Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`LinearSystems`
simulationLTIsystem  |
| {systemstates,controllerstates,disturbancestates,controlinput,disturbanceinput,measurementoutput,controlledoutput,controllersignals}=simulationLTIsystem[system,ICsystem,controller,ICcontroller,disturbancedynamics,ICdisturbance,t0,tf] system controller disturbancedynamics system controller disturbancedynamics ICsystem ICcontroller ICdisturbance t0 tf system controller disturbancedynamics system system system system | |
Examples
(1)
Basic Examples
(1)
In[1]:=
system={{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2,z3,z4},{{-1,2,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-2,-3,-1,1,1,1},{1,0,0,0,0,1,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0},{0,0,0,1,0,0,0},{0,0,0,0,1,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4,5,6}};
In[2]:=
 | controllercanonicalform |
State transformation is xold = transformation.xnew
Out[2]=
True,3,{2,1},,0,0,-,1,0,,,,{x11,x21,x31},{u1,u2,w1,w2},{y1,y2,z1,z2,z3,z4},{0,1,0,0,0,0,2},-,,,1,1,1,1,,-,-,0,1,1,0,,0,0,0,0,1,0,-,1,0,0,0,0,1,,0,0,0,0,0,0,-,1,0,0,0,0,0,{0,0,0,1,0,0,0},{0,0,0,0,1,0,0},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4,5,6}
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In[3]:=
| observercanonicalform |
State transformation is xold = transformation.xnew
Out[3]=
{True,3,{1,2},{{1,0,0},{0,1,0},{2,-3,1}},{{x11,x21,x31},{u1,u2,w1,w2},{y1,y2,z1,z2,z3,z4},{{-1,2,0,0,0,0,1},{0,-4,1,1,1,1,0},{-5,-9,0,2,4,4,-1},{1,0,0,0,0,1,0},{0,1,0,0,0,0,1},{1,0,0,0,0,0,0},{0,1,0,0,0,0,0},{0,0,0,1,0,0,0},{0,0,0,0,1,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4,5,6}}}
In[4]:=
controller={{x1chk,x2chk,x3chk},{y1,y2},{u1,u2},{{-1,1,0,0,1},{-3.10435524768601717601478123947250050901414947573562597081149648344045608933637`51.311650143049405,-1.73594839077805689119557680477137097298363219953713265816251606649319570015058`50.306147744584955,0.87814241965773732109556902688379333054621868686817461835777160853466365674909`50.73865164041571,1,0},{-1.95288711515437031578579767913036750545880308231146871406496998449400271469585`51.110355869039225,-3.12185758034226267890443097311620666945378131313182538164222839146533634325091`50.56102402158889,-3.03843496169831682910376664319936817618033748062912955416207929122130081677137`51.27773662829537,1,1},{-0.07573406626582343011449178017106650177767319671207862837326324947322668732026`50.,-0.30704540521789710614557291582758215176492544320265363826014383751392967844984`49.85484353342589,-0.04171130932197292490033216495841924663672191625134791374007455012201776323977`49.71637050194081,0,0},{-0.02862118142019374590028945930143400723647627902354734243823323396722940201612`49.57739628120991,-0.42890298556015978505000388894378882121870675633447901990237222897926602170074`50.,-0.08014627102028975400409880815778742281705939688047746790215384134331858001114`50.,0,0}},{1,2},{1,2},{1,2},{},{1,2},{}};
In[5]:=
disturbancedynamics=
[Table[0,{i,2},{j,4}]]
 | gainsystem |
Out[5]=
{{},{tempinput1,tempinput2,tempinput3,tempinput4},{tempoutput1,tempoutput2},{{0,0,0,0},{0,0,0,0}},{1,2,3,4},{1,2},{1,2,3,4},{},{1,2},{}}
In[6]:=
{systemstates,controllerstates,disturbancestates,controlinput,disturbanceinput,measurementoutput,controlledoutput,controllersignals}=
[system,{1,0,-1},controller,{0,0,0},disturbancedynamics,{},0,20]
| simulationLTIsystem |
Out[6]=
{systemstates$24688,controllerstates$24688,disturbancestates$24688,controlinput$24688,disturbanceinput$24688,measurementoutput$24688,controlledoutput$24688,controllersignals$24688}
In[7]:=
Plot[systemstates[t],{t,0,20},PlotRangeAll]
Out[7]=
In[8]:=
Plot[controllerstates[t],{t,0,20},PlotRangeAll]
Out[8]=
In[9]:=
Plot[disturbancestates[t],{t,0,20}]
Out[9]=
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""