LINEAR CONTROL SYSTEMS Ali Karimpour Associate Professor Ferdowsi University of Mashhad.
بسم الله الرحمن الرحيم Advanced Control Lecture two Mohammad Ali Fanaei Dept. of...
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Transcript of بسم الله الرحمن الرحيم Advanced Control Lecture two Mohammad Ali Fanaei Dept. of...
بسم الله الرحمن الرحيم
Advanced ControlLecture two
Mohammad Ali Fanaei
Dept. of Chemical Engineering
Ferdowsi University of Mashhad
Reference: Smith & Corripio, “Principles and practice of automatic process control, 3 rd ed., Wiley, 2006
Empirical Modeling (Step Testing)
Final Control Element
Final Control Element
ProcessSensor/
Transmitter
Step Change
Record
m(t) c(t)
1)(
)(
:
0
s
eK
sM
sC
timedeadplusorderfirst
st
Process Gain:
m
cK s
FOPDT Model
Fit 1:
FOPDT Model
Fit 2:
FOPDT Model
Fit 3: 2012 ,)(2
3tttt
Control Valve
Control Valve Action
Control Valve Characteristics
Control valve Capacity
m(t) vp(t) Cv(t) f(t)
Control Valve
1. Control Valve Action
• Fail-Closed (FC) or Air-to-Open (AO) :
• Fail-Open (FO) or Air-to-Close (AC) :
100
)()(
tmtvp
100
)(1)(
tmtvp
Control Valve
2. Control Valve Characteristics
• Linear
• Quick-opening
• Equal percentage
)()( max, tvpCtC vv
1)(max,)( tvp
vv CtC
Rangeabilityparameter
Control Valve
3. Control Valve Capacity
The flow in U.S. gallons per minute (gpm) of water that flows through a valve at a pressure drop of 1 psi across the valve
Liquid Flow :f
vv G
tptCtf
)()()(
gpm
psi
Gas Flow: )148.0()(836)( 31 yyGT
pCtCtf fvs
scfh
Critical flow factor (0.6-0.95) Inlet pressure psia
Inlet temperature oR
1
63.1y
p
p
Cv
f
Where
PID Control
1. Action of Controller
If the action is not correctly selected, the controller will not control
• Reverse action (increase/decrease)
PID Control
• Direct action (increase/increase)
To determine the action of a controller, the engineer must know:
1.The process requirement for control
2.The fail-safe action of the control valve
PID Control
2. Type of PID Controller
• Ideal PID:
• Parallel PID:
• Series PID:
dt
tdeKdtte
KteKmtm Dc
I
cc
)()()()(
ss
KsE
sMsG D
Icc
1
1)(
)()(
1
11
)(
)()(
s
s
sK
sE
sMsG
D
D
Icc
1
111
)(
)()(
s
s
sK
sE
sMsG
D
D
Icc
Range0.05 to 0.2
PID Control
3. Reset Windup
dt
tdeKdtte
KteKmtm Dc
I
cc
)()()()(
PID Control
4. Reset Feedback (RFB)
Internal Reset Feedback
PID Control
4. Reset Feedback (RFB)
PID Control
4. Reset Feedback (RFB)
External Reset Feedback
PID Control
5. Back Calculation
Back-Calculation with internal tracking
Tracking Time ConstantTd < Tt < Ti
PID Control
5. Back Calculation
Back-Calculation with external tracking
External tracking signal
PID Control
5. Proportional and Derivative Kick
dt
tdeKdtte
KteKmtm Dc
I
cc
)()()()(
yyeycyeybyeWheredt
tdeKdtte
KteKmtm
spspdspp
dDc
I
cpc
,,
)()()()(
Proportional Kick Derivative Kick
Range: 0-1 Range: 0-1, Commonly zero
Two Degrees of Freedom or ISA - PID
PID Control