some typical control loops

Prof. Cesar de Prada, ISA, UVA 1

Some typical control loops

Prof. Cesar de Prada Dpt. Systems Engineering and Automatic Control

Univ. of Valladolid


Outline

• Flow control • Level Control • Pressure control • Temperature control


q a

Flow control

FC w u

Centrifugal pump

Flowmeter Control Valve

Pump, valve: sizing, placement

Flowmeter: Type, range

Right order: Pump, flowmeter, valve

Important element: valve selection


Sizing From a design point of view, control valves with a large Cv should be chosen, as they present a lower pressure drops, allowing the use of smaller pumps. Nevertheless, the use of smaller control valves gives wider flow changes making the process more controllable.

q

∆pv

a

∆p0 ∆pb

u


Example Design specifications

Flow: qs = 100 gpm Pressure drop in the line ∆pL = 40 psi Total Pressure difference ∆p0 = -150 psi density = 1 desired valve opening = 50%

Case 1: ∆pv = 20 psi Case 2: ∆pv = 80 psi

q

∆pv

a

∆p0 ∆pb

u Lvb0 pppp ∆+∆=∆+∆

Higher pressure in the line end


Example Case 1: ∆pv = 20 psi Case 2: ∆pv = 80 psi ∆pb = 150+40+20= 210 ∆pb = 150+40+80= 270

q

∆pv

a

∆p0 ∆pb

u 36.22C 72.44C

80C5.0100 20C5.0100

paCq

2v1v

2v1v

vvs

====

ρ∆

=

Lvb0 pppp ∆+∆=∆+∆


Range of operation Assuming that ∆pb is constant Case 1: a=1 , a=0.1 Case 2: a=1, a=0.1

gpm2.24q gpm3.33q

100q40120C1.0q

100q4060C1.0q

gpm141q 115gpmq

100

q40120C1q 100q4060C1q

120150270pp 60150210pp

paCq pppp

min21min

22min

2v2min

21min

1v1min

max21max

22max

2v2max

21max

1v1max

0b0b

vvLb0v

==

−=

−=

==

−=

−=

=−=∆+∆=−=∆+∆ρ

∆=∆−∆+∆=∆

The smaller valve provides a wider range of operation in q


Design

q

qpppCaq

q

qpppC1q

2

s

minLsb0vminmin

2

s

maxLsb0vmax

∆−∆+∆=

∆−∆+∆=

Size the pump (∆pb) and valve Cv as a function of the maximum and minimum flows required for the operation of the process, taking into account the design flow qs and pressures ∆p0, ∆pLs solving:


Design

1q

qa if equations for this existssolution Amin

maxmin <

Otherwise, use a split range control structure

q


q

∆pv

a h

∆p0 ∆pb

]ghq)AfL

Ca1(p[

LA

tdqd

)q(p Avq ALm qCa1p

gAhvAfLpA)pp(Atd

mvd

222

v2

20

22b

22v

2v

2vb0

−++β−αω+ρ

∆=

β−αωρ=∆=ρ=ρ=∆

ρ−ρ−∆−∆+∆=

Flow control

u


Linearized model

aK)p(Kqtdqd

]aqCa2)p([

q2)AfL

Ca1(

1

qtdqd

q2)AfL

Ca1(

LA

1

]aqCa2qq2)

AfL

Ca1()p([

LA

tdqd

]ghq)AfL

Ca1(p[

LA

tdqd

201

0

22v

30

022

v2

022

v2

0

22v

30

22v

20

222

v2

20

∆+∆∆=∆+∆

τ

∆

ρ+∆∆

++βρ=

=∆+∆

++β

∆

+∆

++β−ρ∆∆

=∆

−++β−αω+ρ

∆=


Changes in the operating point

02

2v

22v

22

022

v2

201

)A

CfLa1Ca(a

qK q2)

AfL

Ca1(

LA

1

aK)p(Kqtdqd

++β=

++β=τ

∆+∆∆=∆+∆

τ

q

t

τ grows when the opening of the valve increases K2 decreases when the opening of the valve increases


Linearized model

K2 decreases when the opening of the valve increases

a

u 100 %

A equal percentage valve compensates the change in gain

1

0

0 % uKa

tdad

vv ∆=∆+∆

τ

Valve dynamics must be taken into account very often. Let’s assume that it is approximated by:

q a

u


Block diagram

u %

+ -

W ( ) ( )1s

K1s

K 2

v

v

+τ+τ

Q

( )1sK1

+τ

∆P0

+ ( )sT

1sTK

i

ip +

Kp Ing /%

The transmitter dynamic can be neglected Choose the transmitter gain according to the maximum admissible flow


Field installation

q

The use of the manual valves allows to remove the control valve for repair without stopping the flow to the process

q

A A

A

C

C C


q a

Flow control

FC w u

PI Fast and noisy process Low Kp to decrease the noise effect (0.6 %/%) Low Ti to cancel soon the steady state error (0.1 min)


Positive Displacement pumps Shaft,. Membrane,… Alternating compressors…


q

FC w

u

Positive Displacement pumps Shaft,. Membrane,… Alternating compressors…


Minimum flow in the pump

q a

FC

w

u

FT

FC Fmin

Sometimes, in order to guarantee a minimum flow through the pump, an extra flow loop is added. When w > Fmin the recirculation valve is closed, but if w < Fmin then the extra flow loop opens the recycle to maintain the required flow


q

Flow control

FC w u

When the flow is high, instead of control valves, variable speed pumps are a sensible alternative that allows to save energy. A frequency converter (o similar device) connected to the pump asynchronous motor is required

M

∼


Flow control

FT

FC

Steam

Condensate

Reboiler

Destillation tower


Level Control

q

LC

w

u LT

qi

h

Different alternatives for the level transmitter


Level Control

q

LC w

u LT

qi

h

f0fat0

201

ii

i

phg)p( pghpp

aK)p(Kqtdqd

qqtdhdA qq

tdhdA

Ahm qqtdmd

∆−∆ρ=∆∆−ρ+=∆

∆+∆∆=∆+∆

τ

∆−∆=∆

−=

ρ=ρ−ρ=

uKatdad

vv ∆=∆+∆

τ


Block diagram

u

% +

-

W ( ) ( )1s

K1s

K 2

v

v

+τ+τ Q

( )1sK1

+τ

-∆Pf

+

Kp Ing /%

R(s) +

+

As1 H

gρQi

-


Block diagram

u

%

W ( ) ( )1s

K1s

K 2

v

v

+τ+τ

( )1sK1

+τ

∆Pf

+

Kp Ing /%

R(s) +

12 gKAssA

1sρ++τ

+τH

Qi

- + -


Level Control

q

LC w

u LT

qi

h aKq

tdqd: K smallor f

aK)p(Kqtdqd

qqtdhdA qq

tdhdA

Ahm qqtd

md

21

201

ii

i

∆=∆+∆

τ

∆+∆∆=∆+∆

τ

∆−∆=∆

−=

ρ=ρ−ρ=

uKatdad

vv ∆=∆+∆

τ


Block diagram

u

% +

-

W ( ) ( )1s

K1s

K 2

v

v

+τ+τ

Q

Kp Ing /%

R(s) +

As1 H Qi

-

In practice it behaves as a process with an integrator


Tight /Average control

LC w

u LT h

LC w

u LT qi h

qi

The level must be maintained tightly: PI with “active” tuning

Store liquid + smooth changes in qi : P with “loose” tuning

Surge/Supply tank


Average Control

q

LC

w

u LT

qi

h

Smooth disturbances

P control with low Kp: The level oscillates and there is steady state error but q changes smoothly

u = Kpe + bias

If w = 50%, Kp= 1 and bias = 50%, then u = 100 if h = 100%, u = 0 if h = 0


Units in series

LC w

u LT h

qi

LC w

u LT h

All level control must be placed in the same direction


Several streams

q

LC

w

u LT

qi

h

If possible, then choose the larger stream for control


Pressure control

PC PT

Fi

F

u

a

w

Many different dynamics and aims

Fast process

PI with “tight” tuning


Pressure control

{ }

aKFKptdpd

aap

ppFpaCppp

tdpd

pRTaCppVM

ppp

paCappCFtdpd

RTVM

ppaCFtdpd

RTVM

tankisothermal RTM

p Vm

ppaCFFFtdmd

2i1

0

2f

2

i

0v

2f

2

0v

2f

2

02f

2v02f

2vi

0

2f

2vi

2f

2vii

∆−∆=∆+∆

τ

∆

−

−∆

−

=∆+∆

−

∆

−−∆−−∆=

∆

−−=

ρ=ρ=

−−=−=

Fi

F a

p

pf

uKatdad

vv ∆=∆+∆

τValve:


Block diagram

u %

W ( ) ( )1s

K1s

K 2

v

v

+τ+τ

P

( )1sK1

+τ

∆Fi

( )sT

1sTK

i

ip +

Kp Ing /%

+ - + -


Pressure control

PT PC

Steam

Condensate

Cooling water

w

Column

Condenser

Slow process, PI / PID


Temperature Control

TT

u TC

w

q T

Many architectures / processes Slow process PID Transmitter dynamics can be significant Be careful with the placement of the transmitter in order to avoid transport delays


Temperature Control

TT

u TC

w

q T

The product flow cannot be changed independently


Temperature Control

TT

u TC w

q T

Product by-pass Fast dynamics, low range of control


Temperature Control

TT

u TC

w

q T

The valves operate in opposition, one is air-open and the other one air-close The total product flow is not changed

u 100 %

100 %

B A

B

A


Temperature Control

TT

u TC

w

q T

Three ways valve

Mixing valve at the output or splitting valve at the input


Temperature Control

TT

u TC

w

q T

Heating fluid by-pass Slower dynamics

Configurations with two valves or one three ways valve


Temperature Control

TT

TC

Steam

Condensate

some typical control loops

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