Data processing: measuring – calibrating – or testing – Measurement system – Performance or efficiency evaluation
Reexamination Certificate
1999-09-24
2003-11-04
Wachsman, Hal (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Performance or efficiency evaluation
C702S045000, C702S138000, C702S140000
Reexamination Certificate
active
06643610
ABSTRACT:
BACKGROUND OF THE INVENTION
The invention relates to the field of process measurement and control industry.
The process measurement and control industry employs process variable transmitters to remotely monitor process variables associated with fluids such as flurries, liquids, vapors, gases, chemicals, pulp, petroleum, pharmaceuticals, food and other processing plants. Examples of process variables include pressure, temperature, flow, level, turbidity, concentration, chemical composition, pH and other properties.
Complex mathematical computations are required to determine some process variables. For example, in order to determine flow by measuring differential pressure across an orifice plate, the computation requires the determination of physical properties of the fluid such as fluid density and the gas expansion factor. Calculation of these parameters involves extensive computation which reduces the update time of the transmitter, requires more complex processing equipment and requires increased power.
One technique to reduce the complexity of the calculations is to simply use fixed approximations for some of the parameters. For example, fixed values can be stored in memory rather than calculated using precise formulas. A more accurate technique is the use of straight polynomial curve fitting. In this technique, a process variable is estimated by using a less than complex polynomial rather than perform the precise computation. Such a technique is described in WIPO Publication No. WO 97/04288, filed Jun. 20, 1997 and entitled “TRANSMITTER FOR PROVIDING A SIGNAL INDICATIVE OF FLOW THROUGH A DIFFERENTIAL PRODUCER USING A SIMPLIFIED PROCESS” and U.S. Pat. No. 5,606,513, issued Feb. 25, 1997 and entitled “TRANSMITTER HAVING INPUT FOR RECEIVING A PROCESS VARIABLE FROM A REMOTE SENSOR”. For example, the square root of the reciprocal of the compressibility (Z) of a fluid can be approximated using a “straight” polynomial in the form of:
1
/
Z
=
∑
n
=
0
n
=
j
∑
m
=
0
m
=
k
A
m
,
n
P
m
T
-
n
(
1
)
where P is the absolute pressure of the fluid, T is the absolute temperature and the coefficients A
m,n
are the coefficients of the interpolating polynomial.
FIGS. 3A and 3B
illustrate errors in prior art polynomial curve fitting techniques.
FIG. 3A
shows the curve fit error for ethylene as a function of pressure for 10 different temperature values. The highest powers of pressure P and inverse temperature (1/T) in the interpolating polynomial are eight and six, respectively. The temperatures and pressures for ethylene are not far from saturation pressures and temperatures. The minimum number (63) of pressure and temperature points was used to determine the 63 coefficients A
m,n
of the interpolation polynomial set forth in Equation 1, with j=6 and k=8.
FIG. 3A
illustrates the large error associated with straight polynomial curve fitting, particularly at the pressure extremes.
FIG. 3B
illustrates an even greater error when 32 bit floating point numbers (with 24 bit mantissa) are used. As illustrated in
FIG. 3B
, the results are essentially meaningless, with errors exceeding 10
5
percent. In the example of
FIG. 3B
, the coefficients were determined with 64 bit numbers and the calculation of the fitting polynomial was performed with 32 bit floating point numbers. Note that 32 bits is the typical number of bits used in floating point math performed in microprocessors. The use of a least squares fitting technique reduces the roughness produced by the loss of significant digits. However, the errors produced with such curve fitting are still relatively large in some situations.
This approximation technique is inaccurate, particularly when the highest power in the polynomial exceeds three or four and the polynomial is formed with multiple independent variables. This inaccuracy can cause inaccuracies in the measured process variable. Typically, the only solution has been to use the exact equations which require powerful computers and high power.
SUMMARY OF THE INVENTION
An interpolating polynomial is used to determine a process variable in a transmitter. The interpolating polynomial is “orthogonal” and provides an accurate estimation of the process variable without a significant increase in power consumption. The transmitter includes a sensor configured to couple to a process and having a sensor output related to the process variable. The transmitter also includes a microprocessor coupled to the sensor output and having a process variable output. The process variable output is an orthogonal-polynomial function of the sensor output. A transmitter output is configured to provide an output related to the interpolated process variable.
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Wachsman Hal
Westman Champlin & Kelly P.A.
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