ue aae 09 industrial controllers -...
TRANSCRIPT
1
Industrial controllers
Rferences
• U. Tietze, Ch.Schenk, Electronics Circuits – Handbook for Design and Applications, Springer,2008
• Advertisement materials and Application notes of:
– Linear Technology,
– Analog Device,
– Texas Instruments,
– National Semiconductors
– NEV Corporation
Electronic Controllers
The purpose of a controller is to bring a physical quantity to a predetermined value and hold it at this value
2
Underlying Principles
Where As is the gain of the controlled systemHence, the conytrolled variable is:
ZAA
AW
AAAA
Xsc
s
sc
sc
++
+=
11
)()( ZYAsXandXWAcY +=−=
P-controller
Bode plot of a system with a P-controller
Step response as a function of the
phase margin
Optimum controller
dBdBAporAs
ApAc dB 177lg20714.0
11 =⋅=====
771 =⋅== AsApg
%5.1271
1
1
1 =+
=+
=−gW
XW
The low-frequency limit value of the loop gain is therefore
This gives us a relative deviation of
3
PI-ControllerBode plot of a system
with a PI-Controller
PI-Controller
Block diagram of the PI-Controller Bode plot of the PI-Controller
PI-Controller
PI-Controller
211
2
2
1;
RCf
R
RAp I π
=−=
4
PI-Controller
Error signal for the P-controller sand the PI-controller with an optimum value of fI
PID-Controller
Block diagram of the PID-controllerBode plot of the PID-controller
PID-Controller
Bode plot of system and a PID-controller
−+=++=
ωω
ωω
ωτωτ I
DID jAp
jjApAc 1
1
WhereI
ID
D Apfand
Apf
τππτ 2
1==
5
PID-Controller
Comparison of the transient behavior of
a system with PI-controller and with a
PID-controllerPID-controller
1211
2
2
1;
2
1;
RCf
RCf
R
RAp
DDI ππ
==−=
The PID-Controller withAdjustable Parameters
PID-controller with decoupled parameters
DDDI
P
RCf
RCf
R
RAp
ππ 2
1;
2
1;
111
===
The PID-Controller withAdjustable Parameters
oscIoscDosc TTAcAp 10≈≈≈ ττ
6
Control of nonlinear systemStatic Nonlinearity
Linearization of a system that has static nonlinearity
Control of nonlinear systemDynamic Nonlinearity
Transient behavior of the
controlled variable for a
limited system slew rate Slew rate limiter for the
reference variable.RC
V
dt
dV max0 =
Phase-Locked Loop
Principle of the phase-locked loop (PLL)
7
PLL capture and hold frequency
Input Frequency
Ph.Det. signal
HOLD
CAPTURE
Phase-Locked Loop
ϕ
ϕαkkAc
ff
f
01 −=−
m
f
m
f
f jf
kk
j
kk
V
VAs ϕϕϕ
ωπ
===2
mjωωϕ 1=
∆
∫ ∫∫ ∆=−=t tt
tdtdtd0 0
1
0
2~~~ ωωωϕ
ϕαϕ
α −==k
V
tt mωωω cos)( ∆=∆
tt mm
ωω
ωϕ sin)(∆=
Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector
A sample-and-hold circuit used
as a phase detector Voltage weveform in the phase detector
8
PLL – SH as Ph.Det. - dynamics
ϕϕ sin1̂VV = radVV /1̂ϕϕ ≈
radVd
dVk /1̂==
ϕϕ
ϕ
2221 /
1ffjTj mm eVekk πω
ϕϕ−⋅− ==
2/
1̂
ffjm
f
m
f
mejf
Vk
jf
kkAs π
ϕ ==
2
1
2
ˆ
f
fand
f
Vk
V
VAs m
mm
f
f
ππϕϕ −−===
PLL with a sample-and-hold circuit as phase detector
1;2
1;
2121
2 ==+
= II ARC
fRR
RAp
π
PLL – SH as Ph.Det. - parameters
Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector
Mean absolute value of
the output voltage of a
multiplier for simusoidal
input voltages of
amplitude U
Application of a
synchronous demodulator
for the measurement of
noisy signalsOperation of a
synchronous demodulator
9
Phase-Locked LoopSynchronous Detector as a Phase Detector
PLL with a multiplier as
phase detector for
frequency demodulation
Transconductance multiplier as a switch
Transconductance multiplier as a switch
10
Transconductance multiplier as a switch
Transconductance multiplier as a switch
Multiplying circuit
φ
Gdy φ=0
VCC VCC
11
Synchronous AM detector
Gdy φ=0 To nie jest detekcja szczytowa,
a średnia
VCC VCC
AM synchronous detector
Det. fazy Filtr VCOfin
fout
VCC VCC
Phase-Locked LoopFrequency-Sensitive Phase Detector
Phase detector with
memory for sign of the
phase shift
Input and output signals
of the phase detector
Transfer characteristic of
the phase frequency
detector
12
Phase-Locked LoopPhase Detector with Extensive Range
Phase-Locked LoopPhase Detector with Extensive Range
Detection characteristic of
the phase detector
Frequency synthesis
n
f
k
f outin =
Phase Det. Filtr VCO:k
:n
fin
foutfin/k
fout/n
inout fk
nf =
13
Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector
Phase-Locked LoopSample-and-Hold Circuit as a Phase Detector
PLL applications
• AM Demodulation
• Synchronous detection (LockIn Amp)
• FM, PM demodulation
• Frequency synthesis
• Synchronous telekommunication
14
PLL IC - 4046
4046 phase detector I
4046 phase comparator II
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4046 features
Feature Detektor I (exor) Detektor II
Lack of input signal fwyj=f0 fwyj=fmin
Phase shift on output 90deg for f00 to 180 in the range of 2fT
0deg
Harmonic synchronization synchronize No synchronization
Immunity t noise high low
2fT (lock range) fmax - fmin
2fC (capture range) fC < fT (depends on filter) fC= fT
FM detector
ktuftf
ftmftf
ftmftf
out
out
in
⋅+=∆⋅+=
∆⋅+=
)()(
)()(
)()(
0
0
0
Det. fazy Filtr VCO
fin(t) fout(t)
)()( tmk
ftu
∆=
)()( tmk
ftu
∆=
4046 as FM demodulator
FM signal
10kHz
Follower
16
4046 as AM demodulator
multiplier
PLL IC LM565 (up to 500kHz)
LM565
17
NE564
NE564 (up to 50MHz)
NE567
18
NE567
ADF4360-7
(350-1800MHz)
ADF4360-7 (350-1800MHz)
19
ADF4360-7
generator 500MHz
Summary
• P, PI, PID controllers
– parameters adjustment
• PLL
– Principle of operation
– examples of VCO, filters, phase detectors
– Applications – frequency synthesis, detectors
test questions• What is the practical algorithm for PID controller
parameters adjustment ?
• What is the principle of operation of PLL ?
• What is the principle of operation of PLL as FM
detector ?
• What is the principle of operation of PLL as AM
synchronous detector ?
• What is the principle of operation of PLL as
frequency synthesizer ?