Real Time Simulation of a Turbine Bypass Controller

Luca Pugi1,Carlo Carcasci1, Emanuele Galardi1, Andrea Rindi1, Nicola Lucchesi2

1DIEF: Department of Industrial Engineering

University of Florence

Florence, Italy

email: luca.pugi@unifi.it

2Velan ABV S.p.A.

Lucca, Italy

Abstract— For a fast and safe start up and shut down of steam

power plant, there is a growing interest in the optimization of

turbine bypass controllers and actuators which are mainly used

during transients. This work is focused on the development of a

simple and fast code for real time simulation of a steam plant for

the Hardware In the Loop (HIL) simulation of turbine bypass

controllers and actuators. The aim is to build a Simulink library

of simplified plant components such as valves, turbines, heaters

and so on that could be easily assembled in order to simulate with

a very simplified approach different plants and operating

scenarios. The code, is implemented for a fixed, discrete step

solver and have been tested on a Texas Instrument DSP, as

example of low cost industrial hardware. In particular two

different uses of the developed code should be considered: the

first one is the development of a virtual environment that should

be used for HIL testing of controllers and actuators. The second

one is the creation of Real Time (RT) models of complete plants

or subsystems for the development of model based controllers.

ADOPTED SYMBOLS

ℎ Specific Enthalpy [kJ/kg] DTP Discrete Tortuous Path

𝑃 Pressure [Pa] ECO Economizer

�� Mass Flow Rate [kg/s] ECU Electronic Control Unit

𝑇 Temperature [K] EV Evaporator

𝑄 Heat Flow [kW] HIL Hardware In the Loop

Subscripts: HP/LP High/Low Pressure

BVHP/ BVLP High/Low Pressure Bypass

Valve

MCR Max Continuous Rating

CND Condenser MXHP/MXLP High/Low Pressure Mixer

ECO Economizer PID Proportional Integral

Derivative Controller EV Evaporator

RH/ SH Reheater/ Superheater

FW Feed Water RT Real Time

GAS Gas from the Gas Turbine TBV Turbine Bypass Valve

MXHP/ MXLP High/Low Pressure Mixer TBVHP/TBVLP High/Low Pressure Turbine

Bypass Valve RH/ SH Reheater/ Superheater THP/TLP High/Low Pressure Turbine

THP/TLP High/Low Pressure

Turbine

TVHP/TVLP High/Low Pressure Turbine

Valve WVHP/WVLP High/Low Pressure Spray

Water Valve

WVHP/WVLP High/Low Press Spray Water

Valve

Acronyms: TBS Turbine Bypass System

BVHP/BVLP High Pressure Bypass

Valve

I. INTRODUCTION

In the modern generating units [24], plant efficiency and cost of energy production are continuously improving in terms component size, working pressures and temperatures. In addition, a high flexible operation [11] (e.g., the cyclic operation) is becoming an important specification in the design even of large power plants. Different commercial and technological reasons are enforcing this trend, as example, delocalization of energy production, use of renewable energy sources, liberalization of the energy market [22]. A flexible exercise of the plant involves even higher reliability, availability, and duration of components which are more subjected to potentially dangerous thermo-mechanical stresses [23] especially in the transitional phases (start-up, shut-down) or load disturbances, due to rapid changes in the steam conditions. In particular pressure and temperature conditions are controlled to avoid potentially dangerous working conditions such as extreme pressure and temperature or multiphase flows and to smooth thermal gradients to which are subjected many components such as heat exchangers and turbo-machines. Many companies are recently developing high efficiency Turbine Bypass Systems (TBS), which can contribute to fulfill all these specifications in order to achieve flexible plant operation, including fast and repeated start-up (maximizing the components life) [21] and the quick restoration of the power supply to the network, if any disturbance occurs. Typical applications are in large fossil fired steam plants and more recently in combined gas-steam turbine power plants [24]. In particular, for this second category of applications, fast and frequent start-up and shut-down transients are often required. This involves a difficulty to simulate the controlled plant since most of the components are working in off-design conditions during these transients. Main components of a TBS are described in Figure 1. : an inlet steam mass flow rate goes through a DTP (acronym of Discrete Tortuous Path) lamination valve, represented in Figure 2. , whose internal pressure losses are controlled in order to produce a desired pressure drop.

Figure 1. Typical layout of a TBS (courtesy of ABV Energy S.p.A.).

Figure 2. Scheme of DTP (internal tech doc. of ABV Energy S.p.A.).

A DTP valve (Kwon [9]) is composed by a set of stacked discs on which is produced a tortuous path in radial directions; by changing controlling the axial position of a piston/plug is possible to change linearly the numbers of discs through which the steam can pass through and consequently the equivalent valve orifice area. This kind of construction is robust, reliable and reduces considerably noise and vibrations associated to fluid lamination [10]-[13] Considering typical operating conditions, the flow in the tortuous path is chocked so the valve should be used also to proportionally control the steam mass flow rate in the plant. The lamination process inside this valve can be approximated as an adiabatic, isenthalpic transformation, thus in order to control the outlet steam temperature, the specific enthalpy of the flow is reduced mixing and in the main steam main flow some cold water.

In order to improve the response of the turbine bypass system an efficient design of both actuators and control system is mandatory. In literature there are some examples concerning study and development of TBSs [1],[21] which are typically based on a rigid distinction between simulation and experimental results from field activities. Recently there is an increasing interest in the application of HIL techniques to large energy production facilities, including thermal plant controllers [25], electrical power management systems Errore. L'origine riferimento non è stata trovata. . Aim of this work is to apply the HIL approach to the testing and to the fast prototyping of both controllers and actuators for TBSs reusing a consolidated know-how and the previous experiences taken from vehicular applications as proposed by Pugi, Malvezzi and Allotta [14]-[16]. In particular, the application of HIL techniques involves the development of an efficient and modular approach to implement simulated plant models which have to be implemented in real time on an electronic control

unit. In this work authors proposed to use a bond-graph approach which is often used to obtain simplified lumped models [2]-[3] able to capture the dynamical behavior of complex systems. The effectiveness of the proposed approach is also confirmed by considering previous experiences in the modeling of both Thermal Hydraulic plants [4] (complex lubrication networks of Turbo-Machines auxiliary systems) and pneumatics (railway brake plants) using customized codes [5] or commercial software [6]. As consequence the final goal of this work is to implement on a small cost, low performance hardware, a simplified plant model that should be used both for HIL testing of TBSs with a reasonable quality of simulated results respect to limited available computational resources. In particular to obtain this objective the plant is modeled using an hybrid approach in which simplified dynamical model of the steam boiler available in literature [17] and tabulated data from off-design simulations [8] performed offline are used at the same time.

II. DISCRETIZATION IN RESISTIVE AND

CAPACITIVE ELEMENTS

The dynamical behavior of a continuous fluid system should be properly represented considering the equations governing the mass balance (continuity/mass conservation), momentum (Navier Stokes equations) and energy. Considering even very complex plants, most of the components should be modeled as mono-dimensional elements in which elementary exchanges of mass, momentum or energy occurs; in particular according an approach which is often followed in literature [2]-[3] most of the components of a plant should be approximated in lumped Resistive and Capacitive ones:

Resistive Elements: in resistive elements only a momentum balance is performed, the mass flow �� is calculated considering the inlet and outlet pressure 𝑃 and temperature 𝑇 conditions which are supposed to be calculated by adjacent capacitive elements or by imposed boundary conditions. Typical resistive elements are orifices, valves and almost every component in which drag or inertial effects are dominant while energy and mass exchanges are absent or negligible.

Capacitive Elements: in capacitive elements 𝑃 and 𝑇 of a control volume are calculated imposing mass and energy/enthalpy balances. Balances are performed assuming known mass and energy/enthalpy exchanges as input calculated by external resistive elements or imposed by boundary conditions. Typical components which can be represented as Capacitive elements are tanks, heat exchangers, junctions in which is modeled the mixing of different inlet flows and more general components associated to energy or mass exchanges.

III. RESISTIVE-CAPACITIVE MODEL OF A STEAM

POWER PLANT WITH TWO PRESSURE LEVELS

Figure 3. shows a scheme of a generic steam power plant

[1] which is mainly composed by the following components:

The Boiler (CAPACITIVE ELEMENT): The boiler is

represented by a single block including evaporator (EV)

economizer (ECO) and Superheater Stage (SH). The boiler

model includes also the part concerning the thermal

exchange of the Reheater (RH). 𝑃𝑆𝐻 and 𝑇𝑆𝐻 of the

superheater outlet flow are calculated as functions of the

heat provided by an external source (the burner) and by the

steam flow required by connected HP Turbine Stage and

Bypass Valve.

High Pressure Turbine, THP with its control valve TVHP

(RESISTIVE ELEMENT): the steam flow of the turbine is

calculated as a function of inlet 𝑃𝑆𝐻 , 𝑇𝑆𝐻 and outlet 𝑃𝑅𝐻

conditions which are calculated by adjacent Capacitive

Blocks. Relationship between the flow and the pressure

drop takes count of both the valve state (open/closed) and

the turbine.

Bypass and Spray valves (BVHP, WVHP) of the bypass

system for the HP level (RESISTIVE ELEMENTS): the

steam flow on BVHP and the water flow on WVHP

depends both from inlet and outlet pressure conditions and

by the valve state.

Mixer MXHP and reheater RH (CAPACITIVE): this block

represents the mixing of different flows coming by THP

and by turbine bypass stage and the following reheating in

the RH stage of the boiler. Inlet flows ��𝑇𝐻𝑃, ��𝑊𝑉𝐻𝑃 and

��𝐵𝑉𝐻𝑃, are calculated by turbine and valves resistive

blocks. Performing mass and enthalpy balances is possible

to calculate the corresponding pressure 𝑃𝑀𝑋𝐻𝑃 and

temperature 𝑇𝑀𝑋𝐻𝑃 of the mixed flow. Neglecting pressure

drops in the reheater stage (𝑃𝑀𝑋𝐻𝑃 = 𝑃𝑅𝐻) and knowing the

heat flow 𝑄𝑅𝐻 from the boiler is possible to calculate the

outlet temperature 𝑇𝑅𝐻 .

Low Pressure Turbine (TLP), bypass and spray valves

(BVLP, WVLP ) (RESISTIVE ELEMENTS): as the

corresponding blocks of the high pressure level (the

implementation is the same), these components calculate

their corresponding inlet and outlet flows from known inlet

and outlet pressure conditions.

Condenser CND (CAPACITIVE / boundary conditions)

and low pressure Mixer stage MXLP: this block represents

the condenser which is modeled as a reference (imposed)

boundary pressure condition. Temperature of the mixed

flow obtained by merging ��𝑇𝐿𝑃, ��𝑊𝑉𝐿𝑃 and ��𝐵𝑉𝐿𝑃, is

obtained through a simple enthalpy energy balance.

Figure 3. Simplified scheme of the studied plant with adopted simbols and

corresponding discretization in capacitive (“C” green capital letters) and

resistive (“R” red capital letters ).

Thanks to this modular architecture, this approach should

be easily applied to the simulation of plants with different

pressure levels.

IV. IMPLEMENTATION OF DIFFERENT CONTROL

STRATEGIES

Proposed control strategies differs in the way is supposed

to be controlled the boiler and more generally the plant respect

to the functionality of the turbine bypass system. In particular

to simplify the system description and comprehension, the two

simplified approaches followed in this work are indicated with

the capital letters “A” and “B”. Both the strategies are

implemented in order to control associated to the plant

start/initialization of the plant which is schematized in three

sub-phases:

Bypass Start-up: boiler gradually starts to produce steam

which is not used to feed turbines, since TBVHP and

TBVLP are closed. All the steam flow passes in the bypass

system. 𝑃 and 𝑇 are smoothly increased to reach the

minimal conditions needed to start the turbines.

Turbine Run-up: turbine valves are gradually opened while

an appreciable part of the flow is still passing in the bypass

system. Flow rates through turbines is gradually increasing.

Bypass Shut-down: in this final phase, bypass valves are

gradually closed. At the end of this phase bypass system is

deactivated and all the steam produced by the boiler is

processed by the turbines.

A. Strategy A

The boiler pressure 𝑃𝐸𝑉 , 𝑃𝑆𝐻 is supposed to be controlled as

visible in the simplified scheme of Figure 4. . Pressure 𝑃𝐸𝑉 is

controlled by increasing/decreasing the heat flow provided to

the boiler, considering a simplified approach in which a simple

PID regulator is considered.In particular bypass valves

TBVHP and TBVLP control the steam flows through the two

stages of the plant. As a consequence small changes of the heat

provided to the boiler produces null or negligible changes in

terms of steam flows, respect to appreciable variations of the

boiler pressure PSH. Different control strategies are supposed

to be applied respect to three phases of the plant initialization

described above:

Bypass Start-up and Turbine Run-up phases: TBVLP valve

is regulated in order to control the total steam flow ��𝐶𝑁𝐷,

which is discharged in the condenser. ��𝐶𝑁𝐷 differs from

the corresponding steam flow produced by the boiler ��𝑆𝐻

only for the contribution of the water injected by the two

spray waters WVHP and WVLP. Both WVHP and WVLP

are regulated in order to control respectively 𝑇𝑀𝑋𝐻𝑃 and

𝑇𝑀𝑋𝐿𝑃 in order to protect respectively the reheater and the

condenser from excessive thermal loads and gradients.

Since the flow is mainly regulated by WVLP, the pressure

in the reheater 𝑃𝑅𝐻 is controlled by the WVHP valve. In

this way it’s possible to smoothly start the plant while the

turbines are still excluded (Bypass Start-up) and in the

following Turbine Run-Up where TVHP and TVLP are

opened.

During the Bypass Shut-down, the controllers smoothly

transfer their functions, adopting a bumpless switching

strategy inspired by examples available in bibliography

[19], [20]: TBVHP regulates the mass flow through the

whole high pressure stage and consequently through the

reheater ��𝑀𝑋𝐻𝑃; TBVLP regulates the pressure in the

reheater 𝑃𝑅𝐻 . Also during the Bypass Shut-down, both the

water spray valves WVHP and WVLP continues to

regulate respectively temperatures 𝑇𝑀𝑋𝐻𝑃 and 𝑇𝑀𝑋𝐿𝑃 .

Figure 4. Simplified scheme of strategy A control.

B. Strategy B

In this second case, as shown in the simplified scheme of

Figure 5. , the bypass valve stages TBVHP and TBVLP are

used to control the pressure levels of both boiler 𝑃𝑆𝐻 and

reheater 𝑃𝑅𝐻; as a consequence, a variation of the heat provided

of the boiler produces a null or negligible variation in the boiler

pressures 𝑃𝐸𝑉 respect to the corresponding variation of the

produced steam flow ��𝑆𝐻. For this reason, The boiler is

modeled as a flow controlled system in which a simplified PID

regulator adjust the heat flow 𝑄 provided by the burner to

roughly control the steam flow ��𝑆𝐻. Outlet mean temperatures

of the high and low pressure stages 𝑇𝑀𝑋𝐻𝑃 and 𝑇𝑀𝑋𝐿𝑃 are

regulated with the same approach described for the A Strategy:

spray valves WVHP and WVLP regulate respectively 𝑇𝑀𝑋𝐻𝑃

and 𝑇𝑀𝑋𝐿𝑃 by injecting a variable amount of cold water in the

steam flow.

Figure 5. Simplified scheme of strategy B control.

V. SIMULATION RESULTS

A. Reference Test Case

In order to verify the reliability of the simplified model proposed in this work, results of the proposed models have been compared with a benchmark case available in literature [1]. The proposed benchmark is referred to an oil-fired generating unit, characterized by 4 X 500 MW Power, 1.343.666 kg/h of nominal steam flow, while nominal 𝑃𝑆𝐻 =168 bar and nominal 𝑇𝑆𝐻 = 𝑇𝑅𝐻 = 538 °C. The plant layout is almost equal to the scheme of Figure 3. for a two level

pressure steam plant. For the benchmark plant [1] are also available some reference data which are briefly described in TABLE I. : in particular the values of the main plant parameters during the three phases of the starting transient are shown. These values are referred to a time history which is defined respect to an initial condition in which the initial pressure of the evaporator 𝑃𝐸𝑉 is 68 bar. All the published results are directly referred to the Real-Time code implemented on a TI F28335 board on which the model run with a fixed integrator step. In order to optimize the implementation respect to available numerical resources the simulation was split in various tasks running at different frequencies optimized respect to the dynamical behavior of the corresponding simulated components as visible in TABLE II. In particular communication tasks and filtering of analog signals are implemented only when the system is connected to an external plant or to a component (a tested positioner or other).

TABLE I. BEHAVIOR OF THE REFERENCE PLANT TAKEN FROM

LITERATURE [1].

time[s] 0 200 1000 3000 3300 3600

Unit Operating

phases

Bypass

Start-up Turbine Run-up

Bypass

Shut-down

HP

lev

el

[kg/s] ��𝑀𝑋𝐻𝑃

(total) 0 30 35 60 125 125

[kg/s]

��𝐵𝑉𝐻𝑃 +��𝑊𝑉𝐻𝑃 + (bypass)

0 30 35 60 60 0

[kg/s] ��𝑇𝐻𝑃

(turbine) 0 0 0 0 65 125

LP

lev

el

[kg/s] ��𝑀𝑋𝐿𝑃

(total) 0 35 43 75 130 125

[kg/s] ��𝐵𝑉𝐿𝑃 +��𝑊𝑉𝐿𝑃 +

(bypass)

0 35 43 75 75 0

[kg/s] ��𝑇𝐿𝑃

(turbine) 0 0 0 0 55 125

HP

lev

el [bar] 𝑃𝑆𝐻 68 68 85 117 117 123

[C°] 𝑇𝑆𝐻 571 571 572 573 572 572

[C°] 𝑇𝑀𝑋𝐻𝑃 300 300 300 300 330 330

LP

lev

el

[bar] 𝑃𝑅𝐻 0.5 3.7 4 5.3 5.3 11.75

[C°] 𝑇𝑅𝐻 440 455 500 538 538 538

[bar] 𝑃𝐶𝑁𝐷 0.28 0.28 0.28 0.28 0.28 0.28

[C°] 𝑇𝑀𝑋𝐿𝑃 210 210 210 210 210 210

TABLE II. TASK SCHEULING.

Model

Boiler

(SH,EV,

ECO,RH)

Turbines

(THP/

TLP)

Mixing Capacities

(MXLP, MXHP)

Freq.

[Hz] 0.25Hz 1Hz 10Hz

Model

Control Valves

Valve Controllers/

Positioners Filtering A/D and COM

Freq.

[Hz] 10Hz 100Hz 500Hz

B. Simulation and Verification with Benchmark Test Case

As previously introduced the plant model developed by authors was verified considering as benchmark test-case a plant and the corresponding results from a work available in literature [1] . Bypass valve are controlled using simple PID controllers whose layout is described for the two proposed control strategies “A” and “B” described in Figure 4. and Figure 5. .In order to make clearer how different control plant strategies affect the plant simulation, TABLE III. shows what are the main plant parameters regulated in both cases. In particular some parameters are not directly controlled by valves of the bypass system, while other values are supposed to be regulated by the boiler loop.

TABLE III. REGULATED PLANT PARAMETERS FOR STRATEGIES A AND B

AND BOILER LOOP DURING THE DIFFERENT PHASES OF THE PLANT START-UP.

Operating

phases Bypass Start-up

Turbine Run-up

Bypass Shut-down

HP

Lev

el 𝑃𝑆𝐻

A(boiler loop)

B

A(boiler loop)

B

A(boiler loop)

B

𝑇𝑀𝑋𝐻𝑃 A/B A/B A/B

𝑃𝑅𝐻 A/B A/B A/B

��𝑀𝑋𝐻𝑃 (total) A

��𝐸𝑉 B(boiler loop) B(boiler loop) B(boiler loop)

LP

lev

el 𝑇𝑀𝑋𝐿𝑃 A/B A/B A/B

��𝑀𝑋𝐿𝑃 (total) A A A

All the results shown in this work are referred to the real time implementation of the model directly on the ECU on which the RT Simulink Model is implemented. In Figure 6. some results in terms of simulated mass flow rates are compared considering both strategy “A” and “B” during the bypass the startup, run up and shut down phases: differences between the reference benchmark and simulation are quite small. Higher errors should be noticed in the transition between run up and shut down on the low pressure stage. These differences are mainly caused by the hot gases from the starting turbine stages which is compensated by the temperature controllers increasing the amount of water which is introduced through the spray water valves. It’s also interesting to notice that the mass flows ��𝑀𝑋𝐻𝑃 and ��𝑀𝑋𝐿𝑃 are different for the contribution of the water injected by the spray valves.

Figure 6. Comparison between the reference benchmark and the simulated control strategies (A and B) in terms of mass flow rates.

Pressure behavior, for SH and RH stages; comparison between reference

value and controlled ones for Strategies A and B.

Also good results have been obtained in terms of pressure and temperatures which are respectively visible in 0 and in Figure 7. : according with results commonly available in literature the controlled pressure seems to be very stables, while the temperature control exhibit a more nervous behavior especially at the beginning of the bypass startup phase and during the bypass shut-down. In both cases temperature control performed by spray valve show a nervous behavior

associated to a “chattering” of the controlled temperature. This behavior should be explained considering that when temperature chattering occurs, the steam flow passing through the bypass is quite small; as a consequence also the amount of injected water respect to the size of the spray valve is very small making the control quite difficult to be performed. Finally a statistical analysis of the mean relative error between simulated and desired values of plant pressures, flows, and temperatures are visible in TABLE IV. : for both the proposed control strategies results are quite good, higher values of the relative error are recorded on the regulated flows. In particular for the “A” strategy higher errors are recorded during shut down and start up phases. This behavior can be easily explained considering that the flow control is mainly performed by a single bypass valve in both phases (TBVHP or TBVLP) so the total controlled flow is more affected by disturbances introduced by both boiler dynamics and temperature control performed by spray valves. In the case of strategy “B” higher errors on regulated flows are also recorded in the turbine run up phase. Also in this second case this behavior should be easily explained that in this control configuration bypass valve controls pressure levels and only in an indirect way the flow. As a consequence in the transients associated to the insertion of turbines, pressure behavior is more stable than the flow one, which is also affected by boiler dynamics.

TABLE IV. BEHAVIOR OF THE RELATIVE ERROR BETWEEN SIMULATED

VALUES AND REFERENCE ONES.

Bypass Start-

up

Turbine Run-up Bypass Shut-

down ��𝑴𝑿𝑯𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑨) <4% <0.1% <0.1%

��𝑴𝑿𝑯𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑩) <0.1% <0.1% <0.2%

��𝑴𝑿𝑳𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑨) <0.5% <3.5% <6.5%

��𝑴𝑿𝑳𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑩) <0.7% <6.5% <8.5%

𝑷𝑺𝑯(𝒔𝒕𝒓𝒂𝒕. 𝑨) <0.1% <0.1% <0.1%

𝑷𝑺𝑯(𝒔𝒕𝒓𝒂𝒕. 𝑩) <0.1% <0.1% <0.1%

𝑷𝑹𝑯(𝒔𝒕𝒓𝒂𝒕. 𝑨) <0.1% <0.1% <4%

𝑷𝑹𝑯(𝒔𝒕𝒓𝒂𝒕. 𝑩) <0.1% <0.1% <4%

𝑻𝑴𝑿𝑯𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑨) <0.4% <0.2% <2%

𝑻𝑴𝑿𝑯𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑩) <0.2% <0.3% <0.9%

𝑻𝑴𝑿𝑳𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑨) <0.2% <0.2% <3%

𝑻𝑴𝑿𝑳𝑷(𝒔𝒕𝒓𝒂𝒕. 𝑩) <0.2% <0.4% <3%

Figure 7. Temperature behavior of the outlet mixed mass flows rates after

the bypass turbine stages; comparison between reference value and controlled ones for Strategies A and B.

VI. CONCLUSIONS

In this work a simplified dynamical model of a steam plant has been presented. The proposed model is optimized for RT implementation on low cost commercial DSP board in order to be used for HIL testing and for model based design of plant controllers. In particular in order to reduce needed computational resources the plant is modeled considering an hybrid approach considering both a simplified model of the boiler [17] and tabulated data produced by off-design simulations [8] performed offline. A preliminary validation based on the comparison of results respect to a test case available in literature [1] have produced encouraging results considering that the model was able to reproduce the reference behavior considering two different control configurations of the simulated plant. Also for RT Simulations results are encouraging considering the relatively modest performances of the chosen target hardware. As further development authors are implementing Hardware In the Loop testing of valve positioners (object of a future pubblication).

ACKNOWLEDGMENT

This work was financed as a part of the project High Efficiency Valves (CUP: D55C12009530007) financed by the program POR CRO FESR of Regione Toscana (European Funds for Regional Industrial R&D projects).

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