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Lecture slides for ELEN90055 prepared by Michael Cantoni (c) 2011, 2012
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
http://www.segwaysoutherncross.com/
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
q o (m3/sec)
x (m)
q o
q i
x(t) = x(0) + 1
A
t
0
q (τ ) dτ
q
q i (m3/sec)
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
q o (m3/sec)
x (m)
q o
q ix
x(t) = x(0) + 1
A
t
0
q (τ ) dτ
q
q i (m3/sec)
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
τ dω
dt =
1
J τ
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
τ dω
dt =
1
J τ
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
desired
delay
clock distribution manager
system
clock
SUBSYS1
SUBSYS2
SUBSYS3
lossless tx-line delay τ1
lossless tx-line delay τ2
lossless tx-line delay τ3
back matched
source termination
VS
VS
VS
CLKOUT
CLKOUT
CLKOUT
delay compensator
delay compensator
delay compensator
CLK
CLK
CLK
τM
τM
τM
+ _ +_
-1
_ +
R
R
C
OPAMP
COMPL COMPH
VL VH
CLK
CLKM
VM
τD
VS
CLKOUT
P
Q
D
U
PHASE DETECTORLOSSLESS
TX-LINE
WITH
DELAY τ
BACK-MATCHED
SOURCE
TERMINATION
DELAY COMPENSATOR
τM
VOLTAGE CONTROLLED DELAY (VCD)
VCD
V0
0
0
-V0
VD
V0
0
τ
ref
V D
φD
φ = φD + τ
φ
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
desired
delay
clock distribution manager
system
clock
SUBSYS1
SUBSYS2
SUBSYS3
lossless tx-line delay τ1
lossless tx-line delay τ2
lossless tx-line delay τ3
back matched
source termination
VS
VS
VS
CLKOUT
CLKOUT
CLKOUT
delay compensator
delay compensator
delay compensator
CLK
CLK
CLK
τM
τM
τM
+ _ +_
-1
_
+
R
R
C
OPAMP
COMPL COMPH
VL VH
CLK
CLKM
VM
τD
VS
CLKOUT
P
Q
D
U
PHASE DETECTORLOSSLESS
TX-LINE
WITH
DELAY τ
BACK-MATCHED
SOURCE
TERMINATION
DELAY COMPENSATOR
τM
VOLTAGE CONTROLLED DELAY (VCD)
VCD
V0
0
0
-V0
VD
V0
0
τ
φref
V D
D
φ = φD + τ
φ
sk+1 = sk ek
vk = Apd · skvcd
τ
ek vk
φk
φref
sk+1 = (1−A)sk
+ (φref − τ )
ek+1 = φref − τ − A · sk+1
= (1 −A) · (φref − τ − A · sk)
= (1 −A)ek
ek = φref − φkA
.= Avcd · Apd
en = (1
−A)
n
e0 |
1−A|< 1
|1−A|
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
s
R1
l o
V i V o
f
V s
A
β
β = R2/ R1 + R2
l
R1
s i
o
f
· i
V i = V s − V f
V o = A · V i
V f = β · V o
V o = A · V s − β · V o
V o =
A
1 + β · A
· V s
for large A≈
1
β · V s
R2
R2
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
ϕ
ϕ
http://www.jpk.com/dna-molecule-on-mica.315.en.html
http://www.nanolab.polimi.it/
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
di do
ye u
n
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
yr
f ◦f −1◦
u
r = y = f u+ d ⇐= u = f −1r − d
f ◦ f −1◦
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
y
u
h◦
f ◦
e
ˆy
u = hr − f u =⇒ r − f u = h−1u
=⇒ u = f −1r − h−1ufor high-gain h
≈ u = f −1r =⇒ y ≈ r
yu
ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
http://www.rubicon.com.au/
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ELEN90055 Control Systems: Part IM.Cantoni (c) 2011, 2012
