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18
S.Brock,K.Zawirski
changesofangularposition
∆
θ
i
andtimeperiod
∆
T
i
aremeasured,andnextonthat
basethevalueofspeediscalculatedasanaveragevalueinmeasuredperiod:ω
i
=
∆
θ
i
/
∆
T
i
.
Accuracyofspeedcalculationisdeterminedbyresolutionandaccuracyofen-
coderandmoreoveraccuracyoftimemeasurement.Encoderresolutionisde-
scribedbynumberofcalculatedpulsesperonerevolutionN,howeverencoder
accuracyisdeterminedbyanerrorofpulsesdistributioninonerevolutionδθ.
Usuallyanrelativeerrorisdeterminedδθ
%
=δθ/
∆
θinreferencetotheanglebe-
tweentwosuccessiveimpulses
∆
θ=1/N.
Minimumvalueofmeasurementrangeislimitedbyacceptablemaximumsam-
plingtimeofdigitalcontrolsystem.Foritsdeterminationitcanbeassumedacri-
terionofacceptablechangeofrotationalspeedofanalyseddrive.Itisassumedthat
duringonesamplingperiod,determinedbytimedistancebetweentwosuccessive
encoderimpulses,thespeedmustnotchangemorethan
∆ω
=b
⋅ω
asaresultofload
torquechange
∆
m=a
⋅
M
N
.Aconclusionisthatmaximumvalueofsamplingperiod
T
max
mustbeequal(1)
T
max
=
M
2
π
N
⋅
⋅
J
a
⋅
⋅
b
N
(1)
whereaandbarearbitraryassumedcoefficients.Inpracticethesevaluesareas-
sumedasa=0.1andb=0.5.Insuchawaytheminimumvalueofmeasuredrota-
tionalspeedisdetermined
ω
min
≥
N⋅
1
T
max
(2)
Encoderaccuracydeterminesthemaximumcorrectvalueofmeasuredspeedin
controlsystem.Inthepaperwasassumedacriterionofreferencetorqueripple
limitation.Thereferencetorqueisanoutputsignalofspeedcontroller.Forpre-
sentedanalysisoneassumedaproportionalcontrollerwithgaincoefficientK
p
.
M
z
=
K
p
⋅
(
ω
zad
−
(
ω
±
δω
)
)
(3)
Agoodstartingvalueforcontrollersettingadjustmentcanbedeterminedasa
functionofdelayinacontrolloopanddrivedynamicproperties(4).
K
p
=
0
,
5
⋅
J
⋅
ω
⋅
N
(4)
Insuchacaseripplesofreferencetorque
δ
M
z
involvedbyspeedmeasurement
errors
δ
ω
,shouldbelimited
