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Import.
author Daniele Nicolodi <nicolodi@science.unitn.it>
date Wed, 23 Nov 2011 19:22:13 +0100
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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<HTML>
+<HEAD>
+	<META HTTP-EQUIV="CONTENT-TYPE" CONTENT="text/html; charset=windows-1252">
+	<TITLE></TITLE>
+	<META NAME="GENERATOR" CONTENT="OpenOffice.org 3.1  (Win32)">
+	<META NAME="CREATED" CONTENT="0;0">
+	<META NAME="CHANGEDBY" CONTENT="Adrien G">
+	<META NAME="CHANGED" CONTENT="20090827;17255200">
+</HEAD>
+<BODY LANG="de-DE" DIR="LTR">
+<P>A collection of ssm arrays can be assembled into one ssm using the
+assemble function.</P>
+<H2>Managing inputs/outputs when assembling</H2>
+<P>The order of the systems does not modify the output of .
+The function assemble work by matching inputs and outputs of the same
+name. Of course, they must have the same dimensionality, same
+time-step. However, the check for units is not implemented yet.</P>
+<P>In terms of time-step it is important to assemble all continuously
+linked models together when the system is continuous, and discretize
+it later on. Time discrete models (typically digital systems, and the
+dynamical branch from the actuator input to the sensor output) should
+be assembled together when they are time-discrete. The discretization
+includes a zero hold which models correctly the A/D filter behavior.</P>
+<P>Moreover, a system can be assembled in multiple steps. In this
+case there is a risk of &ldquo;closing a loop&rdquo; multiple times.
+To avoid this, the method &ldquo;assemble&rdquo; suppresses the
+inputs once they are assembled. May the user need the input for a
+simulation later on, he must duplicate it using the function
+&ldquo;inputDuplicate&rdquo;. Built-in models should also have
+built-in duplicated inputs to insert signals.</P>
+<H2>Example using an existing built-in models</H2>
+<DIV CLASS="fragment"><PRE STYLE="margin-bottom: 0.5cm">&gt;&gt; <FONT COLOR="#000000"><FONT FACE="Courier New, monospace">sys = ssm(plist(</FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace"><FONT SIZE=2>'built-in'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>, </FONT></FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace">'standard_system_params'</FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace">, </FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace">'setnames'</FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace">, {</FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace"><FONT SIZE=2>'W'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>}, </FONT></FONT></FONT><FONT COLOR="#a020f0"><FONT FACE="Courier New, monospace"><FONT SIZE=2>'setvalues'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>, 0.2*i ));</FONT></FONT></FONT></PRE></DIV><P>
+Trying sys.isStable with the first and the third system shows a
+different result, the negative stiffness making the latter unstable.
+The system can be made time discrete using the function
+&ldquo;modifTimeStep&rdquo;.
+The input is then duplicated to be used for a controller feedback.</P>
+<DIV CLASS="fragment"><PRE>&gt;&gt; sys = ssm(plist(<FONT COLOR="#a020f0">'built-in'</FONT>, <FONT COLOR="#a020f0">'standard_system_params'</FONT>, <FONT COLOR="#a020f0">'setnames'</FONT>, {<FONT COLOR="#a020f0">'W'</FONT> <FONT COLOR="#a020f0">'C'</FONT>}, <FONT COLOR="#a020f0">'setvalues'</FONT>, [-0.2 -0.5]));
+&gt;&gt; sys.modifTimeStep(0.01);
+&gt;&gt; sys.duplicateInput(<FONT COLOR="#a020f0">'U'</FONT>,<FONT COLOR="#a020f0">'Negative Bias'</FONT>)
+------ ssm/1 -------
+      amats: {  [2x2]  }  [1x1]
+      mmats: {  [2x2]  }  [1x1]
+      bmats: {  [2x1]   [2x2]   [2x1]  }  [1x3]
+      cmats: {  [1x2]  }  [1x1]
+      dmats: {   []     [1x2]    []    }  [1x3]
+   timestep: 0.01
+     inputs:  [1x3 ssmblock]
+         1 : U | Fu [kg m s^(-2)]
+         2 : N | Fn [kg m s^(-2)], On [m]
+         3 : Negative Bias | Fu [kg m s^(-2)]
+     states:  [1x1 ssmblock]
+         1 : standard test system | x [m], xdot [m s^(-1)]
+    outputs:  [1x1 ssmblock]
+         1 : Y | y [m]
+     params: (empty-plist) [1x1 plist]
+    version: $Id: ssm_assemble_content.html,v 1.4 2009/08/28 15:11:53 adrien Exp $--&gt;$Id: ssm_assemble_content.html,v 1.4 2009/08/28 15:11:53 adrien Exp $
+    Ninputs: 3
+ inputsizes: [1 2 1]
+   Noutputs: 1
+outputsizes: 1
+    Nstates: 1
+ statesizes: 2
+    Nparams: 0
+isnumerical: true
+       hist: ssm.hist [1x1 history]
+   procinfo: (empty-plist) [1x1 plist]
+   plotinfo: (empty-plist) [1x1 plist]
+       name: standard_system_params
+description: standard spring-mass-dashpot test system
+    mdlfile: 
+       UUID: 284b0ae3-947d-430a-802e-d9c3738ebb14
+--------------------
+M: running isStable
+ans =
+          2.05114794494015
+warning, system named &quot;standard_system_params&quot; is not stable
+ans =
+     0</PRE></DIV><P>
+Then a controller can be created to make the system stable.</P>
+<DIV CLASS="fragment"><PRE>&gt;&gt; <FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>controller = ssm(plist( </FONT></FONT></FONT><FONT COLOR="#0000ff"><FONT FACE="Courier New, monospace"><FONT SIZE=2>...</FONT></FONT></FONT>
+<FONT COLOR="#000000">   </FONT><FONT COLOR="#a020f0">'amats'</FONT><FONT COLOR="#000000">,cell(0,0), </FONT><FONT COLOR="#a020f0">'bmats'</FONT><FONT COLOR="#000000">,cell(0,1), </FONT><FONT COLOR="#a020f0">'cmats'</FONT><FONT COLOR="#000000">,cell(1,0), </FONT><FONT COLOR="#a020f0">'dmats'</FONT><FONT COLOR="#000000">,{-1}, </FONT><FONT COLOR="#0000ff">...</FONT>
+<FONT COLOR="#000000">   </FONT><FONT COLOR="#a020f0">'timestep'</FONT><FONT COLOR="#000000">,0.01, </FONT><FONT COLOR="#a020f0">'name'</FONT><FONT COLOR="#000000">,</FONT><FONT COLOR="#a020f0">'controller'</FONT><FONT COLOR="#000000">, </FONT><FONT COLOR="#a020f0">'params'</FONT><FONT COLOR="#000000">,plist, </FONT><FONT COLOR="#0000ff">...</FONT>
+<FONT COLOR="#000000">   </FONT><FONT COLOR="#a020f0">'statenames'</FONT><FONT COLOR="#000000">,{}, </FONT><FONT COLOR="#a020f0">'inputnames'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'Y'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'outputnames'</FONT><FONT COLOR="#000000">,{</FONT><FONT COLOR="#a020f0">'U'</FONT><FONT COLOR="#000000">} ));</FONT>
+&gt;&gt; sysCL = assemble(sys, controller);
+&gt;&gt; sysCL.isStable
+
+------ ssm/1 -------
+      amats: {  [2x2]  }  [1x1]
+      mmats: {  [2x2]  }  [1x1]
+      bmats: {  [2x2]   [2x1]  }  [1x2]
+      cmats: {  [1x2]   
+                [1x2]  }  [2x1]
+      dmats: {  [1x2]    []     
+                [1x2]    []    }  [2x2]
+   timestep: 0.01
+     inputs:  [1x2 ssmblock]
+         1 : N | Fn [kg m s^(-2)], On [m]
+         2 : Negative Bias | Fu [kg m s^(-2)]
+     states:  [1x1 ssmblock]
+         1 : standard test system | x [m], xdot [m s^(-1)]
+    outputs:  [1x2 ssmblock]
+         1 : Y | y [m]
+         2 : U | U &gt; 1 []
+     params: (empty-plist) [1x1 plist]
+    version: $Id: ssm_assemble_content.html,v 1.4 2009/08/28 15:11:53 adrien Exp $
+    Ninputs: 2
+ inputsizes: [2 1]
+   Noutputs: 2
+outputsizes: [1 1]
+    Nstates: 1
+ statesizes: 2
+    Nparams: 0
+isnumerical: true
+       hist: ssm.hist [1x1 history]
+   procinfo: (empty-plist) [1x1 plist]
+   plotinfo: (empty-plist) [1x1 plist]
+       name: assembled( standard_system_params + controller))
+description: 
+    mdlfile: 
+       UUID: c6f7397e-add7-4f4c-8eb0-fd0a4841e3cf
+--------------------
+M: running isStable
+System named &quot;assembled( standard_system_params + controller))&quot; is stable
+ans =
+     1</PRE></DIV><P>
+We can then use the system to produce a simulation.</P>
+<P><BR><BR>
+</P>
+</BODY>
+</HTML>
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