Wolfram Cloud Document

I have the following affine state space model

In[]:=

EqnsAffine={

′

vdc

[t]909.0909090909092`i0[t]-1.135578817864623`ic[t]p[t]+22.692646888513092`ic[t]q[t]-907.5386932783704`ic[t]p[t]S[t]-45.414786628553756`ic[t]q[t]S[t]+22.711576357285594`ic[t]p[t]ϕ[t]-453.8529377702641`ic[t]q[t]ϕ[t],

′

[t]-32.64705882352941`ic[t]-294.11764705882354`vcf[t]+0.36739314695620146`p[t]vdc[t]-7.341738699224823`q[t]vdc[t]+293.61545959006094`p[t]S[t]vdc[t]+14.693019203355625`q[t]S[t]vdc[t]-7.347862939121809`p[t]vdc[t]ϕ[t]+146.8347739844972`q[t]vdc[t]ϕ[t],

′

vcf

[t]444444.44444444444`ic[t]-444444.44444444444`is[t],

′

[t]-82.85714285714286`is[t]+2857.1428571428573`vcf[t]-2857.1428571428573`vs[t],

′

[t]100πq[t],

′

[t]-100πp[t]};

that I put into the AffineStateSpaceModel

In[]:=

AffineSS=AffineStateSpaceModel[EqnsAffine,{vdc[t],ic[t],vcf[t],is[t],p[t],q[t]},{S[t],ϕ[t],vs[t],i0[t]},{vdc[t],ic[t],vcf[t],is[t]},t]

Out[]=

vdc[t]	0.+ic[t](-1.13558p[t]+22.6926q[t])	ic[t](-907.539p[t]-45.4148q[t])	ic[t](22.7116p[t]-453.853q[t])	0	909.091
ic[t]	0.-32.6471ic[t]-294.118vcf[t]+0.367393p[t]vdc[t]-7.34174q[t]vdc[t]	293.615p[t]vdc[t]+14.693q[t]vdc[t]	-7.34786p[t]vdc[t]+146.835q[t]vdc[t]	0	0
vcf[t]	444444.ic[t]-444444.is[t]	0	0	0	0
is[t]	0.-82.8571is[t]+2857.14vcf[t]	0	0	-2857.14	0
p[t]	100πq[t]	0	0	0	0
q[t]	-100πp[t]	0	0	0	0
	vdc[t]	0	0	0	0
	ic[t]	0	0	0	0
	vcf[t]	0	0	0	0
	is[t]	0	0	0	0

a simulation with nonzero initial conditions and given inputs is

In[]:=

SimuAffine=OutputResponse[{AffineSS,{400,0,0,0,0,1}},{0.5,0,230Sin[2π50t],1},{t,0,0.5}];Plot[SimuAffine[[1]],{t,0,0.5}]

Out[]=

The response of the system is as expected.
To take advantage of the new predictive control functions of Mathematica I should discretize de system (right?), which I do

In[]:=

dt=1/50/1000;DTAffineSS=ToDiscreteTimeModel[AffineSS,dt]

Out[]=

vdck.	1 50000 0.+ick.-1.13558pk.+22.6926qk.+vdck.	1 50000 ick.-907.539pk.-45.4148qk.	1 50000 ick.22.7116pk.-453.853qk.	0	0.0181818
ick.	ick.+ 1 50000 0.-32.6471ick.-294.118vcfk.+0.367393pk.vdck.-7.34174qk.vdck.	1 50000 293.615pk.vdck.+14.693qk.vdck.	1 50000 -7.34786pk.vdck.+146.835qk.vdck.	0	0
vcfk.	444444.ick.-444444.isk. 50000 +vcfk.	0	0	0	0
isk.	isk.+ 1 50000 0.-82.8571isk.+2857.14vcfk.	0	0	-0.0571429	0
pk.	pk.+ 1 500 πqk.	0	0	0	0
qk.	- 1 500 πpk.+qk.	0	0	0	0
	vdck.	0	0	0	0
	ick.	0	0	0	0
	vcfk.	0	0	0	0
	isk.	0	0	0	0

50000

Everything looking good!
Let us simulate

np=35;u1=Table0.5,k.,0,np;u2=Table0.5,k.,0,np;u3=Table230Sin2π50k.dt,k.,0,np;u4=Table1,k.,0,np;SimuDT=OutputResponse[{DTAffineSS,{400,0,0,0,0,1}},{u1,u2,u3,u4}];ListPlot[SimuDT[[1,All]]]

Out[]=

$Aborted

Out[]=

In[]:=

SimuDT//Dimensions

Out[]=

{4,21}

In[]:=

ListPlot[SimuDT[[2,All]]]

Out[]=