With the increasing demand for green technology, hydrogen and fuel cells are being considered as one of the most promising clean fuel and energy conversion devices, respectively. One of the best examples is Coradia I-Lint, world’s first hydrogen-powered passenger train which was introduced in 2016 in Germany. Fuel cells are electrochemical devices which convert chemical energy to electrical energy as long as fuel and air/oxygen is supplied. The conversion is based on the concept opposite to electrolysis of water, where hydrogen and oxygen ions are separated from a molecule of water by passing electric current through it. Fuel cells are generally classified according to the type of electrolyte used, apart from factors like type of fuel used or the operating temperature. Solid oxides fuel cells (SOFC), phosphoric acid fuel cells (PAFC), direct methanol fuel cells (DMFC), and proton exchange membrane fuel cells (PEMFC) are some of the widely used fuel cell technologies. The ultimate reaction between hydrogen and oxygen to form water is the same in all the cases irrespective of the type of fuel cell used.
PEMFC is a typical fuel cell operating at a lower temperature, generally under 100 ⁰C, which gives it an advantage of faster connection time as compared to other fuel cell types. The transport and the portable device sectors are inclining more towards PEMFCs due to their compact structure, noiseless operation and lightweight characteristics. Furthermore, polymer electrolyte is used in a PEMFC, which makes it easy to manufacture. The physical structure of a PEMFC consists of several components like feeding channels, diffusion layer, membrane, catalytic layer, diffusion layer, and feeding channels in the cathode. The electrodes, membrane, and electrolyte is generally combined in a compact structure which is called Membrane Electrode Assembly (MEA). It is the heart of the fuel cell and is fed with hydrogen and oxygen, generating electrical power with a power density of around 1W cm− 2. Hydrogen acts as fuel to the system and is supplied on the cathode side while air is supplied in most cases instead of pure oxygen on the anode side. The only product of the reaction is water and heat. Auxiliary devices are installed along with the fuel cell for special purposes like thermal management, water management, humidification system and air-fuel flow system.
A single PEMFC produces voltage between 0 and 1 volts depending on the size of the load and fuel cell operating conditions. Usually, the load requires large operating current, so more than one fuel cell is connected in series to form a fuel cell stack to produce the desired voltage. A single cell produces voltage in the range of 0.6 to 0.8 volts, approximately. Since the load requirement is generally large, more than one fuel cell is used in series to form a fuel cell stack, to get higher voltage. The output voltage of the FC stack is generally calculated by multiplying the number of fuel cells used, with the average voltage of a single fuel cell. As with other electrical devices, there are electrical resistances in the fuel cell. The loss associated with the resistance is dissipated in the form of heat. In other words, heat is released from the fuel cell reaction and is considered as one of the by-products along with water (Pukrushpan, 2003).
The literature on PEMFC is quite large and diverse in nature. A lot of research has been conducted from modelling to control of PEM fuel cells. Dutta et al. (2000) and Mann et al. (2000) laid the foundation of steady-state PEMFC stack modelling which were used to derive the aspects of the model related to conductivity and hydration of the membrane. A detailed three-dimensional multi-component PEMFC model was presented by Dutta et al. (2000) with the complicated electrochemical aspects of the model. Coming to the dynamic modelling, Pukrushpan (2003) presented a dynamic PEMFC model to further study and design the control system for air subsystem of the PEMFC model.
One of the earliest works done in the field of control was by Lorenz et al. (1997), where they presented a method to control power of an electric drive unit of a vehicle. While Pukrushpan’s (2003) PhD thesis is considered as one of the major contributions, where the principal focus is on air-in flow control. In a decentralised MIMO control system, basic feedback PID controllers were designed and implemented by Serra et al. (2005) to control stack voltage and hydrogen-air pressure difference by manipulating air stoichiometric ratio and hydrogen stoichiometry, respectively. The implemented control strategy gave the best controllability indices in comparison to other control-manipulated variable pairs. A LQG regulator was developed for a dynamic air supply system presented (Rodatz et al. 2003), apart from faster response time, pressure trace was successfully decoupled from the mass flow trace. Under small load variations a H-infinity controller was designed (Sedghisigarchi and Feliachi 2004) to maintain the output voltage. By control of hydrogen flow rate, variations in the output voltage were kept under 5% during simulations. For a PEMFC system, under varying current conditions, control of air supply system was achieved (Caux et al. 2005). Simulations proposed a species balance model to maintain constant pressure on the cathode (oxygen) compartment and to follow a desired air flow-rate. For a small PEMFC system, using a microcontroller, a novel cascade strategy with a static feed-forward control was proposed (Tae-Hoon Kim et al. 2010).
For a validated non-linear PEMFC model, (Danzer et al. 2009) a constrained feed-forward model predictive control (MPC) was developed of air flow rate. The desired action was achieved by comparing the predicted and actual output current, reducing the error and limiting the oxygen excess ratio to avoid oxygen starvation. Since the MPC for a non-linear system requires a lot of computational time, a linearized model was used (Arce et al. 2007) to reduce the computational time and to generate a faster response for maximum efficiency and starvation control by manipulating the air flow rate. Nejad et al. (2019) proposed genetic algorithm optimization-based approach to obtain optimum control parameters for a traditional lead-lag controller for fuel cell voltage control. The controller was able to achieve less voltage deviation and higher overall efficiency. For a two input two output system, Shankar et al. (2019) developed an experimental hybrid non-linear control structure to maintain the fuel cell operating temperature coupled with an airflow cooling fan, using sliding mode controller and reduced-order sliding mode observer. In terms of disturbance rejection and set point tracking the proposed controller was compared with the traditional PI controller and observed to give better results.
While in the arena of fractional order systems there has been considerable amount of work done in regards with PEMFC. Using Warburg impedance, proposed a fractional order fuel cell transfer function (Taleb et al. 2017). This model was transformed to implement FOM identification. The method used to identify the model’s parameters was based on the least square method extended to fractional order models.
1.1. Motivation and Novelty
Since PEMFCs are mostly employed in the transportation and portable device sectors, the load requirement is quite dynamic in nature according to external conditions. So, a fuel cell is supposed to follow the same trend in the voltage produced, which calls in the control of stack voltage. Stack voltage depends on many factors like stack temperature, moisture content of the membrane, partial pressure of hydrogen and air, out of which inlet rate of hydrogen and air are quite important factors as it affects the rate of reaction and hence the voltage produced. This solves one of the major control problems of a fuel cell that is control of voltage by manipulating the inlet rates of hydrogen and air simultaneously. On the same idea Fu-Cheng Wang et al. (2007) described the dynamics of PEMFC and modelled it as MISO system, with the fixed output resistance to control the output voltage by tuning the hydrogen and air flow rates through a multivariable robust controller. From the experimental results, the proposed robust controller was deemed to achieve robust performance and to reduce hydrogen consumption of the system.
To take this further, in the present study paper a novel control structure, where both fuel and air inlet rates are manipulated simultaneously to control the stack voltage, has been proposed. For this control objective, the integer order MISO model developed by Fu-Cheng Wang et al. is reduced to a fractional order MISO PEMFC model using Indranil Pan’s method based on genetic algorithm as the optimization technique. Using both, the integer as well as the fractional order models, model-based controllers like PI, PID, Model Predictive Control (MPC) and Predictive PID (PPID) are designed for individual feedback loops and for the proposed TISO control unit. The main novelty, contribution and highlights of the study have been summarized below:
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Fractional order model development using genetic algorithm as the optimization technique, followed by model-based control strategy for a Multiple Input and Single Output system
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Proposed a new control structure based on feedback control loop and gain percent contribution for a MISO system focusing on the control of stack voltage
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Control performance evaluated on the basis of set point tracking, disturbance rejection, inverse response and time delay compensation in terms of IAE, ISE and TV values
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While in the literature more focus has been on air flow optimization for compressor or pump performance, this study focuses on both air flow optimization and hydrogen consumption optimization