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Real-time implementation of a neural model-based self-tuning PID strategy for oxygen stoichiometry control in PEM fuel cell
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 1 2 8 1 9 e1 2 8 2 5
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Real-time implementation of a neural model-based self-tuning PID strategy for oxygen stoichiometry control in PEM fuel cell C. Damour a, M. Benne a,*, C. Lebreton a, J. Deseure b,c, B. Grondin-Perez a a
LE2P EA 4079, University of La Reunion, 97715 Saint-Denis, France LEPMI, Univ. Grenoble Alpes, F-38000 Grenoble, France c UMR CNRS 5279, F-38000 Grenoble, France b
article info
abstract
Article history:
This paper proposes a real-time implementable self-tuning PID control strategy to tackle
Received 24 March 2014
oxygen excess ratio regulation challenge of a proton exchange membrane fuel cell.
Received in revised form
Controller parameters are updated on-line, at each sampling time, using a not iterative
3 June 2014
procedure based on an artificial neural network model. The proposed controller takes ac-
Accepted 8 June 2014
count of nonlinear behaviors of the process, while avoiding heavy computations.
Available online 12 July 2014
To assess the efficiency and relevance of the proposed strategy, the controller is implemented on-line, experimentally validated on a real fuel cell and compared to the
Keywords:
built-in controller. In this aim, several control scenarios are considered to evaluate the
Proton exchange membrane fuel cell
controller performance.
Experimental implementation
Experimental results show the excellent tracking capability and disturbances rejection
Real-time control
ability of the controller, regardless of the operating conditions. Moreover, compared to the
Artificial neural network model
built-in controller the proposed strategy demonstrates better disturbances rejection capability. Overall, the proposed neural model-based self-tuning PID controller appears as an excellent candidate to address the oxygen excess ratio regulation issue. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The development of new technologies for energy conversion is mandatory to cope with fossil energy resources depletion and global warming issues. As part of the energy transition, low-carbon energy sources represent promising opportunities to attain significant reductions in the volume of greenhouse gas emissions, there by reducing the
environmental footprint of transport, residential and industrial power consumption. In regard to renewable energies, one of the primary drawbacks is the variability of the supply flows, which raises the key issue of energy storage to counteract the intermittent nature of their conversion. In this context, the hydrogen option represents a promising alternative, as long as the hydrogen is produced from a renewable energy technology (electrolytic hydrogen), and stored to optimize potential gaps and surplus of intermittent
* Corresponding author. Tel.: þ262 262 938 223; fax: þ262 262 938 673. E-mail address: [email protected] (M. Benne). http://dx.doi.org/10.1016/j.ijhydene.2014.06.039 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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production. Downstream the hydrogen chain, electricity is generated from fuel cells, genuine zero-emission power generators. Because their high power density and low operating temperature, proton exchange membrane fuel cells (PEMFC) have proved to be the most suitable fuel cell technology for both transportation and stationary applications. However, several issues still need to be addressed to improve their reliability and energy conversion, reduce their cost or extend their lifetime. Among them, one of the most important is related to their control. To ensure optimal performance of the PEMFC, and avoid voltage degradation or flooding, numerous parameters such as stack temperature or gas pressure need to be properly controlled. In this context, one parameter, namely oxygen excess ratio, requires a special attention. The oxygen excess ratio or stoichiometric ratio represents the ratio of inlet oxygen flow to reacted oxygen flow. A poor control of this parameter could lead to performance degradation, due to oxygen starvation. Prevent oxygen starvation to ensure optimal conversion efficiency and avoid performance deterioration remains a challenging control goal. Recently, several works related to oxygen excess ratio control have been reported. In Ref. [1] a nonlinear second order sliding mode controller was used to regulate the oxygen excess ratio. Robustness and insensitivity properties of the controller have been investigated in simulation environment. Using flatness control theory, Fonseca et al. [2] proposed a nonlinear control strategy based on a simplified model of the PEMFC system. Simulation results showed the good performance of the proposed controller regarding oxygen excess ratio control. Wu et al. [3] proposed a nonlinear model-based predictive control scheme to prevent oxygen starvation. Even if simulation results were promising, the authors emphasized that some devices and design such as inverters have not been taken into account. Becherif et al. [4] used the maximum power point tracking technique to compute the optimal value of excess ratio reference at each sampling period in order to improve the PEMFC efficiency. The proposed approach, tested through simulations, allowed to increase the output power of the PEMFC by over 10%. Feroldi et al., 2007 [5] designed a dynamic matrix predictive control strategy. The proposed controller, implemented in simulation environment, showed good performance, especially in terms of disturbances rejection. Li et al. [6] designed a maximum net power control strategy to determine the optimal oxygen excess ratio value, coupled with an implicit generalized predictive control. The proposed controller showed good tracking capability in simulation. In Ref. [7] an LQR/LQG controller, based on a linearized model of the process, was presented and experimentally tested. Results showed that the proposed linear controller efficiently regulated the oxygen excess ratio, and offered good performance in terms of disturbances rejection. Garcia-Gabin et al. [8] proposed a real-time implementable sliding mode controller. Performance of the controller was experimentally investigated, and its ability to handle load changes was demonstrated. A constrained model predictive control strategy was developed by Ref. [9] to improve oxygen excess ratio regulation. The proposed controller, experimentally implemented, stabilized the
oxygen stoichiometric ratio around the target value approximately five times faster than the original controller. Kunusch et al. [10] designed a Super Twisting controller to regulate oxygen excess ration. The proposed strategy, experimentally tested, showed good tracking capability. Even if many control strategies have been proposed to control oxygen excess ratio, a very few were dedicated to realtime control. In the present paper, a real-time implementable selftuning PID controller is designed to tackle the oxygen excess ratio regulation issue. The proposed control strategy relies on an instantaneous linearization of an artificial neural network (ANN) model of the PEMFC combined with a General Minimum Variance (GMV) control law. ANN model together with GMV design allow to handle nonlinearities of the process, while avoiding heavy computations. On the one hand, compared to others nonlinear model-based approaches, such as nonlinear model-based predictive control, that required heavy computations due to iterative procedures, the proposed auto-tuning PID controller has a very low computational cost. On the other hand, compared to linear controllers, not well suited for nonlinear systems, the ANN model-based approach takes account of the nonlinear behavior of the process. To demonstrate the suitability of the proposed control strategy to address the control problem, the controller is implemented on-line and experimentally validated on a real fuel cell. This work is divided as follows: The experimental
Fig. 1 e Experimental fuel cell test station.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 1 2 8 1 9 e1 2 8 2 5
fuel cell system is presented in Section Experimental system description. Section Control design is dedicated to the realtime implementable neural model-based self-tuning PID controller design. In this section, the procedure used to update on-line, at each sampling time, the controller parameters is detailed, and the ANN model of the PEMFC is designed and experimentally validated. Performance of the proposed controller in terms of tracking capability and disturbances rejection is experimentally investigated in Section Experimental results. Lastly, main conclusions are presented in Section Conclusion and prospects.
Experimental system description In this study, a neural model-based PID controller is proposed to ensure optimal PEMFC performance, while avoiding oxygen starvation. Validation tests are carried out on an experimental unit consisting of a single-cell, various monitoring and control devices, and a programmable electronic load (Fig. 1 and Fig. 2). The single-cell is made of a membrane electrodes assembling (MEA) produced by Paxitech, with an active area of 50 cm2, sandwiched between bipolar plates clamped with a torque of 12 Nm after optimization. The MEA is composed of a Nafion® N115 membrane as the central layer, and gas diffusion layers, made of Pt-doped carbon black (40 wt%/C) deposited by Paxitech onto a carbon felt (0.6 mgPt cm2 mixed with Nafion®), as the two side layers. The Supervisory Control and Data Acquisition (SCDA) system, integrated by Fuel Cell Technologies (FCT), is controlled through a proprietary GUI (graphical user interface)
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composed of a set of modular virtual instruments (VI) implemented with Labview graphical software tool. This makes the experimental unit a flexible environment, allowing to perform a wide range of tests based on various configuration settings: - fuel cell temperature, measured at cathode side, - humidification temperatures, at the anode and cathode, - inlet gas temperatures and mass flows, at the anode and cathode, - and outlet back-pressures, at the anode and cathode. Since VI's can easily be modified or replaced, alternative monitoring and control strategies can be integrated to the SCDA system. As regards innovative control strategies, a set of VIs makes it possible to replace the original built-in controller by model-based approaches. With this setup, the optimal control action, computed on-line in Matlab® environment, is sent through a specific VI to be applied to the experimental unit. Within the scope of this study, pure hydrogen and air are used as fuel and oxidant, respectively.
Control design As previously stated, the oxygen excess ratio is a crucial parameter to ensure optimal PEMFC performance. Indeed, a poor control of this variable could lead to fast performance degradation and irreversible damages to the fuel cell membrane due to a phenomenon called oxygen starvation. Therefore, oxygen excess ratio regulation remains a
Fig. 2 e Simplified process and instrumentation diagram of the system.
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challenging control goal. In this section, a real-time implementable self-tuning PID controller is designed to tackle this control problem. This strategy, based on an ANN model of the PEMFC together with a GMV control design, allows to handle nonlinear behaviors of the process, while avoiding heavy computations.
proposed approach, the minimization of the cost function L is achieved using a not iterative procedure, which is a quite important feature to fulfill real-time implementation requirements. The methodology used to solve the optimization problem and the instantaneous linearization procedure are fully detailed in Refs. [11,12].
Neural model-based self-tuning PID algorithm
ANN model design
The main feature of the proposed approach relies on an instantaneous linearization of the ANN model of the process combined with a GMV control law. A set of coefficients is extracted on-line, at each sampling time, from the ANN model to obtain a linearized model. Controller parameters are then updated using the above mentioned linearized model and a GMV control law (Fig. 3). In the present case, the controlled output y(t) is the oxygen excess ratio, yset(t) denotes the desired value of oxygen excess ratio, e(t) denotes the trajectory tracking error, the manipulated variable u(t) is the air inlet flow rate, ny and nu are the number of past inputs/outputs required, and kc ; ti ; td denote the controller parameters. Since the proposed strategy relies on a classical PID controller, the velocity form of the control action u(t) at time t is computed as follow:
The proposed control strategy involves an ANN model of the PEMFC. This model, expected to predict the system output one step ahead, is used to determine the optimal controller parameters. As previously mentioned, the oxygen excess ratio, namely lO2 , denotes the ratio of oxygen supply to oxygen consumed in the cathode. In this manner, lO2 is a function of inlet air flow rate, load current, relative humidity of air at the cathode inlet, stack temperature and inlet pressure at the cathode. In this paper, regarding real-time control goal, and since lO2 mainly depends on load current and inlet air flow rate [9], a simplified model is proposed. This model is expected to predict lO2 one step ahead, once the load current I and the inlet air flow rate _ air are available. In practice, the load current is a measured m disturbance, whereas the inlet air flow rate is the manipulated variable. Regarding real-time implementation goal, the computational speed of the model is a key component. The model is expected to predict the system output with sufficient accuracy, while avoiding heavy computations. To address this problem, several ANN architectures have been investigated to determine which one provides the best trade-off between prediction accuracy and computational speed. Finally, a fully connected three layers network is designed. The hidden layer has five neurons with a tangent sigmoid activation function 41 , whereas the output layer has one neuron using a linear activation function 42 (Fig. 4). Identification and validation of the ANN model are performed on two different sets of data collected on the PEMFC system presented in Section Experimental system description and sampled with a 3 s period. The data set used for the training phase has to be chosen wisely, regarding the poor extrapolation performance of ANN models. In this aim, the training data set, used to identify the ANN model, covers the whole operating conditions and ranges from minimum to maximum inputs/outputs values. The model identification is
uðtÞ ¼ uðt 1Þ þ DuðtÞ with, Dt td DuðtÞ ¼ kc eðtÞ eðt 1Þ þ ðeðtÞ eðt 1ÞÞ þ ðeðtÞ ti Dt 2eðt 1Þ þ eðt 2ÞÞ and Dt denotes the sampling period. The optimization goal, is to find the optimal set of pab ¼ ½kct t T that minimizes the cost function rameters k i d 2 J ¼ e ðt þ 1Þ þ mDu2 ðtÞ: b ¼ arg min ðJÞ k k
where m is the weighting penalty parameter. However, at time t, eðt þ 1Þ ¼ yset ðt þ 1Þ yðt þ 1Þ is not available since it involves the knowledge of the system output, namely yðt þ 1Þ, at time t þ 1. To address this problem, the linearized model, obtained from the instantaneous linearization of the ANN model, is used to estimate the future output of the system yðt þ 1Þyylin ðt þ 1Þ. ylin ðt þ 1Þ denotes the future system output estimated by the linearized model. Eventually, the optimal controller parameters vector is obtained by minimizing on-line, at each sampling time, the cost In the function L ¼ ðyset ðt þ 1Þ ylin ðt þ 1ÞÞ2 þ mDu2 ðtÞ.
Fig. 3 e Self-tuning PID controller principle.
Fig. 4 e PEMFC ANN model.
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comparison between the built-in controller and the proposed control strategy is made for the second scenario. Note that this comparison cannot be performed for the first and third scenario due to technical constraints. In fact, the built-in controller of the SCDA system, integrated by Fuel Cell Technologies, is designed to operate at constant oxygen excess ratio. In other word, when using the original setup, the oxygen excess ratio value has to be set before the experiments and cannot be modified during the experiments. In the sequel, the inlet air flow rate is taken as manipulated variable, whereas the load current is a measured disturbance. The cell temperature and the sampling period are set to 75 C and 3 s respectively, ny and nu are both set to one, and the weighting penalty parameter m is taken equal to 109. It is assumed here that all other variables, required to ensure safety operation of the fuel cell, are properly controlled. Fig. 5 e PEMFC ANN model validation.
First case scenario: constant load current e variable oxygen excess ratio setpoint
performed using LevenbergeMarquart algorithm with an error goal of 0.001. The validation step is presented in Fig. 5. Two criteria, namely root mean square error qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn b 2 ðRMSE ¼ i¼1 ðyi y i Þ =nÞ and absolute maximal error bi ÞÞ, are considered to assess the one step ðAME ¼ maxðyi y i
ahead prediction performance of the ANN model. n represents b denote experimental and simuthe number of data, y and y lated data, respectively. With an RMSE of 0.003 and an AME under 0.1 the predictive performance accuracy of the ANN model is more than sufficient, especially since it is dedicated to control purposes (Table 1).
Experimental results To assess the performance of the proposed control strategy in terms of tracking capability, disturbances rejection, and robustness against plant-model mismatch, series of experiments are performed on the PEMFC system presented in Section Experimental system description. In this aim, the neural model-based self-tuning PID controller, implemented in Matlab® environment, is executed on-line and communicates in real-time with the SCDA system of the fuel cell. Here, to exemplify the controller performance three control scenarios are considered: The first scenario illustrates the tracking capability of the controller for a constant value of load current. The second scenario is designed to study the controller ability to cope with disturbances. Eventually, the third scenario evaluates the controller performance in terms of setpoint tracking accuracy in presence of disturbances. A
Table 1 e Training and validation results of the ANN model. RMSE AME
Training
Validation
4.726 104 0.079
0.003 0.98
The tracking capability of the controller is evaluated using an oxygen excess ratio setpoint that covers the whole operating condition. In this control scenario, the load current is set to 15 A and kept constant during the entire experiments. Fig. 6 shows that the controller is able to track accurately a variable oxygen excess ratio setpoint, while offering an entirely suitable dynamics for the manipulated variable.
Second case scenario: step changes on load current e constant oxygen excess ratio setpoint To assess the controller performance in terms of disturbances rejection, a set of step changes on the load current is performed. The dynamics of the PEMFC is strongly correlated to the power level. Therefore, to verify that the controller performs accurately whatever the power level, the current steps is chosen to cover the whole operating condition. Several experiments, with different sets of step changes in load current and different oxygen excess ration values, are carried out to compare the performance of the original built-in controller and the proposed control strategy. In each and every case, the proposed self-tuning PID controller preforms better than the built-in controller. Fig. 7 illustrates one of these experiments with the oxygen excess ratio set to 6. The proposed controller demonstrates that it can maintain the oxygen excess ratio to the desired level, even in presence of disturbance. Moreover, compared to the built-in controller, the proposed controller exhibits better disturbances rejection capability. Indeed, for the two first steps in current (t ¼ 17 s and t ¼ 47 s) an overshot is observed with the built-in controller, whereas the proposed controller efficiently rejects the disturbances.
Third case scenario: step changes on load current e variable oxygen excess ratio setpoint This control scenario is designed to assess the controller performance when the oxygen excess ratio setpoint is modified on-line according to the load current. This control scenario, which is a common working scenario in automotive
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Fig. 6 e Experimental tracking capability of the proposed controller: (a) oxygen excess ratio; (b) air flow rate.
Fig. 7 e Experimental disturbances rejection ability: (a) oxygen excess ratio; (b) load current.
Fig. 8 e Experimental tracking capability with step changes on load current: (a) oxygen excess ratio; (b) load current.
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applications, is significantly important. Indeed, several works demonstrated that updating the oxygen excess ratio reference according to the load current could significantly increase the PEMFC efficiency while avoiding oxygen starvation [4,13,14]. The proposed controller demonstrates excellent tracking capability even in presence of disturbances (Fig. 8). The ability of the controller to track efficiently an oxygen excess ratio setpoint, calculated according to a variable load current, is a quite important feature. Indeed, this control scenario appears as one of the most promising options to improve the overall PEMFC efficiency, while ensuring safety operation of the fuel cell. It is important to emphasize that in addition to the presented examples, numerous experiments have been carried out in the whole range of operating conditions. In every case, the proposed control strategy demonstrated highly satisfactory results in terms of tracking capability and disturbances rejection.
Conclusion and prospects In this paper, to address oxygen excess ratio control challenge, a self-tuning neural model-based PID controller has been developed. To achieve real-time control while taking account of nonlinear behaviors of the process, a not iterative procedure based on an ANN model has been designed to update online, at each sampling time, the controller parameters. To assess the efficiency and relevance of the proposed control strategy, the controller has been implemented on-line and experimentally validated on a real fuel cell. In this aim, numerous control scenarios have been experimentally conducted to evaluate the controller performance, especially in terms of setpoint tracking accuracy and disturbances rejection. These control scenarios gather all the possible scenarios in which the system would have to work. In each and every case, the controller demonstrated highly satisfactory results since it tracked efficiently the desired oxygen excess ratio value while compensating disturbances, regardless of the operating conditions. Besides, experimental comparison demonstrated that the proposed controller had better disturbances rejection capability than the built-in controller. The self-tuning PID controller has also proven to have good
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robustness properties against plant/model mismatch. Furthermore, the robustness of the controller can be further improved by introducing the modeling error within the optimization problem. Compared to others nonlinear model-based approaches that usually required heavy computations due to iterative procedures, the proposed auto-tuning PID controller has a very low computational cost since the optimization problem is solved analytically. Indeed, the main asset of the proposed strategy relies on the ANN model. On the one hand, it allows to takes account of process nonlinearities. On the other hand, due to its architecture, the instantaneous linearization of this model allows to rewrite the optimization problem and to solve it analytically. Overall, the proposed self-tuning PID controller appeared to be an excellent trade-off between nonlinear control strategies and linear controllers to tackle oxygen excess ratio regulation issues.
references
[1] Matraji I, Laghrouche S, Jemei S, Wack M. Appl Energy 2013;104:945e57. [2] da Fonseca R, Bideaux E, Gerard M, Jeanneret B, DesboisRenaudin M, Sari A. Appl Energy 2014;113:219e29. [3] Wu W, Xu JP, Hwang JJ. Int J Hydrogen Energy 2009;34:3953e64. [4] Becherif M, Hissel D. Int J Hydrogen Energy 2010;35:12521e30. [5] Feroldi D, Serra M, Riera J. J Power Sources 2007;169:205e12. [6] Li Q, Chen W, Liu Z, Guo A, Liu S. J Power Sources 2013;241:212e8. -Fantova M, Kunusch C, Ocampo[7] Niknezhadi A, Allue Martı´nez C. J Power Sources 2011;196:4277e82. [8] Garcia-Gabin W, Dorado F, Bordons C. J Process Control 2010;20:325e36. [9] Gruber J, Doll M, Bordons C. Control Eng Pract 2009;17(8):874e85. [10] Kunusch C, Puleston PF, Mayosky MA, Fridman L. Control Eng Pract 2013;21:719e26. [11] Chen J, Huang T-C. J Process Control 2004;14:211e30. [12] Beyou S, Grondin-Perez B, Benne M, Damour C, Chabriat JP. In: Proceeding of the world academy of science engineering and technology, Paris; June 2009. pp. 190e5 [ISSN 2070-3724]. [13] Santarelli MG, Torchioa MF, Cali M, Giaretto V. Int J Hydrogen Energy May 2007;32:710e6. [14] Ziogou C, Papadopoulou S, Georgiadis MC, Voutetakis S. J Process Control 2013;23:483e92.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Real-time implementation of a neural model-based self-tuning PID strategy for oxygen stoichiometry control in PEM fuel cell C. Damour a, M. Benne a,*, C. Lebreton a, J. Deseure b,c, B. Grondin-Perez a a
LE2P EA 4079, University of La Reunion, 97715 Saint-Denis, France LEPMI, Univ. Grenoble Alpes, F-38000 Grenoble, France c UMR CNRS 5279, F-38000 Grenoble, France b
article info
abstract
Article history:
This paper proposes a real-time implementable self-tuning PID control strategy to tackle
Received 24 March 2014
oxygen excess ratio regulation challenge of a proton exchange membrane fuel cell.
Received in revised form
Controller parameters are updated on-line, at each sampling time, using a not iterative
3 June 2014
procedure based on an artificial neural network model. The proposed controller takes ac-
Accepted 8 June 2014
count of nonlinear behaviors of the process, while avoiding heavy computations.
Available online 12 July 2014
To assess the efficiency and relevance of the proposed strategy, the controller is implemented on-line, experimentally validated on a real fuel cell and compared to the
Keywords:
built-in controller. In this aim, several control scenarios are considered to evaluate the
Proton exchange membrane fuel cell
controller performance.
Experimental implementation
Experimental results show the excellent tracking capability and disturbances rejection
Real-time control
ability of the controller, regardless of the operating conditions. Moreover, compared to the
Artificial neural network model
built-in controller the proposed strategy demonstrates better disturbances rejection capability. Overall, the proposed neural model-based self-tuning PID controller appears as an excellent candidate to address the oxygen excess ratio regulation issue. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction The development of new technologies for energy conversion is mandatory to cope with fossil energy resources depletion and global warming issues. As part of the energy transition, low-carbon energy sources represent promising opportunities to attain significant reductions in the volume of greenhouse gas emissions, there by reducing the
environmental footprint of transport, residential and industrial power consumption. In regard to renewable energies, one of the primary drawbacks is the variability of the supply flows, which raises the key issue of energy storage to counteract the intermittent nature of their conversion. In this context, the hydrogen option represents a promising alternative, as long as the hydrogen is produced from a renewable energy technology (electrolytic hydrogen), and stored to optimize potential gaps and surplus of intermittent
* Corresponding author. Tel.: þ262 262 938 223; fax: þ262 262 938 673. E-mail address: [email protected] (M. Benne). http://dx.doi.org/10.1016/j.ijhydene.2014.06.039 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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production. Downstream the hydrogen chain, electricity is generated from fuel cells, genuine zero-emission power generators. Because their high power density and low operating temperature, proton exchange membrane fuel cells (PEMFC) have proved to be the most suitable fuel cell technology for both transportation and stationary applications. However, several issues still need to be addressed to improve their reliability and energy conversion, reduce their cost or extend their lifetime. Among them, one of the most important is related to their control. To ensure optimal performance of the PEMFC, and avoid voltage degradation or flooding, numerous parameters such as stack temperature or gas pressure need to be properly controlled. In this context, one parameter, namely oxygen excess ratio, requires a special attention. The oxygen excess ratio or stoichiometric ratio represents the ratio of inlet oxygen flow to reacted oxygen flow. A poor control of this parameter could lead to performance degradation, due to oxygen starvation. Prevent oxygen starvation to ensure optimal conversion efficiency and avoid performance deterioration remains a challenging control goal. Recently, several works related to oxygen excess ratio control have been reported. In Ref. [1] a nonlinear second order sliding mode controller was used to regulate the oxygen excess ratio. Robustness and insensitivity properties of the controller have been investigated in simulation environment. Using flatness control theory, Fonseca et al. [2] proposed a nonlinear control strategy based on a simplified model of the PEMFC system. Simulation results showed the good performance of the proposed controller regarding oxygen excess ratio control. Wu et al. [3] proposed a nonlinear model-based predictive control scheme to prevent oxygen starvation. Even if simulation results were promising, the authors emphasized that some devices and design such as inverters have not been taken into account. Becherif et al. [4] used the maximum power point tracking technique to compute the optimal value of excess ratio reference at each sampling period in order to improve the PEMFC efficiency. The proposed approach, tested through simulations, allowed to increase the output power of the PEMFC by over 10%. Feroldi et al., 2007 [5] designed a dynamic matrix predictive control strategy. The proposed controller, implemented in simulation environment, showed good performance, especially in terms of disturbances rejection. Li et al. [6] designed a maximum net power control strategy to determine the optimal oxygen excess ratio value, coupled with an implicit generalized predictive control. The proposed controller showed good tracking capability in simulation. In Ref. [7] an LQR/LQG controller, based on a linearized model of the process, was presented and experimentally tested. Results showed that the proposed linear controller efficiently regulated the oxygen excess ratio, and offered good performance in terms of disturbances rejection. Garcia-Gabin et al. [8] proposed a real-time implementable sliding mode controller. Performance of the controller was experimentally investigated, and its ability to handle load changes was demonstrated. A constrained model predictive control strategy was developed by Ref. [9] to improve oxygen excess ratio regulation. The proposed controller, experimentally implemented, stabilized the
oxygen stoichiometric ratio around the target value approximately five times faster than the original controller. Kunusch et al. [10] designed a Super Twisting controller to regulate oxygen excess ration. The proposed strategy, experimentally tested, showed good tracking capability. Even if many control strategies have been proposed to control oxygen excess ratio, a very few were dedicated to realtime control. In the present paper, a real-time implementable selftuning PID controller is designed to tackle the oxygen excess ratio regulation issue. The proposed control strategy relies on an instantaneous linearization of an artificial neural network (ANN) model of the PEMFC combined with a General Minimum Variance (GMV) control law. ANN model together with GMV design allow to handle nonlinearities of the process, while avoiding heavy computations. On the one hand, compared to others nonlinear model-based approaches, such as nonlinear model-based predictive control, that required heavy computations due to iterative procedures, the proposed auto-tuning PID controller has a very low computational cost. On the other hand, compared to linear controllers, not well suited for nonlinear systems, the ANN model-based approach takes account of the nonlinear behavior of the process. To demonstrate the suitability of the proposed control strategy to address the control problem, the controller is implemented on-line and experimentally validated on a real fuel cell. This work is divided as follows: The experimental
Fig. 1 e Experimental fuel cell test station.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 1 2 8 1 9 e1 2 8 2 5
fuel cell system is presented in Section Experimental system description. Section Control design is dedicated to the realtime implementable neural model-based self-tuning PID controller design. In this section, the procedure used to update on-line, at each sampling time, the controller parameters is detailed, and the ANN model of the PEMFC is designed and experimentally validated. Performance of the proposed controller in terms of tracking capability and disturbances rejection is experimentally investigated in Section Experimental results. Lastly, main conclusions are presented in Section Conclusion and prospects.
Experimental system description In this study, a neural model-based PID controller is proposed to ensure optimal PEMFC performance, while avoiding oxygen starvation. Validation tests are carried out on an experimental unit consisting of a single-cell, various monitoring and control devices, and a programmable electronic load (Fig. 1 and Fig. 2). The single-cell is made of a membrane electrodes assembling (MEA) produced by Paxitech, with an active area of 50 cm2, sandwiched between bipolar plates clamped with a torque of 12 Nm after optimization. The MEA is composed of a Nafion® N115 membrane as the central layer, and gas diffusion layers, made of Pt-doped carbon black (40 wt%/C) deposited by Paxitech onto a carbon felt (0.6 mgPt cm2 mixed with Nafion®), as the two side layers. The Supervisory Control and Data Acquisition (SCDA) system, integrated by Fuel Cell Technologies (FCT), is controlled through a proprietary GUI (graphical user interface)
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composed of a set of modular virtual instruments (VI) implemented with Labview graphical software tool. This makes the experimental unit a flexible environment, allowing to perform a wide range of tests based on various configuration settings: - fuel cell temperature, measured at cathode side, - humidification temperatures, at the anode and cathode, - inlet gas temperatures and mass flows, at the anode and cathode, - and outlet back-pressures, at the anode and cathode. Since VI's can easily be modified or replaced, alternative monitoring and control strategies can be integrated to the SCDA system. As regards innovative control strategies, a set of VIs makes it possible to replace the original built-in controller by model-based approaches. With this setup, the optimal control action, computed on-line in Matlab® environment, is sent through a specific VI to be applied to the experimental unit. Within the scope of this study, pure hydrogen and air are used as fuel and oxidant, respectively.
Control design As previously stated, the oxygen excess ratio is a crucial parameter to ensure optimal PEMFC performance. Indeed, a poor control of this variable could lead to fast performance degradation and irreversible damages to the fuel cell membrane due to a phenomenon called oxygen starvation. Therefore, oxygen excess ratio regulation remains a
Fig. 2 e Simplified process and instrumentation diagram of the system.
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challenging control goal. In this section, a real-time implementable self-tuning PID controller is designed to tackle this control problem. This strategy, based on an ANN model of the PEMFC together with a GMV control design, allows to handle nonlinear behaviors of the process, while avoiding heavy computations.
proposed approach, the minimization of the cost function L is achieved using a not iterative procedure, which is a quite important feature to fulfill real-time implementation requirements. The methodology used to solve the optimization problem and the instantaneous linearization procedure are fully detailed in Refs. [11,12].
Neural model-based self-tuning PID algorithm
ANN model design
The main feature of the proposed approach relies on an instantaneous linearization of the ANN model of the process combined with a GMV control law. A set of coefficients is extracted on-line, at each sampling time, from the ANN model to obtain a linearized model. Controller parameters are then updated using the above mentioned linearized model and a GMV control law (Fig. 3). In the present case, the controlled output y(t) is the oxygen excess ratio, yset(t) denotes the desired value of oxygen excess ratio, e(t) denotes the trajectory tracking error, the manipulated variable u(t) is the air inlet flow rate, ny and nu are the number of past inputs/outputs required, and kc ; ti ; td denote the controller parameters. Since the proposed strategy relies on a classical PID controller, the velocity form of the control action u(t) at time t is computed as follow:
The proposed control strategy involves an ANN model of the PEMFC. This model, expected to predict the system output one step ahead, is used to determine the optimal controller parameters. As previously mentioned, the oxygen excess ratio, namely lO2 , denotes the ratio of oxygen supply to oxygen consumed in the cathode. In this manner, lO2 is a function of inlet air flow rate, load current, relative humidity of air at the cathode inlet, stack temperature and inlet pressure at the cathode. In this paper, regarding real-time control goal, and since lO2 mainly depends on load current and inlet air flow rate [9], a simplified model is proposed. This model is expected to predict lO2 one step ahead, once the load current I and the inlet air flow rate _ air are available. In practice, the load current is a measured m disturbance, whereas the inlet air flow rate is the manipulated variable. Regarding real-time implementation goal, the computational speed of the model is a key component. The model is expected to predict the system output with sufficient accuracy, while avoiding heavy computations. To address this problem, several ANN architectures have been investigated to determine which one provides the best trade-off between prediction accuracy and computational speed. Finally, a fully connected three layers network is designed. The hidden layer has five neurons with a tangent sigmoid activation function 41 , whereas the output layer has one neuron using a linear activation function 42 (Fig. 4). Identification and validation of the ANN model are performed on two different sets of data collected on the PEMFC system presented in Section Experimental system description and sampled with a 3 s period. The data set used for the training phase has to be chosen wisely, regarding the poor extrapolation performance of ANN models. In this aim, the training data set, used to identify the ANN model, covers the whole operating conditions and ranges from minimum to maximum inputs/outputs values. The model identification is
uðtÞ ¼ uðt 1Þ þ DuðtÞ with, Dt td DuðtÞ ¼ kc eðtÞ eðt 1Þ þ ðeðtÞ eðt 1ÞÞ þ ðeðtÞ ti Dt 2eðt 1Þ þ eðt 2ÞÞ and Dt denotes the sampling period. The optimization goal, is to find the optimal set of pab ¼ ½kct t T that minimizes the cost function rameters k i d 2 J ¼ e ðt þ 1Þ þ mDu2 ðtÞ: b ¼ arg min ðJÞ k k
where m is the weighting penalty parameter. However, at time t, eðt þ 1Þ ¼ yset ðt þ 1Þ yðt þ 1Þ is not available since it involves the knowledge of the system output, namely yðt þ 1Þ, at time t þ 1. To address this problem, the linearized model, obtained from the instantaneous linearization of the ANN model, is used to estimate the future output of the system yðt þ 1Þyylin ðt þ 1Þ. ylin ðt þ 1Þ denotes the future system output estimated by the linearized model. Eventually, the optimal controller parameters vector is obtained by minimizing on-line, at each sampling time, the cost In the function L ¼ ðyset ðt þ 1Þ ylin ðt þ 1ÞÞ2 þ mDu2 ðtÞ.
Fig. 3 e Self-tuning PID controller principle.
Fig. 4 e PEMFC ANN model.
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comparison between the built-in controller and the proposed control strategy is made for the second scenario. Note that this comparison cannot be performed for the first and third scenario due to technical constraints. In fact, the built-in controller of the SCDA system, integrated by Fuel Cell Technologies, is designed to operate at constant oxygen excess ratio. In other word, when using the original setup, the oxygen excess ratio value has to be set before the experiments and cannot be modified during the experiments. In the sequel, the inlet air flow rate is taken as manipulated variable, whereas the load current is a measured disturbance. The cell temperature and the sampling period are set to 75 C and 3 s respectively, ny and nu are both set to one, and the weighting penalty parameter m is taken equal to 109. It is assumed here that all other variables, required to ensure safety operation of the fuel cell, are properly controlled. Fig. 5 e PEMFC ANN model validation.
First case scenario: constant load current e variable oxygen excess ratio setpoint
performed using LevenbergeMarquart algorithm with an error goal of 0.001. The validation step is presented in Fig. 5. Two criteria, namely root mean square error qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn b 2 ðRMSE ¼ i¼1 ðyi y i Þ =nÞ and absolute maximal error bi ÞÞ, are considered to assess the one step ðAME ¼ maxðyi y i
ahead prediction performance of the ANN model. n represents b denote experimental and simuthe number of data, y and y lated data, respectively. With an RMSE of 0.003 and an AME under 0.1 the predictive performance accuracy of the ANN model is more than sufficient, especially since it is dedicated to control purposes (Table 1).
Experimental results To assess the performance of the proposed control strategy in terms of tracking capability, disturbances rejection, and robustness against plant-model mismatch, series of experiments are performed on the PEMFC system presented in Section Experimental system description. In this aim, the neural model-based self-tuning PID controller, implemented in Matlab® environment, is executed on-line and communicates in real-time with the SCDA system of the fuel cell. Here, to exemplify the controller performance three control scenarios are considered: The first scenario illustrates the tracking capability of the controller for a constant value of load current. The second scenario is designed to study the controller ability to cope with disturbances. Eventually, the third scenario evaluates the controller performance in terms of setpoint tracking accuracy in presence of disturbances. A
Table 1 e Training and validation results of the ANN model. RMSE AME
Training
Validation
4.726 104 0.079
0.003 0.98
The tracking capability of the controller is evaluated using an oxygen excess ratio setpoint that covers the whole operating condition. In this control scenario, the load current is set to 15 A and kept constant during the entire experiments. Fig. 6 shows that the controller is able to track accurately a variable oxygen excess ratio setpoint, while offering an entirely suitable dynamics for the manipulated variable.
Second case scenario: step changes on load current e constant oxygen excess ratio setpoint To assess the controller performance in terms of disturbances rejection, a set of step changes on the load current is performed. The dynamics of the PEMFC is strongly correlated to the power level. Therefore, to verify that the controller performs accurately whatever the power level, the current steps is chosen to cover the whole operating condition. Several experiments, with different sets of step changes in load current and different oxygen excess ration values, are carried out to compare the performance of the original built-in controller and the proposed control strategy. In each and every case, the proposed self-tuning PID controller preforms better than the built-in controller. Fig. 7 illustrates one of these experiments with the oxygen excess ratio set to 6. The proposed controller demonstrates that it can maintain the oxygen excess ratio to the desired level, even in presence of disturbance. Moreover, compared to the built-in controller, the proposed controller exhibits better disturbances rejection capability. Indeed, for the two first steps in current (t ¼ 17 s and t ¼ 47 s) an overshot is observed with the built-in controller, whereas the proposed controller efficiently rejects the disturbances.
Third case scenario: step changes on load current e variable oxygen excess ratio setpoint This control scenario is designed to assess the controller performance when the oxygen excess ratio setpoint is modified on-line according to the load current. This control scenario, which is a common working scenario in automotive
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Fig. 6 e Experimental tracking capability of the proposed controller: (a) oxygen excess ratio; (b) air flow rate.
Fig. 7 e Experimental disturbances rejection ability: (a) oxygen excess ratio; (b) load current.
Fig. 8 e Experimental tracking capability with step changes on load current: (a) oxygen excess ratio; (b) load current.
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applications, is significantly important. Indeed, several works demonstrated that updating the oxygen excess ratio reference according to the load current could significantly increase the PEMFC efficiency while avoiding oxygen starvation [4,13,14]. The proposed controller demonstrates excellent tracking capability even in presence of disturbances (Fig. 8). The ability of the controller to track efficiently an oxygen excess ratio setpoint, calculated according to a variable load current, is a quite important feature. Indeed, this control scenario appears as one of the most promising options to improve the overall PEMFC efficiency, while ensuring safety operation of the fuel cell. It is important to emphasize that in addition to the presented examples, numerous experiments have been carried out in the whole range of operating conditions. In every case, the proposed control strategy demonstrated highly satisfactory results in terms of tracking capability and disturbances rejection.
Conclusion and prospects In this paper, to address oxygen excess ratio control challenge, a self-tuning neural model-based PID controller has been developed. To achieve real-time control while taking account of nonlinear behaviors of the process, a not iterative procedure based on an ANN model has been designed to update online, at each sampling time, the controller parameters. To assess the efficiency and relevance of the proposed control strategy, the controller has been implemented on-line and experimentally validated on a real fuel cell. In this aim, numerous control scenarios have been experimentally conducted to evaluate the controller performance, especially in terms of setpoint tracking accuracy and disturbances rejection. These control scenarios gather all the possible scenarios in which the system would have to work. In each and every case, the controller demonstrated highly satisfactory results since it tracked efficiently the desired oxygen excess ratio value while compensating disturbances, regardless of the operating conditions. Besides, experimental comparison demonstrated that the proposed controller had better disturbances rejection capability than the built-in controller. The self-tuning PID controller has also proven to have good
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robustness properties against plant/model mismatch. Furthermore, the robustness of the controller can be further improved by introducing the modeling error within the optimization problem. Compared to others nonlinear model-based approaches that usually required heavy computations due to iterative procedures, the proposed auto-tuning PID controller has a very low computational cost since the optimization problem is solved analytically. Indeed, the main asset of the proposed strategy relies on the ANN model. On the one hand, it allows to takes account of process nonlinearities. On the other hand, due to its architecture, the instantaneous linearization of this model allows to rewrite the optimization problem and to solve it analytically. Overall, the proposed self-tuning PID controller appeared to be an excellent trade-off between nonlinear control strategies and linear controllers to tackle oxygen excess ratio regulation issues.
references
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