Mercurial > hg > ltpda
view m-toolbox/html_help/help/ug/ssm_simulation_content.html @ 47:dd93c9ba6624 database-connection-manager
Fix Java dialog
author | Daniele Nicolodi <nicolodi@science.unitn.it> |
---|---|
date | Tue, 06 Dec 2011 19:07:27 +0100 |
parents | f0afece42f48 |
children |
line wrap: on
line source
<!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;18204600"> </HEAD> <BODY LANG="en-US" DIR="LTR"> <P>The function simulate can use ssm object to produce simulations. </P> <H2>Simulation example. </H2> <P>The following closed loop system is built. </P> <DIV CLASS="fragment"><PRE><FONT SIZE=2>>> sys = ssm(plist(</FONT><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); <FONT SIZE=2>>> sys.duplicateInput(</FONT><FONT COLOR="#a020f0">'U'</FONT>,<FONT COLOR="#a020f0">'Negative Bias'</FONT>); >> controller = ssm(plist( <FONT COLOR="#0000ff">...</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="#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="#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> ------ 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_simulation_content.html,v 1.3 2009/08/28 14:20:07 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: 163d7103-063b-4a57-af7e-b08d22fe42c1 --------------------</PRE></DIV><P> Then we wish to use the inputs of N for a correlated force noise and measurement noise, “Negative Bias” for a sinewave, and there will be an observation DC offset.</P> <P>We want as an output the controller output “U” and the sensor output “y”.</P> <DIV CLASS="fragment"><PRE>>> ao1 = ao(plist(<FONT COLOR="#a020f0">'FCN'</FONT>,<FONT COLOR="#a020f0">'sin(0:0.01:100)'</FONT>)); <FONT COLOR="#000000">>> ao_out = sysCL.simulate( plist(</FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'NOISE VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fn'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'COVARIANCE'</FONT><FONT COLOR="#000000">, [1 0.1 ; 0.1 2] , </FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'AOS VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fu'</FONT><FONT COLOR="#000000">} ,</FONT><FONT COLOR="#a020f0">'AOS'</FONT><FONT COLOR="#000000">, ao1 ,</FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'CONSTANT VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'CONSTANTS'</FONT><FONT COLOR="#000000">, 35, </FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'RETURN STATES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'x'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'RETURN OUTPUTS'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'y'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'U > 1'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'SSINI'</FONT><FONT COLOR="#000000"> , {[100;3]}, </FONT><FONT COLOR="#a020f0">'TINI'</FONT><FONT COLOR="#000000">, 0));</FONT> >> iplot(ao_out([1, 2, 3]));</PRE></DIV><P> <IMG SRC="images/simulate.png" NAME="images1" ALIGN=LEFT WIDTH=567 HEIGHT=454 BORDER=0><BR CLEAR=LEFT>It turns out the system output (blue) is not much like the state (red), causing the control (green) to waste a lot of energy. The state is not experimentally available, but might be obtained through filtering. The kalman method is so far the only filtering method implemented in the toolbox.</P> <DIV CLASS="fragment"><PRE><FONT COLOR="#000000">>> ao_est = sysCL.kalman( plist(</FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'NOISE VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fn'</FONT><FONT COLOR="#000000"> </FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'COVARIANCE'</FONT><FONT COLOR="#000000">, [1 0.1 ; 0.1 2] , </FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'AOS VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'Fu'</FONT><FONT COLOR="#000000">} ,</FONT><FONT COLOR="#a020f0">'AOS'</FONT><FONT COLOR="#000000">, ao1 ,</FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'CONSTANT VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'On'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'CONSTANTS'</FONT><FONT COLOR="#000000">, 35, </FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'OUTPUT VARIABLE NAMES'</FONT><FONT COLOR="#000000">, {</FONT><FONT COLOR="#a020f0">'y'</FONT><FONT COLOR="#000000">}, </FONT><FONT COLOR="#a020f0">'OUTPUTS'</FONT><FONT COLOR="#000000"> , ao_out(2), </FONT><FONT COLOR="#0000ff">...</FONT> <FONT COLOR="#a020f0"> 'RETURN STATES'</FONT><FONT COLOR="#000000">, 1, </FONT><FONT COLOR="#a020f0">'RETURN OUTPUTS'</FONT><FONT COLOR="#000000">, 1 ));</FONT> >> iplot(ao_out(2), ao_est(1), ao_out(1))</PRE></DIV><P> <IMG SRC="images/kalman.png" NAME="images2" ALIGN=LEFT WIDTH=567 HEIGHT=454 BORDER=0><BR CLEAR=LEFT>In this example the estimate (blue) of the state (green) is satisfactory. It leads us to think that such a filter should be used to provide with the input of the controller. </P> <P>However, the DC offset correction by the kalman filter is one information that is not available under usual circumstances. </P> <P><BR><BR> </P> <P STYLE="margin-bottom: 0cm"><BR> </P> <P STYLE="margin-bottom: 0cm"><BR> </P> <P><BR><BR> </P> </BODY> </HTML>