CONTROL VALVE FROM CONTROL LOOP THEORY PERSPECTIVE · PDF file1 Automation Instrumentation...

1

Automation Instrumentation Summit

Castello di Belgioioso, Pavia, 5/6 July 2017

CONTROL VALVE FROM CONTROL LOOP

THEORY PERSPECTIVE:

An overview

Anna Veneroni – SIMECO S.p.A.

Automation Instrumentation Summit – Castello di Belgioioso, Pavia, 5/6 July 2017 Anna Veneroni – Simeco S.p.A. 2

SUMMARY:

1. The valve as control loop element

- Pressure regulation for gas

- Flow regulation for liquids

2. Characteristic of the valve

- Inherent characteristic

- Installed characteristic

3. The gain of a control valve in a loop

4. Regulator synthesis and tuning

INTRODUCTION


Gas pressure regulation loop Control loop principles

1 – THE VALVE AS A REGULATION ELEMENT

REGULATION

VALVE

PRESSURE CONTROLLER

a feedback controller that acts

on the control valve according

to the Set Point and to the

actual pressure in the vessel

EXAMPLE: FEEDBACK CONTROL LOOP

FOR PRESSURE REGULATION OF A VESSEL

Suppose that the pressure in the vessel decrease

as a disturbance effect

The controller takes action in order to guarantee

a proper pressure value in the vessel (direct action)

The valve opening (h) decreases

The valve flow capacity 𝐶𝑣(h) decreases

The outlet flow rate 𝑄 decreases

The net quantity of gas in the vessel increases and therefore also the

pressure in it increases (with T and inlet flow almost constant)

The pressure increase due to the control loop action that allows to

restore the pressure value at the desired Set-Point.


FLOW

CONTROLLER

REGULATION

VALVE

Liquid flow regulation loop Control loop principles


THE VALVE AS THE DISSIPATIVE ELEMENT

IN A HYDRAULIC CIRCUIT

In a hydraulic circuit with a flow rate control loop, suppose to have a flow rate

decrease due to a disturbance effect.

The regulator action opens the valve in order to restore the flow rate value in the

circuit to the Set-Point.

As effect of the controller, the flow rate decreases, the output of the controller

increases (reverse action) and the valve opening (h) increases.

Δ𝑝 3 decrease

𝐶𝑣(h) increases

Δ𝑉 3 decreases

Conductance increases

𝐶𝑣(h) of the valve Variable electrical

conductance (NOT linear)

Q increases I increases


a b

Reference Hydraulic Model

Valve Pressure Profile


Low 𝑞 (the valve is

nearly closed)

Δ𝑝 is concentrated

on the valve

High 𝑞 (the valve is

nearly open)

Δ𝑝 is distribuited

on the lines

p1

p2

p1

p2

p1 = PSource − ∆ppiping a

p2 = PReceiver + ∆ppiping b


DEFINITION OF THE FLOW COEFFICIENT Cv

The Cv coefficient defines the normalized volumetric flow rate which is referred to the following conditions:

•Differential pressure between upstream and downstream of the valve = 1 psi

•The fluid is water at a temperature between 5 and 40°(ρ=1000Kg/m³)

•The unit of measure for the volumetric flow rate is gmp (1gal=3,785l)

∆𝑝(𝑐𝑣) is the static pressure drop, equal to 1 psi

∆𝑝 is the static pressure drop expressed in psi

2 – INHERENT CHARACTERISTIC

𝐶𝑣 = 𝑞𝑣 ∗ ∆𝑝(𝑐𝑣)

∆𝑝∗𝜌

𝜌0



ANSI/ISA–75.01.01–2002 (60534-2-1 Mod) Flow Equations for Sizing Control Valves

Fourth Printing: 15 August 2005

Cv calculation

Sizing equations for incompressible fluids

(Chap. 6 ANSI/ISA–75.01.01–2002 (60534-2-1 Mod)

Turbulent Flow

Non – choked flow

Applicable if ∆𝑃 < 𝐹𝐿𝑃 𝐹𝑃 2(𝑃1 − 𝐹𝐹𝑃𝑉)

Eq. 2 𝐶 =𝑄

𝑁1𝐹𝑃

𝜌1/𝜌0

∆𝑃

Choked flow

Applicable if ∆𝑃 ≥ 𝐹𝐿𝑃 𝐹𝑃 2𝐹𝐿2(𝑃1 − 𝐹𝐹𝑃𝑉)

Eq. 4 𝐶 =𝑄

𝑁1𝐹𝐿𝑃

𝜌1/𝜌0

𝑃1−𝐹𝐹𝑃𝑉



Cv calculation

Sizing equations for compressible fluids

(Chap. 7 ANSI/ISA–75.01.01–2002 (60534-2-1 Mod)

Turbulent Flow

Non-choked flow

Applicable if 𝑥 < 𝐹𝛾 ∗ 𝑥𝑇𝑃

Eq. 11a 𝐶 =𝑄

𝑁9𝐹𝑃𝑃1𝑌

𝑀𝑇1𝑍

𝑥

Choked flow

Applicable if 𝑥 ≥ 𝐹𝛾 ∗ 𝑥𝑇𝑃

Eq. 17a 𝐶 =𝑄

0.667𝑁9𝐹𝑃𝑃1

𝑀𝑇1𝑍

𝐹𝛾𝑥𝑇𝑃


INHERENT CHARACTERISTIC

The inherent characteristic is the relation

between the flow rate and the stroke of

the valve keeping constant the

composition, the temperature, the

pressure upstream and downstream of

the valve.



IEC 60534-2-4

Industrial-process control valves – Part 2-4: Flow capacity -

Inherent flow characteristics and rangeability:

It collects all the criteria that shall be applied from the vendors

to define the correct Cv of a valve.

The valve must operate in an appropriate range, with a declared

tolerance. ø =Cv/Cvmax

INHERENT RANGEABILITY

The inherent rangeability of a valve is typically used during the sizing or during the

operating verifications.

It is the range in which both the prescriptions on the slope of the characteristic curve

and the tolerance on the Cv values are applicable.

It does not represent anyway the effective flow rate capacity of the installed valve.


𝑅 =𝐶𝑣𝑚𝑎𝑥𝐶𝑣𝑚𝑖𝑛

ℎ: 100%

ℎ: 5%


A new and smaller valve has been added in parallel to the existing regulation valve E-10 (FV-017, globe equi%, 12") dedicated to the

regulation of the inlet steam flow rate to the heat exchanger. This new valve is dedicated to the low flow rate regulation (FV-301, globe

equi%, 6").

Applicative example: «Thermal recovery MHC-TAME» for Sarlux

In order to increase the total thermal efficiency of the refinery,

two new heat exchangers have been installed on an existing

etherification plant.

Their function is to heat the etherified gasoline feed in a column

using as hot fluid the GAL available from the near plant MHC.

The GAL flow depends on the operating conditions of the plant

MHC. For this reason the existing heat exchangers, which works

with low pressure steam, shall continue to work though with a

higher range, extending it to low flows.

This condition allows to maintain Set-Point temperature at the

column feed, even if GAL flow rate decreases (for any reason), in

order to optimize the low pressure steam usage.


INCREASE OF THE INHERENT RANGEABILITY USING TWO VALVE IN PARALLEL


N°2 valves equi% in parallel:

• FV-017: 10000 – 25000 Kg/h Pre-existing

• FV-301: 1340 – 10000 Kg/h Installed in order to increase R





Process conditions at switch point:

Q=10000Kg/h

P𝑖𝑛 =3,5barg

Dp =0,5bar

Valve opening and Cv at switch point:

ET-FV-017 𝐶𝑣 =393,1 ⟶ h=37,3%

ET-FV-301 𝐶𝑣 =403,4 ⟶ h=94%

Split range value during valve opening: 35%

Split range value during valve closing: 40%

The valves shall be controlled with a split range. The switch point is selected in order to obtain the extended curve, with continuity of solution

for both the operating valves FV-018 and FV-302.

Moreover, it is necessary to enter a value of hysteresis in order to avoid flow rate oscillations around the switch point value and consequently

an alternate usage of the two valves FV-018 and FV-302.

0

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CvFV-017

CvFV-301



2 – INSTALLED CHARACTERISTIC

INSTALLED CHARACTERISTIC The installed characteristic is the relation between the valve stroke and the related flow rate in a system composed by the

valve and the hydraulic circuit in which the physical properties such as temperature and fluid composition are kept constant.

Pressure trend on flow rate for typical processes:

The installed characteristic is affected by the operating pressure condition of the hydraulic circuit


Note:

If the valve resistance decreases in comparison to

total resistance in the system, Dc decreases.

Therefore the flow rate regulation is similar to an on-

off regulation. 5


INSTALLED CHARACTERISTIC FOR A LINEAR INHERENT CHARACTERISTIC

𝐷𝑐 =∆𝑃

∆𝑃𝑡


Note:

Decreasing Dc, the equi-percentage inherent

characteristic becomes a linear installed characteristic

and the minimum controllable flow rate increases.

5


INSTALLED CHARACTERISTIC WITH AN EQUIPERCENTAGE INHERENT CHARACTERISTIC

𝐷𝑐 =∆𝑃

∆𝑃𝑡


2 – CARATTERISTICA INSTALLATA

Comparison between main characteristics

5

If 𝑄 = 𝑄𝑚𝑎𝑥 and 𝑝𝑣𝑎𝑙𝑣𝑒 > 40% 𝑝𝑡𝑜𝑡 , the linear inherent characteristic

allows to obtain the maximum level of linearity in the installed

characteristic.

If 𝑄 = 𝑄𝑚𝑖𝑛 and 𝑝𝑣𝑎𝑙𝑣𝑒 < 25% 𝑝𝑡𝑜𝑡 , the equi% inherent characteristic

allows to obtain the maximum level of linearity in the installed

characteristic.

Valve with high values of specific 𝐶𝑣 (as rotary valves) can be more

easily influenced by the line effects than globe valves. This is because

the rotary valves have a lower p (5÷10 times smaller) at the same

flow rate.


Block diagram in figure represents

the correspondence between the

valve regulation signal (which

comes from the regulation loop)

and the flow rate in the hydraulic

circuit.

FC regulator

output Flow

Kg/h

Kg/h

Kg/h



How to obtain the valve installed characteristic during engineering:

E.g.: flow rate regulating valve

for low pressure steam


1- Through suitable calculation software for

valve sizing


With a spreadsheet in Excel it is possible to verify the

installed characteristic of the valve.

The initial data involved in the calculation are the

following:

- Liquid density

- Pressure value upstream and downstream of the

valve in both conditions of maximum and minimum

flow rate.

- Inherent characteristic declared in vendor datasheet


E.g.: Flow rate regulating valve for liquid (poor amine)

2 – Using datasheet information and valve

inherent characteristic



28

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00

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12

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76

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41

04

43

68

q [

Kg

/h]

Dp/q

pin

pout

Knowing upstream and downstream valve pressure in both conditions of maximum and minimum flow rate, it is possible to select

the most appropriate pressure trend between typical ones and interpolate the datasheet pressure values accordingly.

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

0 510

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0

h [

%]

Cv/h Inherent characteristis

Cv


Here below are visible the inherent characteristic and the Δp= pin – pout trend entered in calculation sheet:



03,4

56,9

10

,35

13

,817

,25

20

,724

,15

27

,631

,05

34

,537

,95

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,444

,85

48

,351

,75

55

,258

,65

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,165

,55

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,45

75

,979

,35

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,886

,25

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,793

,15

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,6

0

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1000

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4500

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q [Kg/h]/ h [%] Caratteristica Installata

Q


The installed rangeability is:

𝑅 =𝑄 100%

𝑄 5%= 5000

300 = 16.6


𝐷𝑐 =∆𝑃

∆𝑃𝑡

How to calculate the installed characteristic:

- Select a q value in the range

- Read the corresponding p value from plot p/q

- Calculate Cv from the equation 𝐶𝑣 =𝑞𝑣

0,865∗∆𝑃

𝜌/𝜌0

- Read the corresponding valve stroke value h from

inherent characteristic

- Plot (q, h)

- Select another q value in the range and repeat the

steps

𝐷𝑐 = 0,31


INSTALLED RANGEABILITY

The installed rangeability is the actual relation between maximum and minimum

flow rate that valve can adjust during service.

INSTALLED GAIN

The installed gain is the relation between flow rate variation and the corresponding

valve stroke variation.

This ratio correspond to the installed characteristic slope.

Note that, if the installed characteristic is linear, the gain is constant.

A too high gain value could cause high relative errors on flow rate variation (ΔQɛ)

due to relative errors on the valve stroke value (hɛ).

ΔQɛ = G * Δhɛ


𝑅 =𝑄𝑚𝑎𝑥𝑄𝑚𝑖𝑛

𝐺𝑖𝑛𝑠𝑡 =𝑑𝑄𝑝𝑑ℎ


The valve model

Can be approximated by linearization

around every equilibrium flow rate point,

3 – VALVE GAIN IN A CONTROL LOOP Introduction to the control theory….

MODEL LINEARIZATION AROUND THE OPERATING POINT

Applying

Laplace Transform

On linearized system:

If we consider a process operating plant in stationary conditions we can assume that:

the pressure drop of the valve (Δp(t)) is constant, the valve flow rate (Q(t)) is constant and equal to its nominal value 𝑄 and therefore the valve

stroke is equal to the corresponding ℎ in valve installed characteristic.

In these conditions, if the flow rate has very small variations around the nominal value, the installed characteristic of the valve can be

approximated to the straight line with the same slope of the installed characteristic in that point.

𝑄 + 𝛿𝑄 𝑡 = ℎ + 𝐺𝑖𝑛𝑠𝑡 ℎ + δℎ 𝑡

𝑄(𝑡) = 𝑄𝑐 𝑖𝑛𝑠𝑡(ℎ 𝑡 )

Q s = 𝐺𝑖𝑛𝑠𝑡 ℎ ∗ ℎ 𝑠


ACTUATOR STEP RESPONSE

If the controller output u(t) has a step change from the nominal operating condition,

the valve stroke does not reach the new required position instantaneously.

We have to take into account the actuator and the positioner dynamics.

Typically this control action follows a 1°order dynamic (as for the capacitor

regulation in the RC circuit).

Therefore, the dynamic of the valve regulation can be approximated to a I°order

dynamic system which DTF (Dynamic Transfer Function) is the following:

The valve stroke is limited between 0 and 100% and the actuator speed is limited too.

Hence, we must introduce saturations (NON-linearity) in control loop:

3 – VALVE GAIN IN A CONTROL LOOP

𝐹𝑎𝑡𝑡 𝑠 =1

1 + 𝜏𝑠


3 – VALVE GAIN IN A CONTROL LOOP

THE TRANSFER FUNCTION FOR THE FLOW CONTROL LOOP

Note: the process control systems are digital controllers. For the purpose of this discussion, we can neglect this fact and dealing with

analog controllers.

Assuming:

• Ftrasm = 1

𝑄𝑚𝑎𝑥

•Felepos =1

•Fattuat = 1

1+𝑠𝜏

• Ginst = installed gain of the valve

• Neglecting the saturation non-linearity


GENERAL THEORY CONSIDERATION FOR REGULATOR SYNTHESIS

Even if the installed characteristic is nearly linear, the control valve is always a non-linear system.

This is basically due to the control valve 𝐶𝑣 max limitation.

This behavior can be modeled by a saturation.

This non-linearity can be approached using the non-linear control theory.

For historical and practical reasons in the process control it is widespread the usage of linear controllers.

So the regulator synthesis is the construction of a proper Controller Transfer Function.

In addition, it is a very common practice to use standard Controller Transfer Functions (typically PID

regulators) and to define their parameters by tuning.

Then, the actuator saturation is managed taking into account «ad hoc» techniques called ANTI WIND-UP.

4 – REGULATOR SYNTHESIS


Appling Laplace transformation:

PID CONTROLLER

PID controller is the most common controller used in process control.

PID regulators combine 3 actions:

• Kp PROPORTIONAL ACTION: proportional to the error

• Kd DERIVATIVE ACTION: proportional to the derivative of the error

• Ki INTEGRAL ACTION: proportional to the integral of the error


We set Kd=0 because flow rate measures are affected by noise. So we can use PI controller.

Note: Refer to the bibliography for more complex forms and PID implementations in process control systems.

𝑃𝐼𝐷 𝑡 = 𝐾𝑝𝑒(𝑡) + 𝐾𝑑𝑑𝑒(𝑡)

𝑑𝑡+ 𝐾𝑖𝑒 𝑡 𝑑𝑡

𝑡+𝑇

𝑡

𝑃𝐼𝐷 𝑠 = 𝐾𝑝 + 𝑠𝐾𝑑 +𝐾𝑖𝑠

𝑃𝐼𝐷 𝑠 = 𝐾𝑝 +𝐾𝑖𝑠=𝐾𝑝𝑇𝑖

(1 + 𝑇𝑖𝑠)

𝑠


In order to identify the right parameters of the PID controller to guarantee the stability of the process, it is necessary that the

parameters of the process transfer function are almost constant.

The maximum variation of the process gain (ratio valve flow rate/controller output) must be limited.

Empirical value: max 4:1

CONSIDERATIONS ON THE GAIN OF THE INSTALLED VALVE


If the gain exceed this empirical value, will be necessary

have a PID regulator with variable parameters to ensure

a robust control.

Anyway, for the valve system is required that Ginst(q(t)) is

as much as possible constant.

For this reason the valve gain is required to be within a

specific range. For example 0,75÷3 or 0,5÷2 that

comply to general rule:

𝐺𝑖𝑛𝑠𝑡 𝑚𝑎𝑥𝐺𝑖𝑛𝑠𝑡 𝑚𝑖𝑛

< 4


LOOP GAIN AND TRANSFER FUNCTION Q(s)/Q0(s)


𝐿 𝑠 =𝐺𝑖𝑛𝑠𝑡𝑄𝑚𝑎𝑥

𝐾𝑝

𝑇𝑖

(1 + 𝑇𝑖𝑠)

1 + 𝜏𝑠 𝑠

𝐹 𝑠 =𝐿(𝑠)

1 + 𝐿(𝑠)=

(1 + 𝑇𝑖𝑠)

𝛼𝑠2 + 𝛽𝑠 + 1


THE STATIC GAIN OF THE SYSTEM Q(0)/Q0(0)

In time domain, for a Set-Point step variation, after a theoretically infinite time period, Q(s)= 𝑄0(s),

so the error between the Set-Point and the process variable (i.e. the flow rate) is zero.


From a mathematical point of view s=jω=j2πf where f is the frequency.

So, if the signal frequency f goes to zeros the transfer function F(s) goes to one.

If f ⟶ 0 then 𝐹(𝑠) ⟶ 1

F(0)=1

𝐹 𝑠 =(1 + 𝑇𝑖𝑠)

𝛼𝑠2 + 𝛽𝑠 + 1


REGULATOR TUNING


If the time constant of the actuator t is available,

it is possible to choice Ti=t

Hence, F(s) results to be a low-pass filter with gain=1 and critical

pulsation:

ωc = 2πT

(Hz)

It is possible to choose Kp in order to force the desired critical pulsation wc and the response time of the system, of course, within the actuator

valve and process limit.

𝐿 𝑠 = 𝐾(1+𝑇𝑖𝑠)

1+𝜏𝑠 𝑠=𝐾

𝑠 in which 𝐾 =

𝐺𝑖𝑛𝑠𝑡

𝑄𝑚𝑎𝑥

𝐾𝑝

𝑇𝑖

𝐹 𝑠 =1

1+𝑇𝑠 in which 𝑇 =

1

𝐾

𝑃𝐼 𝑠 =𝐾𝑝𝑇𝑖

(1 + 𝑇𝑖𝑠)

𝑠


TUNING METHODS FOR PID CONTROLLER

A ) Tuning methods based on the experimentally process open loop

response to Set-Point step variation

If the process response can be approximated to a I°order system,

we can use:

• Tangent method

• Areas method

• Ziegler-Nichols in open loop

• Cohen-Coon

• Internal Model Control (IMC)

B ) Tuning method based on the experimentally closed loop response

analysis on the system

• Ziegler-Nichols in closed loop



Bibliography:

Béla G. Liptàk, Instrument Engineers’ Handbook - Process Control and Optimization - 4th Edition, CRC Press Taylor &

Francis Group, 2006

P. Muroni, Valvole di regolazione per processi industriali - GISISERVIZI.srl, Milano, 2001

METSO, Flow Control Manual – 6th Edition, METSO AUTOMATION INC., Vantaa, Finland, 2011

F. G. Shinskey: Process Control Systems – 4th Edition, McGraw-Hill,1996

P. Bolzern, R. Scattolini, N. Schiavoni, Fondamenti di controlli automatici – 3° Edizione - McGraw-hill, 2008

ANSI/ISA-75.01.01-2012 (60534-2-1 MOD) Industrial-Process Control Valves - Part 2-1: Flow capacity - Sizing equations

for fluid flow under installed conditions

IEC 60534-2-4, Industrial-process control valves - Part 2-4: Flow capacity - Inherent flow characteristics and rangeability,

Edizione 2.0, 5/13/2009

BIBLIOGRAPHY


THANK YOU FOR YOUR ATTENTION

Simeco S.p.A.

Via Romilli, 22 - 20139 Milano (Italy)

tel. +39.02.99298.1

fax +39.02.56.91.424

www.simecomilano.it

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