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