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| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
|---|---|
| date | Mon, 05 Dec 2011 16:20:06 +0100 |
| parents | f0afece42f48 |
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd"> <html lang="en"> <head> <meta name="generator" content= "HTML Tidy for Mac OS X (vers 1st December 2004), see www.w3.org"> <meta http-equiv="Content-Type" content= "text/html; charset=us-ascii"> <title>Assembling systems (LTPDA Toolbox)</title> <link rel="stylesheet" href="docstyle.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.52.2"> <meta name="description" content= "Presents an overview of the features, system requirements, and starting the toolbox."> </head> <body> <a name="top_of_page" id="top_of_page"></a> <p style="font-size:1px;"> </p> <table class="nav" summary="Navigation aid" border="0" width= "100%" cellpadding="0" cellspacing="0"> <tr> <td valign="baseline"><b>LTPDA Toolbox</b></td><td><a href="../helptoc.html">contents</a></td> <td valign="baseline" align="right"><a href= "ssm_modify.html"><img src="b_prev.gif" border="0" align= "bottom" alt="Modifying systems"></a> <a href= "ssm_simulation.html"><img src="b_next.gif" border="0" align= "bottom" alt="Simulations"></a></td> </tr> </table> <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Assembling systems</h1> <hr> <p> <!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 “closing a loop” multiple times. To avoid this, the method “assemble” 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 “inputDuplicate”. 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">>> <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 “modifTimeStep”. The input is then duplicated to be used for a controller feedback.</P> <DIV CLASS="fragment"><PRE>>> 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])); >> sys.modifTimeStep(0.01); >> 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 $-->$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 "standard_system_params" is not stable ans = 0</PRE></DIV><P> Then a controller can be created to make the system stable.</P> <DIV CLASS="fragment"><PRE>>> <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> >> sysCL = assemble(sys, controller); >> 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 > 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 "assembled( standard_system_params + controller))" is stable ans = 1</PRE></DIV><P> We can then use the system to produce a simulation.</P> <P><BR><BR> </P> </BODY> </HTML> </p> <br> <br> <table class="nav" summary="Navigation aid" border="0" width= "100%" cellpadding="0" cellspacing="0"> <tr valign="top"> <td align="left" width="20"><a href="ssm_modify.html"><img src= "b_prev.gif" border="0" align="bottom" alt= "Modifying systems"></a> </td> <td align="left">Modifying systems</td> <td> </td> <td align="right">Simulations</td> <td align="right" width="20"><a href= "ssm_simulation.html"><img src="b_next.gif" border="0" align= "bottom" alt="Simulations"></a></td> </tr> </table><br> <p class="copy">©LTP Team</p> </body> </html>