictlon
! normally associated with other forms of hydraulic actuators consist-
ing of a cylinder and piston without a diaphragm.
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The opposite end of the upper chamber 52 is fluidically coupled
directly to the servovalve 30 which regulates the flow of fluid from
the actuator 58 to tlle accumulator 54. The accumulator 54 stores
the lncompressible hydraulic fluid under pressure in a manner such
5 that pressure changes due to fluid volume changes are small. The
static pressure in the vibration isolaticn system 10 is controlled
by a pressurized compressible fluid contained within the accumulator
54. A flexlble fabric-reinforced elastomeric diaphragm o2 sealed to
the lnner wall of the support cylinder 50 separates the accumulator
lO 54 into subchambers 84 and 86, having therein the hydraulic fluld
and the compressible fluid, respectively. Due to diaphragm 82,
subchambers 84, 86 each have variable volumes and therefor are
expansible in response to relative pressure changes therein. The
device utilized for the accumulator 54 can indeed be a commercially
15 available hydraulic accumulator or the lower pressure version of the
hydraulic accumulator, the hydraulic snubber.
- The hydraulic fluid within the upper chamber 52 and subchamber
84 can be any incompressible fluid which is compatible with the
system and the environment within which the system must function.
Examples of the incompressible fluid are ordinary low viscosity
hydraulic oil, brake fluids normally utilized in automotive braking
systems, or mixtures of water and ethylene glycol type antifreeze if
extremely low operating temperatures are required.
The compressible fluid in the subchamber 86, for example, can
be a gas or ordinary air. The choice of the compressible fluid in
con~unction with its volume and the area of the hydraulic load
supporting actuator 58 establish the resonance characteristics of
:: .
the vibration isolation system.
The function of the accumulator 54 is two-fold. First, the
30 trapped compressible fluid acts as a pneumatic spring to give the
vibration isolation system a substantially linear spring stiffness,
defining the isolation system undamped natural frequency. The
; - second function is to provide a reservoir for hydraulic fluid which
h is maintained under a moderately high and substantially constant
35 pressure. This provides the lift in con~unction with the load
support area of the support cylinder 50 to support the static load
of the payload 16.
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The compressible fluid is introduced into subchamber 86 by
pneumatic fitting 88.
C. Optional Height Sensing and Control
The electromechanical viscous damper as heretofore described is
suitable for applications in which the weight of the payload does
not fluctuate appreciably. For those applications in which it does,
manual introduction of the compressible fluid might be undesirable.
Rather, a system for automatically adjusting the lift of the damper
in response to the payload weight would be advantageous.
This can be achieved by employing a height sensing control
device 90 to adjust the pressure of the compressible fluid in
subchamber 86 so as to maintain the quiescent relative height of the
payload 16. A supply of pressurized compressible gaseous fluid from
a source (not shown) is coupled to a three-way valve 91 at inlet
conduit 92. Axial positioning of a double-headed valve spool 93
regulates admission of pressurized fluid to the subchamber 86 by
conduit 94. Valve spool g3 similarly regulates the relief of
pressure from the subchamber 86 through the e~haust conduit 95.
Valve body 96 is secured to the base 18 by, for example,
linkage 97 so as to be maintained against movement in the axial
2Q direction identified by arrow "a". The valve spool 93 is affixed to
rod 98 which, at the other end thereof, is secured to payload 16.
Relative height fluctuations of the payload 16 with respect to the
base 18 introduce fluid flow into or release fluid flow from the
subchamber 86 by the opening or closing of the fluld flow path.
Thus the pressure in the subchamber 86 is adjusted automatically to
acco~modate different payload welghts.
A further understanding of the height sensing and control
device 90 can be had by reference to U.S. Patent ~o. 2,965,372
issued December 20, 1960 to R.D. Cava~naugh and entitled "Pneumatic
Isolator".
D. Response_Sens_rs_12, 14
As discussed above, the payload 16 and the base 18 are provided
with response sensors 12, 14 which generate or derive after
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processlng signals representive of the velocity of the payload 16,
abbrevlated "dX,"and the velocity of the excitation of thelbase 18,
abbreviated "dU", respectively.
Response sensor 12 is operatively coupled with the payload 16
either directly or via the payload support 56 which is secured to
the payload 16. Response sensor 14 is operatively coupled with the
base 18 either directly or via the support cylinder 50 which is
secured to the base 18.
The response sensors 12, 14 can be accelerometers such as
piezo-electric accelerometers, having their outputs integrated to
yield a velocity signal, or electro-mechanical velocity sensors such
as and preferrably a geophone type mechanism. Geophones are
dlscussed extensively in the earlier application, of which this is a
contInuation-in-part. The informational content of the sensor
signals is not substantially utilized for frequencies below the
isolation system undamped resonant frequency; thus the motion sensor
frequency response need not extend down to extremely low
frequencies.
The implementation of each of the sensors 12, 14 should be such
that the sensor resonant frequency should be at least one octave in
frequency below the resonant frequency of the isolation system
j actuator. This, then, limits the application of electro-mechanical
velocity sensors such as geophones to vibration isolation systems
having resonant frequencies above approximately ten cycles per
second. Integrated accelerometers can be utilized as velocity
sensors for vibration isolation systems having resonant frequencies
-~ below about ten cycles per second.
E. Electronic Servo-Controller 22
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The servo-controller 22 shown in Figure 4 uses the two velocity
' signals and the feedback signal to generate a control function to be
applied to the servovalve 30 as the command signal in the form
required by EQ t10) . While an all analog system is shown, it can
be converted to a digital system using analog to digital and digital
to analog converters for communication with the response sensors 12,
14 and the servo-controller 22. These changes are well within the
skill of an engineer in the art.
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The flow path of the control system slgnals starts with
applying the output voltages EX and EU from the sensors 12, 14 to
coupling means 102, 104, respectively. The function of the coupling
means 102, 104 ls to convert the high impedance signal from the
velocity sensors 12, 14 to low impedance signals which can undergo
additional manipulatlon without the input impedances of other
clrcuit eléments altering them, i.e., impedance matchin~. The
coupllng ampllfier means 102, 104 may include, where appropriate,
circuit elements (not shown) such as an amplifier to establish a
deslred voltage scale factor for the velocity signal; and/or
frequency manipulation circuits to artificially lower the resonant
frequency of the sensor, or integration circuits to integrate the
acceleration signals from accelerometer sensors where used for the
`, response sensors 12, 14 instead of velocity sensors.
15The circuit used to artificially lower the resonant frequency
of the sensor comprises one or two operational amplifiers (not
shown) used to generate a double lag-lead transfer function.
;~ Details of this circuit and the integration circuit are well within
the skill of one in this art. Details of the synthesis of linear
transfer functions utilizing operational amplifiers, can be found in
my prior application, of which this is a continuation-in-part.
, The output signals from the coupling amplifier means 102, 104
-,(which signals for simplicity shall be still referred to as EX and
Eu, respectively) are fed to a substraction circuit 106 to form a
25 voltage signal, "Ed" which is the difference between the signals EX
and EU and represents the relative velocity.
~iThe signals Ex and EU are then inputted into processing means
' 108, 110 for converting them to their absolute values.
t li !The two absolute valued signals are then fed into an analog
30 divider circuit 112 which also acts as an output voltage limiter; EX
-is fed to the numerator and EU is fed to the denominator.
,The divider circuit's output is the velocity ratio ER which is
limited to voltages und~r the maximum magnitude El.
The velocity ratlo is then applied to the input of an amplifier
35 114 having gain G. 1 -
Next, the amplified velocity ratio signal is fed to a summer
116, where a constant voltage "Eb" of, for example, 1.0 volt is
i
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-17-
added to the veloclty ratio as a bias. The output of the summer 116
---i is a control function signal.
- The remaining control electronics compensate for specific
characteristics of`the servovalve 30 used in the vibration isolation
system 10. For example, for the electro-mechanical servovalve 30
described herein, these characteristics are the velocity squared
nature of non-viscous fluid flow damping, and the nature of the
displacement and positioning of the valve spool 32. The description
of these compensation circuits 120 follows.
The control function signal from the summer 116 is applied as
the denominator, and the relative velocity voltage dV from the
subtracting summer 106 is applied as the numerator, of a second
divider 122.
The circuitry shown in Figure 3 is for a bidirectional servo
valve. For a unidirectional servo valve, the signal representing
the relative velocity dV will be applied to the second divider 122
; from the output of the processing means 108, 110 instead of from the
subtraction circuit 106, thus insuring that the output of the second
divider 122 will always be of one polarity.
The second divider's output is fed to a square root function
generator 124, which for a unidirectional servovalve can be single
quadrant but for a bidirectional servovalve can be two quadrant to
preserve the sign of the output of the second divider 122. Note
that if it is desired to have a bidirectional servovalve act as an
unidirectional servovalve, the only change needed is to replace the
two quadrant function generator by a single quadrant function
generator so as to generate only a single polarity command signal.
The output voltage, Es, from the square root function generator
i 124 is amplified (or attenuated) by amplifier 126 which has a gain R
defined in E~ (9). This sets the magnitude of the resulting damping
coefficient to the proper scaling magnitude, such that the damping
coefficient when EX is zero is equal, to the damping coefficient
Zetazero of the vibration isolation system 10. The resulting
voltage signal is fed into the valve controller to control the
servovalve's openings' area as given above in EQ (10). It is this
signal which is applled as the command signal to control the
` electro-mechanical means and thereby close the servo-control loop.
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