U.S. patent application number 13/034207 was filed with the patent office on 2011-08-04 for mass flow controller with improved dynamic response.
This patent application is currently assigned to Brooks Instrument, LLC. Invention is credited to John Michael Lull.
Application Number | 20110191038 13/034207 |
Document ID | / |
Family ID | 41697154 |
Filed Date | 2011-08-04 |
United States Patent
Application |
20110191038 |
Kind Code |
A1 |
Lull; John Michael |
August 4, 2011 |
MASS FLOW CONTROLLER WITH IMPROVED DYNAMIC RESPONSE
Abstract
A system and method of characterizing or controlling a flow of a
fluid is provided that involves a sensor conduit and a bypass. A
plurality of fluids may be utilized in the flow control device
based on characteristic information of the device generated during
calibration thereof. The characteristic information, in turn is
based on a dimensionless parameters, such as adjusted dynamic
pressure and adjusted Reynolds number.
Inventors: |
Lull; John Michael;
(Fullerton, CA) |
Assignee: |
Brooks Instrument, LLC
|
Family ID: |
41697154 |
Appl. No.: |
13/034207 |
Filed: |
February 24, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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12197888 |
Aug 25, 2008 |
7905139 |
|
|
13034207 |
|
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Current U.S.
Class: |
702/47 ;
73/202.5 |
Current CPC
Class: |
G05D 7/0635 20130101;
G01F 1/6847 20130101; G01F 1/6965 20130101 |
Class at
Publication: |
702/47 ;
73/202.5 |
International
Class: |
G06F 19/00 20110101
G06F019/00; G01F 1/68 20060101 G01F001/68 |
Claims
1. A mass flow controller for measuring flow of a fluid,
comprising: a flow meter for providing a signal corresponding to
mass flow through the flow meter, the flow meter including a flow
sensor; an adjustable valve for controlling the passage of fluid
out of the mass flow controller; a fluid path through the mass flow
controller, the fluid path including an inventory volume between
the flow sensor and the adjustable valve; a pressure transducer for
providing a signal corresponding to the fluid pressure at a
position in the flow path before the adjustable valve; and a signal
processor to determine the compressibility of the gas in the fluid
path using the fluid temperature and pressure and to correct the
signal from the flow sensor for inaccuracies caused by a change in
pressure, the correction depending on the compressibility of the
gas; and a controller to adjust the adjustable valve to control the
flow through the mass flow controller in accordance with the
corrected signal corresponding to the fluid flow.
2. The mass flow controller of claim 1 in which the signal
processor is programmed to calculate compressibility using a form
of the virial coefficients.
3. The mass flow controller of claim 1 in which the signal
processor is programmed to determine a signal that compensates for
the change in pressure using a value proportional to the change in
gas in the inventory volume.
4. The mass flow controller of claim 3 in which value proportional
to the change in gas in the inventory volume includes a pressure
term, a compressibility term, and a temperature term.
5. The mass flow controller of claim 3 in which value proportional
to the change in gas in the inventory volume is proportional to the
pressure and inversely proportional to the temperature and
compressibility of the gas.
6. The mass flow controller of claim 1 in which the signal
processor is positioned on the flow meter.
7. The mass flow controller of claim 1 in which the signal
processor is part of the controller.
8. The mass flow controller of claim 1 further comprising a
temperature sensor.
9. A method of determining fluid flow through a mass flow
controller including a flow sensor, comprising: measuring pressure
in a fluid path; measuring temperature in the fluid path;
determining compressibility of the gas using the pressure and
temperature measurement; and modifying, using the determined
compressibility of the gas, a signal from the flow sensor to
correct for changes in pressure.
10. The method of claim 9 in which modifying a signal from the flow
sensor includes modifying a signal derived from one or more
temperature sensitive elements.
11. The method of claim 10 in which the one or more temperature
sensitive elements comprise heated resistive winding positioned
along a tube through which the fluid being measured flows.
12. The method of claim 10 in which the one or more temperature
sensitive elements comprise a thermocouple or a thin film
resistor.
13. The method of claim 9 in which modifying a signal from the flow
sensor includes modifying a signal derived from applying heat in
the flow path and sensing temperature at one or more points in the
flow path, the temperatures being determined in part by the gas
flow.
14. The method of claim 13 in which applying heat in the flow path
includes applying by one or more resistive windings and in which
sensing temperature at one or more points in the flow path includes
sending temperature using resistive windings, a thermocouple, or a
thin film resistor.
15. The method of claim 9 in which modifying, using the determined
compressibility of the gas, a signal from the flow sensor to
correct for changes in pressure includes modifying the signal using
a change in the amount of gas in an inventory volume.
16. The method of claim 10 in which modifying the signal using a
change in the amount of gas in an inventory volume includes using
the change in the amount of gas in inventory as the input of a
filter.
17. The method of claim 16 in which modifying the signal using a
change in the amount of gas in an inventory volume includes using
the change in the amount of gas in inventory as the input of a
series of cascading filters.
18. The method of claim 17 in which modifying the signal using a
change in the amount of gas in an inventory volume includes using
the change in the amount of gas in inventory as the input of a
series of cascading second order filters.
19. The method of claim 9 in which modifying a signal from the flow
sensor to correct for changes in pressure includes modifying a
signal that has been normalized and calibrated to a particular
gas.
20. A method of determining gas flow through a mass flow controller
including a flow sensor, comprising: measuring pressure in a fluid
path; measuring temperature in the fluid path; determining
compressibility of the gas using the pressure and temperature
measurement; and generating a sensor output signal derived from two
resistors in a flow sensor; modifying the sensor output signal to
produce a corrected sensor output signal, the corrected sensor
output signal being normalized, linearized with respect to the
sensor fluid flow, and corrected for changes in pressure using the
compressibility of the gas.
21. The method of claim 20 further comprising controlling a gas
flow valve in accordance with the corrected sensor output.
22. The method of claim 20 in which modifying the sensor output
signal to produce a corrected sensor output signal includes
calibrating and linearizing the sensor output before correcting the
sensor output for changes in pressure.
23. The method of claim 20 in which determining compressibility of
the gas using the pressure and temperature measurement includes
using a form of a virial expansion.
24. The method of claim 20 in which modifying the sensor output
signal to produce a corrected sensor output signal includes
determining a change in the amount of gas in the inventory
volume.
25. The method of claim 24 in which modifying the sensor output
signal to produce a corrected sensor output signal includes using
the change in the amount of inventory volume as an input to an
electronic filter.
26. The method of claim 24 in which the filter produces a false
flow signal that is subtracted to produce the corrected sensor
output signal.
27. A method of controlling a valve, comprising: receiving a set
point corresponding to a desired flow rate of fluid through the
valve; determining a valve drive signal to be provided to the valve
that corresponds to the desired flow rate, the valve drive signal
corresponding to a first displacement of the valve under a first
set of pressure conditions in a flow path leading to the valve;
measuring at least one pressure in a flow path that corresponds to
a second set of pressure conditions that is different than the
first set of pressure conditions; determining the compressibility
of the fluid as a function of temperature and pressure measured in
the flowpath; and modifying the valve drive signal to compensate
for a difference in a displacement of the valve due to a difference
between the first set of pressure conditions and the second set of
pressure conditions.
28. The method of claim 27 in which determining the compressibility
of the fluid as a function of temperature and pressure measured in
the flow path includes determining compressibility using a form of
the virial coefficients.
29. The method of claim 27 in which modifying the valve drive
signal includes modifying the drive signal by an amount determined
by the change in gas in the inventory volume.
30. The method of claim 29 in which modifying the drive signal by
an amount determined by the change in gas in the inventory volume
includes modifying the drive signal by an amount determined by
value proportional to the change in gas in the inventory
volume.
31. The method of claim 29 in which modifying the drive signal by
an amount determined by the change in gas in the inventory volume
includes modifying the drive signal by an amount determined by a
value proportional to the pressure and inversely proportional to
the temperature and compressibility of the gas.
32. A mass flow meter, comprising: a fluid path for passage of a
fluid; a flow sensor through which a fluid flows, the flow sensor
connected to the fluid path, the flow sensor producing an
electrical signal corresponding to the flow of fluid through the
flow sensor; a flow restriction in the fluid path, the volume of
the fluid path between the flow sensor and the restriction defining
an inventory volume; a pressure transducer for providing a signal
corresponding to the fluid pressure at a position in the flow path
before the flow restriction; and a signal processor programmed to
determine the compressibility of the gas in the fluid path using
the fluid temperature and pressure and to correct the electrical
signal from the flow sensor for inaccuracies caused by a change in
pressure, the correction depending on the compressibility of the
gas.
33. The mass flow meter of claim 32 in which the signal processor
is programmed to calculate compressibility using a form of the
virial coefficients.
34. The mass flow meter of claim 32 in which the signal processor
is programmed to determine a signal that compensates for the change
in pressure using a value proportional to the change in gas in the
inventory volume.
35. The mass flow meter of claim 34 in which value proportional to
the change in gas in the inventory volume includes a pressure term
and a compressibility term.
36. The mass flow meter of claim 34 in which value proportional to
the change in gas in the inventory volume is proportional to the
pressure and inversely proportional to the temperature and
compressibility of the gas.
37. A mass flow controller for measuring flow of a fluid,
comprising: a fluid inlet; a flow meter connected to the fluid
inlet for providing a signal corresponding to mass flow through the
flow meter, the flow meter including a flow sensor; an adjustable
valve for controlling the passage of fluid out of the mass flow
controller through a fluid outlet; a fluid path through the mass
flow controller from the fluid inlet to the fluid outlet, the fluid
path including an inventory volume between the flow sensor and the
adjustable valve; a pressure transducer for providing a signal
corresponding to the fluid pressure at a position in the flow path
before the adjustable valve; and a signal processor to determine
the compressibility of the gas in the fluid path using the fluid
temperature and pressure and to correct the signal from the flow
sensor for inaccuracies caused by a change in pressure, the
correction depending on the compressibility of the gas; and a
controller to adjust the adjustable valve to control the flow
through the mass flow controller in accordance with the corrected
signal corresponding to the fluid flow.
38. A mass flow controller for measuring flow of a fluid,
comprising: a fluid inlet; an adjustable valve connected to the
fluid inlet for controlling the passage of fluid through the mass
flow controller; a flow meter connected to a fluid outlet for
providing a signal corresponding to mass flow through the flow
meter, the flow meter including a flow sensor; a fluid path through
the mass flow controller from the fluid inlet to the fluid outlet,
the fluid path including an inventory volume between the adjustable
valve and the flow sensor; a pressure transducer for providing a
signal corresponding to the fluid pressure at a position in the
flow path after the adjustable valve; a signal processor to
determine the compressibility of the gas in the fluid path using
the fluid temperature and pressure and to correct the signal from
the flow sensor for inaccuracies caused by a change in pressure,
the correction depending on the compressibility of the gas; and a
controller to adjust the adjustable valve to control the flow
through the mass flow controller in accordance with the corrected
signal corresponding to the fluid flow.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a Continuation Application of
application Ser. No. 12/197,888 filed on Aug. 25, 2008, entitled
MASS FLOW CONTROLLER WITH IMPROVED DYNAMIC, the entire contents of
which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
Technical Field of the Invention
[0002] The present invention relates generally to methods and
systems for determining the mass flow rate of a fluid, and more
particularly to the operation of mass flow controllers.
[0003] Many industrial processes require precise control of various
process fluids. For example, in the pharmaceutical and
semiconductor industries, mass flow controllers are used to
precisely measure and control the amount of a process fluid that is
introduced to a process tool. A fluid can be any type of matter in
any state that is capable of flow such as liquids, gases, and
slurries, and comprising any combination of matter or substance to
which controlled flow may be of interest.
[0004] Conventional mass flow controllers (MFCs) generally include
four main portions: a flow meter, a control valve, a valve
actuator, and a controller. The flow meter measures the mass flow
rate of a fluid in a flow path and provides an electrical signal
indicative of that flow rate. Typically, the flow meter may include
a mass flow sensor and a bypass. The mass flow sensor measures the
mass flow rate of fluid in a sensor conduit that is fluidly coupled
to the bypass. The mass flow rate of fluid in the sensor conduit is
related to the mass flow rate of fluid flowing in the bypass, with
the sum of the two being the total flow rate through the flow path
controlled by the mass flow controller.
[0005] FIG. 1 shows schematically a typical mass flow controller
100 that includes a block 110, which is the platform on which the
components of the MFC are mounted. A thermal mass flow meter 140
and a valve assembly 150 containing a valve 170 are mounted on the
block 110 between a fluid inlet 120 and a fluid outlet 130. The
thermal mass flow meter 140 includes a bypass 142 through which
typically a majority of fluid flows and a thermal flow sensor 146
through which a smaller portion of the fluid flows.
[0006] Thermal flow sensor 146 is contained within a sensor housing
102 (portion shown removed to show sensor 146) mounted on a
mounting plate or base 108. Sensor 146 is a small diameter tube,
typically referred to as a capillary tube, with a sensor inlet
portion 146A, a sensor outlet portion 146B, and a sensor measuring
portion 146C about which two resistive coils or windings 147, 148
are disposed. In operation, electrical current is provided to the
two resistive windings 147, 148, which are in thermal contact with
the sensor measuring portion 146C. The current in the resistive
windings 147, 148 heats the fluid flowing in measuring portion 146
to a temperature above that of the fluid flowing through the bypass
142. The resistance of windings 147, 148 varies with temperature.
As fluid flows through the sensor conduit, heat is carried from the
upstream resistor 147 toward the downstream resistor 148, with the
temperature difference being proportional to the mass flow rate
through the sensor.
[0007] An electrical signal related to the fluid flow through the
sensor is derived from the two resistive windings 147,148. The
electrical signal may be derived in a number of different ways,
such as from the difference in the resistance of the resistive
windings or from a difference in the amount of energy provided to
each resistive winding to maintain each winding at a particular
temperature. Examples of various ways in which an electrical signal
correlating to the flow rate of a fluid in a thermal mass flow
meter may be determined are described, for example, in commonly
owned U.S. Pat. No. 6,845,659, which is hereby incorporated by
reference. The electrical signals derived from the resistive
windings 147,148 after signal processing comprise a sensor output
signal.
[0008] The sensor output signal is correlated to mass flow in the
mass flow meter so that the fluid flow can be determined when the
electrical signal is measured. The sensor output signal is
typically first correlated to the flow in sensor 146, which is then
correlated to the mass flow in the bypass 142, so that the total
flow through the flow meter can be determined and the control valve
170 can be controlled accordingly. The correlation between the
sensor output signal and the fluid flow is complex and depends on a
number of operating conditions including fluid species, flow rate,
inlet and/or outlet pressure, temperature, etc.
[0009] The process of correlating raw sensor output to fluid flow
entails tuning and/or calibrating the mass flow controller and is
an expensive, labor intensive procedure, often requiring one or
more skilled operators and specialized equipment. For example, the
mass flow sensor may be tuned by running known amounts of a known
fluid through the sensor portion and adjusting certain signal
processing parameters to provide a response that accurately
represents fluid flow. For example, the output may be normalized,
so that a specified voltage range, such as 0 V to 5 V of the sensor
output, corresponds to a flow rate range from zero to the top of
the range for the sensor. The output may also be linearized, so
that a change in the sensor output corresponds linearly to a change
in flow rate. For example, doubling of the fluid output will cause
a doubling of the electrical output if the output is linearized.
The dynamic response of the sensor is determined, that is,
inaccurate effects of change in pressure or flow rate that occur
when the flow or pressure changes are determined so that such
effects can be compensated.
[0010] A bypass may then be mounted to the sensor, and the bypass
is tuned with the known fluid to determine an appropriate
relationship between fluid flowing in the mass flow sensor and the
fluid flowing in the bypass at various known flow rates, so that
the total flow through the flow meter can be determined from the
sensor output signal. In some mass flow controllers, no bypass is
used, and the entire flow passes through the sensor. The mass flow
sensor portion and bypass may then be mated to the control valve
and control electronics portions and then tuned again, under known
conditions. The responses of the control electronics and the
control valve are then characterized so that the overall response
of the system to a change in set point or input pressure is known,
and the response can be used to control the system to provide the
desired response.
[0011] When the type of fluid used by an end-user differs from that
used in tuning and/or calibration, or when the operating
conditions, such as inlet and outlet pressure, temperature, range
of flow rates, etc., used by the end-user differ from that used in
tuning and/or calibration, the operation of the mass flow
controller is generally degraded. For this reason, the flow meter
can be tuned or calibrated using additional fluids (termed
"surrogate fluids") and or operating conditions, with any changes
necessary to provide a satisfactory response being stored in a
lookup table. U.S. Pat. No. 7,272,512 to Wang et al., for "Flow
Sensor Signal Conversion," which is owned by the assignee of the
present invention and which is hereby incorporated by reference,
describes a system in which the characteristics of different gases
are used to adjust the response, rather than requiring a surrogate
fluid to calibrate the device for each different process fluid
used.
[0012] Control electronics 160 control the position of the control
valve 170 in accordance with a set point indicating the desired
mass flow rate, and an electrical flow signal from the mass flow
sensor indicative of the actual mass flow rate of the fluid flowing
in the sensor conduit. Traditional feedback control methods such as
proportional control, integral control, proportional-integral (PI)
control, derivative control, proportional-derivative (PD) control,
integral-derivative (ID) control, and
proportional-integral-derivative (PID) control are then used to
control the flow of fluid in the mass flow controller. A control
signal (e.g., a control valve drive signal) is generated based upon
an error signal that is the difference between a set point signal
indicative of the desired mass flow rate of the fluid and a
feedback signal that is related to the actual mass flow rate sensed
by the mass flow sensor. The control valve is positioned in the
main fluid flow path (typically downstream of the bypass and mass
flow sensor) and can be controlled (e.g., opened or closed) to vary
the mass flow rate of fluid flowing through the main fluid flow
path, the control being provided by the mass flow controller.
[0013] In the illustrated example, the flow rate is supplied by
electrical conductors 158 to a closed loop system controller 160 as
a voltage signal. The signal is amplified, processed and supplied
to the control valve assembly 150 to modify the flow. To this end,
the controller 160 compares the signal from the mass flow sensor
140 to predetermined values and adjusts the proportional valve 170
accordingly to achieve the desired flow.
[0014] FIG. 2 illustrates a schematic block diagram of a typical
mass flow controller 200. The mass flow controller illustrated in
FIG. 2 includes a flow meter 210, a Gain/Lead/Lag (GLL) controller
250, a valve actuator 260, and a valve 270.
[0015] The flow meter 210 is coupled to a flow path 203. The flow
meter 210 senses the flow rate of a fluid in the flow path, or in a
portion of the flow path, and provides a raw flow signal indicative
of the sensed flow rate. The raw flow signal is typically
conditioned, that is, it is normalized, linearized, and compensated
for dynamic response. A conditioned flow signal FS2 is provided to
a first input of GLL controller 250. The conditioned flow signal
FS2 is also provided to a signal filter 220, which provides
appropriate signal levels as input to a display 225, which displays
the flow rate to an operator.
[0016] In addition, GLL controller 250 includes a second input to
receive a set point signal SI2. A set point refers to an indication
of the desired fluid flow to be provided by the mass flow
controller 200. The set point signal SI2 may first be passed
through a slew rate limiter or filter 230 prior to being provided
to the GLL controller 250. Filter 230 serves to limit instantaneous
changes in the set point in signal SI2 from being provided directly
to the GLL controller 250, such that changes in the flow take place
over a specified period of time. It should be appreciated that the
limiter or filter 230 may be omitted, and that any of a variety of
signals capable of providing indication of the desired fluid flow
is considered a suitable set point signal. The term set point,
without reference to a particular signal, describes a value that
represents a desired fluid flow.
[0017] Each of the components of MFC 200 has an associated gain,
which gains can be combined to determine a system gain. In block
240, a reciprocal gain term G is formed by taking the reciprocal of
a system gain term and applying it as one of the inputs to the GLL
controller. It should be appreciated that the reciprocal gain term
may be the reciprocal of all or fewer than all of the gain terms
associated with the various components around the control loop of
the mass flow controller. For example, improvements in control and
stability may be achieved by forming the reciprocal of the product
of the individual component gain terms. However, in preferred
embodiments, gain term G is formed such that the loop gain remains
a constant (i.e., gain G is the reciprocal of the system gain
term).
[0018] Pressure sensed at the inlet 208 or elsewhere provides a
pressure signal 290 to flow meter 210 to compensate for spurious
indications due to pressure transients. Further, the pressure
signal may be used by GLL controller 250 for feed forward control
of the valve. Also, the pressure signal may be used to adjust the
gain in a GLL controller.
[0019] Based in part on the flow signal and the set point signal
SI2, the GLL controller 250 provides a drive signal DS to the valve
actuator 260 that controls the valve 270. The valve 270 is
typically positioned downstream from the flow meter 210 and permits
a certain mass flow rate depending, at least in part, upon the
displacement of a controlled portion of the valve 270. The
controlled portion of the valve 270 may be a moveable plunger
placed across a cross-section of the flow path 203. The valve 270
controls the flow rate in the fluid path by increasing or
decreasing the area of an opening in the cross section where fluid
is permitted to flow. Typically, mass flow rate is controlled by
mechanically displacing the controlled portion of the valve by a
desired amount. The term displacement is used generally to describe
the variable of a valve on which mass flow rate is, at least in
part, dependent. As such, the area of the opening in the cross
section is related to the displacement of the controlled portion,
referred to generally as valve displacement.
[0020] The displacement of the valve is often controlled by a valve
actuator, such as a solenoid actuator, a piezoelectric actuator, a
stepper actuator etc. In FIG. 2, valve actuator 260 is a solenoid
type actuator; however, the present invention is not so limited, as
other alternative types of valve actuators may be used. The valve
actuator 260 receives drive signal DS from the controller and
converts the signal DS into a mechanical displacement of the
controlled portion of the valve. Ideally, valve displacement is
purely a function of the drive signal. However, in practice, there
may be other variables that affect the position of the controlled
portion of the valve.
[0021] When the input pressure changes, for a brief period of time
the sensor output does not accurately indicate the mass flow. To
mitigate this effect, some mass flow controllers include a pressure
transducer. Pressure transducers allow tuning of the dynamic
response of the device as a function of pressure, which in turn can
provide a faster response, especially at low inlet pressures. For
example, U.S. Pat. No. 7,273,063 to Lull et al., which is commonly
owned with the present application and which is hereby incorporated
by reference, uses signals from a pressure transducer to modify the
sensor signal to compensate for some pressure related transient
effects and provides some compensation for changes in the amount of
gas in the inventory volume.
[0022] There is some unavoidable internal volume between the flow
meter and the control valve. That volume, referred to as an
"inventory volume," (e.g. 140 of FIG. 1, and 280 of FIG. 2)
contains a small amount of gas that varies with pressure and
temperature. An inventory volume exists between the flow meter and
any downstream restriction, with the control valve being an example
of a restriction. As the input pressure to the flow meter changes,
a certain net amount of fluid flows into or out of the inventory
volume to equalize the inventory volume pressure with that of the
rest of the system, thus changing the amount, that is the mass, of
fluid stored in that inventory volume. When input or output
pressure changes, there is a net flow into or out of the inventory
volume, and this leads to a discrepancy between the flow through
the flow meter and the flow actually delivered to the process. U.S.
Pat. No. 7,273,063 compensates for this by simply differentiating
the inlet pressure and subsequently applying a filter, for example,
to generate a transient compensating signal that nominally matches
that spike for the signal inside the flow meter. The transient
compensating signal is subtracted from the signal from the flow
meter to compensate for the pressure change. The technique of U.S.
Pat. No. 7,273,063 provides accurate sensor output for some gases,
but does not provide sufficiently accurate signals for other
gases.
[0023] While the presence of the inventory volume is known and
attempts have been made to compensate for the volume to properly
indicate flow, present methods are insufficiently accurate for the
increasingly demanding standards of industry.
SUMMARY OF THE INVENTION
[0024] An object of the invention is to provide improved accuracy
in flow sensors and flow controllers.
[0025] The present invention provides a more accurate indication of
gas flow through a flow controller by accounting for the
compressibility of the gas when correcting a flow signal for
inaccuracies caused by changes in pressure.
[0026] The foregoing has outlined rather broadly the features and
technical advantages of the present invention in order that the
detailed description of the invention that follows may be better
understood. Additional features and advantages of the invention
will be described hereinafter. It should be appreciated by those
skilled in the art that the conception and specific embodiment
disclosed may be readily utilized as a basis for modifying or
designing other structures for carrying out the same purposes of
the present invention. For example, both pressure and temperature
are required for calculations of the preferred embodiments. The
pressure measurement used can be obtained, for instance, directly
from inlet pressure, from a transducer exposed directly to the
inventory volume, or approximated. Similarly, the temperature
measurement used can be obtained, for instance, from the flow
sensor body temperature or average gas temperature in the inventory
volume. It should also be realized by those skilled in the art that
such equivalent constructions do not depart from the spirit and
scope of the invention as set forth in the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0027] For a more through understanding of the present invention,
and advantages thereof, reference is now made to the following
descriptions taken in conjunction with the accompanying drawings,
in which:
[0028] FIG. 1 illustrates a conventional thermal mass flow
controller;
[0029] FIG. 2 illustrates a schematic block diagram of a mass
flow;
[0030] FIG. 3 is a flow chart showing one preferred method of the
present invention.
[0031] FIG. 4 is a chart illustrating normalized outputs of the
stages of a preferred signal filter of the present invention.
[0032] FIG. 5 is a chart illustrating the scaled filter section
outputs of FIG. 4 and the resulting sum for a preferred embodiment
of the present invention.
[0033] FIG. 6 illustrates an algorithm of a preferred embodiment of
the present invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0034] While the mass flow controller described in U.S. Pat. No.
7,273,063 adequately compensates the sensor readings for pressure
transients for some applications, it suffers from three significant
shortcoming:
[0035] 1. It does not adequately account for gas
compressibility;
[0036] 2. It does not adequately deal with nonlinearities in the
flow meter; and
[0037] 3. It does not adequately compensate for changes in flow
meter dynamic response on different gasses or at different flow
rates.
[0038] When the input pressure to an MFC changes the flow meter
provides an inaccurate flow signal that does not correspond to the
actual flow of gas through the valve and to the process tool. A
portion of the inaccurate signal corresponds to the actual amount
of gas that flows into or out of the inventory volume; another
portion of the inaccurate signal is caused by the dynamic response
of the flow meter to the transient changes in the gas flow through
the meter as the pressure changes. Thus, an accurate correction not
only compensates for the gas flowing into or out of the inventory
volume, but also for the inaccuracy of the flow sensor signal
caused by the unsettled thermal environment in the flow sensor
caused by the change in flow. While the actual flow into or out of
inventory volume is thought to occur relatively quickly, on the
order of a millisecond, the portion of the inaccurate signal caused
by the dynamic response of the meter is thought to last longer, on
the order of a second, which, if not corrected, can lead to a
significant distortion of the measured flow.
[0039] Preferred embodiments correct for this transient response to
changes in pressure causing net flow into or out of the inventory
volume, so that a more accurate flow is reported to the control
system of a mass flow controller to adjust the valve position and
is reported to the process tool operator. Preferred embodiments of
the present invention compensate for the inventory space by
properly accounting for gas compressibility, non-linearities in the
flow meter, and changes in flow meter dynamic response on different
gasses and at different flow rates.
[0040] Embodiments of the invention substantially improve flow
measurement accuracy, particularly on non-ideal gases, such as
SF.sub.6, and on highly non-linear flow meters, by substantially
improving pressure-transient performance compared to prior art mass
flow controllers. Accounting for the compressibility significantly
improves the measurement accuracy for gases that do not follow the
ideal gas law (PV=nRT).
[0041] FIG. 3 shows an overview of the steps of a preferred
embodiment of the present invention. Several of the steps are
explained later in more detail. In step 302, the system verifies
that pressure information is available. If no pressure information
is available, for example, because the pressure transducer is not
providing a pressure signal input to the flow meter, then pressure
effects on gas in the inventory volume cannot be calculated and the
process ends at block 304. The cause of the lack of pressure
information is preferably investigated by an operator and corrected
before the process restarts.
[0042] If pressure information is available, the compressibility of
the fluid is determined in step 306. The compressibility depends on
the gas species and the pressure and the temperature of the gas. In
step 308, the system determines whether it is in an operating state
in which inventory gas compensation is required. For example, if
the operator sets the valve to stop the gas flow, then the gas flow
rate through the valve is known to be zero, and so no adjustment to
the sensor output is required to indicate an accurate flow rate. If
no inventory gas compensation is required, the process ends at step
310.
[0043] If inventory gas compensation is required, the process
continues in step 312, in which a value related to gas-in-inventory
is calculated. As described above, there is a difference between
the flow indicated by the flow sensor and the actual flow through
the valve if, after passing through the flow sensor, there is a net
gain or loss of gas in the inventory volume. Thus, the inventory
volume compensation depends not on the actual amount of gas in the
inventory volume itself, but on the change of the amount of gas in
the inventory volume. If the amount of gas in the inventory volume
remained constant, then no compensation for the inventory volume
would be required. It is therefore not necessary to actually
calculate the exact amount of gas in the inventory volume, it is
only necessary to determine the change in the amount of gas. The
change can be determined from a value related to the amount gas in
the inventory volume, without calculating the actual amount of the
gas in the inventory volume. For example, an inventory value that
is proportional to the inventory amount can be calculated.
[0044] In step 314, a value proportional to the derivative with
respect to time of gas-in-inventory is calculated from the
inventory values determined in step 312.
[0045] In step 316, the value proportional to the derivative
determined in step 314 is applied to a signal filter to produce a
signal corresponding to the inaccurate flow signal produced by the
flow sensor in response to an input pressure change. Because the
input to the filter is the value related to the time related change
of gas amount in the inventory volume determined in step 314, the
signal produced by the filter will depend on the variables used to
produce the derivative, that is, the compressibility of the gas,
the change in pressure, and the temperature of the gas. Thus, the
signal from the filter can more accurately reflect the actual
operating conditions of the flow meter.
[0046] In step 318, a gain factor, specific for the process gas
being used in the MFC, is applied to the signal calculated in step
316 to produce a compensation signal that matches the magnitude of
the inaccurate flow signal from the flow meter on the actual
process gas. In step 320, the compensation signal is subtracted
from the output of the sensor, which eliminates the effects of
changes in inventory value from the flow signal so that the flow
meter is more accurately indicating the actual fluid flow to a
process tool.
[0047] Below are described in more detail several exemplary methods
of carrying out some of the steps of FIG. 3. The invention is not
limited to these exemplary methods. For determining the
compressibility of the gas in step 306, various algorithms are
known. Some calculations of compressibility are very accurate over
a wide range of pressure and temperature, but are not well suited
for implementation directly in the device firmware. A preferred
algorithm is sufficiently accurate to provide flow information at
the required accuracy, while requiring relatively little processing
and little data storage. One algorithm expresses the
compressibility, Z(P,T), as a function of pressure and temperature
using the alternate form of the well known virial expansion, which
expresses the pressure of a many-particle system in equilibrium as
a power series in the pressure. A suitable implementation truncates
the power series at the second order term.
Z(P,T)=1+B'(T)*P+C'(T)*P2 [Equation.1]
[0048] where:
[0049] P is the absolute pressure of the gas in the inventory
volume, for computational convenience P may be expressed as a
fraction of the full scale range of the absolute pressure signal
available to the flow meter (P2=P*P is the notation for the second
order term).
[0050] B' and C' are the alternate form of the second and third
virial coefficients.
[0051] T is the absolute temperature of the gas in the inventory
volume, expressed in degrees Kelvin (K).
[0052] The alternate form of the 2nd & 3rd virial coefficients
can each be approximated over a reasonable temperature range as
cubic polynomials of 1/T:
B'(T).about.B(T)=B0+B1/T+B2/T2+B3/T3
C'(T).about.C(T)=C0+C1/T+C2/T2+C3/T3
[0053] Values of Z(P,T) may be obtained spanning the range of
operating pressures and temperatures anticipated for the flow
meter. The Z(P,T) values may come from measurement data or may be
computed using a suitable equation of state model. One suitable
model for computing Z(P,T) is that of Lee and Kesler using the
three-parameter principle of corresponding states of Pitzer. For a
particular temperature Ti the values of Z(P,Ti) at several
different pressures (e.g. P1, P2, P3, . . . , Pn) form a curve that
may be fit by suitable mathematical process to determine B'(Ti) and
C'(Ti) satisfying Equation.1 at temperature Ti over the pressure
range P1-Pn. The values of B'(T) and C'(T) may be thus determined
at several different temperatures (e.g. T1, T2, T3, . . . , Tn).
The temperature related sequence of values B'(T1), B'(T2), B'(T3),
. . . , B'(Tn) form a curve that may be fit by a suitable
mathematical process to determine the approximation B(T). Similarly
the temperature related sequence of values C'(T1), C'(T2), C'(T3),
. . . , C'(Tn) form a curve that may be fit by a suitable
mathematical process to determine the approximation C(T). Least
squares fitting is one example of a suitable mathematical process
for determining B(T) and C(T) as cubic polynomials of 1/T. A
preferred algorithm then uses the compressibility
approximation:
Za(P,T)=1+(B0+B1/T+B2/T2+B3/T3)*P+(C0+C1/T+C2/T2+C3/T3)*P2
[Equation.2]
[0054] To determine a value related to the gas in inventory for
step 312, one can first determine an expression for the actual
amount gas in inventory, and then derive a simpler expression
proportional to the gas in inventory, the simpler expression being
used by firmware during operation of the MFC. The actual amount of
gas in inventory does not need to be calculated. The
gas-in-inventory can be calculated as:
Ig = Vi Z ( P , T ) P P 0 T 0 T [ Equation . 3 ] ##EQU00001##
[0055] where:
[0056] Ig=gas stored in the inventory volume (standard
cm.sup.3)
[0057] Vi=Inventory volume (cm.sup.3)
[0058] P=Pressure of the gas in the inventory volume (Pa)
[0059] P0=standard pressure (Pa)
[0060] T=Temperature of the gas in the inventory volume (K)
[0061] T0=standard temperature (K); and
[0062] Z(P,T)=Compressibility of the process gas at pressure P and
temperature T (per Equation.1 above).
[0063] As it well known, 1 standard cm.sup.3= 1/22414 mole
[0064] Because the process requires only an expression proportional
to the gas in inventory, the constant terms Vi, P0, and T0 can
therefore be omitted and the remaining expression will still
represent a value, Mg, proportional to gas-in-inventory,
leaving:
Mg=(P/(Za(P,T)*T) [Equation.4]
[0065] where:
[0066] Za(P,T)=approximated compressibility of the process gas at
pressure P and temperature T (per Equation.2 above);
[0067] While the value of Mg above is an example of a value
proportional to the gas in inventory that can be used in a
preferred algorithm, the invention is not limited to any particular
value calculation.
[0068] In step 314, a value proportional to the change in time of
the amount of gas in the inventory volume is determined. The values
of Mg can be calculated repeatedly as data from the pressure and
temperature sensors are updated. The values of Mg thus form a time
series of discrete values, equally spaced in time by a period .tau.
and designated . . . , Mg.sub.n-1, Mg.sub.n, Mg.sub.n+1, . . . ,
the derivative of Mg with respect to time can be approximated over
the interval between samples n-1 and n as simply:
Mg n t = Mg n - Mg n - 1 .tau. [ Equation . 5 ] ##EQU00002##
[0069] Since the system requires only a value proportional to the
derivative of the amount of gas in inventory over time, and not the
derivative itself, and because .tau. is fixed for any given device,
the system omits the constant .tau. from the calculation and uses
the quantity Mg.sub.n-Mg.sub.n-1 as a value proportional to the
derivative. The subscripts n and n-1 represent the value of the
corresponding variables for the current and previous signal
processing cycles, respectively.
[0070] In step 316, the value proportional to the derivative is
filtered to produce a signal matching the dynamics of the
inaccurate flow signal. The change in Mg in response to a step
change in pressure is dictated by the acoustic propagation delay
and pneumatic RC time constant of the flow meter and inventory
volume. Since flow meters generally have a very low flow
resistance, and the inventory volume is minimized as much as
possible in the design of the MFC, the pneumatic time constant is
typically very short. Since the bypass is generally physically
short and relatively open, the acoustic propagation delay is short
as well, typically less than a millisecond.
[0071] Flow meter response, however, is far slower. Flow meter
dynamic response is dominated by multiple thermal time constants in
the flow sensor itself--some of which are on the order of a second.
Prior art flow meters response is typically compensated to settle
in a fraction of a second, but this still leaves a significant
discrepancy between the actual flow into or out of the inventory
volume and the corresponding spike in indicated flow.
[0072] To more accurately indicate flow, the system of the present
invention produces a compensation signal closely matching the
waveform of the pressure transient induced "inaccurate flow" signal
from the flow meter. The compensation signal is derived from the
actual flow into or out of the inventory volume. This compensation
signal could be produced through a wide variety of signal filters.
While one preferred filter is described below, the invention is not
limited to any particular filter, and skilled persons can readily
determine other filters that can accomplish this task.
[0073] One suitable filter comprises a cascade of six, two-pole
infinite impulse response, low-pass filter sections to produce a
series of six "smeared out" pulses from an impulse input. These
"smeared out" pulses are then scaled and summed to produce a
waveform to compensate for the inaccurate sensor signal.
[0074] Each filter section implements the equation:
J.sub.m,n=2*J.sub.m,n-1-J.sub.m,n-2+((I.sub.m,n-J.sub.m,n-1)*Qm-(J.sub.m-
,n-1-J.sub.m,n-2))*P.sub.m
[0075] where:
[0076] I.sub.m,n is the input to filter section m on signal
processing cycle n
[0077] J.sub.m,n is the output of filter section m on signal
processing cycle n
[0078] P.sub.m and Q.sub.m are tuning parameters controlling the
impulse response of filter section m. The parameters P.sub.m and
Q.sub.m are determined empirically as described below.
[0079] The input, I.sub.1,n, to the first filter section is the
value related to the change in inventory volume calculated in step
312, that is, Mg.sub.n-Mg.sub.n-1. For the second and subsequent
cascaded filter sections, the input I is the output from the
previous section, that is, I.sub.m,m=J.sub.m-1,n. FIG. 4 shows the
outputs of each filter section in the cascade for a unit impulse in
to the cascade, for typical values of P and Q. Each output in the
figure is normalized to a peak value of 1 for easy visibility. The
filter described produces a waveform that closely matches the shape
of the inaccurate flow signal, but at some arbitrary magnitude.
This signal must then be scaled to match the actual magnitude of
the inaccurate flow signal on a specific device. Lines 401-406
represent respectively, the output of the filter stages one through
six.
[0080] Each of the filter section outputs is scaled by a gain
factor G.sub.m and summed to get a simulated inaccurate flow signal
for each time interval n for the specific process gas being
used.
Simulated False Signal n = m = 1 6 G m J m , n ##EQU00003##
[0081] FIG. 5 shows the scaled filter section outputs (Gm*Jm,n) and
the resulting sum for a typical application. Lines 501-506
represent respectively, the scaled output of the filter stages one
through six.
[0082] This scaling must take into account several factors: [0083]
The inventory volume varies from device to device. [0084] The
magnitude of the filter output varies depending on the inventory
volume and the fitting procedure used to select the specific set of
G values to be used. [0085] The range of the flow meter varies from
device to device, and from process gas to process gas on a specific
device.
[0086] All of the required parameters--P.sub.m, Q.sub.m, and
G.sub.m--can be determined during production of the flow meter
comprised of a sensor and a bypass by a procedure that includes
changing the input pressure to the flow meter by a representative
amount at a representative rate and then observing the sensor
electrical output and measuring the actual flow. The discrepancy
between the actual measured fluid flow and the sensor output
represents the "false flow." Software optimizes the filter
parameters to give a waveform closely matching the shape of the
measured inaccurate flow signal, and matching its amplitude
expressed in sccm, or standard cm.sup.3 per minute.
[0087] The P and Q values can be selected by an N-dimensional
nonlinear minimizer, using for each trial G values obtained by a
linear least squares fit
[0088] If sensor response and response compensation are
sufficiently reproducible, then nominal P, Q, and G values can be
determined for a typical sensor through testing with very fast
pressure transients on a few sample sensors and the average values
applied across some larger population.
[0089] Note that the specific G values used are somewhat arbitrary,
though their relative values are critical to the filter
performance. The entire waveform may be scaled up or down,
adjusting all G values by the same factor in order to match their
magnitudes to that of a specific flow meter. In some embodiments, a
single scale factor is applied in step 318 to the filter output, in
addition to the individual scale factors applied to each filter
section.
[0090] The gain factor applied in step 318 is inversely
proportional to the nominal flow range of the device on a specific
process gas, expressed in sccm. This proportionality constant is
required because the flow rate, at the point where the compensation
signal is injected, is expressed as a fraction of the nominal flow
range of the device on the selected process gas. If the flow signal
were expressed directly in sccm, no gain adjustment would be
needed. This is because the filter input is directly proportional
to the net flow rate (in sccm) into or out of the inventory
volume--completely independent of gas species--so long as the
compressibility calculation and measured temperature and pressure
are correct.
[0091] If the filter parameters for the inventory volume
compensation are determined at the factory before the sensor is
calibrated, the indicated flow signal during the inventory volume
compensation correction will be incorrect by an amount dependent on
the flow rate, and the gain factor needs to compensate for this
error. The gain factor can be determined empirically, or from the
non-linearity of the sensor and the maximum net flow into or out of
the inventory volume.
[0092] In other embodiments, it may be desirable to record the
compensation transient data at a point where it is convenient in
terms of the manufacturing process, and then convert the data to a
calibrated flow signal and perform the curve fit and gain
adjustment after final calibration. Skilled person can determine a
gain constant based on an understanding of a particular flow sensor
device and a particular production process flow.
[0093] In some embodiments, the inventory volume correction can be
confined to flow rates where the flow meter is essentially linear,
and then the software could scale based on the difference between
the estimated low-flow slope of the calibration curve (during the
compensation process) and the final low-flow slope of the
calibration curve once a valid curve is determined.
[0094] Note that while the filter parameters are preferably
determined at the factory and fixed for the sensor, the gain
adjustment is determined during operation because it is
proportional to the fluid flow.
[0095] The algorithm used for the compensation for the inventory
volume is typically stored in firmware on the circuit board of the
mass flow controller. Depending on the processing power available
in the specific application, the inventory volume compensation
filter cascade can be run at less than the full signal processing
rate, with a portion of the filter being run on each processing
cycle.
[0096] The algorithm described above compensates for the linearized
flow signal rather than the raw sensor output. Skilled persons
could readily create algorithms to operate on the raw flow signal.
When correcting the linearized flow signal, either the final
inventory gas compensation gain adjustment must be made after the
device is calibrated for a particular gas, or the calibration
process must provide a calibration to convert sensor output to
determine the inventory gas compensation gain adjustment for the
particular gas used. This is because the parameters used in the
filter, P, Q, and G, will vary with the gas used. If the gas used
in the process is different from the gas used to determine the
filter parameters, then the sensor output will need to be
compensated for the different gas. This can be done either by
performing calibration on every unit with nitrogen and using known
methods of adjusting for the process gas, or by performing a final
inventory gas compensation gain adjustment as part of a calibration
process using the process gas or suitable surrogate gas. The
correction signal should coincide temporally with the sensor output
signal being corrected. Due to relatively long time constants
associated with heat diffusion in the mechanical structures of a
heated capillary flow sensor there is typically some delay between
detection of a change in pressure and the output of the false
signal from the flow meter. The delay inherent in the signal
processing, particularly in the multistage filter, may be adequate
to temporally coordinate the correction signal with the sensor
false signal; if not, an additional delay element may be added to
the circuit.
[0097] Also, since the algorithm above is compensating the
linearized flow signal, the result will be sensitive to any
discrepancy between the derivative of the linearization curve and
the derivative of the actual flow meter output-versus-flow curve.
Such nonlinearities would most often arise at low flow rates due to
uncorrected sensor offsets during final calibration, such as
residual valve heating effects, potentially leading to a low-flow
"hook" in the derivative of the linearization curve. Such
irregularities can degrade accuracy of the inventory gas
compensation algorithm, and should be avoided in most
embodiments.
[0098] Because temperature changes relatively slowly, calculation
of temperature dependent virial coefficients can be scheduled at
the convenience of the firmware. They are preferably updated at
least 10 times per second, but updating them more often than the
temperature is updated is not useful. Calculation of flow
compensation is preferably performed as part of normal flow meter
processing on every signal processing cycle, and should occur as
soon as the linearized flow rate becomes available.
[0099] All other firmware calculations defined above, such as the
compressibility, the value corresponding to the inventory value,
the value corresponding to the amount of gas in the inventory
volume, the value corresponding to the derivative of the amount of
gas in the inventory volume, and the compensation signal are
preferably preformed on every signal processing cycle. These
calculations can begin as soon as the normalized flow rate
calculation is available, and are preferably completed before the
drive signal to the valve actuator is produced.
[0100] Although the present invention and its advantages have been
described in detail, it should be understood that various changes,
substitutions and alterations can be made herein without departing
from the spirit and scope of the invention as defined by the
appended claims. For example, while the embodiment described above
compensates for input pressure transients, skilled persons can
recognize that embodiments could also compensate for changes in
output pressure in the case of devices wherein the flow meter is
not substantially isolated from the output pressure by action of
the control valve (e.g. in a reverse flow device having the control
valve upstream of the flow meter). Moreover, the scope of the
present application is not intended to be limited to the particular
embodiments of the process, machine, manufacture, composition of
matter, means, methods and steps described in the specification.
For example, both pressure and temperature are required for
calculations of the preferred embodiments. The pressure measurement
used can be obtained, for instance, directly from inlet pressure,
from a transducer exposed directly to the inventory volume, or
approximated. Similarly, the temperature measurement used can be
obtained, for instance, from the flow sensor body temperature or
average gas temperature in the inventory volume. The invention is
not limited to any particular means for generating an electrical
signal corresponding to the flow. While an embodiment using two
resistive coils is described, other embodiments can use three or
any number of resistive coils, or other temperature sensitive
elements, such as thermocouples or thin film resistors. Also, the
invention is not limited to mass flow meters, but could be applied
to other types of flow meters, such as volume flow meters.
[0101] While the inventory volume was described in the embodiment
above as comprising the volume between the flow sensor and the
adjustable valve, the inventory volume could comprise any volume
between the flow sensor and a flow restriction, such as an orifice.
As one of ordinary skill in the art will readily appreciate from
the disclosure of the present invention, processes, machines,
manufacture, compositions of matter, means, methods, or steps,
presently existing or later to be developed that perform
substantially the same function or achieve substantially the same
result as the corresponding embodiments described herein may be
utilized according to the present invention. Accordingly, the
appended claims are intended to include within their scope such
processes, machines, manufacture, compositions of matter, means,
methods, or steps.
* * * * *