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Applicationofdigitalfiltersinactiveserialcompensation...
Fig.2.Activeseriescompensatorcontrolstructure
Fig.3.Adaptivecontrolstructurebasedondigitalfilterunit
23
Anunknownsystemisinthisinstancethenetworknodealongwithasourceof
theadditivevoltage.Theweightcoefficientsofadaptivefilterarecalculatedbased
onspecificadaptivealgorithm[7,8].Theadaptivealgorithmcalculatesanunknown
discretesequenceofcontrolsignal.Thiscalculationsarebeingmadethroughthe
optimizationprocess,whichincludessteeringquality.Inmostcasesitisimpossible
toachieveanoptimalsequence-itdependsonassumedsteeringqualityfactor.
Oneofthemostcommonrealizationofadaptivealgorithms,usedfordevice
control,areWienerfiltersandKalmanfilterstechniques[7,8].
TheWienerfiltertheoryisbasedonsocalledtransversalfilter[7,8,10].A
transversalfiltercontains
N
−
1
delayingunits.Aninputsignalis
u
(n
)
,whichis
currentvalueofinputsignalrelatedtodiscreettime.Remainingsamplesare
rememberedbyfilterpriorvaluesofthatsignal.Thesesamplesarebeing
multiplicatedbyrelatedtothemweight
h
1
,
h
2
,
K
,
h
N
.Sumoftheseproductsgives
anansweroffilter:
N
y
ˆ
(
n
|
U
n
)
=∑
h
k
u
(
n
−
k
+
1
)
=
h
T
u
()
n
(1)
k
=1
where:
y
ˆ
(
n
|
U
n
)
isanestimateofsignal,
h
T
=
[
h
1
,
h
2
,
K
,
h
N
]
isavectoroffilter
weightcoefficients,and
u
(n
)
-aninputsignalsamplesvector.
U
n
describes
u
(n
)
samplesvectorspace.
Filteroutputgives
y
ˆ
(
n
|
U
n
)
signaltreatedasestimateofreferencesignal
