There is an increasing interest in the use of proton exchange membrane fuel cells (PEMFCs) as environmentally friendly power sources for mobile and stationary applications. The key issues limiting the widespread commercialization of fuel cell technology are performance and cost. To achieve better operating performance, it is necessary to develop effective control schemes that can manage the complex dynamics of the PEMFC. One way to define better performance is to obtain maximum possible power density from the PEMFC with minimum input effort, and model based control schemes are well-suited for this task. Dynamic models of fuel cells available in literature developed from first principles include mass transport, reaction mechanism, electron transportation and overpotential of voltage throughout the process. These models are complex, and are difficult to develop and use directly for controller design. Thus, the use of data driven time series models, which can be developed with significantly less effort, is an attractive option for controller development.

To the best of our knowledge, the literature does not contain any instances of controller design for the PEMFC based on data driven models. Grujicic et al. [1] have employed black box model-based feed forward control strategies for maintaining the partial pressure of oxygen at the cathode during abrupt changes in current demand. As this scheme is sensitive to modeling errors, they recommend the inclusion of separate feedback control for power regulation. Ren et al. [2] have used a modeling and predictive control scheme developed based on support vector regression machine for control of humidification at the anode. Choe et al. [3] have presented an integrated model of PEM fuel cell power system along with a PWM DC/DC converter. They have implemented two control strategies, static feedback and static feedforward for oxygen starvation and temperature, respectively. Methekar et al. [4] have proposed an IMC based multi-loop PID control scheme for controlling average power density and average solid temperature of the PEMFC. They also implemented a ratio control strategy to avoid oxygen starvation, but found response times for tracking set points to be large. In another recent publication, Bedi et al. [5] have developed nonlinear internal model control (IMC) schemes for peak power control in PEMFC using deterministic nonlinear output error models. While schemes such as static feedforward control and multi-loop PI are relatively easy to develop, they are not suitable for managing multi-variable interactions and unmeasured disturbances. Internal model and predictive control schemes appear promising approaches for handling PEMFC control problems. However, the approaches discussed above do not attempt to model unmeasured disturbances and use these models for controller development.

In this work, we develop multivariable control schemes using data driven models under the IMC and linear quadratic Gaussian (LQG) optimal control framework. The LQG controller is an infinite horizon controller that guarantees asymptotic local stability. Moreover, these control schemes are relatively easy to tune for achieving desired performance. Since fuel cells have relatively fast dynamics (of the order of seconds) and since the servo control requirements in load following applications are stringent, the controller must be able to decide on the manipulated variable action within a very small sampling period. Since IMC and LQG approaches yield closed form control laws these are easy to implement in real-time for managing the fast transients in these systems. We investigate the problem of controlling average power density and temperature of the PEMFC using inlet molar flow rate of hydrogen and coolant. While simulating system dynamics, it is assumed that manipulated inputs entering the system are subject to unknown fluctuations and measurements are corrupted with noise. An innovation form of linear state space model is identified from input-output data generated by simultaneously introducing random binary signal (RBS) perturbations in both the manipulated inputs. The main advantage of this model form is that the stationary unmeasured disturbances are explicitly modeled together with the deterministic signals. Thus, the use of these models for controller design can significantly improve regulatory performance of the controller. These state space models, after appropriate state augmentation for dealing with plant-model mismatch, are used for the development of a state estimator (Kalman filter) and further for implementing state feedback control laws.

The process dynamics of the PEMFC are simulated using the mechanistic model given by Golbert and Lewin [6]. This model is a distributed parameter model, which accounts for spatial dependency and dynamics in temperature. The efficacy of the designed controllers is tested by simulating servo and regulatory control problems associated with the PEMFC, and the resulting performances are compared with the performance of IMC based multi-loop PI control scheme. Simulation results show that the proposed control schemes successfully track large variations in the power demand for the PEMFC. Also, as can be expected, the LQG controller outperforms the IMC based PI and IMC based multivariable controllers.

REFERENCES:

[1] M. Grujicic, K. M. Chittajallu, E. H. Law and J. T. Pukrushpan. Model-based control strategies in the dynamic interaction of air and fuel cell. J. Power and Energy 2004; 218A: 487-499.

[2] Y. Ren, G.-Y. Cao and X.-J. Zhu. Predictive control of proton exchange membrane fuel cell (PEMFC) based on support vector regression machine. Proc. Machine learning and cybernetics Conference. 2005; 18-21.

[3] S.-Y. Choe, J.-G. Lee, J.-W. Ahn and S.-H. Baek. Integrated modeling and control of a PEM fuel cell power system with a PWM DC/DC Converter. J. Power Sources. 2007; 164: 614-623.

[4] R. N. Methekar, V. Prasad and R. D. Gudi. Dynamic analysis and linear control strategies for proton exchange membrane fuel cell using a distributed parameter model. J. Power Sources. 2007; 165(1): 152-170.

[5] P. Bedi, R. Methekar, S.C. Patwardhan, V. Prasad, and R.D. Gudi. Nonlinear Internal Model Control of PEM Fuel Cell, accepted for presentation in DYCOPS – 2007.

[6] J. Golbert and D. R. Lewin. Model based control of fuel cells: (1) Regulatory control. J. Power Sources. 2004; 135: 135-151.

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