Issue 
Mechanics & Industry
Volume 19, Number 3, 2018



Article Number  311  
Number of page(s)  11  
DOI  https://doi.org/10.1051/meca/2018028  
Published online  04 October 2018 
Regular Article
Realtime simulation testbed for an industrial gas turbine engine’s controller
Systems Simulation and Control Laboratory, School of Mechanical Engineering, Iran University of Science and Technology,
Tehran, Iran
^{*} email: alirezamiran@mecheng.iust.ac.ir; s.alireza.miran@gmail.com
Received:
20
August
2017
Accepted:
18
May
2018
A hardwareintheloop (HIL) test for a control unit of an industrial gas turbine engine is performed to evaluate the designed controller. Although the dynamic performance of the studied gas turbine is strictly related to the variable inlet guide vain (VIGV) position, one of the main challenges is to develop an engine model considering VIGV variations. The model should also be capable of real time simulation. Accordingly, the gas turbine is numerically modeled using bond graph concepts. To demonstrate the operational reliability of the engine’s control strategy, the control algorithm is implemented on an industrial hardware as an embedded system. This is then put into a HIL test along with the engine model. The actual component (controller) and the virtual engine model are the hardware and software parts of the HIL test, respectively. In this experiment, the interaction between the real part and the rest of the system is compared with that of the completely numerical model in which the controller is a simulated softwarebased model as is the engine itself. Finally, the results indicate that the physical constraints of the engine are successfully satisfied through the implementation of control algorithms on the utilized hardware.
Key words: Bond graph / industrial gas turbine engine / electronic control system / hardwareintheloop simulation
© AFM, EDP Sciences 2018
1 Introduction
A key factor in designing complex systems and structures is the ability to test every subsystem in each design stage to ensure a convergent design strategy. In this regard, various theoretical and experimental procedures have been considered. The hardwareintheloop (HIL) simulation has proven to be one of most efficient method for testing complicated and costly systems. HIL simulation has been used extensively in a variety of fields for realtime testing and development of interconnected physical components of a system replaced virtually by computer models. Interaction between hardware and software during the test is accomplished via electric signals transferred by data acquisition cards. Consequently, HIL simulation is widely used in numerous applied fields and industries. Using this approach, it is possible to test the performance of real mechanical parts of a system along with softwarebased simulated models of other parts in real time [1,2].
One of the requirements of HIL test is designing and constructing a testsystem so as to experiment with different parts of a complex system in accordance with the defined rules. Furthermore, to make HIL more costeffective, the main system in which we are interested to design should be numerically modeled. These hardware and software models are then put into a loop together for experiment.
Hanselman [3] benefited from HIL simulation in the control development of electronic control units (ECUs) used in engines, vehicles and other components. Cao et al. [4] verified the validity of their control scheme based on adaptive networkbased fuzzy inference engine using HIL test. Gans et al. [5] presented another HIL simulation to control unmanned vehicles. In that study, a real camera captured pictures of a virtual 3D environment which would later be used in the control system. Aerospace is another field where HIL has progressively been utilized as Maclay [6] enumerated several examples. Canadian Space Agency successfully applied HIL in meticulously tuning controllers used in the International Space Station. A nongravity environment for the controllers was simulated using HIL. The simulation results were acceptable compared to practical tests [7]. In the gas turbine industry, HIL applications are innumerable, specifically for designing, testing and performance verification of the gas turbine engine’s ECU or fuel control unit (FCU). HIL simulation studies have been reported for rapid prototyping of ECU of turbofan engines [8,9] and turbojet engines [10,11]. An HIL simulation is reported by MontazeriGh et al. [12] for ECU performance verification of a turboshaft engine. Another HIL simulation is presented by MontazeriGh et al. [13] for testing a fuel control unit of a jet engine.
Despite numerous reports on HIL simulation of a gas turbine engine’s ECU or FCU, there has not been any publication regarding HIL simulation of a twoshaft industrial gas turbine engine modeled using bond graph methodology. As an example of bond graph power in modeling gas turbine engines, Novinzadeh et al. used this method to simulate an ideal turbocharger [14]. Montazeri et al. [15] showed how bond graph approach can be utilized for modeling the cold start phase of a microjet engine.
Moreover, Krikelis and Papadakis [16] modeled a simple cycle of the singleshaft gas turbine using bond graph model. By linearization of the model around an operation point, they designed a PI controller for it. In addition, they utilized several parameters including the pressure, temperature and torque as the effort variables, as well as the mass flow rate and engine speed (rpm) as the flow variables.
Sanei et al. [17] considered the effects of kinetic energy and momentum (in the convergentdivergent nozzles with supersonic fluid flows) using the pseudobond graph approach.
Uddin and Gravdahl [18] developed the bond graph model of a radial compressor system, and complemented it with a control system. They also developed certain methods to prevent the surge in the compressor. Montazeri and MiranF [19] presented the bond graph approach application for modeling the industrial gas turbine engine. The bond graph model developed in that study was applicable to the real time implementation. A more comprehensive study using bond graph was later accompanied by the modeling and simulation of the propulsion system of a twoshaft gas turbine including a platetype clutch [20] as well as another related study on JetQuard aerial robot [21]. This was similar to other gas turbine nonlinear models [22–24] involving thermodynamics equations as well as compressor and turbine performance maps. Therefore, the bond graph model seems appropriate for controlling purposes during an HIL simulation as is the case in present study.
In this article, the designed control system of a twoshaft industrial gas turbine engine, along with the engine’s ECU (as a physical model), is tested in an HIL simulation. The utilized ECU is an electronic hardware called PC/104, which is an embedded system on which the control algorithm has been implemented via C++ programming language. The engine model is actually a bond graph model simulated on a personal computer using 20SIM and Matlab/Simulink. The interface between hardware and software subsystems is realized by an I/O data acquisition card.
To examine the performance of ECU to ensure the accuracy of its operation, the results are compared with the simulation results of the same system in which the ECU is numerically simulated. Such simulation is called softwareintheloop (SIL) simulation.
2 System description
The schematic of the system as well as the interaction of different parts in HIL and SIL test is shown in Figure 1a–c. It is a feedback control system composed of two main subsystems including the plant and the controller. Only the plant is simulated numerically, while the ECU is a hardware within the HIL simulation. The plant, a twoshaft industrial engine (SGT600) [25] with two outputs and two inputs, is a gas turbine engine model. The engine specifications at the design point are given in Table 1 [25]. The plant’s inputs are the required fuel flow rate to the combustion chamber of the gas turbine engine and the required variable inlet guide vain (VIGV) position. The engine outputs are the angular velocities of the power gas turbine engine shaft (N_{PT}) and the gas generator shaft (N_{GG}). The gas turbine engine has two bleed valves which are considered to be closed during the engine modeling process at a specific state in this article. This state is demonstrated in Figure 2, indicating that their effect is negligible. The plant controller, known as the ECU, calculates the appropriate fuel flow rate and the required VIGV at every moment based on its inputs, and accordingly generates control signals towards the plant. VIGV position is a function of N_{GG} and thus, the effects of VIGV variations are considered in the engine’s performance maps. The ECU has three inputs, two of which are the angular velocities of the engine that are fed back to the ECU, and a reference angular velocity which is set by the user. RRV is a preferred angular velocity with which the power turbine shaft rotates. The outputs are the fuel flow rate and VIGV, as stated previously.
Fig. 1 Schematics of (a) complete system, (b) HIL test, and (c) SIL test 
2.1 Plant
The engine components [19] (compressor, combustor and turbine) are simulated according to the bond graph theory. Every component is assumed to be an energy field interacting with other components, i.e. mass, energy and work are permanently exchanged in all components. The gas turbine engine is considered to be a thermofluid system, and the effort and flow variables are selected as introduced by Karnopp [19,26]. According to this variable selection, the pseudobond graph is advantageous over the true bond graph. The effort and flow variables of the compressor and turbine are torque and engine speed. Mass flow rate and pressure are the flow and effort variables in one pseudobond while energy flow and temperature are the variables for another pseudobond. In order to obtain a gas turbine model using the bond graph theory, it is necessary to take the following criteria into consideration:

model simplicity;

inclusion of the control model in engine model to observe the physical limitations of the engine;

dynamic operation and steady state performance predictability;

considering the change in the composition of working medium.
Generally, two different approaches are employed to develop the model of compressor or turbine. One is based on the turbomachinery fundamental equations. Such approach requires not only a thorough understanding of the machine, but also considering some simplifying assumption that may lead to limited accuracy.
The other approach requires taking the state performance maps into account. These maps contain valuable performance information of the machine over a large operational range. Also, no mass and energy accumulation within the compressor and turbine models are considered (quasisteady assumption). As a result, the performance map for steady state condition is valid even during transient operation.
Finally, to show the accuracy of utilized bond graph model, the reader is referred to references [19,20] where it was used for a gas turbine and good agreement was obtained.
2.1.1 Compressor model equations
The isentropic efficiency and corrected mass flow rate of the compressor vary in accordance with three compressor parameters: inlet guide vanes, pressure ratio and corrected rotor speed [19,22]. These are described as $${\mathit{\Gamma}}_{\text{C}}={f}_{1}({\pi}_{\text{C}},{N}_{\text{C},\text{cor}},{\theta}_{\text{VIGV}}),\text{\hspace{1em}}{\eta}_{\text{is},C}={f}_{2}({\pi}_{\text{C}},{N}_{\text{C},\text{cor}},{\theta}_{\text{VIGV}}),$$(1) $${\mathit{\Gamma}}_{\text{C}}=\frac{{{\displaystyle \dot{m}}}_{C}\sqrt{\theta}}{\delta},\text{\hspace{1em}}{N}_{\text{C},\text{cor}}=\frac{{N}_{\mathrm{G}\mathrm{G}}}{\sqrt{\theta}},\text{\hspace{1em}}{\pi}_{\text{C}}=\frac{{P}_{\text{out}}}{{P}_{\text{in}}}\text{,}$$(2) $${M}_{\text{C}}=\frac{30}{\pi}\left[\frac{{{\displaystyle \dot{m}}}_{\text{C}}({h}_{\text{is,out}}{h}_{\text{in}})}{{\eta}_{\text{is,C}}N}\right],{T}_{\text{out}}{T}_{\text{in}}=\frac{{T}_{\text{in}}}{{\eta}_{\text{C}}}\left[{\left(\frac{{P}_{\text{out}}}{{P}_{\text{in}}}\right)}^{\frac{\gamma 1}{\gamma}}1\right]\text{,}$$(3) $${{\displaystyle \dot{E}}}_{\text{in}}={{\displaystyle \dot{m}}}_{\text{C}}{h}_{\text{in,C}}\text{,}$$(4) where Γ_{C}, π_{C}, N_{C,cor}, η_{is,C}, M_{C} and ${{\displaystyle \dot{m}}}_{\text{C}}$ are, respectively, the corrected mass flow rate, pressure ratio, corrected rotor speed, isentropic efficiency, torque and air mass flow rate of the compressor. Moreover, N_{GG} is the gas generator speed, P_{out} is the outlet pressure, (P_{in}, h_{in}) are the inlet pressure and enthalpies, h_{is,out} is the outlet isentropic enthalpy, (T_{out}, T_{in}) are the outlet and inlet temperatures and γ is the specific heat ratio. Finally, E being the internal energy, (${{\displaystyle \dot{E}}}_{\text{in}}$, ${{\displaystyle \dot{E}}}_{\text{out}}$) describe the energy flow in and out of the compressor.
By definition, the dimensionless pressure and temperature are defined as $\delta ={P}_{\text{in}}/{P}_{\text{ref}}$ and $\theta ={T}_{\text{in}}/{T}_{\text{ref}}$, respectively, where P_{ref} and T_{ref} represent the standard pressure and temperature (ISA).
2.1.2 Combustion chamber model equations
For the combustion chamber, the following assumptions are considered: volume of the chamber is constant and physical and chemical properties of fuel and air mixture are the same throughout the chamber [19,22]. Based on the conservation laws of mass (Eq. (5)) and energy (Eq. (6)), the combustion chamber equations are expressed as $$\frac{\mathrm{d}m}{\mathrm{d}t}={{\displaystyle \dot{m}}}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}}\text{,}$$(5) $$\frac{dU}{\mathrm{d}t}={{\displaystyle \dot{m}}}_{\text{in}}{h}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}{h}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}}({h}_{\text{f}}+\mathrm{L}\mathrm{H}\mathrm{V}{\eta}_{\text{cc}})\text{,}$$(6) where $\mathrm{L}\mathrm{H}\mathrm{V}$ is the heat value of fuel, m_{f} is the fuel mass, m_{air} is the air mass and η_{cc} is the combustor efficiency. By differentiation the above equations, one can obtain $$\frac{\text{d}U}{\text{d}t}={C}_{\text{v}}T\frac{\text{d}m}{\text{d}t}+{C}_{\text{v}}m\frac{\text{d}T}{\text{d}t}\text{,}$$(7)where C_{v} is the specific heat at constant volume. Setting equation (6) equal to equation (7), and then using the ideal gas law, the temperature and pressure of chamber exhaust are described as $$\frac{\text{d}T}{\text{d}t}=\frac{{{\displaystyle \dot{m}}}_{\text{in}}{h}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}{h}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}}({h}_{\text{f}}+\text{LHV}{\eta}_{\text{cc}}){C}_{\text{v}}T({{\displaystyle \dot{m}}}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}})}{{C}_{\text{v}}m}\text{,}$$(8) $$\frac{P}{m}({{\displaystyle \dot{m}}}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}})+\frac{P}{T}\left[\frac{{{\displaystyle \dot{m}}}_{\text{in}}{h}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}{h}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}}({h}_{\text{f}}+\text{LHV}{\eta}_{\text{cc}}){C}_{\text{v}}T({{\displaystyle \dot{m}}}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}+{{\displaystyle \dot{m}}}_{\text{f}})}{{C}_{\text{v}}m}\right]=\frac{\text{d}P}{\text{d}t}\text{.}$$(9)
Finally, the fueltoair ratio is expressed by $$f=\frac{{m}_{\text{f}}}{{m}_{\text{air}}}=\frac{{m}_{\text{f}}}{m{m}_{\text{f}}}\text{.}$$(10)
2.1.3 Gas generator turbine model equations
In a similar manner, the isentropic efficiency and corrected mass flow rate of the turbine are dependent on two turbine parameters: expansion ratio and corrected rotor speed [19,22], written in the form $$\Gamma {\hspace{0.17em}}_{\text{T}}={g}_{1}({\pi}_{\text{T}},{N}_{\text{T},\text{cor}}),\text{\hspace{1em}}{\eta}_{\text{is},\text{T}}={g}_{2}({\pi}_{\text{T}},{N}_{\text{T},\text{cor}})\text{,}$$(11) $${\Gamma}_{\text{T}}=\frac{{{\displaystyle \dot{m}}}_{\text{c}}\sqrt{\theta}}{\delta},\text{\hspace{1em}}{N}_{\text{T},\text{cor}}=\frac{{N}_{\text{GG}}}{\sqrt{\theta}},\text{\hspace{1em}}{\pi}_{\text{T}}=\frac{{P}_{\text{in}}}{{P}_{\text{out}}}\text{,}$$(12) $${M}_{\text{T}}=\frac{30}{\pi}\left[\frac{{\eta}_{\text{T}}{{\displaystyle \dot{m}}}_{\text{T}}({h}_{\text{u}}{h}_{\text{d,is}})}{N}\right]\text{,}$$(13) $${{\displaystyle \dot{E}}}_{\text{in}}={{\displaystyle \dot{m}}}_{\text{T}}{h}_{\text{u,T}}\text{,}$$(14) $${{\displaystyle \dot{E}}}_{\text{out}}={{\displaystyle \dot{m}}}_{\text{T}}\left[{h}_{\text{u,T}}+\frac{({h}_{\text{u}}{h}_{\text{d,is}})}{{\eta}_{\text{T}}}\right]\text{,}$$(15) where g represents a function, i.e. the corrected mass flow rate (Γ_{T}) and isentropic efficiency (η_{is,T}) are both functions of expansion ratio and corrected rotor speed.
2.1.4 Plenum equations
The plenum is taken as an isentropic passage in which energy and flow speed are not significant and thus are neglected. The governing equations to obtain the plenum pressure in addition to the temperature variation caused by the mass accumulation can be written as $$\begin{array}{l}{V}_{\text{p}}\frac{\text{d}{\rho}_{\text{out}}}{\text{d}t}=\frac{{V}_{P}}{\delta R{T}_{\text{out}}}\frac{\text{d}{p}_{\text{out}}}{\text{d}t}={{\displaystyle \dot{m}}}_{\text{in}}{{\displaystyle \dot{m}}}_{\text{out}}\hfill \\ \frac{\text{d}{T}_{\text{out}}}{\text{d}t}=\frac{\delta}{\rho {c}_{\text{p}}{V}_{\text{p}}}\left[{({c}_{\text{p}}T{\displaystyle \dot{m}})}_{\text{in}}{({c}_{\text{p}}T{\displaystyle \dot{m}})}_{\text{out}}\right]+\frac{{T}_{\text{out}}}{\rho {V}_{\text{p}}}({{\displaystyle \dot{m}}}_{\text{out}}{{\displaystyle \dot{m}}}_{\text{in}})\hfill \end{array}\text{,}$$(16) where V_{p} is the plenum volume. Moreover, c_{p} and ρ are the constant pressure heat capacity, respectively. δ can be estimated by the specific heat ratio [19,22].
2.1.5 Gas turbine shaft model equations
The gas generator shaft acceleration is due to the difference between the turbine output shaft power and the input power to the compressor. It should be noted that the variations in the load applied to the power turbine shaft causes changes in the power turbine speed. This leads to the acceleration of the connector shaft between the power turbine and generator (load). Accordingly, the gas generator shaft along with the power turbine shaft can be described using mathematical relations as in $$\begin{array}{l}{M}_{\text{fric,GG}}={\eta}_{\text{mech,GG}}{M}_{\text{GG.Turb}}\hfill \\ {M}_{\text{fric,PT}}={\eta}_{\text{mech,PT}}{M}_{\text{Power.Turb}}\hfill \end{array}\text{,}$$(17) $$\frac{\text{d}{N}_{\text{GG}}}{\text{d}t}=\frac{30}{\pi {I}_{\text{GG}}}({M}_{\text{GG.Turb}}{M}_{\text{C}}{M}_{\text{fric,GG}})\text{,}$$(18) $$\frac{\text{d}{N}_{\text{PT}}}{\text{d}t}=\frac{30}{\pi {I}_{\text{PT}}}({M}_{\text{Power.Turb}}{M}_{\text{L}}{M}_{\text{fric,PT}})\text{,}$$(19) where η_{mech,GG} and η_{mech,PT} represent the mechanical efficiency of, respectively, the gas generator and power turbine. In addition, (M_{fric,GG}, M_{GG.Turb}) and (M_{fric,PT}, M_{Power.Turb}) are the friction and turbine torque of, respectively, the gas generator and power turbine. Furthermore, M_{L} signify the consumed torque as a result of applied load on the power turbine shaft.
Figure 3 shows the component models. The compressor, combustion chamber and turbine are modeled via modulated energy fields (MR, MC and MR). IGV and fueltoairratio (f) signals are transferred to the compressor and turbine by informative bonds. When the bond graphs of all submodels are coupled, a complete gas turbine engine dynamic model would be constructed, as shown in Figure 4.
Fig. 4 Complete bond graph model of the engine. 
2.2 ECU
ECU is the master mind of the system. It computes the necessary amount of required fuel as well as the appropriate IGV position for the engine to provide a satisfactorily operation and ensure a safe performance. The fuel control algorithm is based on the MinMax control strategy. The IGV control algorithm is a function of the angular velocity of the gas generator shaft. Upon designing the control algorithm in 20SIM [27] and Matlab/Simulink, its precise and nondestructive performance is tested by the computer. As in every gas turbine engine design and construction process, ECU eventually needs to be implemented on a hardware. In this study, a microprocessor called PC/104 has been used. In addition, the MinMax control strategy for fuel controlling along with the IGV control function are implemented using C++ language. The models of plant [19] and ECU [12,28] as well as PC/104 specifications used for this study were discussed in detail in previous studies.
The MinMax controller is composed of five transient control loops and a single steady state control loop, as depicted in Figure 5. In each loop, the required fuel to fulfill the needs of that loop is calculated. Next, a MinMax algorithm is used for fuel selection throughout the engine operation. This algorithm is written as [12]
$${F}_{\text{trans}}=\text{Max}\left[{F}_{\text{dec}},\text{Min}\left({F}_{\text{acc}},{F}_{{\text{NGG}}_{\text{max}}},{F}_{{\text{NPT}}_{\text{max}}},{F}_{{\text{NPT}}_{\text{requried}}}\right)\right]\text{,}$$(20)
$${F}_{\text{total}}={F}_{\text{trans}}+{F}_{\text{steady}}\text{.}$$(21)
The description of each parameter is presented in Table 2.
In order to assess the performance of this controller, an input load is applied to the engine, as demonstrated in Figure 6. As shown in Figures 7–9, N_{GG} (NGG), N_{PT} (NPT) and their rate of change have been kept within allowable limits. Also, N_{PT} approximately remains at its desired set value.
Fig. 6 Load input to the gas turbine model. 
Fig. 7 Variation of the gas generator turbine shaft acceleration. 
Fig. 8 Variation of the gas generator shaft speed. 
Fig. 9 Variation of the power turbine shaft speed. 
3 HIL setup
In order to evaluate the performance accuracy of the ECU and its proper implementation, a real time HIL simulation testbed is prepared as displayed in Figure 10.
The gas turbine engine model, created using 20SIM and Simulink/Matlab, is loaded on a PC labeled “1” in the figure. The control algorithm is embedded on VDX6354 PC/104 (labeled “2”) as the ECU, via a C++ code.
The VDX6354 family of controllers is designed as a plugin replacement to support legacy software and help extend the existing product life cycle without heavy reengineering. VDX6354 is suitable for a broad range of dataacquisition tasks, industrial automation, process control, automotive controller, AVL, intelligent vehicle management device, medical device, human machine interface, robotics, machinery control, in addition to applications that require small footprint, lowpower and lowcost hardware with open industry standard such as PC/104. Transmission of signals from softwarebased engine model to the hardwarebased ECU model and vice versa is rendered by a data acquisition card, Advantech PCL812PG I/O (labeled “3”). PC/104 VGA output is connected to a monitor (labeled “4”) to enable the user to edit the C++ code of the control algorithm.
Fig. 10 HIL simulation of the testbed. 
4 HIL results
To conduct an HIL simulation, an input load is designated by the user. In this study, the load is selected to be a combination of some ramp and step inputs, as indicated in Figure 11. The load starts from its minimum value and remains constant for about 20 s, then increases to its maximum load value in two consecutive steps after 60 s and finally returns to its initial value. This should be considered as the worstcase scenario of load since it involves acceleration along with deceleration for a very short period of time with a relatively steep trend. Should the assumed control strategies keep the system operating in the desired range, they will most likely do for other load function.
The HIL simulation results are compared with those of SIL simulation when subjected to the same load.
Figure 12 shows the result of N_{GG} in SIL and HIL simulations. It shows that N_{PT} closely follows the load trend, and a rise or fall in the load will cause the same effect in N_{GG} plot. In addition, N_{GG} changes based on the change in load with virtually no observed lag for both case of SIL and HIL simulations. This indicates that the control strategies on N_{GG} are satisfactory and the implementation is properly carried out for HIL test.
Normalized N_{PT} from HIL and SIL simulations are illustrated in Figure 13. NPT tends to remain at its desired set value (RRV). However, the ECU designates a new fuel demand for the engine when a sudden change in the load occurs. As a result, some oscillations occur in N_{PT} until it reaches its defined value. Fuel mass flow rate for HIL simulation and SIL tests are demonstrated in Figure 14. Upon load deviation, the fuel flow to the engine is decreased and vice versa, as indicated by the simulation results.
Sampling time plays a key role in HIL simulations for the physical part of the test system, i.e. PC/104 microprocessor. Choosing an appropriate sampling time for every HIL simulation is an essential part of the test. Figure 15 shows the effect of different sampling times (53 ms, 75 ms and 102 ms) for the same HIL simulation described in the previous section.
As can be observed, the higher the sampling time, the more oscillatory the test results are. Nevertheless, relative accuracy is reached for the sampling time of about 53 ms. To put it more accurately, sampling time greatly affects the results stability. By choosing a small sampling time, the simulation time for a sampled data may not match the require time and addition of new sampled data may end in results divergence. A similar discussion can be made on long simulation time where the simulation may be left with no data input for a period, which may lead to instability. There are recommendations for choosing sampling time, but the best one is obtained through trial and error, as carried out in this study.
Fig. 11 Applied load to the HIL simulation. 
Fig. 12 HIL and SIL simulation results for N_{GG} signal. 
Fig. 13 HIL and SIL simulation results for N_{PT} signal. 
Fig. 14 HIL and SIL simulation results for fuel flow signal. 
Fig. 15 Fuel flow signal for three HIL simulations with different sampling times. 
5 conclusion
In this article, an industrial gas turbine engine with two shafts and variable IGVs was studied. The VIGV position and the engine inlet fuel were considered as the controlling parameters of the engine. Since the performance characteristic of the engine is highly dependent on VIGVs, a modeling procedure was chosen to take this effect into account (bond graph modeling). The ECU of this gas turbine engine provides the required fuel flow as well as VIGV operational position. To evaluate the accuracy of the designed control system, the control strategy was implemented on an electronic hardware and tested in real time via some comprehensive HIL simulations. Every physical constraint of the engine is satisfied by fuel and VIGV position, indicating the successful implementation of the control algorithm on the PC/104 hardware. Changes in bleed valves can be the subject and future studies, while HIL test can be carried out at lower speed and in the startup phase of gas turbine. A small rounding of the load ramp corner is also necessary to obtain better results. Finally, a more advanced control system such as model predictive control can be used to perform HIL test.
Nomenclature
c_{p}: Constant pressure specific heat
_{Cv}: Constant volume specific heat
CAMF: Compressor air mass flow
CPR: Compressor pressure ratio
N_{GG}, NGG: Gas generator speed
N_{PT}, NPT: Power turbine speed
RRV: Desired power turbine speed
VIGV: Variable inlet guide vane
Subscripts
ref: Standard value (of pressure or temperature)
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Cite this article as: M. MontazeriGh, S.A. Miran Fashandi, S. Abyaneh, Realtime simulation testbed for an industrial gas turbine engine’s controller, Mechanics & Industry 19, 311 (2018)
All Tables
All Figures
Fig. 1 Schematics of (a) complete system, (b) HIL test, and (c) SIL test 

In the text 
Fig. 2 Schematics of the bleed valve (BV) and IGV functions of the gas turbine [29]. 

In the text 
Fig. 3 Pseudobond graph models of the gas turbine components [19]. 

In the text 
Fig. 4 Complete bond graph model of the engine. 

In the text 
Fig. 5 Controller structure [19]. 

In the text 
Fig. 6 Load input to the gas turbine model. 

In the text 
Fig. 7 Variation of the gas generator turbine shaft acceleration. 

In the text 
Fig. 8 Variation of the gas generator shaft speed. 

In the text 
Fig. 9 Variation of the power turbine shaft speed. 

In the text 
Fig. 10 HIL simulation of the testbed. 

In the text 
Fig. 11 Applied load to the HIL simulation. 

In the text 
Fig. 12 HIL and SIL simulation results for N_{GG} signal. 

In the text 
Fig. 13 HIL and SIL simulation results for N_{PT} signal. 

In the text 
Fig. 14 HIL and SIL simulation results for fuel flow signal. 

In the text 
Fig. 15 Fuel flow signal for three HIL simulations with different sampling times. 

In the text 
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