FP_SCALE

Perform linear interpolation of discrete values

This FP instruction renders the value y at position x by performing a linear interpolation based on the neighboring reference points Pw_{(xw, yw)} and Pw+1_{(xw+1, yw+1)}. In this example, w is the nearest reference point whose x value is smaller than the input value s1_x, i.e. the function connects the individual reference points in series and renders the output value d_y based on the input value s1_x.

Parameters

Input

s1_x

Input value

On 16-bit PLC types: (INT, DINT, REAL)
On 32-bit PLC types: (INT, DINT, UINT, UDINT, REAL, LREAL)

s2_xyData (user defined DUT; INT, UINT, WORD (ANY16))

Apply the first element of the user-defined DUT, i.e. the number of xy values, to this input. See description of DUT structure below.

Output

d_y

Result

On 16-bit PLC types: (INT, DINT, REAL)
On 32-bit PLC types: (INT, DINT, UINT, UDINT, REAL, LREAL)

Remarks

Application examples:

Linearizing measured values, e.g. with non-linear sensors
Rendering a heater’s flow temperature y in relation to the outside temperature x

Error flags

sys_bIsOperationErrorHold (turns to TRUE and remains TRUE)

if the area specified using the index modifier exceeds the limit.
if the number of reference points is outside the range of 2–256.
if s2_xyData is out of range.
if the x values of the reference points are not in ascending order.

sys_bIsOperationErrorNonHold (turns to TRUE for one scan)

if the area specified using the index modifier exceeds the limit.
if the number of reference points is outside the range of 2–256.
if s2_xyData is out of range.
if the x values of the reference points are not in ascending order.

Limitations of the output value y:

If the input value x is smaller than the x-coordinate of the first reference point (P1: x< x1), the output y is set to the first reference point’s y-coordinate (output y = y1, horizontal dashed line in the graph’s upper left corner).
If the input value x is greater than the x-coordinate of the last reference point (P8: x > x8), the output y is set to the last reference point’s y-coordinate (output y = y8, horizontal dashed line in the graphic’s upper right corner).

DUT for the xy value pairs (reference points P1, P2, ...):

The reference points (P1, P2, ...) are copied to the function via an DUT-type variable that contains the number of reference points and the xy value pairs (number; x1, x2, ...; y1, y2; ...).

Structure of the user-defined DUT:

Element: number of reference points z (INT). The number of reference points (xy value pairs) can be set anywhere between 2–100. In the graph, eight reference points (P1–P8) are used.
Element: Variable of the data type ARRAY[1..z] OF INT (on 16-bit PLC types: INT, DINT, REAL; on 32-bit PLC types: (INT, DINT, UINT, UDINT, REAL)) or ARRAY[0..z-1] of INT (on 16-bit PLC types: INT, DINT, REAL; on 32-bit PLC types: (INT, DINT, UINT, UDINT, REAL)) that contains the x values. Here z represents the place marker for the number of reference points (see entry 1).
Element: Variable of the data type ARRAY[1..z] OF INT (on 16-bit PLC types: INT, DINT, REAL; on 32-bit PLC types: (INT, DINT, UINT, UDINT, REAL)) or ARRAY[0..z-1] of INT (on 16-bit PLC types: INT, DINT, REAL; on 32-bit PLC types: (INT, DINT, UINT, UDINT, REAL)) that contains the y values. Here z represents the place marker for the number of reference points (see entry 1).

NOTE

FP_SCALE supports the following data types:

On 16-bit PLC types (FP-Sigma, FP-X): INT, DINT, REAL
On 32-bit PLC types (FP7): INT, DINT, REAL, UINT, UDINT

Example

DUT

With a Data Unit Type (DUT) you can define a data unit type that is composed of other data types. A DUT is first defined in the DUT pool and then processed like the standard data types (BOOL, INT, etc.) in the list of global variables or the POU header.

POU header

All input and output variables used for programming this function have been declared in the POU header. The same POU header is used for all programming languages.

VAR
		bStart: BOOL:=FALSE;
		iInput: INT:=50;
		xy_data: xy_data_dut;
		iScaledOutput: INT:=0;
		@'': @'';
	END_VAR

POU body

When the variable bStart is set to TRUE, the function is carried out.

LD body

BODY
    WORKSPACE
        NETWORK_LIST_TYPE := NWTYPELD ;
        ACTIVE_NETWORK := 0 ;
    END_WORKSPACE
    NET_WORK
        NETWORK_TYPE := NWTYPELD ;
        NETWORK_LABEL :=  ;
        NETWORK_TITLE :=  ;
        NETWORK_HEIGHT := 6 ;
        NETWORK_BODY
B(B_CONTACT,,bStart,4,2,6,4,);
B(B_F,FP_SCALE!,,17,1,25,6,,?DEN?Ds1_x?Ds2_xyData?AENO?Cd_y);
B(B_VARIN,,iInput,15,3,17,5,);
B(B_VAROUT,,iScaledOutput,25,3,27,5,);
B(B_VARIN,,xy_data.iNumberOfValues,15,4,17,6,);
L(1,0,1,6);
L(1,3,4,3);
L(6,3,17,3);
        END_NETWORK_BODY
    END_NET_WORK
END_BODY

ST body

IF (bStart) then
    FP_SCALE(s1_x := iInput, 
             s2_xyData := xy_data.iNumberOfValues, 
             d_y => iScaledOutput);
END_IF;