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Import.
| author | Daniele Nicolodi <nicolodi@science.unitn.it> |
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| date | Wed, 23 Nov 2011 19:22:13 +0100 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/m-toolbox/html_help/help/ug/ssm_introduction.html Wed Nov 23 19:22:13 2011 +0100 @@ -0,0 +1,174 @@ +<!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>Introduction to Statespace Models with LTPDA (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.html"><img src="b_prev.gif" border="0" align= + "bottom" alt="Statespace models"></a> <a href= + "ssm_building.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Building Statespace models"></a></td> + </tr> + </table> + + <h1 class="title"><a name="f3-12899" id="f3-12899"></a>Introduction to Statespace Models with LTPDA</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;17351600"> +</HEAD> +<BODY LANG="en-US" DIR="LTR"> +<H2>What is a ssm object?</H2> +<P>The ssm class is a class to use “state space models” +for simulation, identification and modeling in the toolbox. A state +space model is a mathematical object constituted of</P> +<UL> + <LI><P>A time model represented by the field “timestep”, + either discrete or continuous (“timestep” is then 0)</P> + <LI><P>A linear differential equation, which turns into a difference + equation it the model is time discrete. This equation is written + using a state space x in the form x' = Ax + Bu where A is the state + transition matrix and B the state input matrix, u being the + exogenous input signal. In this setup, x and u are time series.</P> + <LI><P>An observation equation which allows for linear observation + of the input and the state : y = Cx+Du. The variable y is the output + of the system.</P> +</UL> +<P>Input and output variables (lines in u and y) may be named and +assigned a unit. However for the state x there is more of a choice +since if free of choice via a basis change. The most usual choice is +that x contents the same units as y and it derivatives, or the same +units as u and its integrals. In general the size of the state space +is equal to the number of poles in the system.</P> +<P>In the LTPDA toolbox, lines in u,y,x are grouped in blocks (input +blocks, state blocks, output blocks) to ease the understanding of a +large system. This means the matrices A, B, C, and D are also split +into blocks of the corresponding size. The diagonal blocks of A may +represent the dynamics of a LTP subsystem (the controller, the +propulsion …) or the coupling between two systems (from the +propulsion to the equations of motion)... In addition the dynamic +equation also contains an inertia matrix M so that the parametric +equation is made simple. The equation becomes M x' = Ax + Bu. If not +user set M is supposed to be the identity.</P> +<P>Below we build a standard system to show the contents of the +object.</P> +<DIV CLASS="fragment"><PRE>>> <FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>system = ssm(plist(</FONT></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"><FONT SIZE=2>'standard_system_params'</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>'withparams'</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>'ALL'</FONT></FONT></FONT><FONT COLOR="#000000"><FONT FACE="Courier New, monospace"><FONT SIZE=2>))</FONT></FONT></FONT> +M: running ssm/ssm +M: running ssmFromBuiltinSystem +M: looking for models in C:\Documents and Settings\Adrien.IFR-NB01\My Documents\MATLAB2008\LTPDA_SSM_MODELS\ltp_ssm_models +M: looking for models in C:\Users\Adrien.IFR-NB01\My Documents\MATLAB2008\ltpda_toolbox\ltpda\classes\@ssm\..\..\m\built_in_models +M: running buildParamPlist +M: running ssm/ssm +M: running ssm/ssm +M: running fromStruct +M: running ssm/ssm +M: running validate +M: running validate +M: running display +------ ssm/1 ------- + amats: { [2x2] } [1x1] + mmats: { [2x2] } [1x1] + bmats: { [2x1] [2x2] } [1x2] + cmats: { [1x2] } [1x1] + dmats: { [1x1] [1x2] } [1x2] + timestep: 0 + inputs: [1x2 ssmblock] + 1 : U | Fu [kg m s^(-2)] + 2 : N | Fn [kg m s^(-2)], On [m] + states: [1x1 ssmblock] + 1 : standard test system | x [m], xdot [m s^(-1)] + outputs: [1x1 ssmblock] + 1 : Y | y [m] + params: (W=0.2, C=0.5, C1=0, C2=0, B=1, D=0) [1x1 plist] + version: $Id: ssm_introduction_content.html,v 1.3 2009/08/28 14:20:07 adrien Exp $-->$Id: ssm_introduction_content.html,v 1.3 2009/08/28 14:20:07 adrien Exp $ + Ninputs: 2 + inputsizes: [1 2] + Noutputs: 1 +outputsizes: 1 + Nstates: 1 + statesizes: 2 + Nparams: 6 +isnumerical: false + 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: 8eafd65e-9052-4800-a694-9482e2bd7b70 +--------------------</PRE></DIV><P> +The fields “amats”, “mmats”, “bmats”, +“cmats”, “dmats” contain the matrices of the +differential and observation equation of a mass spring system with +dampening.</P> +<P>The systems inputs/states/outputs are listed by blocks. There are +two input blocks, which correspond to the commanded signal (U) and +the noise (N). There is one state block and one output block. Each +input has its name displayed followed with individual input variable +names and units. Note that the empty ssm object does not have an +input block, a state block and an output block of size 0, it has no +such blocks, and the size fields are empty.</P> +<P>The “params” field is the 1x1 default plist with no +parameter. This is the case when the system is fully numerical, +parameters are deleted from the field “params” as they +get substituted .</P> +<P>Inputs, states and output sizes are summed up in the fields N* and +*sizes.</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.html"><img src= + "b_prev.gif" border="0" align="bottom" alt= + "Statespace models"></a> </td> + + <td align="left">Statespace models</td> + + <td> </td> + + <td align="right">Building Statespace models</td> + + <td align="right" width="20"><a href= + "ssm_building.html"><img src="b_next.gif" border="0" align= + "bottom" alt="Building Statespace models"></a></td> + </tr> + </table><br> + + <p class="copy">©LTP Team</p> +</body> +</html>