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% Verbal description for system PIe (PIe_desc.tex)
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% %% Revision 1.1  2000/12/28 09:13:38  peterg
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   The acausal bond graph of system \textbf{PIe} is
   displayed in Figure \Ref{fig:PIe_abg.ps} and its label
   file is listed in Section \Ref{sec:PIe_lbl}.

\textbf{PIe} implements a collocated PI controller where:
\begin{description}
\item[w] is the (flow) setpoint at port [w]
\item[y] is the (flow) system output at port [yu]
\item[u] is the (effort) system input (control signal) at port [yu]
\end{description}

The controller transfer-function is:
\begin{equation}
  u(s) = \left [ k_p + \frac{k_i}{s} \right ] e(s) 
\end{equation}
where the \emph{error} $e(s) = w(s) - y(s)$.