Transcript 01_1 - Ferdowsi University of Mashhad

‫بسم هللا الرحمن الرحيم‬
Advanced Control
Lecture 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)
Step
Change
Record
m(t)
Final
Control
Element
Process
Sensor/
Transmitter
c(t)
first order plus dead tim e:
C ( s ) K e t 0 s

M ( s)  s  1
Process Gain:
c s
K
m
FOPDT Model
Fit 1 :
FOPDT Model
Fit 2 :
FOPDT Model
Fit 3 :
3
  (t2  t1 ) ,
2
t0  t 2  
Control Valve
m(t)
vp(t)
Control
Valve Action
Cv(t)
Control Valve
Characteristics
f(t)
Control valve
Capacity
Control Valve
1. Control Valve Action
•
Fail-Closed (FC) or Air-to-Open (AO) :
•
Fail-Open (FO) or Air-to-Close (AC) :
vp (t ) 
m(t )
100
vp (t )  1 
m(t )
100
Control Valve
2. Control Valve Characteristics
•
Linear
•
Quick-opening
•
Equal percentage
Cv (t )  Cv,max vp(t )
Cv (t )  Cv,max  vp(t )1
Rangeability
parameter
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:
gpm
Gas Flow:
scfh
Where
psi
pv (t )
f (t )  Cv (t )
Gf
Critical flow factor (0.6-0.95)
f s (t )  836Cv (t )C f
Inlet temperature oR
y
1.63 pv
Cf
p1
Inlet pressure psia
p1
( y  0.148y 3 )
GT
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:
Kc
de(t )
m(t )  m  K c e(t ) 
e(t )dt  K c D
I 
dt


M ( s)
1

Gc ( s) 
 K c 1 
  D s 
E ( s)
 Is

•
Parallel PID:
•
Series PID:

M ( s)
1
 Ds 
Gc ( s) 
 K c 1 


E ( s)

s

s

1
I
D



M ( s)
1    D s  1 
 

Gc ( s) 
 K c 1 
E ( s)
  I s    D s  1 
Range
0.05 to 0.2
PID Control
3. Reset Windup
m(t )  m  K c e(t ) 
Kc
I
 e(t )dt  Kc D
de(t )
dt
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
Tracking Time Constant
Td < Tt < Ti
Back-Calculation with internal tracking
PID Control
5. Back Calculation
External tracking signal
Back-Calculation with external tracking
PID Control
5. Proportional and Derivative Kick
m(t )  m  K c e(t ) 
Kc
I
 e(t )dt  Kc D
Proportional Kick
de(t )
dt
Derivative Kick
Two Degrees of Freedom or ISA - PID
ded (t )
I
dt
Where e p  bysp  y, ed  cysp  y, e  ysp  y
m(t )  m  K c e p (t ) 
Range: 0-1
Kc
 e(t )dt  Kc D
Range: 0-1, Commonly zero
PID Control