Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
ZigangPan`SystemofSystems`
EZDCFSS  |
| {vectorrelativedegree,relativedegrees,highfrequencygain,transformation,extzerodynamics}=EZDCFSS[listofSystems,θ] listofSystems θ vectorrelativedegree relativedegrees highfrequencygain transformation extzerodynamics | |
Examples
(1)
Basic Examples
(1)
In[1]:=
Needs["ZigangPan`Examples`"]
In[2]:=
system1={{x11,x12,x13,x14,x15},{u11,u12,u21,y31,y32,wg1,wg2,wg3,wg4,wg5,wg6},{y11,y12,z11,z12},{{0,1,0,θb11,0,2θb11,θb12,0,θb11,-θb12,0,0,0,0,0,θb11},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,-θb13,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1,0,0,-2,1,-θb11,-θb12,0,θb11,θb12,0,0,0,0,0,θb12},{0,0,0,-1/2,-1,0,0,1/6*θb12,θb11,-θb12,0,0,0,0,0,θb12},{1,0,0,0,0,θb11,θb12,0,0,0,1,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,0,0,0,1,0,0,0,0},{1,0,0,0,0,θb11,θb12,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,-θb12,θb11,0,0,0,0,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4,5,6,7,8,9,10,11},{1,2},{3,4}};systemcheck[system1]
In[3]:=
θbar1={θb11,θb12,θb13};
In[4]:=
system2={{x21,x22,x23,x24},{u21,u31,u32,y11,y12,wg1,wg2,wg3,wg4,wg5,wg6},{y21,z21},{{-θb21,1,0,0,θb21,0,0,0,0,0,0,0,0,0,θb21},{-θb21,0,1,0,3θb21,0,0,θb21,θb22,0,0,0,0,0,3θb21},{-θb22,0,0,1,3θb21,-θb22,θb21,-θb22,θb21,0,0,0,0,0,3θb21},{θb22,0,0,0,θb21,θb21,θb22,θb21,θb22,0,0,0,0,0,-θb21},{1,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{1},{1},{1},{2,3,4,5,6,7,8,9,10,11},{1},{2}};systemcheck[system2]
Out[4]=
True
In[5]:=
θbar2={θb21,θb22};
In[6]:=
system3={{x31,x32,x33,x34,x35,x36},{u31,u32,u11,u12,y21,wg1,wg2,wg3,wg4,wg5,wg6},{y31,y32,z31,z32},{{1+θb31,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1+θb33},{1+θb31,-1+θb32,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1+θb34},{1-θb32,-1+θb31,0,0,1,0,1+θb33,1+θb34,0,0,1+θb31,0,0,0,0,0,1+θb31},{1+θb33,1+θb34,0,0,0,1,-1-θb34,1+θb33,0,0,-1-θb32,0,0,0,0,0,-1-θb32},{1-θb34,0,0,0,-1,1,0,0,1+θb33,0,1+θb34,0,0,0,0,0,1-θb34},{0,-1+θb33,0,0,-1,-1,0,0,0,1+θb34,0,0,0,0,0,0,-1+θb33},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}},{1,2},{1,2},{1,2},{3,4,5,6,7,8,9,10,11},{1,2},{3,4}};systemcheck[system3]
Out[6]=
True
In[7]:=
θbar3={θb31,θb32,θb33,θb34}
Out[7]=
{θb31,θb32,θb33,θb34}
In[8]:=
$Assumptions=$Assumptions&&assumeReal[Join[system1〚1〛,system2〚1〛,system3〚1〛,system1〚2〛,system2〚2〛,system3〚2〛,system1〚3〛,system2〚3〛,system3〚3〛]]&&assumePositive[Join[θbar1,θbar2,θbar3]]
Out[8]=
x11∈&&x12∈&&x13∈&&x14∈&&x15∈&&x21∈&&x22∈&&x23∈&&x24∈&&x31∈&&x32∈&&x33∈&&x34∈&&x35∈&&x36∈&&u11∈&&u12∈&&u21∈&&y31∈&&y32∈&&wg1∈&&wg2∈&&wg3∈&&wg4∈&&wg5∈&&wg6∈&&u21∈&&u31∈&&u32∈&&y11∈&&y12∈&&wg1∈&&wg2∈&&wg3∈&&wg4∈&&wg5∈&&wg6∈&&u31∈&&u32∈&&u11∈&&u12∈&&y21∈&&wg1∈&&wg2∈&&wg3∈&&wg4∈&&wg5∈&&wg6∈&&y11∈&&y12∈&&z11∈&&z12∈&&y21∈&&z21∈&&y31∈&&y32∈&&z31∈&&z32∈&&θb11>0&&θb12>0&&θb13>0&&θb21>0&&θb22>0&&θb31>0&&θb32>0&&θb33>0&&θb34>0
In[9]:=
{vrd,rds,hfg,trans,ezdcf}=
[{system1,system2,system3},Join[θbar1,θbar2,θbar3]];
 | EZDCFSS |
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
State transformation is xold = transformation.xnew
In[10]:=
vrd
Out[10]=
True
In[11]:=
rds
Out[11]=
{0,0,1,2,2}
In[12]:=
hfg//MatrixForm
Out[12]//MatrixForm=
1 | 1 | 0 | 0 | 0 |
-1 | 1 | 0 | 0 | 0 |
0 | 0 | θb21 | 0 | 0 |
0 | 0 | 0 | 1+θb33 | 1+θb34 |
0 | 0 | 0 | -1-θb34 | 1+θb33 |
In[13]:=
systemoperation[FullSimplify[ezdcf],{"View"}];
""