<!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 statespace 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 andassigned a unit. However for the state x there is more of a choicesince if free of choice via a basis change. The most usual choice isthat x contents the same units as y and it derivatives, or the sameunits as u and its integrals. In general the size of the state spaceis equal to the number of poles in the system.</P><P>In the LTPDA toolbox, lines in u,y,x are grouped in blocks (inputblocks, state blocks, output blocks) to ease the understanding of alarge system. This means the matrices A, B, C, and D are also splitinto blocks of the corresponding size. The diagonal blocks of A mayrepresent the dynamics of a LTP subsystem (the controller, thepropulsion …) or the coupling between two systems (from thepropulsion to the equations of motion)... In addition the dynamicequation also contains an inertia matrix M so that the parametricequation is made simple. The equation becomes M x' = Ax + Bu. If notuser set M is supposed to be the identity.</P><P>Below we build a standard system to show the contents of theobject.</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/ssmM: running ssmFromBuiltinSystemM: looking for models in C:\Documents and Settings\Adrien.IFR-NB01\My Documents\MATLAB2008\LTPDA_SSM_MODELS\ltp_ssm_modelsM: looking for models in C:\Users\Adrien.IFR-NB01\My Documents\MATLAB2008\ltpda_toolbox\ltpda\classes\@ssm\..\..\m\built_in_modelsM: running buildParamPlistM: running ssm/ssmM: running ssm/ssmM: running fromStructM: running ssm/ssmM: running validateM: running validateM: 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: 1outputsizes: 1 Nstates: 1 statesizes: 2 Nparams: 6isnumerical: false hist: ssm.hist [1x1 history] procinfo: (empty-plist) [1x1 plist] plotinfo: (empty-plist) [1x1 plist] name: standard_system_paramsdescription: 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 thedifferential and observation equation of a mass spring system withdampening.</P><P>The systems inputs/states/outputs are listed by blocks. There aretwo input blocks, which correspond to the commanded signal (U) andthe noise (N). There is one state block and one output block. Eachinput has its name displayed followed with individual input variablenames and units. Note that the empty ssm object does not have aninput block, a state block and an output block of size 0, it has nosuch blocks, and the size fields are empty.</P><P>The “params” field is the 1x1 default plist with noparameter. This is the case when the system is fully numerical,parameters are deleted from the field “params” as theyget substituted .</P><P>Inputs, states and output sizes are summed up in the fields N* and*sizes.</P></BODY></HTML>
