Element ¶ Element (Folder) IsLinkedElem (Property) IsListMemberOf (Method) NextElem (Property) PrevElem (Property) TypedElement (FunctionBlock)

Element (FB) ¶ FUNCTION_BLOCK Element IMPLEMENTS IElement , IElementHelper Properties: IsLinkedElem NextElem PrevElem Methods: IsListMemberOf Structure: IsLinkedElem (Property) IsListMemberOf (Method) NextElem (Property) PrevElem (Property)

TypedElement (FB) ¶ FUNCTION_BLOCK TypedElement EXTENDS Element IMPLEMENTS ITypedElement Properties: IsLinkedElem , inherited from Element NextElem , inherited from Element PrevElem , inherited from Element Methods: IsListMemberOf , inherited from Element

List ¶ List (Folder) AppendElem (Method) InsertElem (Method) PopBackElem (Method) PopElem (Method) PushElem (Method) RemoveElem (Method) ListBase (FunctionBlock) HeadElem (Property) ListIsEmpty (Property) ListSize (Property) TailElem (Property) TypedList (FunctionBlock) AppendElem (Method) InsertElem (Method) PopBackElem (Method) PopElem (Method) PushElem (Method) RemoveElem (Method)

List (FB) ¶ FUNCTION_BLOCK List EXTENDS ListBase IMPLEMENTS IList Properties: HeadElem , inherited from ListBase ListIsEmpty , inherited from ListBase ListSize , inherited from ListBase TailElem , inherited from ListBase Methods: AppendElem InsertElem PopBackElem PopElem PushElem RemoveElem Structure: AppendElem (Method) InsertElem (Method) PopBackElem (Method) PopElem (Method) PushElem (Method) RemoveElem (Method)

CAA Mathematics ¶ This library provides some helpful mathematical program units. The standardized in- and outputs of function blocks are described in detail with the CAA guidelines, so that we will omit this aspect here. Functions Transformations LinearTrafo (FunctionBlock) fmod (Function) analog monitors Hysteresis_DINT (FunctionBlock) Hysteresis_LREAL (FunctionBlock) LimitAlarm_DINT (FunctionBlock) LimitAlarm_LREAL (FunctionBlock) sgn (Function) analytical functions CalcRootLin (FunctionBlock) CalcRootParable (FunctionBlock) Derivative (FunctionBlock) Integral (FunctionBlock) PolynomialValue (Function) function manipulators CharCurve_DINT (FunctionBlock) CharCurve_LREAL (FunctionBlock) geometrical functions Line Functions ProjectPointOnLine (Function) Plane Functions CalcHesseRepresentation (FunctionBlock) ProjectPointOnPlane (Function) Polar coordinates CartesianToPolar (FunctionBlock) PolarToCartesian (FunctionBlock) Vector Functions AddMultiplicatedVector (Function) CrossProduct (FunctionBlock) CrossProductNormed (FunctionBlock) MakeNormed3D (Function) Norm3D (Function) ScalProd3D (Function) ScalProd3DStand (Function) SubVector (Function) signals MeasureFrequence (FunctionBlock) statistical functions Statistics_DINT (FunctionBlock) Statistics_LREAL (FunctionBlock) Variance (FunctionBlock) trigonometrical functions atan2 (Function) Global Variables GlobalConstants (GVL) Structs LINE_3D (Struct) PLANE_H (Struct) POINT2_DINT (Struct) POINT2_LREAL (Struct) VECTOR3D (Struct)

Functions ¶ Transformations LinearTrafo (FunctionBlock) fmod (Function) analog monitors Hysteresis_DINT (FunctionBlock) Hysteresis_LREAL (FunctionBlock) LimitAlarm_DINT (FunctionBlock) LimitAlarm_LREAL (FunctionBlock) sgn (Function) analytical functions CalcRootLin (FunctionBlock) CalcRootParable (FunctionBlock) Derivative (FunctionBlock) Integral (FunctionBlock) PolynomialValue (Function) function manipulators CharCurve_DINT (FunctionBlock) CharCurve_LREAL (FunctionBlock) geometrical functions Line Functions ProjectPointOnLine (Function) Plane Functions CalcHesseRepresentation (FunctionBlock) ProjectPointOnPlane (Function) Polar coordinates CartesianToPolar (FunctionBlock) PolarToCartesian (FunctionBlock) Vector Functions AddMultiplicatedVector (Function) CrossProduct (FunctionBlock) CrossProductNormed (FunctionBlock) MakeNormed3D (Function) Norm3D (Function) ScalProd3D (Function) ScalProd3DStand (Function) SubVector (Function) signals MeasureFrequence (FunctionBlock) statistical functions Statistics_DINT (FunctionBlock) Statistics_LREAL (FunctionBlock) Variance (FunctionBlock) trigonometrical functions atan2 (Function)

Transformations ¶ LinearTrafo (FunctionBlock) fmod (Function)

LinearTrafo (FB) ¶ FUNCTION_BLOCK LinearTrafo This function will calculate the linear transformation \(y \in \mathbb{R}\) of \(x \in \mathbb{R}\) according to \[ \begin{align}\begin{aligned}\frac{y - y_{1}}{y_{2}-y_{1}} = \frac{x-x_{1}}{x_{2}-x_{1}}\\\mathrm{with}\ x_{1}, x_{2}, y_{1}, y_{2} \in \mathbb{R}\ \mathrm{and}\ x_{1} \neq x_{2} \land x_{1} \leq x \leq x_{2}\end{aligned}\end{align} \] InOut: Scope Name Type Comment Input lrInputValue LREAL Value \(x\) to be transformated lrInput1 LREAL Coefficient \(x_{1} \in \mathbb{R}\) lrInput2 LREAL Coefficient \(x_{2} \in \mathbb{R}\) lrOutput1 LREAL Coefficient \(y_{1} \in \mathbb{R}\) lrOutput2 LREAL Coefficient \(y_{2} \in \mathbb{R}\) Output lrOutputValue LREAL Linear transformation \(y \in \mathbb{R}\) of \(x \in \mathbb{R}\) xOutOfLimits BOOL Error flag TRUE : If \(x_{1} = x_{2} \lor x < x_{1} \lor x > x_2\)

fmod (FUN) ¶ FUNCTION fmod : LREAL This function will return the modulo of the integral division \(\frac{x}{m}\) : \[x\ \mathrm{mod}\ m = x - \left \lfloor \frac{x}{m} \right \rfloor \cdot m\] Note The invalid input \(m=0\) will result in the return 0. InOut: Scope Name Type Comment Return fmod LREAL Input lrX LREAL Dividend \(x\) lrM LREAL Divisor \(m\)