Transcript Chapter 10 Analog Controllers

Princess Sumaya Univ.
Electronic Engineering Dept.
3442
Industrial Instruments 2
Chapter 10
Analog Controllers
Dr. Bassam Kahhaleh
Princess Sumaya University
3442 - Industrial Instruments 2
10: Analog Controllers
Electronic Controllers
 Error Detector

Voltage difference.
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3442 - Industrial Instruments 2
10: Analog Controllers
Electronic Controllers
 Error Detector
Voltage difference.
 Floating Power Supply.

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10: Analog Controllers
Electronic Controllers
 Error Detector
Voltage difference.
 Floating Power Supply.

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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral … etc)

Two-Position (ON / OFF)
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Two-Position (ON / OFF)
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3442 - Industrial Instruments 2
10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Two-Position (ON / OFF)
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Two-Position (ON / OFF)
0
Vin > VSP
+ VSP
0
0
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Two-Position (ON / OFF)
VO
+
VSP
0
+VO
Vin + (R1/R2)VO < VSP
– [ Vin + (R1/R2)VO]
Vin < VSP – (R1/R2)VO
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (On / Off):
Level measurement in a tank:
Transducer output 0.2 V / m
Turn-on pump when level > 2 m
Turn-off pump when level < 1.5 m
Pump turn-on voltage = 5 V
VSP = 0.4 V
R1 / R2 = 0.02
VH = 0.4 V
VL = 0.3 V
VO = 5 V
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Three-Position
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (3-Position):
Level control in a tank:
Transducer output 0.45 V / m
Valve opening: 0 to 8 V
level < 2 m: valve = 20% open
2 m < level < 3 m valve = 65% open
3 m < level
valve = 100% open
Comparator output voltage = 5 V
VB = 1.6 V
R3 / R1 = 0.72
VSP1 = 0.9 V
VSP2 = 1.35 V
VOut = 1.6 V
VOut = 5.2 V
R3 / R2 = 0.56
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3442 - Industrial Instruments 2
10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Floating
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (Floating):
Trip Voltages: 2 & 4 V
3-Position Controller O/P: 0, ± 2 V
Integrator: 1 MΩ, 1 μF
t = 1 sec
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (Floating):
Assume an inverter is used at
the output of the integrator:
Vo 
1
1 sec
2V
-2 V
 Vc
dt
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Proportional
p  K P eP  pO
V o  G P Ve  V O
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (Proportional):
O/P Scaling: 0 – 10 V  0 – 100 %
Zero error controller O/P: 50 %
Proportional Band: 20 %
Error Range: 10 V
K
K
P
P


p
eP
 VO
 Ve
(

V 2  V min
V max  V min
(
r  b2
b max  b min
x100 %)  (
x100 %)  (
GP = 5
V 1  V min
V max  V min
r  b1
b max  b min
VO = 5 V
PB = 100 / KP
KP = 100 / 20 = 5
x100 %)
x100 %)
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Integral
t
p (t )  K I
e
P
( t ) dt  p I ( 0 )
0
t
VO  G I
V
e
dt  V O ( 0 )
0
1/RC
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (Integral):
Measurement range: 0.4 – 2 V
Output range:
0 – 6.8 V
KI = 4% / (%-min)
4
K
I

4%

1 % min
( 6 .8  0 ) V
100
1
( 2  0 . 4 ) V ( 60 sec)
100
GI 
0 . 272 V
0 . 96 V sec
 0 . 283 s
1
RC = 3.53 sec
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10: Analog Controllers
Electronic Controllers
 Single Mode (Proportional, Integral …)

Derivative
p (t )  K
VO  G D
de P
D
dt
dV e
dt
R2C
<< 1/R1C
R1 << 1/C
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10: Analog Controllers
Electronic Controllers
 Single Mode
Example (Derivative):
Valve Control
Flow surge: minimum period 2.2 sec
Input signal range: 0.4 – 2 V
Output range:
0.0 – 5 V
KD = 0.04% / (%/min)
0 . 04
K
D

0 . 04 % min
 100
1%
fmax = 0.45 Hz
max = 2.826 r/s
o = 28.3 r/s
( 5  0 ) V ( 60 sec)
1
( 2  0 .4 ) V
R1C = 1/28.3
100
GD 
0 . 12 V sec
0 . 016 V
 7 .5 s
R2C = 7.5 sec
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10: Analog Controllers
Electronic Controllers
 Composite Modes

Proportional-Integral (PI)
p  K P eP  K P K I
e
Vo  G P Ve  G P G I
R2/R1
1/R2C
P
dt  p O
V
e
dt  V O
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10: Analog Controllers
Electronic Controllers
 Composite Mode
Example (PI):
Input signal range: 0.4 – 2 V
Output range:
0.0 – 10 V
PB = 30 %
KI = 0.1% / (% - sec)
0 .1
K
I

GI 
0 .1 %

1 % sec
(10  0 ) V
100
1
( 2  0 . 4 ) V sec
100
0 . 01 V
0 . 016 V sec
 0 . 625 s
1
KP = 100 % / 30 %
GP 
(10  0 ) * 100 %
( 2  0 . 4 ) * 30 %
R2/R1 = 20.83
R2C = 1.6 sec
 20 . 83
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10: Analog Controllers
Electronic Controllers
 Composite Modes

Proportional-Derivative (PD)
p  K P eP  K P K D
de P
dt
Vo  G P Ve  G P G D
R2/(R1+R3)
 PO
dV e
R3C
R1//R3 << XC
dt
 VO
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10: Analog Controllers
Electronic Controllers
 Composite Mode
Example (PD):
Input signal range: 0.4 – 2 V
Output range:
0.0 – 5 V
KP = 5 % / %
KD = 0.08% / (%/min)
Minimum period: 1.5 sec
0 . 08
K
D

0 . 08 % min
 100
1%
0 . 24 V sec
0 . 016 V
 15 s
(5  0 ) * 5 %
( 2  0 .4 ) * 1 %
 15 . 625
R2/(R1+R3)= 15.625
fmax = 0.67 Hz
max = 4.187 r/s
o = 41.9 r/s
( 5  0 ) V ( 60 sec)
1
100
GD 
GP 
( 2  0 .4 ) V
(R1//R3)C = 1/41.9
R3C = 15 sec
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10: Analog Controllers
Electronic Controllers
 Composite Modes

Proportional-Integral-Derivative (PID)
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10: Analog Controllers
End of Chapter 10