Elsevier

Journal of Power Sources

Volume 194, Issue 1, 20 October 2009, Pages 338-348
Journal of Power Sources

Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization

https://doi.org/10.1016/j.jpowsour.2009.04.077Get rights and content

Abstract

By utilizing the state feedback exact linearization approach, a nonlinear robust control strategy is designed based on a multiple-input multiple-output (MIMO) dynamic nonlinear model of proton exchange membrane fuel cell (PEMFC). The state feedback exact linearization approach can achieve the global exact linearization via the nonlinear coordinate transformation and the dynamic extension algorithm such that H robust control strategy can be directly utilized to guarantee the robustness of the system. The proposed dynamic nonlinear model is tested by comparing the simulation results with the experimental data in Fuel Cell Application Centre in Temasek Polytechnic. The comprehensive results of simulation manifest that the dynamic nonlinear model with nonlinear robust control law has better transient and robust stability when the vehicle running process is simulated. The proposed nonlinear robust controller will be very useful to protect the membrane damage by keeping the pressure deviations as small as possible during large disturbances and prolong the stack life of PEMFC.

Introduction

As a renewable energy source, fuel cells are one of the promising energy technologies for sustainable future due to their high energy efficiency and environment friendliness. Compared with the other types of fuel cells, a proton exchange membrane fuel cell (PEMFC) shows promising results with its advantages such as low temperature, high power density, fast response, and zero emission if it is run with pure hydrogen, and it is suitable for use in portable power supply, vehicles, and residential and distributed power plants [1], [2], [3].

PEMFC is a nonlinear, multiple-input and output, and strongly coupled dynamic system. Its working process is accompanied with liquid/vapor/gas mixed flow transportation, heat conduction and electrochemical reaction. The output current changes when the drove load changes, and electrochemical reaction is accelerated, simultaneously. If the flow rate of oxygen is too low in cathode, the output power of PEMFC system could be decreased because of lacking oxygen, which is so-called starvation. Therefore, in order to generate a reliable and efficient power response and prevent membrane damage as well as detrimental degradation of the stack voltage and oxygen depletion, it is so significant to design an effective control scheme to achieve optimal air and hydrogen inlet flow rates.

At present, many control strategies have been adopted for controlling the PEMFC system. Vahidia et al. [4] adopted a predicting control method to design the controller for fuel cell vehicle and it could satisfy the quickness response of air supply. Golbert and Lewind [5] who made fuel cell model linearization used predicting control to satisfy the need of power. Yuan et al. [6] imposed a predicting control method based on support vector machine to fuel cell control system. Schumacher et al. [7] proposed a water management of PEMFC method using fuzzy control. According to the experimental data, Almeda and Smoesm [8] proposed an artificial neural network control method to control output voltage of fuel cell and optimize the parameters in the system. Pukrushpan co-workers [9], [10] used feed-forward and feedback strategies to control the flow rate of compressor in the PEMFC air supply system. However, the existing control approaches used for PEMFC were based on linear models which were linearized at a specific operating point. Chiu et al. [11] proposed a linear PEMFC models which was used Jacobian linearization via a Taylor series expansion at the nominal operating point. However, the proposed model could not easily achieve satisfactory dynamic performance under large disturbances because of the operational parametric uncertainties such as the uncertainties of parametric coefficients for each cell on kinetic, thermodynamic and electrochemical foundations, and the resistivity of the membrane for the electron flow. Na co-workers [12], [13] presented a nonlinear controller which was designed based on the nonlinear model to prolong the stack life of fuel cells. The simulation results showed that the proposed nonlinear controls had better transient performances than the linear controls. However, the feedback linearization approach was used to only achieve the local linearization without the nonlinear coordinate transformation because of lacking the relative degree of the system. The proposed nonlinear controller could not guarantee the robustness with the operational parametric uncertainties and the internal dynamics problem would be appeared out. Therefore, an accurate nonlinear dynamic model needs to be developed for PEMFC as well as an advanced controller design technique, considering the nonlinearity and uncertainty that need to be proposed.

Recently, the state feedback exact linearization for nonlinear dynamic models, a well-known nonlinear approach, has been widely used to achieve more robust transient behavior [14], [16], [17]. The state feedback exact linearization uses a nonlinear transformation to transform an original nonlinear dynamic model into a linear model by diffeomorphism mapping. An optimal control theory is also applied to obtain a linear control that is transformed back to the original space by using the nonlinear mapping. The purpose of the dynamic extension algorithm is to construct an extended system in which the relative degree is equal to the order of the system [15]. After using the dynamic extension algorithm, the internal dynamics problem can be avoided and the nonlinear system becomes global linearized via the state feedback exact linearization.

H control approach has a broad base of support because of its robustness to uncertainties and reliable design algorithms [18], [19], [20]. The weighting functions chosen to shape the sensitivity functions are obtained through analysis of the uncertainties present in the system as well as from frequency-domain and time-domain requirements. Therefore, in the framework of H mixed sensitivity design, the nonlinear H robust control based on the state feedback exact linearization could make the system possess better robust stability.

In this paper, a MIMO dynamic nonlinear model that is appropriate for developing a nonlinear robust controller is proposed. The state feedback exact linearization with the dynamic extension algorithm is applied to design the proposed robust controller, based directly on the nonlinear dynamic PEMFC model. The dynamic response of the proposed model is tested by fuel cell test system. The control law obtained from the state feedback exact linearization is expected to be more robust in the presence of large disturbances when the vehicle running process is simulated. Furthermore, PEMFC life can be prolonged and protected by minimizing the deviations between the hydrogen and oxygen partial pressures.

Section snippets

The theory of PEMFC

The fuel cell is an electrochemical energy device that converts the chemical energy of fuel directly into electricity and heat with water as a byproduct of the reaction. The hydrogen and oxygen work as fuel and oxidant and they need to be humidified before they are fed into the cell/stack. The positively charged protons diffuse from anode through one side of the membrane and migrate toward the cathode [21], [22], [23], [24]. The electrons pass from the anode to the cathode through an exterior

Nonlinear control by state feedback exact linearization

For chemical process control, nonlinear control theory developed from differential geometry, known as exact linearization or feedback linearization, has more attractive because many chemical processes are basically of high nonlinearity [31], [33]. Hence, one of the main motivations of utilizing state feedback exact linearization for a PEMFC system is inherently a nonlinear chemical process.

Nonlinear robust control of PEMFC

In this section, a MIMO dynamic nonlinear model of PEMFC is developed by Eqs. (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), and it is then used to design a nonlinear robust controller by adopting state feedback exact linearization in order to minimize the pressure deviation between the hydrogen and oxygen. The main purpose

Experimental

The PEMFC test system was set up in the Fuel Cell Application Centre (FAC), Temasek Polytechnic Engineering School.

Model validation and simulation results

In this paper, the Matlab/Simulink is used to setup the PEMFC system dynamic model with nonlinear robust controller. To verify the validity of model, an experimental of a 1 kW PEMFC stack with 20 cells was conducted. The performances of the stack, such as output voltage versus current (VI) curve and power versus current (PI) curve, are presented in Fig. 5. It can be seen that the stack can give a 1 kW output at about 70 A of current.

Fig. 7 shows the measurement results of the transient voltage

Conclusions

In this paper, a MIMO nonlinear dynamic model of PEMFC which is implemented in Matlab/Simulink environment is proposed for designing a nonlinear robust control by the state feedback exact linearization with the dynamic extension algorithm. By adding H robust control to the state feedback control law, the steady-state error due to parameter uncertainty can be reduced and the system is guaranteed to have better robustness. The comparison between the experimental data and simulation results shows

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