#FIG 3.2
Portrait
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 1575 3375 2925 3375 2700 3600
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 3375 3375 4725 3375 4500 3600
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 4950 3150 4950 1800 5175 2025
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 5175 3375 6525 3375 6300 3600
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 3
	 3150 3150 3150 1800 3375 2025
2 1 0 2 0 7 100 0 -1 0.000 0 0 -1 0 0 2
	 6525 3150 6525 3600
2 4 0 2 31 7 51 0 -1 0.000 0 0 7 0 0 5
	 7875 4275 7875 900 450 900 450 4275 7875 4275
4 1 0 100 0 18 18 0.0000 4 195 150 3150 3465 0\001
4 1 0 100 0 18 18 0.0000 4 195 150 4950 3465 1\001
4 2 4 100 0 18 18 0.0000 4 270 870 1530 3465 SS:[in]\001
4 0 4 100 0 18 18 0.0000 4 270 1065 6660 3465 SS:[out]\001
4 1 0 100 0 18 18 0.0000 4 270 780 3150 1665 C:k_p\001
4 1 0 100 0 18 18 0.0000 4 270 765 4950 1665 R:k_d\001

% -*-latex-*- Put EMACS into LaTeX-mode
% Verbal description for system PDe (PDe_desc.tex)
% Generated by MTT on Tue May 1 09:26:33 BST 2001.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  2000/12/28 09:13:38  peterg
% %% Initial revision
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   The acausal bond graph of system \textbf{PDe} is
   displayed in Figure \Ref{fig:PDe_abg.ps} and its label
   file is listed in Section \Ref{sec:PDe_lbl}.
   The subsystems are listed in Section \Ref{sec:PDe_sub}.

   This is a proportional + derivative (PD) controller for a
   collocated sutuation where the control signal is an effort and the
   measured signal is a (collocated) flow.

   The controller can be thought of as controlling \emph{integated
   flow}, and it is with respect to this that the P and D terms are defined.

 The setpoint is a \emph{flow}; and must be generated to give the
 desired \emph{integrated} flow.

 Physically, the controller is a \textbf{C} and an \textbf{R}
 component - for mechanical systems a mass and a spring.
 
 Mathematically, in integral causality, the equations are:
%file: pde_{dae}.tex
%differential-algebraic equations
 \begin{equation}
   \begin{aligned}
     \dot x_{1} &=
     {
       f_d - f
       }
   \end{aligned}
 \end{equation}
 \begin{equation}
   \begin{aligned}
     u &=
     {
       - k_{d} f + k_{p} x_{1}
       }
   \end{aligned}
 \end{equation}

 The state $x_1$ is the the integrated difference between 
 \emph{desired} flow $f_d$ and the actual flow  $f$. Thus the control
 signal $u$ is $k_p$ multiplied by the position error minus $k_d$ time
 the flow.

%% Label file for system PDe (PDe_lbl.txt)
%SUMMARY PDe: Proportional + Derivative controller with effort output
%DESCRIPTION 

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% Version control history
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %% $Id$
% %% $Log$
% %% Revision 1.1  2000/12/28 09:13:38  peterg
% %% Initial revision
% %%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Port aliases
%ALIAS	in	in
%ALIAS	out	out

% Argument aliases
%ALIAS	$1	k_p
%ALIAS	$2	k_d

%% Each line should be of one of the following forms:
%	     a comment (ie starting with %)
%	     component-name	cr_name	arg1,arg2,..argn
%	     blank

% ---- Component labels ----

% Component type C
	k_p	lin		state,k_p

% Component type R
	k_d	lin		flow,k_d

% Component type SS
	[in]	SS		internal,external
	[out]	SS		external,external