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author Daniele Nicolodi <nicolodi@science.unitn.it>
date Mon, 05 Dec 2011 16:20:06 +0100
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<P>Built-in models enable to build fast predefined models to use
later in simulations. 
</P>
<H2>Modifying using the setter functions</H2>
<P><FONT COLOR="#000000">It is possible to set the content of the
fields &ldquo;input&rdquo;, &ldquo;output&rdquo;, &ldquo;states&rdquo;,
as well as the field &ldquo;params&rdquo;.</FONT></P>
<P><FONT COLOR="#000000">Here is a simple model</FONT></P>
<DIV CLASS="fragment"><PRE><FONT COLOR="#000000">&gt;&gt; name = </FONT><FONT COLOR="#a020f0">'sys'</FONT><FONT COLOR="#000000">;</FONT>
&gt;&gt; timestep = 0;
&gt;&gt; amats = cell(3,3);
&gt;&gt; bmats = cell(3,3);
&gt;&gt; cmats = cell(3,3);
&gt;&gt; dmats = cell(3,3);
<FONT COLOR="#000000">&gt;&gt; amats{1,1} = -(sym(</FONT><FONT COLOR="#a020f0">'OMEGA'</FONT><FONT COLOR="#000000">));</FONT>
&gt;&gt; amats{2,2} = -2;
&gt;&gt; amats{3,3} = [0 1 ; -0.05 -0.01];
&gt;&gt; amats{3,1} = [-1;-3];
&gt;&gt; bmats{1,1} = 1;
&gt;&gt; bmats{2,2} = 2;
&gt;&gt; bmats{3,3} = 3*eye(2);
&gt;&gt; cmats{1,1} = 1;
&gt;&gt; cmats{2,2} = 1;
&gt;&gt; cmats{3,3} = eye(2);
&gt;&gt; dmats{1,3} = [6 6];
&gt;&gt; dmats{2,1} = 6;
&gt;&gt; dmats{3,2} = [6;6];
<FONT COLOR="#000000">&gt;&gt; sys = ssm(plist( </FONT><FONT COLOR="#0000ff">...</FONT>
<FONT COLOR="#a020f0">'amats'</FONT><FONT COLOR="#000000">,amats, </FONT><FONT COLOR="#a020f0">'bmats'</FONT><FONT COLOR="#000000">,bmats, </FONT><FONT COLOR="#a020f0">'cmats'</FONT><FONT COLOR="#000000">,cmats, </FONT><FONT COLOR="#a020f0">'dmats'</FONT><FONT COLOR="#000000">,dmats, </FONT><FONT COLOR="#0000ff">...</FONT>
<FONT COLOR="#a020f0">'timestep'</FONT><FONT COLOR="#000000">,timestep, </FONT><FONT COLOR="#a020f0">'name'</FONT><FONT COLOR="#000000">,name));</FONT>
<FONT COLOR="#000000">&gt;&gt; sys.setParams(plist({</FONT><FONT COLOR="#a020f0">'OMEGA'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'system frequency'</FONT><FONT COLOR="#000000">}, 2))</FONT>
<FONT SIZE=2><FONT FACE="Courier New, monospace"><FONT COLOR="#000000">M: running ssm/ssm</FONT></FONT></FONT>
M: running ssmFromDescription
M: running validate
M: running ssm/setParams
M: running display
------ ssm/1 -------
amats: { [1x1] [] [] 
[] [1x1] [] 
[2x1] [] [2x2] } [3x3]
mmats: { [1x1] [] [] 
[] [1x1] [] 
[] [] [2x2] } [3x3]
bmats: { [1x1] [] [] 
[] [1x1] [] 
[] [] [2x2] } [3x3]
cmats: { [1x1] [] [] 
[] [1x1] [] 
[] [] [2x2] } [3x3]
dmats: { [] [] [1x2] 
[1x1] [] [] 
[] [2x1] [] } [3x3]
timestep: 0
inputs: [1x3 ssmblock]
1 : input 1 | input 1 &gt; 1 []
2 : input 2 | input 2 &gt; 1 []
3 : input 3 | input 3 &gt; 1 [], input 3 &gt; 2 []
states: [1x3 ssmblock]
1 : state 1 | state 1 &gt; 1 []
2 : state 2 | state 2 &gt; 1 []
3 : state 3 | state 3 &gt; 1 [], state 3 &gt; 2 []
outputs: [1x3 ssmblock]
1 : output 1 | output 1 &gt; 1 []
2 : output 2 | output 2 &gt; 1 []
3 : output 3 | output 3 &gt; 1 [], output 3 &gt; 2 []
params: (OMEGA=2) [1x1 plist]
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
Ninputs: 3
inputsizes: [1 1 2]
Noutputs: 3
outputsizes: [1 1 2]
Nstates: 3
statesizes: [1 1 2]
Nparams: 1
isnumerical: false
hist: ssm.hist [1x1 history]
procinfo: (empty-plist) [1x1 plist]
plotinfo: (empty-plist) [1x1 plist]
name: sys
description: 
mdlfile: 
UUID: 227fd0a2-1de0-4e01-855f-d0548e1eb1ff
--------------------</PRE></DIV><P>
<BR><BR>
</P>
<P>In then we set the names and descriptions of the input blocks, the
names, descriptions and units of the port variables:</P>
<DIV CLASS="fragment"><PRE><FONT COLOR="#000000">&gt;&gt; sys.setBlockNames(plist(</FONT><FONT COLOR="#a020f0">'field'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'inputs'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'blocks'</FONT><FONT COLOR="#000000">, [1 2 3], </FONT><FONT COLOR="#a020f0">'names'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'myinput1'</FONT><FONT COLOR="#000000">,</FONT><FONT COLOR="#a020f0">'myinput2'</FONT><FONT COLOR="#000000">,</FONT><FONT COLOR="#a020f0">'myinput3'</FONT><FONT COLOR="#000000">} ));</FONT>
<FONT COLOR="#000000">&gt;&gt; sys.setBlockDescriptions(plist(</FONT><FONT COLOR="#a020f0">'field'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'inputs'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'blocks'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'myinput1'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'descriptions'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'myinput1 description'</FONT><FONT COLOR="#000000">} ));</FONT>
<FONT COLOR="#000000">&gt;&gt; sys.setPortNames(plist(</FONT><FONT COLOR="#a020f0">'field'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'inputs'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'block'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'myinput3'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'ports'</FONT><FONT COLOR="#000000">, [1 2], </FONT><FONT COLOR="#a020f0">'names'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'my port 3-1'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'my port 3-2'</FONT><FONT COLOR="#000000">} ));</FONT>
<FONT COLOR="#000000">&gt;&gt; sys.setPortDescriptions(plist(</FONT><FONT COLOR="#a020f0">'field'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'inputs'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'block'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'myinput3'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'ports'</FONT><FONT COLOR="#000000">, [1 2], </FONT><FONT COLOR="#a020f0">'descriptions'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'first description'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'second description'</FONT><FONT COLOR="#000000">} ));</FONT>
<FONT COLOR="#000000">&gt;&gt; sys.setPortUnits(plist(</FONT><FONT COLOR="#a020f0">'field'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'inputs'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'block'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'myinput3'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'ports'</FONT><FONT COLOR="#000000">, [1 2], </FONT><FONT COLOR="#a020f0">'units'</FONT><FONT COLOR="#000000">, [unit(</FONT><FONT COLOR="#a020f0">'kg m^-2'</FONT><FONT COLOR="#000000">) unit(</FONT><FONT COLOR="#a020f0">'m'</FONT><FONT COLOR="#000000">)] ));</FONT>
&gt;&gt; sys.inputs
M: running ssm/setBlockNames
M: running ssm/setBlockDescriptions
M: running ssm/setPortNames
------ ssmport/1 -------
name: my port 3-1
units: [] [1x1 unit]
description: 
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
------------------------
------ ssmport/2 -------
name: my port 3-2
units: [] [1x1 unit]
description: 
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
------------------------
M: running ssm/setPortDescriptions
------ ssmport/1 -------
name: my port 3-1
units: [] [1x1 unit]
description: first description
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
------------------------
------ ssmport/2 -------
name: my port 3-2
units: [] [1x1 unit]
description: second description
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
------------------------
M: running ssm/setPortUnits
------ ssmblock/1 -------
name: myinput1
ports: input 1 &gt; 1 [] [1x1 ssmport]
description: myinput1 description
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
-------------------------
------ ssmblock/2 -------
name: myinput2
ports: input 2 &gt; 1 [] [1x1 ssmport]
description: 
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
-------------------------
------ ssmblock/3 -------
name: myinput3
ports: my port 3-1 [kg m^(-2)], my port 3-2 [m] [1x2 ssmport]
description: 
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
<FONT SIZE=2><FONT FACE="Courier New, monospace"><FONT COLOR="#000000">-------------------------</FONT></FONT></FONT></PRE></DIV><H2>
Modifying the parameter values</H2>
<P>Once the parameter field &ldquo;params&rdquo; is set, one may want
to set or modify (like in an optimizer) the parameter values. This is
done by the functions &ldquo;*Parameters.m&rdquo;. The function
setParameters takes two inputs ('setnames' and 'setvalues') which are
the names of the parameters to modify and the values assigned to
them.</P>
<DIV CLASS="fragment"><PRE>&gt;&gt; sys.params
<FONT COLOR="#000000">&gt;&gt; sys.setParameters(</FONT><FONT COLOR="#a020f0">'OMEGA'</FONT><FONT COLOR="#000000">, 0.002);</FONT>
&gt;&gt; sys.params
----------- plist 01 -----------
n params: 1
---- param 1 ----
key: OMEGA
val: 2
desc: system frequency
-----------------
description: 
UUID: 84ff1ed8-eee2-406c-89d8-7e6e703d36dd
--------------------------------
M: running setParameters
M: running ssm/ssm
----------- plist 01 -----------
n params: 1
---- param 1 ----
key: OMEGA
val: 0.002
desc: system frequency
-----------------
description: 
UUID: 84ff1ed8-eee2-406c-89d8-7e6e703d36dd
--------------------------------</PRE></DIV><P>
The function subsParameterskeep and Parameters substitute numerical
values to the symbolic expressions, using a list of the parameters to
substitute (or its complementary). All parameters substituted are
removed from the &ldquo;params&rdquo; field. The call
&lt;system&gt;.keepParameters substitues all the parameters. The
field isnumerical is then set to 1, unless a parameter in the
matrices was forgotten in the params field.</P>
<DIV CLASS="fragment"><PRE>&gt;&gt; sys.keepParameters;
&gt;&gt; sys.params
&gt;&gt; sys.isNumeric

M: running keepParameters
----------- plist 01 -----------
n params: 0
description: 
UUID: 84ff1ed8-eee2-406c-89d8-7e6e703d36dd
--------------------------------
ans =
1</PRE></DIV><H2>
Modifying the inputs/states/outputs</H2>
<P><FONT COLOR="#000000">Les us first build a simple system
constituted of four parallel 1</FONT><FONT COLOR="#000000"><SUP>st</SUP></FONT><FONT COLOR="#000000">
order systems.</FONT></P>
<DIV CLASS="fragment"><PRE><FONT COLOR="#000000">&gt;&gt; name = </FONT><FONT COLOR="#a020f0">'sys'</FONT><FONT COLOR="#000000">;</FONT>
&gt;&gt; timestep = 0;
&gt;&gt; amats = {diag([-1 -2 -3 -4])};
&gt;&gt; bmats = {diag([1 2 0 0])};
&gt;&gt; cmats = {[diag([1 0 3 0]) ; [0 0 0 0 ]]};
&gt;&gt; dmats = {[diag([0 0 0 0]) ; [0 0 0 0 ]]};
<FONT COLOR="#000000">&gt;&gt; sys = ssm(plist( </FONT><FONT COLOR="#0000ff">...</FONT>
<FONT COLOR="#a020f0">'amats'</FONT><FONT COLOR="#000000">,amats, </FONT><FONT COLOR="#a020f0">'bmats'</FONT><FONT COLOR="#000000">,bmats, </FONT><FONT COLOR="#a020f0">'cmats'</FONT><FONT COLOR="#000000">,cmats, </FONT><FONT COLOR="#a020f0">'dmats'</FONT><FONT COLOR="#000000">,dmats, </FONT><FONT COLOR="#0000ff">...</FONT>
<FONT COLOR="#a020f0">'timestep'</FONT><FONT COLOR="#000000">,timestep, </FONT><FONT COLOR="#a020f0">'name'</FONT><FONT COLOR="#000000">,name));</FONT>
<FONT COLOR="#000000">It is possible to obtain the structural realization of the system using sMinReal. This function deletes states which are either not observable or controllable. However, there may still exist such linear combinations of states.</FONT>
<FONT COLOR="#000000">The process only modify the states, here the 2</FONT><FONT COLOR="#000000"><SUP>nd</SUP></FONT><FONT COLOR="#000000"> and 4rt states disappear since they are not observable, and the 3</FONT><FONT COLOR="#000000"><SUP>rd</SUP></FONT><FONT COLOR="#000000"> and 4</FONT><FONT COLOR="#000000"><SUP>th</SUP></FONT><FONT COLOR="#000000"> disappear since they are not controllable.</FONT>
&gt;&gt; sys.sMinReal
M: running ssm/ssm
M: running ssmFromDescription
M: running validate
M: running ssm/sMinReal
M: running display
------ ssm/1 -------
amats: { [1x1] } [1x1]
mmats: { [1x1] } [1x1]
bmats: { [1x4] } [1x1]
cmats: { [5x1] } [1x1]
dmats: { [] } [1x1]
timestep: 0
inputs: [1x1 ssmblock]
1 : input 1 | input 1 &gt; 1 [], input 1 &gt; 2 [], input 1 &gt; 3 [], input 1 &gt; 4 []
states: [1x1 ssmblock]
1 : state 1 | state 1 &gt; 1 []
outputs: [1x1 ssmblock]
1 : output 1 | output 1 &gt; 1 [], output 1 &gt; 2 [], output 1 &gt; 3 [], output 1 &gt; 4 [], output 1 &gt; 5 []
params: (empty-plist) [1x1 plist]
version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $
Ninputs: 1
inputsizes: 4
Noutputs: 1
outputsizes: 5
Nstates: 1
statesizes: 1
Nparams: 0
isnumerical: true
hist: ssm.hist [1x1 history]
procinfo: (empty-plist) [1x1 plist]
plotinfo: (empty-plist) [1x1 plist]
name: sys
description: 
mdlfile: 
UUID: 349cd9c4-ad91-4151-b542-63d34b01bed8
--------------------</PRE></DIV><P>
Then we can work on the input/outputs to simplify the model.</P>
<P>The user must specify which block variable he want to keep, and
three syntaxes are allowed. 
</P>
<UL>
	<LI><P>'ALL'
	meaning all ports in all blocks are kept</P>
	<LI><P>{&lt;varname1&gt;
	&lt;varname2&gt; &hellip;} giving the name of each port to keep, in
	this case one must ensure ports of different blocks have different
	names.</P>
	<LI><P>{&lt;logical
	index for block1&gt; &lt;double index for block2&gt; &lt;varnames
	cellstr for block3&gt; &ldquo;ALL&rdquo; &ldquo;NONE&rdquo;} using a
	different index for each individual block.</P>
</UL>
<P>This
syntax is also used for any converter to select the inputs and
outputs in the ssm.</P>
<P>It is important to note that this removes lines and columns in the
system's matrices, but no parameters are removed. So second order
parameters that should be remove (by setting them to a neutral value)
must be taken care of separately.</P>
<DIV CLASS="fragment"><PRE><FONT FACE="Courier New, monospace"><FONT COLOR="#000000">&gt;&gt; sys.simplify(plist(</FONT><FONT COLOR="#a020f0">'inputs'</FONT><FONT COLOR="#000000">, {[1 2]} , </FONT><FONT COLOR="#a020f0">'states'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'ALL'</FONT><FONT COLOR="#000000"> , </FONT><FONT COLOR="#a020f0">'outputs'</FONT><FONT COLOR="#000000">, { </FONT><FONT COLOR="#a020f0">'output 1 &gt; 1'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'output 1 &gt; 4'</FONT><FONT COLOR="#000000">}))</FONT></FONT>
<FONT FACE="Courier New, monospace"><FONT COLOR="#000000"><FONT SIZE=2>M: running ssm/simplify</FONT></FONT></FONT>
<FONT FACE="Courier New, monospace">M: running ssm/ssm</FONT>
<FONT FACE="Courier New, monospace">M: running ssm/simplify</FONT>
<FONT FACE="Courier New, monospace">M: running display</FONT>
<FONT FACE="Courier New, monospace">------ ssm/1 -------</FONT>
<FONT FACE="Courier New, monospace">amats: { [1x1] } [1x1]</FONT>
<FONT FACE="Courier New, monospace">mmats: { [1x1] } [1x1]</FONT>
<FONT FACE="Courier New, monospace">bmats: { [1x2] } [1x1]</FONT>
<FONT FACE="Courier New, monospace">cmats: { [2x1] } [1x1]</FONT>
<FONT FACE="Courier New, monospace">dmats: { [] } [1x1]</FONT>
<FONT FACE="Courier New, monospace">timestep: 0</FONT>
<FONT FACE="Courier New, monospace">inputs: [1x1 ssmblock]</FONT>
<FONT FACE="Courier New, monospace">1 : input 1 | input 1 &gt; 1 [], input 1 &gt; 2 []</FONT>
<FONT FACE="Courier New, monospace">states: [1x1 ssmblock]</FONT>
<FONT FACE="Courier New, monospace">1 : state 1 | state 1 &gt; 1 []</FONT>
<FONT FACE="Courier New, monospace">outputs: [1x1 ssmblock]</FONT>
<FONT FACE="Courier New, monospace">1 : output 1 | output 1 &gt; 1 [], output 1 &gt; 4 []</FONT>
<FONT FACE="Courier New, monospace">params: (empty-plist) [1x1 plist]</FONT>
<FONT FACE="Courier New, monospace">version: $Id: ssm_modify_content.html,v 1.2 2009/08/28 15:11:53 adrien Exp $</FONT>
<FONT FACE="Courier New, monospace">Ninputs: 1</FONT>
<FONT FACE="Courier New, monospace">inputsizes: 2</FONT>
<FONT FACE="Courier New, monospace">Noutputs: 1</FONT>
<FONT FACE="Courier New, monospace">outputsizes: 2</FONT>
<FONT FACE="Courier New, monospace">Nstates: 1</FONT>
<FONT FACE="Courier New, monospace">statesizes: 1</FONT>
<FONT FACE="Courier New, monospace">Nparams: 0</FONT>
<FONT FACE="Courier New, monospace">isnumerical: true</FONT>
<FONT FACE="Courier New, monospace">hist: ssm.hist [1x1 history]</FONT>
<FONT FACE="Courier New, monospace">procinfo: (empty-plist) [1x1 plist]</FONT>
<FONT FACE="Courier New, monospace">plotinfo: (empty-plist) [1x1 plist]</FONT>
<FONT FACE="Courier New, monospace">name: sys</FONT>
<FONT FACE="Courier New, monospace">description: </FONT>
<FONT FACE="Courier New, monospace">mdlfile: </FONT>
<FONT FACE="Courier New, monospace">UUID: 8e55110a-eb07-44d2-aaee-4f839a5fb155</FONT>
<FONT FACE="Courier New, monospace">--------------------</FONT>
</PRE></DIV>
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