Tydgebied Spesifikasies / Time Domain Specifications
ω n2
Vir die oordragfunksie / For the transfer function: G (s ) =
s 2 + 2ζω n s + ω n2
met / with: σ = ζω n
en / and ωd = ωn 1 − ζ 2
en / and ζ = sin θ
1 .8
Stygtyd / Rise Time : tr ≈ (10%-90%)
ωn
π
Piektyd / Peak Time : tp =
ωd
− πζ
1−ζ 2
ln 2 M p
Oorskiet / Overshoot : Mp =e ; ζ =
π 2 + ln 2 M p
3
ts = (5%)
σ
4
Wegsterftyd / Settling Time : ts = (2%)
σ
4.6
ts = (1%)
σ
Overshoot for Additional Zero Rise Time for Additional Pole
Bladsy 1 - Page 1
, Frekwensiegebied Spesifikasies / Frequency Domain Specifications
1 1
Resonante Piek / Resonant Peak : Mr = ≈
2ζ 1 − ζ 2 2ζ
Fasegrens / Phase Margin: PM ≈ 100ζ
Wortellokus / Root Locus
180° + 360°(l − 1)
φl = , l = 1,2,..., n − m
Asimptote / Asymptotes: n−m
α=
∑ pi − ∑ z i
n−m
φdep = ∑ψ i − ∑ φi − 180°
Wegtrek- en aankomshoeke / ψ arr = ∑φ − ∑ψ + 180°
i i
Departure and arrival angles: qφl , dep = ∑ψ − ∑ φ − 180° − 360°(l − 1)
i i
qψ l , arr = ∑ φ − ∑ψ + 180° + 360°(l − 1)
i i
Moontlike inbreek/uitbreekpunte / da ( s ) db( s ) b( s )
b( s ) − a(s) = 0 where Gol ( s ) =
Possible break-out/break-in points: ds ds a( s)
Kompenseerders / Compensators
Ts + 1
D( s) = α <1
αTs + 1
1 − sin φ max 1−α
Voorloop / Lead: α= sin φmax =
1 + sin φ max 1+ α
1
ωmax =
T α
Ts + 1
Naloop / Lag: D( s) = α α >1
αTs + 1
Ziegler-Nichols Reëls / Ziegler-Nichols Tuning Rules
Bladsy 2 - Page 2
ω n2
Vir die oordragfunksie / For the transfer function: G (s ) =
s 2 + 2ζω n s + ω n2
met / with: σ = ζω n
en / and ωd = ωn 1 − ζ 2
en / and ζ = sin θ
1 .8
Stygtyd / Rise Time : tr ≈ (10%-90%)
ωn
π
Piektyd / Peak Time : tp =
ωd
− πζ
1−ζ 2
ln 2 M p
Oorskiet / Overshoot : Mp =e ; ζ =
π 2 + ln 2 M p
3
ts = (5%)
σ
4
Wegsterftyd / Settling Time : ts = (2%)
σ
4.6
ts = (1%)
σ
Overshoot for Additional Zero Rise Time for Additional Pole
Bladsy 1 - Page 1
, Frekwensiegebied Spesifikasies / Frequency Domain Specifications
1 1
Resonante Piek / Resonant Peak : Mr = ≈
2ζ 1 − ζ 2 2ζ
Fasegrens / Phase Margin: PM ≈ 100ζ
Wortellokus / Root Locus
180° + 360°(l − 1)
φl = , l = 1,2,..., n − m
Asimptote / Asymptotes: n−m
α=
∑ pi − ∑ z i
n−m
φdep = ∑ψ i − ∑ φi − 180°
Wegtrek- en aankomshoeke / ψ arr = ∑φ − ∑ψ + 180°
i i
Departure and arrival angles: qφl , dep = ∑ψ − ∑ φ − 180° − 360°(l − 1)
i i
qψ l , arr = ∑ φ − ∑ψ + 180° + 360°(l − 1)
i i
Moontlike inbreek/uitbreekpunte / da ( s ) db( s ) b( s )
b( s ) − a(s) = 0 where Gol ( s ) =
Possible break-out/break-in points: ds ds a( s)
Kompenseerders / Compensators
Ts + 1
D( s) = α <1
αTs + 1
1 − sin φ max 1−α
Voorloop / Lead: α= sin φmax =
1 + sin φ max 1+ α
1
ωmax =
T α
Ts + 1
Naloop / Lag: D( s) = α α >1
αTs + 1
Ziegler-Nichols Reëls / Ziegler-Nichols Tuning Rules
Bladsy 2 - Page 2
