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\textbf{Preloading Integral}\\
A rising edge at the \emph{Enable} inport enables the controller and preloads the integral.\\
One may choose from two options how to preload the integral value:
\begin{itemize}
	\item Preload the integral from the \emph{Init} inport.
	\item Preload the integral such that the first output of the controller matches the current value at the \emph{Init} inport.
	\newline This option allows controller switching without disturbing the control.
\end{itemize}

\paragraph{Note:}Each fixed point implementation uses the next higher integer data type for the integral value storage variable.


\noindent
\textbf{Transfer function} (zero-order hold discretization method):\\
When the block is enabled, the PID controller realizes the following transfer function:
\begin{eqnarray*}
	G(z) = K_{\mathrm{p}} + K_{\mathrm{i}}T_{\mathrm{s}}\frac{1}{z-1} + K_{\mathrm{d}}2 \pi f_{\mathrm{c}}\frac{z-1}{z-e^{-2 \pi f_{\mathrm{c}} T_{\mathrm{s}}}}
\end{eqnarray*}

\paragraph{FiP8 bug:} When using the TI compiler the step response of the derivative part does not return to zero, but generates an overflow at zero crossing if the derivative parameter value is too high.
\paragraph{Developer note:} For the fixed point implementations the source code of block \textit{PIDLimit} is used.