An Efﬁcient and Robust Current Control for Polymer Electrolyte Membrane Fuel Cell Power System

: Taking into account the restricted ability of polymer electrolyte membrane fuel cell (PEMFC) to generate energy, it is compulsory to present techniques, in which an efﬁcient operating power can be achieved. In many applications, the PEMFC is usually coupled with a high step-up DC-DC power converter which not only provides efﬁcient power conversion, but also offers highly regulated output voltage. Due to the no-linearity of the PEMFC power systems, the application of conventional linear controllers such as proportional-integral (PI) did not succeed to drive the system to operate precisely in an adequate power point. Therefore, this paper proposes a robust non-linear integral fast terminal sliding mode control (IFTSMC) aiming to improve the power quality generated by the PEMFC; besides, a digital ﬁlter is designed and implemented to smooth the signals from the chattering effect of the IFTSMC. The stability proof of the IFTSMC is demonstrated via Lyapunov analysis. The proposed control scheme is designed for an experimental closed-loop system which consisted of a Heliocentric hy-Expert™ FC-50W, MicroLabBox dSPACE DS1202, step-up DC-DC power converter and programmable DC power supplies. Comparative results with the PI controller indicate that a reduction of 96% in the response time could be achieved using the suggested algorithm; where, up to more than 91% of the chattering phenomenon could be eliminated via the application of the digital ﬁlter.


Introduction
In the recent few decades, global warming has been characterized by an abrupt increase due to the carbon dioxide emissions caused by human activities [1]. As a solution for this matter and in order to reduce its development, coal plants over the world are being replaced by clean and renewable energies such as wind turbines, solar panels, bio-oils and fuel cells [2].
Polymer electrolyte membrane fuel cells (PEMFCs) are among the most efficient electrical generators due to several properties like high energy density, performance and high robustness [3], which leads to multiple applications such as portable power generation, cars, aircrafts and space shuttles [4][5][6][7][8][9][10]. In such application, DC-DC high step-up power converters are usually desired not only for boosting the PEMFC low voltage, but also to provide regulated output voltage for end use. The DC-DC power converter, which could be an inductive switching converter or a switched capacitor converter [11], is an adaptation stage circuit that is inserted between the load and the PEMFC stack. One of the most common adaptation stage circuits is the DC-DC boost converter, which is classified as one of the most and simplest used converters. This latter has the ability to step-up a lower input voltage into a higher output voltage via controlled pulse-width-modulation (PWM) switching technique.
In order to have an efficient power conversion from the PEMFCs to the DC link (or load), many control techniques and algorithms have been adopted during the recent years. The advantages and disadvantages of the most recent reported ones are enlisted in Table 1. Hence, in [12], an appropriate power point was obtained using a proportional-integral-derivative (PID) for a PEMFC power system. Results showed that by selecting the accurate parameters, the proposed approach could provide satisfactory results in terms of high tracking efficiency. The application of fuzzy logic control (FLC) on PEMFC power systems was introduced by [13]. In comparison with perturb and observe (P&O), satisfactory results such as a reduction of 90% in the signal ripples were obtained using the proposed control scheme. In [14], a back-stepping technique was proposed for a high step-up converter to keep the PEMFC power system operating at the maximum power point. Results have indicated the out-performance of the proposed technique over the proportional integral control in terms of robustness and settling time. Authors of [15,16] used conventional sliding mode control (SMC) aiming to overcome the drawbacks of the classical linear PI controller; their proposed method showed acceptable results in terms of robustness against sharp load variation, but since the SMC was used, the chattering phenomenon was present during the tests. However, as a solution for the chattering phenomenon, authors of [17][18][19] have, respectively, proposed quasi-continuous, twisting and super twisting algorithms. Results have demonstrated that chattering reduction of 91%, 82% and 84% can be achieved via the proposed algorithms.
Recently, terminal sliding mode controls (TSMCs) have attracted the attention of many researchers due to their capabilities to overcome the drawbacks of the conventional SMC while offering several superior properties such as speeding up the convergence rate and providing high precision control [20][21][22] Shotorbani et al. [20] compared the performance of the distributed terminal sliding mode controller (DTSMC) with divers control schemes such as PI, SMC, proportional finite-time control (PFTC), proportional asymptotic convergent control (PACC) and proportional-integral finite-time control (PIFTC). Results have confirmed the effectiveness of the proposed DTSMC over the other controllers; in terms of accuracy, smooth tracking and robustness when facing external disturbances. A fast terminal sliding mode control (FTSMC) was designed by Gudey and Gupta [21], for a low-voltage PEMFC based micro-grid system. Experimental results have demonstrated the effectiveness of the proposed FTSMC (faster convergence and slighter steady-state error) to overcome the inability of the classical SMC to regulate the micro-grid bus voltage. An integral terminal sliding mode control (ITSMC) was designed by [22] for a hybrid AC/DC micro-grids based on a wind turbine and PEMFC generator source. Improved performance in terms of robustness was obtained using the proposed ITSMC scheme with respect to control Lyapunov function (CLF) and SMC.
With respect to state of the art, the main contribution of this work is the real-time implementation of a robust no-linear integral fast terminal sliding mode control (IFTSMC), which is a combination of FTSMC [21] and ITSMC [22], aiming to keep the PEMFC system operating at an appropriate and efficient power point; besides, a digital filter is designed and implemented to smooth the signals from the chattering effect of the IFTSMC. The stability proof of the IFTSMC is demonstrated via Lyapunov analysis. The control objective is not only to remain the fuel cell running at an adequate efficient power point, but also to pursuit the trajectory with high tracking performance. This paper is arranged as follows: Section 2 presents the materials and methods including the models, the control design, as well as the system set-up; whereas the results and discussions are presented in Section 3; finally, conclusions are presented in Section 4. -Problem of intrinsic singularity.
-Can not be applied to higher order systems.
-The boundary information of system uncertainties is usually required to be known in advance.
-Problem of intrinsic singularity.
-High tracking accuracy.
-Robust to parameter uncertainties and disturbances.
-Applicable to high order systems.
-Requires the knowledge of the system boundary uncertainties.
-Problem of intrinsic singularity.

Materials and Methods
The closed-loop system consists of the PEMFC which is the source of the electricity, a DC-DC boost converter that manipulates the produced DC voltage to feed the load demand, and finally, a digital controller that drives the converter commutations to keep the PEMFC working at an efficient and adequate power point. The diagram of the closed-loop system is presented in Figure 1.

Polymer Electrolyte Membrane Fuel Cell
According to [23], the electrical energy generated by the PEMFC can be expressed as Equation (1). This is derived from a thermo-dynamical analysis of the device which takes into account the temperature and fuels partial pressures. Therefore, the looses are not considered in this theoretical expression.
where T (K) is the stack temperature; P H 2 (atm) and P O 2 (atm) are, respectively, the partial pressure of H 2 and O 2 . In order to make a realistic expression derived from Equation (1), three main electric losses which could be classified as activation (e act ), ohmic (e ohm ) and concentration (e con ) losses, are added to the Equation (1). Hence, a realistic PEMFC output voltage is expressed as Equation (2) [24,25].
The parameters σ 1 , σ 2 , σ 3 and σ 4 are parametric coefficients determined by the constructor, I is the current of the PEMFC, C O2 is the oxygen concentration in the catalysts (mol·cm −3 ), ψ is a constant parameter, J is the current density, J max is the maximum current density, R mem is the internal resistance of the electrolyte membrane, and R con is the resistance occurred due to the contact between the bipolar plates and the carbon electrodes.
The power generated by the PEMFC stack can be calculated using Equation (4); where N cell represents the number of cells used in the stack [25].
The efficiency of the PEMFC is determined as the ratio of the electric power provided by the stack P stack (W) to the one provided by the stack input P in . This latter can be written as Equation (5); where, LHV is the hydrogen lower heating value (J/kg), andṁ H 2 is the hydrogen mass flow rate (kg/s).
Therefore, using Equation (4) and (5), the efficiency of the PEMFC can expressed as Equation (6) [28,29]. This equation was used with experimental data in order to plot the efficiency which process is explained in further sections.

DC-DC Boost Converter
A DC-DC boost converter is a switch-mode power supply which converts a direct voltage coming from a DC source into another higher direct voltage value by adjusting the switch duty cycle d. The output voltage of the DC-DC boost converter can be calculated as Equation (7) [30,31].
As shown in Figure 2, a boost converter is consisted of an inductance, a metal oxide semiconductor field-effect transistor (MOSFET) switch, a Schottky diode, a capacitor, and a load resistance. The DC-DC converter operates in two modes, continuous conduction mode (CCM) and discontinuous conduction mode (DCM), depending on its storage capacity and the switching period T [32,33]. By assuming that the boost converter operates in the CCM, and by applying the Kirchhoff's laws to the circuit, the averaged state-space representation can be determined as Equation (8)

Control Design
In this section, a proportional-integral (PI) and an integral fast terminal sliding mode control (IFTSMC) are designed to stabilize and remain the PEMFC operating at an efficient and adequate power point.

PI Control
PI controller is widely used in most power electronic closed-loop systems. It is the most straightforward classical control which uses a feedback loop to generate an error e r . More specifically, the controller must track a set-point or a reference by adjusting the appropriate signal that supplied to the system. Hence, the controller uses the reference and the feedback, which is a measurement acquired by a sensor, to generate the control signal. The overall control function u of the PI controller is given in Equation (10) [36][37][38]; where e r is the error between the PEMFC current i L and the reference current i re f (expressed in Equation (9)). K p and K i represents, respectively, the proportional and the integral coefficients.
The major drawback of the PI controller appears in determining its proportional and integral gain coefficients that correspond, respectively, with K P and K i . Besides, its vulnerability, due to the load variations, could be a major problem. However, in order to decrease the complexity of selecting the gain coefficients, the Ziegler-Nichols tuning method was used since it is an efficient trial and error method.

Integral Fast Terminal Sliding Mode Control (IFTSMC)
IFTSMC is a new type of terminal sliding mode control which was invented by the scientist Venkataraman and Gulati [39] in the Jet Propulsion Laboratory. It is a nonlinear and a robust control based on the concept of the conventional TSMC and through a development of SMC. The command law u of the IFTSMC consists of two terms, a discontinuous term u sw that remains the system on the sliding surface, and an equivalent term u eq that brings the system to the sliding surface [40]. The total command law can be expressed as Equation (11).
The discontinuous term u sw is defined in Equation (12); where, where k is a positive constant and sign(s) is the signum function [41].
The time derivative of the surface can be expressed as in Equation (14).
Also, the error expression was already defined in the Equation (9). As the reference current is constant, therefore, a derivative expression can be obtained from (8) which results in the following Equation (15).ė Thus, through a combination of Equation (14), with the latter Equation (15), a complete expression of the surface derivative is gathered in the following Equation (16).
Finally, stating that thatṡ = 0, the equivalent term of the control law is achieved as in Equation (17).
Previous remarks in terms of the chosen surface, provided certain limitations to take into account at the moment of the constants tuning. However, these have also been adjusted through the minimization of the integral of the absolute error (IAE) that belongs to the Equation (18). This aims to achieve a suitable performance by taking into account the error reduction in real time.

IFTSMC Stability Proof
The previous obtained control law can be analyzed in terms of the Lyapunov theory of stability. This states that if there exist a positive definite function: R n → R so that V (x) > 0, V (0) = 0, V(∞) = ∞ andV(x) < 0, ∀ x = 0; therefore the dynamical system is asymptotically stable. Consequently, to prove the stability of the PEMFC system, a positive definite Lyapunov candidate function is chosen as the Equation (19).
Thus, the derivative of the latter expression is established in the next expression such thatṡ from (16) is replaced as follows.
The replacement of the control term u with the Equations (11), (12) and (17), yields to the following expression. Further mathematical development as follows, accomplishes with the Lyapunov stability proof sinceV(s) is concluded to be less or equal to zero.

Digital Filter Design
In order to reduce ripples and chattering phenomenon, a digital filter was designed in Matlab. The command filter(b,a,x) requires the numerator b and denominator a coefficients which represent a rational transfer function, whereas the data input is defined as x.
Provided that a = 1 and b = 1/N, the result is a moving-average expression that filters the high frequency signals along the the number of elements N to be filtered (this is also known as the filter order) expressed in Equation (22) [45].
The implementation of previous expression has been done through a Finite Impulse Filter (FIR) block in Simulink. The filter order was defined along the research as it is explained in the following sections. The sampling frequency was chosen is 10 kHz since it fits with the hardware limitations and data acquired.

Description of the Test Bench
The experimental test bench, which is shown in Figure 3, was built at the laboratory of advanced control in the university of Vitoria-Gasteiz, Spain. It is consisted of a Heliocentric hy-Expert™ FC-50W and its auxiliaries, MicroLabBox dSPACE DS1202, step-up DC-DC power converter and programmable DC power.  Table 2 lists the technical specifications of the Heliocentric FC-50; where this latter consists of 10 cells stacked together to generate a rated power around 40 W.
The host computer has an INTEL processor type I7 7700k 4.5 GHz based on Kaby Lake architecture, and a powerful RAM of 32GB. It is used to design the controller and manage the system via the Matlab/Simulink™ environment software. The input and output signals are measured and observed via the ControlDesk software tools. The control algorithm has been implemented on a dSPACE DS1202 card to generate the pulse width modulation (PWM) signal, which activates the IGBT trigger of the boost converter. This latter was constructed by the research-group-TEP192 with the characteristics listed in Table 3. The MicroLabBox dSPACE DS1202 is a powerful tool that used to linkage between the software (Simulink) and the hardware (the converter), via its real-time interface (RTI). It has the ability to receive and send the information among the converter, the Matlab/Simulink™ and ControlDesk software, as well as monitoring the signals of the real processes throughout the operation. It contains two digital input/output PWM ports, two RS232, two CAN, as well as 48 input/output channels which make it adapted to many different functions and activities. Furthermore, it has a powerful CPU of 2GHz and a field-programmable gate array (FPGA) that allows the user to make tests even for speedy control loops. A block diagram of the integrated MicroLabBox with the PEMFC, the boost converter, the host computer as well as the programmable DC power is shown in Figure 4. The programmable DC power is manufactured by BK-PRECISION, type 8500B, and it is used as a variable load resistance in order to test the performance of the proposed control algorithm.
The design of the digital controller on the Simulink™ graphical interface as well as its connections with the RTI blocks are shown in Figure 5.

Results and Discussion
The current/voltage and current/power characteristics of the practical FC-50W for diverse temperatures, are presented in Figure 6. It is noticed that the performance of the FC-50W is enhanced by the increase of temperature from 20°C to 46°C which could be interpreted by the rise of the membrane conductivity, and by the improvement in the exchange of the current density which will results in diminishing the activation losses. Notwithstanding these improvements, at higher temperatures such as T > 46°C, the conductivity of the membrane starts to drop due to the lack of the relative humidity; which will result in a reduction in the performance of the PEMFC. It should be noted that the performance study of the FC-50W was limited due to the constraints in the oxygen and hydrogen partial pressures; these were narrowed since the rates are automatically controlled by an integrated control. When studying the performance and the behaviour of the PEMFC, a contrast between the maximum operating power point and maximum efficiency operating point must be made. In Figure 7, the current/efficiency characteristics of the Heliocentric hy-Expert™ FC-50W are presented. This was obtained based on Equation (6) through a variation of the stack current and gathering the mass flow rate variation of the hydrogen which was given by the Heliocentris software. Therefore, the curve was possible to be achieved. According to this figure, it can be seen that the best efficiency is obtained at low load currents [1-2 A]. However, according to Figure 6, the optimum operating power point is obtained at a high current range [6-8 A]. Therefore, it is mandatory to choose between the optimum power or efficiency, and this could be selected depending on the required power for the specific application. In this work, the authors preferred to establish an efficient operating power point while providing an important amount of power. Thus, by designing a suitable controller that able to remain the FC-50W operating at I = 4 A, an efficiency of almost 50% while producing a power of 25 W can be achieved. To hold and keep the FC-50W operating at the selected reference current I re f = 4 A, PID and IFTSMC controllers were proposed. Their coefficient parameters obtained through Ziegler-Nichols and min{I AE} are enlisted in Table 4.

IFTSMC PI
In order to test and view the performance of the proposed controllers, variations in the load resistance are adjusted, respectively, from 20 Ω to 50 Ω at t = 20 s, and from 50 Ω to 20 Ω at t = 40 s. These load variations, the duty cycle signal for both PI and IFTSMC, as well as their generated errors, are presented in Figure 8. Despite the sharp variations of the load resistance, it is clearly shown that both of controllers succeeded to converge the error to zero value; which will guarantee as a result the stability of the system. Figure 8 also demonstrates the drawbacks of the PI controller in terms of the converging time; hence, it takes up to more than 12 s to reach the equilibrium point while the proposed IFTSMC algorithm takes only 0.45 s. The electric outputs of the FC-50W stack, under the application of PI and IFTSMC, are presented in Figure 9; where the three graphs shows, respectively, the stack current, stack voltage and stack power. At t = 20 s, by applying load variation from 20 Ω to 50 Ω, the PI shows an undershoot of 2.006 A in current, an overshoot of 1.147 V in voltage, and an undershoot of 10.05 W in power; while the proposed IFTSMC shows an undershoot of 1.997 A in current, an overshoot of 1.107 V in voltage, and an undershoot of 9.99 W in power. On the other hand, at t = 40 s, by applying load variation from 50 Ω to 20 Ω, the PI shows an overshoot of 4.086 A in current, an undershoot of 2.014 V in voltage, and an overshoot of 9.17 W in power; while the proposed IFTSMC shows an overshoot of 4.141 A in current, an undershoot of 2.012 V in voltage, and an overshoot of 9.26 W in power. According to these results, it is clear that both of PI and IFTSMC have almost the same performance in term of overshoots and undershoots; where the IFTSMC has an improvement of 0.06 W over the PI when increasing the load resistance, while the PI has an improvement of 0.09 W over the IFTSMC when decreasing the load resistance. However, it is clearly shown that the feature of the proposed IFTSMC appears in its capability to converge the system to the reference value with high speed (response time = 0.45 s).  Figure 10 shows the output signals behaviour of the step-up DC-DC converter. According to this figure, gradual and smooth movements to the desired value are obtained. However, in spite of the chattering phenomenon which is caused by the proposed IFTSMC control during the steady state, its robustness to converge the system in a short times which will results in a high tracking accuracy, is an important advantage over the conventional PI.
According to Figures 9 and 10, it is noticed that the chattering phenomenon, which is a normal behavior of sliding mode control, occurred in the steady state could represent an obstacle for the proposed IFTSMC control; therefore, to eliminate these ripples, a a digital filter that diminished the high frequency components along 400 points was applied to the duty cycle (command law). The filtered signals of the FC-50W stack are presented in Figure 11. This latter demonstrates that by applying a digital filter, a chattering reduction from 0.65 A, 0.33 V, 2.76 W (Figure 9) to 0.08 A, 0.03 V, 0.36 W (Figure 11), are respectively obtained. By means of power percentage, a chattering reduction up to 91% is obtained which results in a soft and smooth signals.  According to these results, it is clearly seen that the IFTSMC with the application of the digital filter has succeeded to keep the FC-50W stack operating at the desired power point while providing high tracking performance. Hence, high convergence speed with chattering reduction up to more than 91% are obtained using the proposed IFTSMC algorithm. Besides, soft and fast dynamic behavior while guaranteeing the system stability are also obtained.

Conclusions
A Heliocentric hy-Expert™ FC-50W feeding programmable DC power supplies via a controlled boost converter is studied in this work. The closed-loop system which includes the FC-50W and its auxiliaries, the converter, the host computer and the programmable DC power supplies are implemented and linked to the MicroLabBox dSPACE DS1202. The suggested IFTSMC control scheme is designed to keep the PEMFC power system operating at an appropriate and efficient power point as well as to pursuit the trajectory with high tracking performance. The stability proof of the proposed IFTSMC is demonstrated via Lyapunov analysis; where its chattering phenomenon is cancelled via the application of a digital filter.
The experimental characteristics of the FC-50W for diverse temperatures are investigated and it is concluded that the performance of the PEMFC is enhanced by the increase of temperature from 20°C to 46°C, while it is reduced for higher temperatures. On the other hand and based on the efficiency characteristics of the PEMFC, it is concluded that for the performance improvement, it is mandatory to to choose between the optimum power point or the optimum efficiency.
An experimental comparative study is investigated between the IFTSMC and the well-known PI controller so as to reveal the merits of the proposed technique. Results have indicated that despite the sharp variations of the load resistance, both of controllers succeeded to converge the error to zero value; where, gradual and smooth movements to the desired value with global system stability are obtained. Results also have indicated that both of PI and IFTSMC have almost the same performance in term of overshoots and undershoots; however, it is clearly proven that the feature of the proposed IFTSMC appears in its capability to converge the system to the reference value with high speed (response time = 0.45 s).
The experimental comparative study also has proven the effectiveness of the LFP application, hence, up to more than 91% of the chattering phenomenon of the IFTSMC could be eliminated. Therefore, it is clearly proven that the IFTSMC with the application of the digital filter has succeeded to keep the FC-50W stack operating at the desired power point while providing high tracking performance such as high convergence speed with significant chattering reduction. Finally, the obtained results of this work are quite encouraging and they give prospects for further advanced research to enhance and improve the performance of the PEMFC.  Acknowledgments: The authors would like to acknowledge the Algerian government and the UPV/EHU for supporting this work.

Conflicts of Interest:
The authors declare no conflict of interest.