## Scaling Data - Polynomials, Spans & FunctionsThe Scaling data is principally used for converting or linearizing the electrical signals measured on the input channels, into units of the physical quantity that is being measured. Other reasons for scaling data include adjusting for attenuation of inputs, specifying the resistance of current shunts, changing the magnitude of data, etc. The methods available for scaling data with the Automatic Scaling Channel Factors Spans Polynominals Intrinsic Functions Calculations ## Automatic ScalingThe input channels of the The fundamental signal types supported by the Sensors with standardised characteristics such as thermocouples, RTD's, IC temperature sensors, vibrating wire transducers, and thermistors are automatically linearized to physical units such as temperature by internal polynomials, prior to being returned to the host or logged. Automatic scaling of input channels is illustrated in the following program BEGIN In this example the 1V 1283.67 mV The ## Channel FactorThe simplest method of scaling raw data from an input channel or internal channel is by applying a Channel Factor directly to the channel data. The raw data is simply multiplied by the Channel Factor. The Channel Factor has a predefined function for most of the input signal types supported by the Voltage, Thermocouples, LM335 ñ the Channel Factor specifies an attenuation factor for these signal types if inputs have been externally attenuated. External attenuation mainly applies to voltage signals which exceed the input voltage range of the Current, Current Loop, AD590, AD592 – the Channel Factor specifies the resistance of the current shunt used for measuring the current signals. The default current shunt resistance is 100.0 OhmsΩ, however larger and smaller shunt resistances can be used to suit different current magnitudes to be measured. The shunt resistance is used by the Bridge ñ the Channel Factor specifies the arm resistance for current excited resistance bridges. The default Channel Factor is 350.0 Ohms. RTDs ñ the Channel Factor specifies the resistance of the RTD element at 0°C. However RTDs with a different resistance at 0°C can be supported by the System Timers, Counters ñ the Channel Factor specifies the maximum or terminal count. The range of the counters can be customised by specifying different maximum or terminal counts as a Channel Factor. The default Channel Factor varies for System Timers, and is 65535 Counts for counters. Frequency and Period ñthe Channel Factor sets the minimum measurable frequency, by defining the longest period. The default Channel Factor is 30 mSec, for 33Hz minimum frequency. Vibrating Wire ñthe Channel Factor sets the delay between plucking the wire and reading the wire frequency. The default Channel Factor is 200 mSec. Resistance, Channel Variables, System Variables ñ the Channel Factor is undefined, and so can be used to scale the data by a linear factor. Digital ñ the Channel Factor is for various functions, depending on the signal types. The Channel Factor is entered as a Channel Option (See Section III ñ Channel Options) for the input channel as follows RA5S 1V(10.1) 4PT385(250.0) 7F(1000) 3CV(2.2) 1V(10.1) ñ an externally attenuated voltage is applied to analog channel 1. The 4PT385(200.0) ñ a platinum RTD connected to analog channel 4 has a resistance of 250Ω Ohms at 0°C. The 7F(1000) ñ a low frequency signal connected to analog channel 7 is less than the default minimum measurable frequency of 33 Hz. The Channel Factor sets maximum period to 1000mSec, enabling a minimum measurable frequency of 1 Hz. The data stored in Channel Variable number 3 is simply scaled up by the factor of 2.2. ## Intrinsic FunctionsThe The Intrinsic Functions are applied as Channel Options for the input channel or Channel Variable (See Section III ñ Channel Options). The Intrinsic Functions are mutually exclusive , such that only one Intrinsic Function can be applied to each channel or Channel Variable. The Intrinsic Functions supported by the
* (See Section III ñThe Digital Input Channels When Intrinsic Functions are applied to input channels or Channel Variables, the data is returned with the units text appropriate to the channel, appended with the units text modifier for the Intrinsic Function. Using DeTransfer, Intrinsic Functions are applied to input channels and Channel Variables for example BEGIN which will return data in the format 1V 0.036 mV (Inv) The channel number and units text are returned with the data according to the settings of the (/n /N) and (/u /U) Switches, Parameter22 and Parameter24 (See Section III ñ Format of Returned Data). Using DeLogger, the Intrinsic Functions are applied to input channels and Channel Variables in the
in the Program Builder by first defining the channel or Channel Variable, then right click on the Data Use icon, select PropertiesÖ, select the Intrinsic tab in the Channel Properties dialog, and select the required function. Intrinsic Functions can also be selected by right clicking on the channel icon, and follow the walking menu through Channel Options:Data Conversion:Calculation:Intrinsics and select the required Function from the list of Functions.
## Introduction to Polynomials and SpansThe Polynomials and Spans extend the flexibility of the Polynomials are used to convert sensors with either curvilinear (non-linear) and linear calibrations, to engineering units. Spans are used to convert sensors with linear calibrations to engineering units. Spans are particularly suited to current loop transmitters, which by definition have linear scaling. The Polynomial and Span declarations are stored in a common area of ## PolynomialsA Polynomial describes the relationship between the output signal from a sensor (which is plotted on the X axis of a graph), and the physical parameter that the sensor is measuring (which is plotted on the Y axis of a graph). They are used to convert signals from sensors that have both curvilinear (non-linear) or linear calibrations. The The polynomials can be defined as a 1st, 2nd, 3rd, 4th or 5th order polynomial, and units text can be defined appropriate to the new data. Higher polynomial orders describe greater degrees of non-linearity in the relationship between the sensor signal and the physical parameter measured. The polynomials are described mathematically as follows ï first order (linear) Y = a + bX where Y is the calculated data in terms of the physical parameter measured ## Declaring PolynomialsThe Polynomial coefficients are entered into the Yn=a,b,c,d,e,f"units text" where Y is the polynomial identifier The Polynomial number must be in the range of 1 to 20, and must not be a number used for a Span (see below). The "units text" string is optional, and allows engineering units appropriate for the physical parameter being measured to be defined. The units text string is limited to a maximum of 7 characters, and may contain control characters which are entered in the two character format of eg. ^G (Bell) ^M (CR) ^J (LF) etc. The dynamic range for the calculated data from polynomials is ±1.00e-18 to ±1.00e18. An example of a curvilinear calibration between the output voltage and the applied load for a load cell is illustrated below
Figure 129 - A Load Cell Calibration The polynomial for the curvilinear relationship between the millivolt output and applied load for the load sensor is obtained by a regression for example Y=1.42+7.04X-0.099X The Polynomial is defined to the Using DeTransfer, the polynomial is entered into the Y1=1.42,7.04,-0.099,0.001,-2.88e-6,3.93e-9"Kgm" where the polynomial coefficients only are listed. The coefficients are separated by commas, and there must be no included spaces. Any zero coefficients must be included to enable the following coefficients to be given the correct ascendancy. The polynomial coefficients can be entered either in floating point format (1.42, 0.099), or exponential format (1.55e-3, 3.0e2) While polynomials up to the 5th order (6 coefficients) are permitted, lower order polynomials can be used and are entered as follows Y2=3.67,-1.22"KWatts" which in this case describes a second order polynomial, which is a linear relationship. Using DeLogger, Polynomials are entered in the Program Builder. Click on the Settings tab, right click on the Polynomial button and select PropertiesÖ to open the Polynomials dialog. Click on the tab for the Polynomial number you are defining, and Enter the coefficients and units text for the new Polynomial. Click Apply to store the values, and either click on the tab for the next Polynomial number to define, or click OK to finish.
DeLogger only allows 10 Polynomials and 10 Spans to be defined rather than any mix totalling 20 as the ## Using PolynomialsDefined Polynomials are specified as a Channel Option for input channels, Channel Variables, etc to linearise the original data. Using DeTransfer, this is illustrated in the following program Y1=1.42,7.04,-0.099,0.001,-2.88e-6,3.93e-9"Kgm" which will result in data of the format 5V 224.37 Kgm The channel number and units text are returned with the data according to the settings of the (/n /N) and (/u /U) Switches, Parameter22 and Parameter24 (See Section III ñ Format of Returned Data). Polynomials can be specified as a Channel Option to sequences of channels using DeTransfer, as follows R1H 1..5V(Y1) 6..10R(Y2) where Polynomial Y1 is specified as a Channel Option to channels 1 through 5, and the Polynomial Y2 is specified as a Channel Option to channels 6 through 10. Using DeLogger, defined Polynomials are specified as a Channel Option for input channels, Channel variables, etc in the Program Builder. Firstly, enter the input channel or Channel Variable into the work area. Right click on the channel icon, and follow the walking menu through Channel Options:Data Conversion:Scaling:Polynomial and select the required Polynomial from the list of defined Polynomials.
The channel will then change to show the Polynomial being applied between the channel icon and the data use icon. ## Using Polynomials for Other PurposesPolynomials can also be used to carry out various mathematical processing on data, and to attach custom units text to data. A number of standard mathematical functions which can be implemented using polynomials, for example squaring of data Y1=0,0,1 cubing of data Y1=0,0,0,1 scaling data by a constant multiplier Y1=0, adding a constant offset to data Y1= Dummy Polynomials can be used to add custom units text to data. This is particularly useful with Channel Variables which do not have units text. For example Y1=0,1"Widgets" where Y1 is defined as a dummy polynomial (does not change the magnitude of the data) but has a custom units text which is applied to any data that the Polynomial is applied to. ## Obtaining the Polynomial for a SensorThe polynomial calibration for sensors can usually be obtained from the manufacturer of the sensor. However in some cases it may be necessary to calculate the sensor polynomial from calibration tables or lookup tables supplied by the manufacturer. This can be done using one of the many statistical software packages available, which have functions for calculating polynomials or for fitting polynomials by least squares regression. The Microsoft Excel spreadsheet package has these functions. ## SpansA Span describes the linear relationship between the output signal from a sensor (plotted on the X axis of a graph), and the physical parameter that the sensor is measuring (plotted on the Y axis of a graph). Spans are used to convert signals from sensors which have linear calibrations, into units in terms of the physical parameter being measured. Spans are particularly suited to converting data from current loop transmitters which by definition have linear scaling. The Spans are described mathematically as follows
where S is the calculated data in terms of the physical parameter ## Declaring SpansSpans are entered into the Sn=a,b,c,d"units text" where S is the span identifier The span number must be in the range of 1 to 20, and must not be a number used for a Polynomial (see above). The "units text" string is optional, and allows the engineering units for the physical parameter being measured to be defined. The units text string is limited to a maximum of 7 characters, and may contain control characters which are entered in the two character format of eg. ^G (Bell) ^M (CR) ^J (LF) etc. The dynamic range for the calculated data from spans is ±1.00e-18 to ±1.00e18. An example of a linear calibration between the output voltage and temperature for an infrared detector is illustrated below
Figure 130 ñ Infrared Detector Calibration
The infrared detector has an output of 200mV for a temperature of 320°C, and 500mV for a temperature of 1170°C. Using DeTransfer, the Span for the linear relationship between the temperature and millivolt output signal from the infrared detector is entered into the S1=320.0,1170.0,200.0,500.0"Deg C" The Span co-ordinates are separated by commas, and there must be no included spaces. Embedded zero co-ordinates must be included to enable following co-ordinates to be given correct ascendancy. The span co-ordinates may be entered either in floating point format (12.63, 0.001), or in exponential format (1.55e-3, 3.0e2) Using DeLogger, Spans are entered in the Program Builder. Click on the Settings tab, right click on the Span button and select PropertiesÖ to open the Span dialog. Click on the tab for the Span number you are defining, and Enter the co-ordinates and units text for the new Span. Click Apply to store the values, and either click on the tab for the next Span number to define, or click OK to finish.
DeLogger only allows 10 Polynomials and 10 Spans to be defined rather than any mix totalling 20 as the ## Using Declared SpansDefined Spans are specified as a Channel Option for input channels, internal channels, Channel Variables, etc to linearise the original data. Using DeTransfer, this is illustrated in the following program S1=0.0,1500.0,100.0,600.0"Deg C" which will result in data of the format 1V 845.36 Deg C The channel number and units text are returned with the data according to the settings of the (/n /N) and (/u /U) Switches, Parameter22 and Parameter24 (See Section III ñ Format of Returned Data). Spans may also be specified as a Channel Option to sequences of channels using DeTransfer as follows R1H 1..5V(S1) 6..8R(S2) the Span S1 is specified as a Channel Option to input channels 1 - 5, and Span S2 is specified as a Channel Option to input channels 6 - 8. Using DeLogger, defined Spans are specified as Channel Option for input channels, Channel variables, etc in the Program Builder. Firstly, enter the input channel or Channel Variable into the work area of the appropriate Schedule. Right click on the channel icon, and follow the walking menu through Channel Options:Data Conversion:Scaling:Span and select the required Span from the list of defined Spans.
The channel will then change to show the Span being applied between the channel icon and the data use icon. ## Spans for Current LoopsWhile the The When declaring Spans for current loop inputs, only the two physical span co-ordinates need to be declared. The Using DeTransfer, declaring and using Spans for current loop inputs is illustrated below S5=0.0,250.0"KPa" In this example the sensor pressure range of 0 to 250KPa corresponds to 4 - 20 mA or 0 to 100% of output by the current loop device.
Spans for current loop devices can also be specified as a Channel Option to sequences of channels using DeTransfer as follows R1H 3..5L(S1) where Span S1 is specified as a Channel Option to channels 3 to 5. ## Checking the Declaration of Polynomials and SpansThe Polynomials and Spans that have been declared to Using DeTransfer, the Polynomials and Spans is checked using the STATUS command as follows STATUS which produces a general report which includes details similar to
166350,0 Internal Data Points Free,Stored 79265,1670 Card Data Points Free,Stored 4090,0 Program Characters Free,Stored /a/C/d/E/f/h/J/K/l/M/N/o/Q/R/S/t/U/v/w/x/y/Z and the command STATUS4 produces a detailed report of defined Polynomials and Spans similar to 2 Polynomials/Span Limits Defined Using DeLogger, the number of defined Polynomials and Spans can be checked by the dataTaker : Status option from the main menu bar, or the Status button on the main toolbar. However the actual definition of the Polynomials and Spans are not shown here. These can be found in the Program Builder where the Polynomials and Spans were originally defined. ## Obtaining the Span for a SensorThe span calibration for sensors and current loop transmitters can usually be obtained from the sensor manufacturer. This information is usually provided either as direct statement of the physical parameter and signal range end points, or a tabulation of the sensor calibration. If a sensor is being used to measure a physical parameter over a smaller range than the full range of the sensor, then a span can be declared for this sub-range to provide greater resolution. |
## Page Content## Section 1Construction of the dataTaker 50 Construction of the dataTaker 500 600
## Section 2Powering Sensors from the dataTaker The RS232 COMMS Serial Interface Measuring 4-20mA Current Loops Measuring Frequency and Period Measuring Temperature with Thermocouples Measuring Temperature with RTDs Measuring Temperature with IC Temperature Sensors Measuring Temperature with Thermistors Measuring Bridges and Strain Gauges Measuring Vibrating Wire Strain Gauges Installing The Panel Mount Display
## Section 3Communication Protocols and Commands Entering Commands and Programs |