Derivative (FB)

FUNCTION_BLOCK Derivative

This function block will approximate the first derivative \(f\prime\) of a function \(f = f(t)\) at the actual time \(t_{n}\) with the respect to the values of the last three function calls according to the BDF method:

\[f\prime (t_{n}) \doteq \frac{3 (f(t_{n}) - f(t_{n-3})) + f(t_{n-1}) - f(t_{n-2})}{3(t_{n-2}-t_{n-3})+4(t_{n-1}-t_{n-2})+3(t_{n}-t_{n-1})}\]

InOut:

Scope	Name	Type	Comment
Input	xEnable	BOOL	reset
	lrInputValue	LREAL	actual function value
	udiTM	UDINT	length of time interval \([t_{n-1}, t_{n}]\) (equals time passed since last call to function)
Output	lrDerivative	LREAL	approxmated value of first derivative
	xValid	BOOL	Validity of result FALSE: If the number of calls neccessary for approximating has not been executed yet.