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File mttroot/mtt/lib/comp/compound/Control/Collocated/Pe/Pe_desc.tex artifact dc170f25ad part of check-in e76e07bbf8

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system Pe (Pe_desc.tex)
% Generated by MTT on Wed May 15 10:28:28 BST 2002.

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% %% Version control history
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% %% $Id$
% %% $Log$
% %% Revision 1.1  2002/05/15 11:01:24  gawthrop
% %% New PI controller component
% %%
% %% Revision 1.1  2000/12/28 09:13:38  peterg
% %% Initial revision
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   The acausal bond graph of system \textbf{Pe} is
   displayed in Figure \Ref{fig:Pe_abg.ps} and its label
   file is listed in Section \Ref{sec:Pe_lbl}.

\textbf{Pe} implements a collocated P 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) = k_p e(s) 
\end{equation}
where the \emph{error} $e(s) = w(s) - y(s)$.