Download - Basic Concepts
Basic Concepts
Block diagram representation of control systems
Transfer functions Analysis of block diagrams P, PI and PID controllers ( Continuous
and discrete forms) Stability of feedback control systems
PID:Process Instrumentation Diagram
TT101
temperaturetransmitter
Thermocouple
TC101
temperaturecontroller
cooling waterinlet
cooling waterout
Feed
electronictransmissionline
ProductManualValve
sensor
pneumaticline
Automatic ControlValve
Block Diagram of Feedback Control System
CONTROLVALVE
TANKCONTROLLER
TRANSMITTER
WATERFLOW
VALVETset
SETPOINTERROR
ACTUATOR PROCESS
TEMPERATURE
Tm (MEASURED VARIABLE)
SIGNAL TO
CONTROLLEROUTPUT
MANIPULATEDVARIABLE
CONTROLLERVARIABLE
Common Signals
Name Function, f(t) Laplace transform, F(s)
Unit step function 0 0 ttu
0 1 ttu s
1
Unit impulse function(Diracdelta function)
0 , tt 0 0 tt
1
Ramp function 0 0 ttr
0 tkttr 2s
k
Sine function wttx sin 22
s
Properties of Laplace Transform
P r o p e r t yD e s c r i p t i o n
L i n e a r i t y P r o p e r t y
co n stan t w h ere
11
2121
K
tfLktfkL
tfLtfLtftfL
T i m e D e l a y sFe
tfLetfLs
s
D i f f e r e n t i a t i o n ofsFsd t
tfdL
I n t e g r a t i o n sFs
d ttfLt
o
1
F i n a l V a l u e T h e o r e m lim t
f t lim s 0
s F s
p r o v i d e d t h e l i m i t o n t h e l e f t
h a n d s i d e e x i s t s .
Transfer functions
0)0(),()()(
121 xtubtxadt
tdxa (BC.3)
subsxa0xsxsa 121
su1s
K
suasa
bsx
21
1
(BC.4)
1s
KsG
(BC.5)
Proportional Integral Derivative (PID) Control
dt
de dt e te K tm D
Ic
1
)()1
1()( sess
Ksm DI
c
)()1
11()( se
s
s
sKsm D
Ic
Common Transfer Functions
0)0(',0)0(,22
22 xxKu x
dt
dx
dt
xd
Second-Order Transfer Functions
su s s
sx
1222
Stability and Pole Location
Imaginary Axis
Real Axis
Oscillatory growth
Exponential growth
Oscillatory growth
Expnential Decay
Oscillatory Decay
Oscillatory Decay
Sustained Oscillations
Sustained Oscillations
"For a transfer function to be stable, all its poles must lie to the left of the imaginary axis in the com-plex plane, i.e. in the left half plane (LHP)".
Stability of Closed Loop SystemsCONTROLLER ACTUATOR PROCESS OUTPUT
TRANSMITTERMEASURED VARIABLE
yset + e(s) m(s) q(s) y(s) sGc
G (s)
sGv sGp
sGT sym
-
01 Tvcp GGGG
setTvcp
pvcy
GGGG
GGGy
1
Root Locus
Table BC.4 Table of roots of the character’s equation for various valves of cK
Kc root1 root2 root30.10.20.390.61.010.020.030.060.0100.0
-3.0467-3.0880-3.1564-3.2212-3.3247-4.3089-4.8371-5.2145-6.0000-6.7134
-1.8990-1.7909-1.4218 - 0.0542i-1.3894 - 0.3442i-1.3376 - 0.5623i-0.8455 - 1.7316i-0.5814 - 2.2443i-0.3928 - 2.5980i0 - 3.3166i0.3567 - 3.9575i
-1.0544-1.1211-1.4218 + 0.0542i-1.3894 + 0.3442i-1.3376 + 0.5623i-0.8455 + 1.7316i-0.5814 + 2.2443i-0.3928 + 2.5980i0 + 3.3166i0.3567 + 3.9575I
CONTROLLER TUNING)()
)1(
111()( ses
ssKsm D
Ic
0
0 .2
0 .4
0 .6
0 .8
1
1 .2
1 .4
0 1 2 3 4 5 6
N e w s e t p o i n t
O v e r s h o o t , AR i s e t i m e , T r
B
e ( t ) , E r r o r i n c o n t r o l
I S E e d t
D e c a y R a t i o B A
2
/
4PeriodTime Rise
Penod
eRatioDecay
eOvershoot
2
12
1
12
2
2
12
122
ss
sG