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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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1 <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
2 <HTML>
3 <HEAD>
4 <META HTTP-EQUIV="CONTENT-TYPE" CONTENT="text/html; charset=windows-1252">
5 <TITLE></TITLE>
6 <META NAME="GENERATOR" CONTENT="OpenOffice.org 3.1 (Win32)">
7 <META NAME="CREATED" CONTENT="0;0">
8 <META NAME="CHANGEDBY" CONTENT="Adrien G">
9 <META NAME="CHANGED" CONTENT="20090827;17351600">
10 </HEAD>
11 <BODY LANG="en-US" DIR="LTR">
12 <H2>What is a ssm object?</H2>
13 <P>The ssm class is a class to use &ldquo;state space models&rdquo;
14 for simulation, identification and modeling in the toolbox. A state
15 space model is a mathematical object constituted of</P>
16 <UL>
17 <LI><P>A time model represented by the field &ldquo;timestep&rdquo;,
18 either discrete or continuous (&ldquo;timestep&rdquo; is then 0)</P>
19 <LI><P>A linear differential equation, which turns into a difference
20 equation it the model is time discrete. This equation is written
21 using a state space x in the form x' = Ax + Bu where A is the state
22 transition matrix and B the state input matrix, u being the
23 exogenous input signal. In this setup, x and u are time series.</P>
24 <LI><P>An observation equation which allows for linear observation
25 of the input and the state : y = Cx+Du. The variable y is the output
26 of the system.</P>
27 </UL>
28 <P>Input and output variables (lines in u and y) may be named and
29 assigned a unit. However for the state x there is more of a choice
30 since if free of choice via a basis change. The most usual choice is
31 that x contents the same units as y and it derivatives, or the same
32 units as u and its integrals. In general the size of the state space
33 is equal to the number of poles in the system.</P>
34 <P>In the LTPDA toolbox, lines in u,y,x are grouped in blocks (input
35 blocks, state blocks, output blocks) to ease the understanding of a
36 large system. This means the matrices A, B, C, and D are also split
37 into blocks of the corresponding size. The diagonal blocks of A may
38 represent the dynamics of a LTP subsystem (the controller, the
39 propulsion &hellip;) or the coupling between two systems (from the
40 propulsion to the equations of motion)... In addition the dynamic
41 equation also contains an inertia matrix M so that the parametric
42 equation is made simple. The equation becomes M x' = Ax + Bu. If not
43 user set M is supposed to be the identity.</P>
44 <P>Below we build a standard system to show the contents of the
45 object.</P>
46 <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>
47 M: running ssm/ssm
48 M: running ssmFromBuiltinSystem
49 M: looking for models in C:\Documents and Settings\Adrien.IFR-NB01\My Documents\MATLAB2008\LTPDA_SSM_MODELS\ltp_ssm_models
50 M: looking for models in C:\Users\Adrien.IFR-NB01\My Documents\MATLAB2008\ltpda_toolbox\ltpda\classes\@ssm\..\..\m\built_in_models
51 M: running buildParamPlist
52 M: running ssm/ssm
53 M: running ssm/ssm
54 M: running fromStruct
55 M: running ssm/ssm
56 M: running validate
57 M: running validate
58 M: running display
59 ------ ssm/1 -------
60 amats: { [2x2] } [1x1]
61 mmats: { [2x2] } [1x1]
62 bmats: { [2x1] [2x2] } [1x2]
63 cmats: { [1x2] } [1x1]
64 dmats: { [1x1] [1x2] } [1x2]
65 timestep: 0
66 inputs: [1x2 ssmblock]
67 1 : U | Fu [kg m s^(-2)]
68 2 : N | Fn [kg m s^(-2)], On [m]
69 states: [1x1 ssmblock]
70 1 : standard test system | x [m], xdot [m s^(-1)]
71 outputs: [1x1 ssmblock]
72 1 : Y | y [m]
73 params: (W=0.2, C=0.5, C1=0, C2=0, B=1, D=0) [1x1 plist]
74 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 $
75 Ninputs: 2
76 inputsizes: [1 2]
77 Noutputs: 1
78 outputsizes: 1
79 Nstates: 1
80 statesizes: 2
81 Nparams: 6
82 isnumerical: false
83 hist: ssm.hist [1x1 history]
84 procinfo: (empty-plist) [1x1 plist]
85 plotinfo: (empty-plist) [1x1 plist]
86 name: standard_system_params
87 description: standard spring-mass-dashpot test system
88 mdlfile:
89 UUID: 8eafd65e-9052-4800-a694-9482e2bd7b70
90 --------------------</PRE></DIV><P>
91 The fields &ldquo;amats&rdquo;, &ldquo;mmats&rdquo;, &ldquo;bmats&rdquo;,
92 &ldquo;cmats&rdquo;, &ldquo;dmats&rdquo; contain the matrices of the
93 differential and observation equation of a mass spring system with
94 dampening.</P>
95 <P>The systems inputs/states/outputs are listed by blocks. There are
96 two input blocks, which correspond to the commanded signal (U) and
97 the noise (N). There is one state block and one output block. Each
98 input has its name displayed followed with individual input variable
99 names and units. Note that the empty ssm object does not have an
100 input block, a state block and an output block of size 0, it has no
101 such blocks, and the size fields are empty.</P>
102 <P>The &ldquo;params&rdquo; field is the 1x1 default plist with no
103 parameter. This is the case when the system is fully numerical,
104 parameters are deleted from the field &ldquo;params&rdquo; as they
105 get substituted .</P>
106 <P>Inputs, states and output sizes are summed up in the fields N* and
107 *sizes.</P>
108 </BODY>
109 </HTML>