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<H2>What is a ssm object?</H2>
<P>The ssm class is a class to use &ldquo;state space models&rdquo;
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 &ldquo;timestep&rdquo;,
	either discrete or continuous (&ldquo;timestep&rdquo; 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 &hellip;) 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>&gt;&gt; <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 $--&gt;$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 &ldquo;amats&rdquo;, &ldquo;mmats&rdquo;, &ldquo;bmats&rdquo;,
&ldquo;cmats&rdquo;, &ldquo;dmats&rdquo; 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 &ldquo;params&rdquo; 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 &ldquo;params&rdquo; as they
get substituted .</P>
<P>Inputs, states and output sizes are summed up in the fields N* and
*sizes.</P>
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author	Daniele Nicolodi <nicolodi@science.unitn.it>
date	Sun, 04 Dec 2011 21:23:09 +0100 (2011-12-04)
parents	f0afece42f48
children