FB_CTRL_TRANSFERFUNCTION_2

FB_CTRL_TRANSFERFUNCTION_2 1:

This function block calculates a discrete transfer function with the second standard form shown below. The transfer function here can be of any order, n.

The coefficients for the following transfer functions are stored in the parameter arrays:

Description of the transfer behavior

The internal calculation is performed in each sampling step according to the second standard form, for which the following block diagram applies:

FB_CTRL_TRANSFERFUNCTION_2 3:

The transfer function can be brought into the form shown in the block diagram by means of some transformations:
FB_CTRL_TRANSFERFUNCTION_2 4:

The coefficients of the counter polynomial are calculated according to the following rule:
FB_CTRL_TRANSFERFUNCTION_2 5: FB_CTRL_TRANSFERFUNCTION_2 6:
FB_CTRL_TRANSFERFUNCTION_2 7:

The programmer must create the following arrays in the PLC if this function block is to be used:

aNumArray    : ARRAY[0..nTfOrder] OF FLOAT;
aDenArray    : ARRAY[0..nTfOrder] OF FLOAT;
aStTfData    : ARRAY[0..nTfOrder] OF ST_CTRL_TRANSFERFUNCTION_2_DATA;

The coefficients "b₀" to "b_n" are stored in the array aNumArray. This must be organized as follows:

aNumArray[0]:= b0;
aNumArray[1]:= b1;
...
aNumArray[n-1] := bn-1;
aNumArray[n] := bn;

The coefficients "a₀" to "a_n" are stored in the array aDenArray. This must be organized as follows:

aDenArray[0]:= a0;
aDenArray[1]:= a1;
...
aDenArray[n-1] := an-1;
aDenArray[n] := an;

The internal data required by the function block is stored in the array aStTfData. This data must never be modified from within the PLC program. This procedure is also illustrated in the sample program listed below.

VAR_INPUT

VAR_INPUT
    fIn          : FLOAT;
    fManValue    : FLOAT;
    eMode        : E_CTRL_MODE;
END_VAR

Name	Type	Description
fIn	FLOAT	Input to the transfer function
fManValue	FLOAT	Input whose value is present at the output in manual mode.
eMode	E_CTRL_MODE	Input that specifies the operation mode of the function block.

VAR_OUTPUT

VAR_OUTPUT
    fOut        : FLOAT;
    eState      : E_CTRL_STATE;
    bError      : BOOL;
    eErrorId    : E_CTRL_ERRORCODES;
END_VAR

Name	Type	Description
fOut	FLOAT	Output from the transfer function
eState	E_CTRL_STATE	State of the function block
bError	BOOL	Supplies the error number when the output `bError` is set.
eErrorId	E_CTRL_ERRORCODES	Becomes TRUE, as soon as an error occurs.

VAR_IN_OUT

VAR_IN_OUT
    stParams    : ST_CTRL_TRANSFERFUNCTION_2_PARAMS;
END_VAR

Name	Type	Description
stParams	ST_CTRL_TRANSFERFUNCTION_2_PARAMS	Parameter structure of the function block

stParams consists of the following elements:

TYPE
ST_CTRL_TRANSFERFUNCTION_2_PARAMS:
STRUCT
    tTaskCycleTime                : TIME; 
    tCtrlCycleTime                : TIME := T#0ms; 
    nOrderOfTheTransferfunction   : USINT;
    pNumeratorArray_ADR           : POINTER TO FLOAT := 0;
    nNumeratorArray_SIZEOF        : UINT;
    pDenominatorArray_ADR         : POINTER TO FLOAT := 0;
    nDenomiantorArray_SIZEOF      : UINT;
    pTransferfunction2Data_ADR    : POINTER TO
ST_CTRL_TRANSFERFUNCTION_2_DATA;
    nTransferfunction2Data_SIZEOF : UINT;
END_STRUCT
END_TYPE

Name	Type	Description
tTaskCycleTime	TIME	Cycle time with which the function block is called. If the function block is called in every cycle this corresponds to the task cycle time of the calling task.
tCtrlCycleTime	TIME	Cycle time with which the control loop is processed. This must be greater than or equal to the TaskCycleTime. The function block uses this input value to calculate internally whether the state and the output values have to be updated in the current cycle.
nOrderOfTheTransferfunction	USINT	Order of the transfer function [0...]
pNumeratorArray_ADR	POINTER TO FLOAT	Address of the array containing the numerator coefficients
nNumeratorArray_SIZEOF	UINT	Size of the array containing the numerator coefficients, in bytes
pDenominatorArray_ADR	POINTER TO FLOAT	Address of the array containing the denominator coefficients
nDenomiantorArray_SIZEOF	UINT	Size of the array containing the denominator coefficients, in bytes
pTransferfunction2Data_ADR	POINTER TO ST_CTRL_ TRANSFERFUNCTION_2_DATA	Address of the data array
nTransferfunction2Data_SIZEOF	UINT	Size of the data array in bytes

Sample:

PROGRAM PRG_TRANSFERFUNCTION_2_TEST
VAR CONSTANT
    nTfOrder : USINT := 2;
END_VAR
VAR
    aNumArray           : ARRAY[0..nTfOrder] OF FLOAT;
    aDenArray           : ARRAY[0..nTfOrder] OF FLOAT;
    aStTfData           : ARRAY[0..nTfOrder] OF ST_CTRL_TRANSFERFUNCTION_2_DATA;
    eMode               : E_CTRL_MODE;
    stParams            : ST_CTRL_TRANSFERFUNCTION_2_PARAMS;
    eErrorId            : E_CTRL_ERRORCODES;
    bError              : BOOL;
    fbTansferfunction   : FB_CTRL_TRANSFERFUNCTION_2;
    bInit               : BOOL := TRUE;
    fIn                 : FLOAT := 0;
    fOut                : FLOAT;
    b_0, b_1, b_2       : FLOAT;
    a_0,a_1,a_2         : FLOAT;
END_VAR
IF bInit THEN
    aNumArray[0] := 1.24906304658218E-007;
    aNumArray[1] := 2.49812609316437E-007;
    aNumArray[2] := 1.24906304658218E-007;
    aDenArray[0] := 0.998501124344101;
    aDenArray[1] := -1.99850062471888;
    aDenArray[2] := 1.0;
    stParams.tTaskCycleTime    := T#2ms;
    stParams.tCtrlCycleTime    := T#2ms;
    stParams.nOrderOfTheTransferfunction := nTfOrder;
    eMode := eCTRL_MODE_ACTIVE;
    bInit := FALSE;
END_IF
stParams.pNumeratorArray_ADR := ADR(aNumArray);
stParams.nNumeratorArray_SIZEOF := SIZEOF(aNumArray);
stParams.pDenominatorArray_ADR := ADR(aDenArray );
stParams.nDenominatorArray_SIZEOF := SIZEOF(aDenArray );
stParams.pTransferfunction2Data_ADR := ADR(aStTfData );
stParams.nTransferfunction2Data_SIZEOF := SIZEOF(aStTfData);
fbTansferfunction (fIn := fIn,
                   eMode := eMode,
                   stParams := stParams,
                   fOut => fOut,
                   eErrorId => eErrorId,
                   bError => bError);