Control-oriented thermal management of solid oxide fuel cells based on a modified Takagi–Sugeno fuzzy model

Thermal management for a solid oxide fuel cell (SOFC) is actually temperature control, due to the importance of cell temperature for the performance of an SOFC. An SOFC stack is a nonlinear and multi-variable system which is difficult to model by traditional methods. A modified Takagi–Sugeno (T–S) fuzzy model that is suitable for nonlinear systems is built to model the SOFC stack. The model parameters are initialized by the fuzzy c-means clustering method, and learned using an off-line back-propagation algorithm. In order to obtain the training data to identify the modified T–S model, a SOFC physical model via MATLAB is established. The temperature model is the center of the physical model and is developed by enthalpy-balance equations. It is shown that the modified T–S fuzzy model is sufficiently accurate to follow the temperature response of the stack, and can be conveniently utilized to design temperature control strategies.     

Nonlinear predictive control of a molten carbonate fuel cell stack

Operating temperature of a molten carbonate fuel cell stack should be controlled within a special range in order to improve the performance of fuel cell. In this paper, a nonlinear predictive control algorithm based on the Takagi–Sugeno fuzzy model is developed for the temperature of a molten carbonate fuel cell stack. Through predicting the outputs on a Takagi–Sugeno fuzzy model, a discrete optimization of the control action is adopted according to the principle of branch-and-bound method. The simulation results show the potential to introduce the predictive control based on Takagi–Sugeno fuzzy model for the development of fuel cells.     

Control‐oriented nonlinear modelling of molten carbonate fuel cells

Performance and availability of molten carbonate fuel cells (MCFC) stack are greatly dependent on its operating temperature. Control of the operating temperature within a specified range and reduction of its temperature fluctuation are highly desirable. The models of MCFC stack existing are too complicated to be suitable for design of a controller because of its lack of clear input–output relations. In this paper, according to the demands of control design, a quantitative relations model of control‐oriented MCFC between the temperatures of the stack and flowrates of the input gases is developed, based on conservation laws. It is an affine nonlinear model with multi‐input and multi‐output, the flowrates of fuel and oxidant gases as the manipulated vector and the temperatures of MCFC electrode–electrolyte plates, separator plates as the controlled vector. The modelling and simulation procedures are given in detail. The simulation tests reveal that the model developed is accurate and it is suitable to be used as a model in designing a controller of MCFC stack. Copyright © 2004 John Wiley & Sons, Ltd.     

Identification of the Hammerstein model of a PEMFC stack based on least squares support vector machines

This paper reports a Hammerstein modeling study of a proton exchange membrane fuel cell (PEMFC) stack using least squares support vector machines (LS-SVM). PEMFC is a complex nonlinear, multi-input and multi-output (MIMO) system that is hard to model by traditional methodologies. Due to the generalization performance of LS-SVM being independent of the dimensionality of the input data and the particularly simple structure of the Hammerstein model, a MIMO SVM-ARX (linear autoregression model with exogenous input) Hammerstein model is used to represent the PEMFC stack in this paper. The linear model parameters and the static nonlinearity can be obtained simultaneously by solving a set of linear equations followed by the singular value decomposition (SVD). The simulation tests demonstrate the obtained SVM-ARX Hammerstein model can efficiently approximate the dynamic behavior of a PEMFC stack. Furthermore, based on the proposed SVM-ARX Hammerstein model, valid control strategy studies such as predictive control, robust control can be developed.     

基于自适应竞争聚类的多输人多输出热工过程模糊辨识

针对多输入多输出（MIM0）热工过程的非线性、强耦合、变工况及参数时变等特点,提出了一种基于系统输入输出数据和模糊自适应竞争聚类的模型辨识新方法．该方法首先依据系统的各个典型运行工况,使用模糊自适应竞争聚类对输入输出数据进行聚类划分,并对T—S模糊模型进行结构辨识,以确定系统的模型结构和参数;然后采用最小二乘递推算法对模型后件参数进行辨识,同时对结构辨识参数进行精确修正．将所提出的模型辨识方法用于锅炉一汽轮机非线性系统的模型辨识,仿真结果验证了该方法的有效性．     

熔融碳酸盐燃料电池（MCFC）系统建模与控制的研究现状与发展

详细介绍了MCFC的电极,单电池、电堆,系统四个层次的建模以及MCFC控制的研究现状,指出了现有模型的不足;讨论了电堆和系统两级建模的发展方向,分析了MCFC系统的非线性,大时滞、分布参数、多输入多输出,有约束和随机干扰等特征,提出了两种适宜的控制方法。     

Nonlinear dynamic modeling for a SOFC stack by using a Hammerstein model

Solid oxide fuel cell (SOFC) is a kind of nonlinear, multi-input–multi-output (MIMO) system that is hard to model by the traditional methodologies. For the purpose of dynamic simulation and control, this paper reports a dynamic modeling study of SOFC stack using a Hammerstein model. The static nonlinear part of the Hammerstein model is modeled by a radial basis function neural network (RBFNN), and the linear part is modeled by an autoregressive with exogenous input (ARX) model. To estimate the hidden centers, the radial basis function widths and the connection weights of the RBFNN, a new gradient descent algorithm is derived in the study. On the other hand, the least squares (LS) algorithm and Akaike Information Criteria (AIC) are used to estimate the parameters and the orders of the ARX model, respectively. The applicability of the proposed Hammerstein model in modeling the nonlinear dynamic properties of the SOFC is illustrated by the simulation. At the same time, the experimental comparisons between the Hammerstein model and the RBFNN model are provided which show a substantially better performance for the Hammerstein model. Furthermore, based on this Hammerstein model, some control schemes such as predictive control, robust control can be developed.     

Predictive control of solid oxide fuel cell based on an improved Takagi-Sugeno fuzzy model

Thermal management of a solid oxide fuel cell (SOFC) stack essentially involves control of the temperature within a specific range in order to maintain good performance of the stack. In this paper, a nonlinear temperature predictive control algorithm based on an improved Takagi-Sugeon (T-S) fuzzy model is presented. The improved T-S fuzzy model can be identified by the training data and becomes a predictive model. The branch-and-bound method and the greedy algorithm are employed to set a discrete optimization and an initial upper boundary, respectively. Simulation results show the advantages of the model predictive control (MPC) based on the identified and improved T-S fuzzy model for an SOFC stack.     

应用模糊辨识方法对DMFC电堆的温度特性建模

从甲醇燃料电池（DMFC）电堆实际应用的角度出发,利用模糊技术对DMFC电堆非线性系统进行模型辨识和预测。以阴阳极燃料的流速为的输入量,电堆的工作温度为输出量,利用1000组实验数据作为样本,建立了不同燃料流速下电堆工作温度的动态响应模型。仿真结果证明采用模糊辨识建模的方法是有效的,建立的模型精度较高,从而为设计DMFC电堆实时控制系统奠定了基础。     

Predictive control of SOFC based on a GA-RBF neural network model

Transients in a load have a significant impact on the performance and durability of a solid oxide fuel cell (SOFC) system. One of the main reasons is that the fuel utilization changes drastically due to the load change. Therefore, in order to guarantee the fuel utilization to operate within a safe range, a nonlinear model predictive control (MPC) method is proposed to control the stack terminal voltage as a proper constant in this paper. The nonlinear predictive controller is based on an improved radial basis function (RBF) neural network identification model. During the process of modeling, the genetic algorithm (GA) is used to optimize the parameters of RBF neural networks. And then a nonlinear predictive control algorithm is applied to track the voltage of the SOFC. Compared with the constant fuel utilization control method, the simulation results show that the nonlinear predictive control algorithm based on the GA-RBF model performs much better.     

Nonlinear model predictive control of SOFC based on a Hammerstein model

To protect solid oxide fuel cell (SOFC) stack and meet the voltage demand of DC type loads, two control loops are designed for controlling fuel utilization and output voltage, respectively. A Hammerstein model of the SOFC is first presented for developing effective control strategies, in which the nonlinear static part is approximated by a radial basis function neural network (RBFNN) and the linear dynamic part is modeled by an autoregressive with exogenous input (ARX) model. As we know, the output voltage of the SOFC changes with load variations. After a primary control loop is designed to keep the fuel utilization as a steady-state constant, a nonlinear model predictive control (MPC) based on the Hammerstein model is developed to control the output voltage of the SOFC. The performance of the MPC controller is compared with that of the PI controller developed in [Y.H. Li, S.S. Choi, S. Rajakaruna, An analysis of the control and operation of a solid oxide fuel-cell power plant in an isolated system, IEEE Trans. Energy Convers. 20 (2) (2005) 381–387]. Simulation results demonstrate the potential of the proposed Hammerstein model for application to the control of the SOFC, while the excellence of the nonlinear MPC controller for voltage control of the SOFC is proved.     

Intelligent uninterruptible power supply system with back-up fuel cell/battery hybrid power source

This paper presents the development of an intelligent uninterruptible power supply (UPS) system with a hybrid power source that comprises a proton-exchange membrane fuel cell (PEMFC) and a battery. Attention is focused on the architecture of the UPS hybrid system and the data acquisition and control of the PEMFC. Specifically, the hybrid UPS system consists of a low-cost 60-cell 300 W PEMFC stack, a 3-cell lead–acid battery, an active power factor correction ac–dc rectifier, a half-bridge dc–ac inverter, a dc–dc converter, an ac–dc charger and their control units based on a digital signal processor TMS320F240, other integrated circuit chips, and a simple network management protocol adapter. Experimental tests and theoretical studies are conducted. First, the major parameters of the PEMFC are experimentally obtained and evaluated. Then an intelligent control strategy for the PEMFC stack is proposed and implemented. Finally, the performance of the hybrid UPS system is measured and analyzed.     

A boiler-turbine system control using a fuzzy auto-regressive moving average (FARMA) model

This paper presents an application of an online self-organizing fuzzy logic controller to a boiler-turbine system of a fossil power plant. The control rules and the membership functions of the proposed fuzzy logic controller are generated automatically without using a plant model. A boiler-turbine system is described as a multi-input multioutput (MIMO) nonlinear system in this paper. Then, three single-loop fuzzy logic controllers are designed independently. Simulation shows robust results for various kinds of electric load demand changes and parameter variations of boiler-turbine system.     

Study on the levelling process of the current collector for the molten carbonate fuel cell based on curvature integration method

The current collector for the molten carbonate fuel cell (MCFC) is manufactured from the sheet metal forming process. After the forming process, the current collector is bent resulting in a specific curvature (κ_i) in the direction in which trapezoidal protrusions are formed due to springback. In the stack of the MCFC, small deformation of the current collector can bring about defects in the electrolyte, non-uniform contact and difficulties in assembling the stack. Therefore, the curvature of the current collector should be minimized in order to reduce defects which can cause critical damage in the long-term operation. In order to straighten the current collector, the levelling process using three rolls was employed. In this work, a simple and effective method for designing the levelling process was proposed. An analytic model and the finite element analysis were used in combination. The optimal curvature minimizing the resultant curvature and the resultant moment of the current collector down to zero was calculated from the bending moment–curvature relationship. The bending moment–curvature relationship of the current collector was determined from the finite element analysis of uniform bending using the simulation results of the three-stage forming process. In the analytic model based on curvature integration method, the proper roll arrangement corresponding to the optimal curvature was calculated. Experiments were conducted using the calculated roll arrangement. The current collector was levelled nearly flat using the levelling process. After the levelling process, the flattened current collector was easily assembled with a centre plate and ensuring uniform contact with the electrolyte.     

Experimental study on the dynamic characteristics of kW-scale molten carbonate fuel cell systems

The aim of this work is to develop dynamic models for two types of kW-scale molten carbonate fuel cell (MCFC) systems on the basis of experimental data. The dynamic models are represented as a 3×3 transfer function matrix for a multi-input and multi-output (MIMO) system with three inputs and three outputs. The three controlled variables which severely affect the stack performance and lifetime are the temperature difference in the stack and the pressure drop at the anode and the cathode. Three manipulated variables, namely, current load, fuel and oxidant utilization, are selected to keep the three controlled variables within their safety limits for the reliable operation and protection of the system in case of emergency. Each element in the transfer function matrix is in the form of a first-order model using a simple, unit step, response test during operation. The non-zero off-diagonal elements in the transfer function matrix show that some interactions exist among the operating variables, and two zeros show no interaction between fuel and oxidant flow without gas cross-over. The stability of both dynamic models is analyzed using the relative gain array (RGA) method. Large diagonal elements in the RGA matrix show that the pairing between the manipulated and controlled variables is appropriate. Proper pairing is also proven by the singular value analysis (SVA) method with a smaller singular value in each system.     

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

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.     

Modelling,simulation and control of a proton exchange membrane fuel cell (PEMFC) power system

Fuel cell power systems are emerging as promising means of electrical power generation on account of the associated clean electricity generation process, as well as their suitability for use in a wide range of applications. During the design stage, the development of a computer model for simulating the behaviour of a system under development can facilitate the experimentation and testing of that system's performance. Since the electrical power output of a fuel cell stack is seldom at a suitable fixed voltage, conditioning circuits and their associated controllers must be incorporated in the design of the fuel cell power system. This paper presents a MATLAB/Simulink model that simulates the behaviour of a Proton Exchange Membrane Fuel Cell (PEMFC), conditioning circuits and their controllers. The computer modelling of the PEMFC was based on adopted mathematical models that describe the fuel cell's operational voltage, while accounting for the irreversibilities associated with the fuel cell stack. The conditioning circuits that are included in the Simulink model are a DC–DC converter and DC–AC inverter circuits. These circuits are the commonly utilized power electronics circuits for regulating and conditioning the output voltage from a fuel cell stack. The modelling of the circuits is based on relationships that govern the output voltage behaviour with respect to their input voltages, switching duty cycle and efficiency. In addition, this paper describes a Fuzzy Logic Controller (FLC) design that is aimed at regulating the conditioning circuits to provide and maintain suitable electrical power for a wide range of applications. The model presented demonstrates the use of the FLC in conjunction with the PEMFC Simulink model and that it is the basis for more in-depth analytical models.     

Modeling a SOFC stack based on GA-RBF neural networks identification

In this paper, a nonlinear offline model of the solid oxide fuel cell (SOFC) is built by using a radial basis function (RBF) neural network based on a genetic algorithm (GA). During the process of modeling, the GA aims to optimize the parameters of RBF neural networks and the optimum values are regarded as the initial values of the RBF neural network parameters. Furthermore, we utilize the gradient descent learning algorithm to adjust the parameters. The validity and accuracy of modeling are tested by simulations. Besides, compared with the BP neural network approach, the simulation results show that the GA-RBF approach is superior to the conventional BP neural network in predicting the stack voltage with different temperature. So it is feasible to establish the model of SOFC stack by using RBF neural networks identification based on the GA.     

Modelling and simulation of the steady-state and dynamic behaviour of a PEM fuel cell

The performance of a fuel cell can be expressed by the voltage–load current (V–I) characteristics. In this study, two mathematical modelling for computing the steady-state and dynamic voltage–current (V–I) characteristics of PEM fuel cell stacks have been developed. For determining the humidity of the membrane in steady-state conditions, mathematical and theoretical equations are considered. This value is not an adjustable parameter. The goal of dynamic modelling is to find the response of the system against the load variations. In this research, in addition to the charge double layer phenomenon, the effects of temperature and gas flows are taken into account, then the fuel cell system is divided into three control volumes and thus a lumped-parameter model for these sub-systems is established using the mass and heat transfer equations. The proposed models are implemented in Matlab/Simulink environment. Additionally, these models were tested for the SR-12Modular PEM Generator, the Ballard Mark V FC, the BCS 500-W stack and various experimental data in open literature. They exhibit excellent agreement with other simulation and experimental results.