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
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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