6. Analysis of the regulations

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6. Analysis of the regulations

6.1. Software environment and the methodology followed

The purpose of the study is to optimize/validate the performances of the two control loops introduced in the previous chapter. This will be done with frequency analysis and so a linear model of the loops is required.

After performing the study in the frequency domain, a time domain simulation is required to account for non-linearities that are in the model. It is clear that the software to be used must provide the ability to perform this kind of analysis in a common and highly integrated environment in order to assure coherence of data, easy management of the results, fast model modification for sensitivity purposes, etc.

At the moment Matlab®/Simulink® is able to satisfy these requirements and so it is the software platform selected to implement the model of the system.

Matlab® is a software environment devoted to technical and scientific computing. It integrates computation, visualization and programming in only one platform. Its name stands for MAtrix LABoratory highlighting that its basic data element is the array. Moreover it features a series of application specific add-ons; they are sets of Matlab® functions or also toolboxes which provide a user interface. These add-ons are highly integrated in Matlab®.

Most relevant add-ons for the purpose of this thesis are Simulink® and the Control Systems toolbox.

Simulink® is a dynamic simulator which allows continuous and discrete time simulation or even hybrid. It features a graphic interface to implant the model by dragging and dropping basic blocks which implement mathematical or Matlab® functions. The graphic interface is very useful for model modification, but also for accessibility to variable: it is sufficient to add a block to record the time trend of a variable.

The Control Systems toolbox is integrated with Simulink® and Matlab®. It embeds functions and an interface related to frequency analysis, manipulation of transfer functions, linearization, etc. Since it runs in parallel with Simulink® it is possible to inspect and store

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various configurations of the controller, load the corresponding parameters into the controller and run a Simulink® simulation to test the time domain behaviour of the system.

The Control System toolbox can linearize a Simulink® model around a point by means of analytic methods or numeric perturbations. Analytic methods rely on the pre-programmed Jacobian matrix of a function, so it is used when there is a “standard” function in the model (e.g. sinus, exponential, power, etc.); numeric perturbation is used in other cases. Its algorithm is inspected in the following.

A linearized system around a point can be written in the following way:

( )

t x

( )

t u

( )

t y t u t x t x r r r & r r r &

δ

D C B A + = + =

The state-space matrices A, B, C, and D of this linearized model represent the Jacobians of the block. To compute the matrices, the states and inputs are perturbed, one at a time, and the response of the system to this perturbation is measured by computing δ and δx& y. The perturbation and the response are then used to compute the matrices in the following way:

( )

0 , 0 , , x x x x i m i p xpi r r r & r & − − = A

( )

0 , 0 , , u u x x i m i p upi r r r & r & − − = B

( )

0 , 0 , , x x y y i m i p xpi r r & r r − − = C

( )

0 , 0 , , u u y y i m i p upi r r r r − − = D where: i p

xr _, is the state vector whose ith component is perturbed from the operating point value;

0

xr is the state vector at the operating point;

i p

ur _, is the input vector whose ith component is perturbed from the operating point value;

0

ur is the input vector at the operating point;

i p x x , r

& _{is the value of x} r

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i p u x , r

& _{is the value of x} r

& at ur_p_,_i, xr₀;

0

x

r

& is the value of x r

& at the operating point;

i p x y , r is the value of yr at xr_p_,_i, ur₀; i p u y , r is the value of yr at ur_p_,_i, xr₀; 0

yr is the value of yr at the operating point.

The default difference between the perturbed value and the operating point value is

(

x0,i

)

5

1

10− + for perturbation based linearization, where x₀_,_i is the operating point value. This default value has been adopted in the study.

6.1.1. Frequency domain analysis

In the following the input of the system is always the set point, the output is the controlled variable and all other variables which act on the plant but on which controller has no information are disturbances.

Referring to Figure 18 it is clear that each controller does not receive information about the upstream/downstream part of the system or about other physical quantities of the controlled system. Obviously the two systems interact in some way and the result of this interaction is a disturbance on the controlled variable (variable on which controller receive information by means of process deviation). In other words the controller acts the controlling variable only by means of information about the controlled variable, that is, the control system is of the SISO type. So it is possible to analyze each control loop separately, independently from the other one.

Resulting loops are:

̶ closed loop regulation: pressure upstream vacuum pump (representative of RCP

pressure): controlled variable (the output of the system) is pressure into the RCP as read by PT1, controlling variable is mass flow rate entering the RCP and the input of the system is pressure set point;

̶ closed loop regulation: pressure downstream vacuum pump (approximated by the

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the pipe from pump outlet nozzle to separator inlet nozzle): controlled variable (the output of the system) is pressure into the separator as read by PT2, controlling variable is by passed mass flow rate and the input of the system is pressure set point.

This requires some boundary conditions to be provided for each TH-system in order to find its operating point (that will be then the linearization point): in fact the pump extracts some mass from the system RCP (see Figure 18) and this phenomenon is going to be lost by system separation. Boundary conditions are chosen at their nominal value according to Ref. [2].

Pressure upstream vacuum pump

RCP pressure set point bara 0.8

Mass flow rate to RPE kg/s 3.47e-2

(Injected mass flow rate by SGN system kg/s 3.47e-2)

Pressure upstream CV1 bara 11

Pressure downstream vacuum pump

Pressure set point bara 1

Pressure downstream BP bara 0.8

Mass flow rate to TEG kg/s 3.47e-2

Table 5: Boundary conditions and set point

Another point that needs clarification is the structure of the loop: according to control theory a closed loop control system has the basic form shown on the left hand side of Figure 20.

The output of the plant, if required, is acquired by means of another transducer that could have worse dynamic performances than the feedback transducer and hence cheaper.

Since in considered control schemes there is only one transducer used either to generate the feedback signal and the signal displayed in the MCR, transducer has been included in the feed forward signal path. This has an influence on the structure of the closed loop transfer function of the system.

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Figure 20: Loops architectures

The transfer function that corresponds to the configuration on the left is:

) ( ) ( 1 ) ( ) ( s T s F s F s H + =

while that one related to the loop configuration on the right is:

) ( 1 ) ( ) ( s F s F s H + = where:

̶ F(s)= open loop feed forward branch transfer function; ̶ T(s)= feed back transducer transfer function;

̶ H(s)= closed loop transfer function.

The following procedure has been adopted to find the operating point of the two sub systems:

1. Isolation of the sub systems and imposition of the boundary conditions;

2. Removal of non linear blocks that affect linearization (the only one is backslash used

to simulate a dead band);

3. Running time simulation of the model to achieve steady state conditions at the set point of the controlled variable. In order to do so a guess set of controller parameters has been used: the PI controller is already in the loop and controls the actuators of the loop. In this first phase it is important that the model reaches steady state with a negligible steady state error and so simulation length has been chosen accordingly (an error of 10-10 was the target);

4. Acquisition of the operating point by means of the function “Simulation Snapshot” at

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After it possible to:

5. Linearize the model by means of the “Control System Toolbox”: once the input of the

system, the output of the system and eventually disturbances are provided it is possible to plot the open or closed loop response of system relative to input to output or disturbances to output;

6. Perform the study of validation, and eventually optimization, to assure following frequency domain specification:

Gain Margin 20<GM<50 dB Phase Margin 60<PM<90 deg

Table 6: Frequency domain specifications

6.1.2. Time domain analysis

Since the model of the TH system is non linear and in the linearized model some non linear blocks are neglected (e.g. valves are considered to open instantaneously, i.e. they have an infinite speed), it is required to perform time domain analysis to check if the controller configuration obtained relying on stability margins is robust enough to withstand deviation from a perfectly linear behaviour of the model.

Moreover, time domain analysis is required to verify time domain requirements of Table 7 and register following quantities too:

100 max sp sp P P P OVERSHOOT = − min 100 sp sp P P P UNDERSHOOT = − pert t t time Settling = _{± %}₅ − 100 sp sp P P P Error= − ∞

Table 7: Time domain specifications

Table 7 requirements are inspired by EUR requirements of §4.1.6.

- Controlled variable must not oscillate after a perturbation of the system; - Controlled variable must remain in ±5% set point range;

- Controlled variable must settle on the new set point or on the set point after a perturbation.

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Time domain analysis has been performed using steps in the set point and in main disturbance variable of the sub systems (information about the amplitude of the step are provided later). Following points describe the method:

1. Running various simulation to obtain a steady state error of 10-5;

2. Substituting the required block with a step block and extending the simulation length to at

least twice the length found in pt.1. The step is sent at half of simulation length;

3. Running the simulation with step;

4. Running another simulation with a further increase in the length in the case the steady state has not been reached.

6.2. Modelling of Thermal Hydraulic components

To study the performances of the two control loops (whatever in the frequency or time domain), it is required to have a model of the physical system on which they act that is the equipment that they control. In other words it is required to fill the block “Plant” of Figure 20. This block is going to relate the controlled variable with the controlling variable. In both loops of §6.1.1 the controlled variable is pressure and the controlling variable is mass flow rate.

Obtaining the correct solution by means of a CFD or system code approach is not required by the study. In fact the accuracy of these methods will not be retained by the linearization process with the only consequence of increasing computational time. In fact, for the purpose of the study, it is better to have a fast running model to perform sensitivity analysis to asses the robustness of the control system.

According to this consideration a 0-Dimensional model is going to be implemented, but some hypotheses need to be verified and some simplifying assumptions need to be done.

Components or systems that are going to be modelled are:

̶ The RCP;

̶ The vacuum pump

̶ The water separator;

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6.2.1. General assumptions

Following assumptions have been postulated in deriving the TH model:

̶ All gas flows considered are of dry N2;

̶ Gas flow is considered incompressible in components that are not modelled as

volumes (e.g. pipes) in order to use Bernoulli’s equation to find the pressure at a given section of a pipeline;

̶ Use of ideal gas model;

̶ Pressure drop coefficients are considered constant because they do not vary a lot with

gas properties and speed of flow;

̶ Components are considered adiabatic toward the environment because of their thermal

insulation if not otherwise specified;

̶ Systems that are involved in the processes but that are not modelled provide their output at the nominal value for that particular operating condition.

6.2.2. Reactor Coolant System (RCP) Volume modelling

INITIAL AND BOUNDARY CONDITIONS

It seems worthy to note the state in which some pipelines are just before the sweeping starts. In fact they affect the condition of the gas that flows trough them and consequently the modelling choice.

Water and structures belonging to the primary system are at a fixed temperature of 70°C PRZ hemispherical head and a part of the PZR vent line are at T=230°C because of the previous flowing of hot steam to vent the PRZ and their thermal insulation; remaining pipelines till the pump inlet are at room temperature and not insulated from the external environment

Pressure in the RCP at the beginning of sweeping is assumed to be atmospheric.

MODELLING

Because three different boundary conditions exist, at least three 0-D (lumped) components will be used to model the system RCP:

̶ Constant temperature zone;

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̶ Heat subtraction zone.

Constant temperature zone

This region of the RCP encompasses: the hot and cold legs, SGs volume, MCPs volume, vessel upper head, PRZ surge line, PRZ until the hemispherical head and will be named Volume A in the following. Injection pipelines are not considered in this section of the model since they do not affect the pressure at the section were the transducer is installed (see Figure 22 and Figure 23).

Following additional assumptions apply to this section:

̶ Negligible speed of the gas trough the equipment involved;

̶ Negligible pressure drops across the circuit that follows from the large sections of the

legs and the vessel;

̶ Constant and homogeneous temperature of structure and water contained into the

equipment;

̶ Homogeneous temperature of the gas flowing into the volume (stratification and

convective phenomena are neglected);

̶ All the five injection points are collapsed into only one inlet since CV1 control valve

is upstream the branching off of the line (it is no possible to know flow repartition among the injection lines);

Volume A has been modelled with the following equations: Mass balance equation;

Energy balance equation; State equation for the ideal gas;

         = − + − − − = − = ) ( ) ( ) ( )) ( ( ) ) ( )( ( ) )( ( ) ( ) ( ) ( ) ( ) ( 2 1 1 2 1 t RT t m V t P t T T A h c T t T t m c T T t m dt t dT c t m t m t m dt t dm A A A A A W conv p ref p ref A v A A & & & & where:

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A is the total surface of structure and water touched by the gas;

R is the universal ideal gas constant divided by the molecular weight [J/kgK];

Tw is the temperature of RCP water inventory and RCP steel masses.

Heat addition zone

This zone is made by the PRZ hemispherical head and the first part of the PZR venting pipeline.

It is going to be modelled as a heat exchanger with time varying heat power. The time variation is due to convective cool-down provided by gas flow trough the pipeline.

This lumped component will be named HE1 in the following.

Pressure drops in this pipe line is accounted for by means of an orifice upstream HE1. This orifice will be named O1 in the following (see Figure 22 and Figure 23).

HE1 has been modelled with the following equations: Mass balance equation;

Energy balance equation;

Heat exchange equation for Tpipe;

(

)

    = + − = 0 ) ( ) ( ) ( ) ( ) ( ) ( 4 2 4 2 t Q t T t T t m c t m t m hot A p & & & &      − = = ) ( ) ( ) ( ) ( int , 1 , int , 1 t T A h dt t dT M c t T A h t Q ml he c ml st st p ml he c hot & where:

Ahe1,int is the internal surface of the pipeline touched by the gas;

cp,st is the heat capacity of stainless steel;

Mst is the mass of the pipeline;

Tml is the logarithmic mean temperature difference..

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This zone is made up by remaining pipelines from the PZR venting line up to the section where PT1 is located.

It is going to be modelled as and heat exchanger with time varying heat power. The time variation is due to convective heat-up provided by gas flow trough the pipeline and the cool-down due to convective heat exchange trough the external environment.

This lumped component will be named HE2 in the following.

Pressure drops in this pipeline is accounted for by means of an orifice upstream HE2. This orifice will be named O2 in the following (see Figure 22 and Figure 23).

HE2 has been modelled with the following equations: Mass balance equation;

Energy balance equation;

Heat exchange equation for Tpipe;

(

)

    = − − = 0 ) ( ) ( ) ( ) ( ) ( ) ( 6 4 4 6 4 t Q t T t T t m c t m t m cold p & & & &

(

)

(

)

(

)

(

)

(

)

(

)

         − + − = − − − − − = − = − − − − 4 4 2 , 2 , , , 4 4 2 , 2 , , 2 , , 2 , ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( concr pipe he ext room pipe he ext R P c room air air p concr pipe he ext room pipe he ext R P c pipe av he c G P c pipe st st p pipe av he G P c cold T t T A t T t T A h dt t dT M c T t T A t T t T A h t T t T A h dt t dT M c t T t T A h t Q σε σε & where:

Aext,he2 is the external surface of the pipeline;

Tav is the average temperature of the gas in the pipe.

The RCP volume is upstream the vacuum pump which imposes the extracted mass flow rate according to its characteristic mass flow rate vs. Psuction. It is therefore possible to estimate the pressure read by the transducer on the pipeline using the Bernoulli’s equation (TR stands for the section of the pipeline where the transducer PT1 is installed):

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[

( ) ( )

]

) ( 2 ) ( ) ( ) ( 1 ) ( ) ( 6 2 2 2 3 2 4 2 4 2 1 , t t t A t m K K t A t A K t P t P TR TR TR tot tot TR TR tot tot s A TR

ρ

τ

=         + +       + − − = & where:

τ is the delay due sound propagation into considered gas;

Ki accounts for the distributed and concentrated pressure losses in the lines; they

are splitted according to pipe diameter.

AREMARK

Heat transfer that takes place in the pipelines can be neglected for frequency analysis purposes; in fact pressure at the transducer section varies slightly with the temperature and this variation is bounded by the incertitude on the measure acquired by the transducer.

Figure 21 shows the influence of gas temperature on the pressure losses from the RCP volume up to the section where PT1 is installed. As can be seen the variation from 70 °C to 230 °C is of about 1 kPa that is in the range of the transducer incertitude on the measurement (refer to Table 8).

∆

∆P vs. Temperature

0,0150 0,0200 0,0250 0,0300 0,0350 0,0400 334,15 344,15 354,15 364,15 374,15 384,15 394,15 404,15 414,15 424,15 434,15 444,15 454,15 464,15 474,15 484,15 494,15 504,15 514,15 Temp [K] ∆∆∆∆ P [ b a r] Q=100Nm3/h Q=110Nm3/h Q=90Nm3/h

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Moreover, since the flux in the pipe is considered incompressible, the density at the transducer will be the same in volume A delayed by the transit time in the pipeline,

τ

_{l ,}_tot, computed for the nominal mass flow rate.

According to this the Bernoulli’s equation can be rearranged in:

[

( ) ( )

]

) ( 2 ) ( 1 ) ( ) ( , 2 2 2 3 2 2 4 2 1 , tot l A TR line A TR tot tot TR tot tot s A TR t t t A t m K K A A K t P t P

τ

ρ

τ

ρ

τ

− = −         + +       + − − = &

HE1 and HE2 have been introduced in the Simulink® library of the study to inspect the behaviour of invalidities and protection signals (refer to §5.2.2) in the case of a follow up of the present study.

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Figure 23: 0-D model of the RCP

6.2.3. Nuclear Island Vent and Drain (RPE) Vacuum pump

It is modelled as an isothermal compressor with its own characteristic and compression ratio and respecting steady state mass balance. According to the constructive technology, the compression power is transferred to a water ring; due to the geometry of the impeller, the water ring creates an eccentric path for the gas so the gas firstly is extracted by means of a depression and then it is expelled from the pump by a compression. Moreover since the service water and the gas are in intimate contact, water may cool down or heat up the gas. The verse of the heat exchange depends on the temperature of the service water and of the incoming gas.

The characteristic mass flow rate vs. Psuction is placed into a “Look up table” block: knowing the pressure in the RCP it is possible to determine the extracted mass flow rate.

In reality a protection on the power absorbed by the electric motor is provided in order to stop the pump from pressurizing the circuit downstream it. For the same purpose a safety valve is placed on the outlet pipeline of the separator. This arrangement is simulated by a check over the pressures upstream the pump and into the separator. (K is the compression ratio of the pump).     < = = > = = separator up in pump out pump separator up upstr in pump out pump P KP m m P KP P f m m 0 ) ( , , , , & & & &

An orifice plate is placed at the inlet nozzle of the vacuum pump by the constructor. This arrangement is needed to provide a pressure difference between the interior of the pump and the water supply system of the water ring: in this way water enters the pump without the need

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of pump. The orifice plate is accounted by considering a discrete loss at the pump inlet; the K of the loss has been derived from constructor’s data using the following equation:

2 2 w K P_nom = _orifice

ρ

∆

In order to determine the pressure loss caused by the orifice, the mass flow rate at the previous time step is used; it is then possible to calculate the mass flow rate for the new time step which will determine the pressure in the Volume A.

6.2.4. Nuclear Island Vent and Drain (RPE) water separator

It is modelled as a volume (same approach used for the RCP volume of §6.2.2). It is the only component on the RPE side, together with the pump, where the gas is considered compressible.

Consequently the equations used to describe this component are: Mass balance equation;

Energy balance equation; State equation for the ideal gas.

(

)

         = − + − − = − − = ) ( ) ( ) ( ) ) ( ( ) ( ) ( ) ) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( , , , , , , , t RT t m V t P T t T c t m t m T t T c t m dt t dT c t m t m t m t m dt t dm sep sep sep sep ref sep p sep bp sep out ref sep in p sep in sep v sep sep bp sep out sep in sep & & & & & &

6.2.5. Nuclear Island Vent and Drain (RPE) T-Junctions

These components are modelled as opened, stationary components; in other words they have to satisfy mass and energy balance at steady state in each instant of time.

    − = − + − = + − − − ) ( ) ( ) ( ₆ 6 6 ref out p out ref pass by p pass by ref p out pass by T T c m T T c m T T c m m m m & & & & & &

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6.2.6. Nuclear Island Vent and Drain (RPE) Pipes

RPE pipes do not introduce any head loss. They are modelled as nodes (according to the nomenclature characteristic of TH codes), that is, lines connecting blocks in Simulink® software.

Since head losses in the pipelines are neglected, pressure upstream the by-pass valve BP is the same present in the separator and read by the pressure transducer PT2; pressure downstream the by-pass valve BP is the same read by pressure transducer PT1.

6.2.7. Nuclear Island Vent and Drain (RPE) initial and boundary

conditions

At the starting of the sweeping phase, that is t=0 sec, pipelines, the separator, the pump, structures and gas, are considered at environmental temperature. The separator is at atmospheric pressure.

Since the pump involves the usage of demineralised water during its work, the temperature of this water is considered constant at T=40°C and the amount of power removed by the pump from the compressed gas is considered constant too.

Figure 24: RPE vacuum unit modelled compoenets

6.2.8. Vacuum pulling/maintaining during filling

Standing previous assumptions and modelling choices, it is possible to introduce further simplifications in the model built for this phase.

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̶ In particular, RCP temperature is considered constant at 30°C (it must be <50°C). So the block “Energy equation” is not anymore present in the RCP subsystem.

̶ The T-junction upstream the vacuum pump is neglected since valve BP is closed: no

mass flow control is required since evacuated gas is routed to EBA.

̶ Phase separator is not anymore included into the vacuum unit. This decision follows

from the following reasoning: if it had been included in the model, the pressure at its outlet would have been atmospheric pressure as a consequence of the lack of modelling pipelines between vacuum unit and the TEG/EBA systems; moreover it was modelled as a volume without pressure losses except an entrance pressure loss. The exposed configuration is equivalent to a compressor – vacuum pump whose discharge nozzle is at atmospheric pressure. This has little influence on the model: in fact pressure losses would raise the pressure into the separator until the required ∆P to assure mass flow is reached.

̶ The assumption of constant Ks in the pipeline from the PZR top up to the vacuum pump is not anymore valid in this field of pressures (because of heavy changes in density of the gas), so they have been neglected and the pressure at the pump inlet is considered equal to the pressure in the RCP. The effect is to underestimate the time to reach a pressure of 0.2 bara in the RCP.

6.3. Modelling of I&C components

I&C equipment encompasses all hardware devices (valves, transducers, actuators) and software tools (implemented in the complex blocks) needed to control process variables. Principal equipments of this category that play a relevant role in closed loop regulation (and so in the study) are:

̶ Transducers;

̶ Signal acquisition and processing hardware and software (FUM230 and its related acquisition complex block ACQ);

̶ Control valves;

̶ Controllers, that is, the step PI controller implemented in the CTRL complex block or

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6.3.1. Transducers

Three different pressure transducers are used to acquire the measure. They are analogical capacitive pressure transducers with 4-20 mA output; their characteristic [bara] vs. [mA] is linear in the measuring range.

They are based on the principle that geometric variation, induced on the plates of a capacitor by the pressure, affects capacitor capacity which in turn affects the impedance seen by an oscillating voltage across the capacitor. As a result the current across the capacitor will be proportional to the pressure on the plates.

CV j I = ω

Moreover according to its capacitive nature, this kind of transducer will show the characteristic behaviour of a first order filter with a time constantτ . This has been simulated wit the block “LTI model” and not “Transfer function” in order to provide the initial condition.

Main characteristics of the transducers are reported in Table 8:

NUCLEAR ISLAND VENT AND DRAIN [RPE]TRANSDUCERS

Transducer PT1

Manufacturer ****

Location Upstream vacuum pump

MR 0 to 249 kPa (span=24.9 kPa) absolute

Accuracy in normal conditions ± ****% span

Characteristic Linear with an incertitude of ****% MR

Response time **** seconds

Technology Analogue capacitive transducer – 4-20 mA output

Manufacturer ****

Location Outlet of phase separator

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REACTOR COOLANT SYSTEM [RCP]TRANSDUCERS

Manufacturer ****

Location On PRZ top

MR 0 to 210 kPa absolute

Table 8: Transducers main characteristcs

6.3.2. Signal acquisition

The complex block (ACQ) that performs this task, is in charge also of other functions different from signal acquisition and pre-processing. In fact it manages signal invalidities, generation of minimum and maximum signals and hardware (transducer) monitoring.

When possible these functions have been implemented in the model (it has no sense implementing the function for hardware monitoring when there is no hardware available). Even if the all these relevant functions have been implemented, only the following signal path is relevant to the scope of frequency analysis.

Analogue signal provided by the transducer is sampled and scaled and converted to a digital value in the range 0 – 10000. The digital signal is filtered by means of a software first order filter and then, still in digital format, it is corrected if required. At the end it is rescaled to process unit according to the measuring range required for the process. Signal saturates when reaching of ±10% of the scaling range (0 – 10000). Also this time the filter has been modelled with the LTI block in order to provide the initial condition.

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Since the I&C functions studied are **** the acquisition process is carried out in the **** sub-system by acquisition and actuating modules of the TXP platform (cfr. §4.3). The resulting processing chain implemented in Simulink® is presented in Figure 25.

Figure 25: Signal acquisition chain

6.3.3. Control valves

Control valves CV1 and BP allow actuating the controlling variable of the process: mass flow rate in both control loops.

The core of their model is their Cv vs. opening percentage characteristic that has been

interpolated by polynomial fitting and the resulting coefficients in a “Polynomial” Simulink®

block. Consequently this component has one input, opening percentage, and one output, mass flow rate. By means of valve characteristic it is possible to find the Cv; by means of Bernoulli’s equation, knowing the ∆P across the valve and fluid density, it is possible to derive the mass flow trough the valve.

The valve is driven by a stepped electrical motor and so it moves with a finite and constant speed: this is accounted for by adding a limitation on the first time derivative of the signal produced by the PI controller. Moreover since mechanical effects of pressure are negligible, valve will set just at the position defined by the controller (i.e. the positioner is not needed).

6.3.4. Controllers

As for previous acquisition block the complex blocks CTRL and DRV perform other tasks than that ones relevant in the study.

The CTRL main feature is the step PI controller that it contains: it receives the process deviation and outputs a positioning command to the actuator of the valve. Other tasks performed by this block are check back signals acquisition from the limit switches of the actuator, monitoring of the actuator, selection of the operating mode of the actuator (e.g. automatic or manual).

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s I P s

F( )= +

and it is perfectly suited by the PID block available in Simulink®. Figure 26 shows the processing of the process deviation.

Figure 26: Process deviation processing

The control block DRV manages the electrical motor of the vacuum pump in an ON/OFF sense. It manages priority between different commands (manual, automatic, protection) and emits the command to the switchgear. Figure 27 shows the logic used in Simulink® to implement its tasks.

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References

[1] Matlab® R2006b/Simulink® user’s guide

[2] Areva’s internal documentation

[3] “Controlli Automatici” (5th edition) – G. Marro Zanichelli [4] “Handbook of hydraulic resistance” – 3rd edition Idelchik