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.     

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.     

Parameter optimization for tubular solid oxide fuel cell stack based on the dynamic model and an improved genetic algorithm

The tubular solid oxide fuel cell (SOFC) stack has important parameters that need to be identified and optimized for the control of high performance. In this paper, a simple SOFC electrochemical model which its parameters need to be optimized is introduced to implement stack control for high output power. A dynamic SOFC model is built based on three sub-models to provide a large numbers simulated data and different condition for optimization. Unlike the traditional parameter optimization method--simple genetic algorithm (SGA), an improved genetic algorithm (IGA) is introduced. The proposed method shows more accuracy and validity by comparing the different results using SGA and IGA methods, the simulated data, and experimental data. The models and IGA method are adapted to control processes.     

Thermal management of an independent steam reformer for a solid oxide fuel cell with constrained generalized predictive control

In this paper a systematic method for the development of a constrained generalized predictive control (CGPC) system for a steam reformer is presented. Firstly, a control-oriented dynamic model deriving from physical conservation laws is established and validated by experimental data. Based on the physical model, the control system adopts the Takagi-Sugeno (T-S) fuzzy model to rapidly and accurately predict the reforming temperature. This is identified on-line using the forgetting factor recursive least square (FFRLS) technique. In order to handle input amplitude constraints, the Lagrange Multiplier method is implemented in GPC while the optimal control sequence is obtained by minimizing a multistage objective function. The numerical test results demonstrate that the CGPC control system cannot only achieve rapid and smooth responses, but also possesses excellent disturbance rejection capability which allows it to maintain the reforming temperature during fuel flow rate fluctuations due to SOFC system load variation.     

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.     

Generalized predictive control for fractional order dynamic model of solid oxide fuel cell output power

An adaptive generalized predictive control (GPC) system is presented for the management of output power of solid oxide fuel cells (SOFCs). The dynamics of SOFC output power are characterized by a fractional order model, which is more accurate than an integer order model to depict the dynamics; the fractional order dynamic model is taken as the controlled plant of the GPC system. The GPC algorithm adopts a linear approximation method that uses a linear predictive model to approximate locally and dynamically the nonlinear dynamics of SOFC output power at each sampling period. Moreover, the parameters of the predictive model are identified online to overcome the time-varying dynamics of SOFC output power via introducing a forgetting factor recursive least squares (FFRLS) algorithm. Finally, according to the future power outputs predicted by the predictive model, an optimal current control sequence is obtained by solving a multistage cost function. The results demonstrate that the dynamic responses of the GPC system are quick and smooth, and the change of the current control sequence is slow and smooth. The quick and smooth dynamics are important for satisfying the rapid load following of SOFC generating systems and for prolonging the lifetime of SOFC stack.     

Thermal modeling of a solid oxide fuel cell and micro gas turbine hybrid power system based on modified LS-SVM

For a solid oxide fuel cell (SOFC) integrated into a micro gas turbine (MGT) hybrid power system, SOFC operating temperature and turbine inlet temperature are the key parameters, which affect the performance of the hybrid system. Thus, a least squares support vector machine (LS-SVM) identification model based on an improved particle swarm optimization (PSO) algorithm is proposed to describe the nonlinear temperature dynamic properties of the SOFC/MGT hybrid system in this paper. During the process of modeling, an improved PSO algorithm is employed to optimize the parameters of the LS-SVM. In order to obtain the training and prediction data to identify the modified LS-SVM model, a SOFC/MGT physical model is established via Simulink toolbox of MATLAB6.5. Compared to the conventional BP neural network and the standard LS-SVM, the simulation results show that the modified LS-SVM model can efficiently reflect the temperature response of the SOFC/MGT hybrid system.     

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.     

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.     

一种基于T-S模型的模糊PID控制器的设计及应用研究

基于Tзkзgi和Sugeno的模糊控制模型，设计了一种基于T-S模型的模糊PID控制器，这种设计方法可以充分借鉴常规PID控制器参数调整的各种成熟经验，使模糊控制规则的制定和参数的调整更简单易行，且物理意义明确。通过对电加热炉的仿真和实时控制表明，该控制器有着很强的适应性和鲁棒性，改善了系统的动静态性能。     

Nonlinear fuzzy modeling of a MCFC stack by an identification method

This paper reports a nonlinear fuzzy modeling study of a molten carbonate fuel cell (MCFC) stack by an identification method. MCFC is a complex nonlinear, multi-input and multi-output (MIMO) system that is hard to model by traditional methodologies. The Takagi–Sugeno (T–S) fuzzy model is suitable to model a large class of nonlinear MIMO system. In this paper, a MIMO T–S fuzzy model is used to represent MCFC. An identification method is used to determine both the nonlinear parameters of the antecedents and the linear parameters of the rules consequent in the T–S fuzzy model. The simulation tests reveal that obtained T–S fuzzy model using the identification method can efficiently approximate the static and dynamic behavior of a MCFC stack. Furthermore, based on this proposed T–S fuzzy model, valid control strategy studies such as predictive control, robust control can be developed.     

基于T-S模型的质子交换膜燃料电池控制建模

对PEMFC非线性复杂被控对象,提出了一种在线辨识模糊预测算法,用模糊聚类和线性辨识方法在线建立PEMFC控制系统的T—S模糊预测模型,仿真实验结果表明了该模糊辨识建模方法具有建模简单、模型精度高等优点,亦证明了该算法的有效性和优越性。研究结果对质子交换膜燃料电池控制系统的建模和控制具有一定的实用价值。     

Power decoupling control of a solid oxide fuel cell and micro gas turbine hybrid power system

Solid Oxide Fuel Cell (SOFC) integrated into Micro Gas Turbine (MGT) is a multivariable nonlinear and strong coupling system. To enable the SOFC and MGT hybrid power system to follow the load profile accurately, this paper proposes a self-tuning PID decoupling controller based on a modified output-input feedback (OIF) Elman neural network model to track the MGT output power and SOFC output power. During the modeling, in order to avoid getting into a local minimum, an improved particle swarm optimization (PSO) algorithm is employed to optimize the weights of the OIF Elman neural network. Using the modified OIF Elman neural network identifier, the SOFC/MGT hybrid system is identified on-line, and the parameters of the PID controller are tuned automatically. Furthermore, the corresponding decoupling control law is achieved by the conventional PID control algorithm. The validity and accuracy of the decoupling controller are tested by simulations in MATLAB environment. The simulation results verify that the proposed control strategy can achieve favorable control performance with regard to various load disturbances.     

Control of a solid oxide fuel cell stack based on unmodeled dynamic compensations

To guarantee solid oxide fuel cell (SOFC) safe operation, plenty control strategies have been developed to control stack temperature and voltage within a reasonable range. However, these control approaches ignore unmodeled dynamics of the SOFC system, which may lead to unsatisfactory control results, sometimes even make the system unstable. To overcome this challenge, a unique control strategy which considers unmodeled dynamic compensations of the SOFC system is proposed in this paper. A model of the SOFC system is firstly built, which includes a known linear model and an unmodeled nonlinear dynamic estimation. A nonlinear controller based on the unmodeled dynamic compensation is then developed to force the SOFC to track desired stack temperature and voltage. To evaluate the control performance, the proposed control method is compared with a traditional sliding mode controller. The simulation results show if the unmodeled dynamics have a small effect on the SOFC, both the sliding mode controller and the proposed controller can achieve a precise tracking. If the unmodeled dynamics have a great impact on the SOFC, the temperature and voltage can be well controlled with the proposed control strategy. However, in the sliding mode controller, the temperature and voltage trajectories deviate largely from the reference values.     

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.     

Fault-tolerant control for steam fluctuation in SOFC system with reforming units

Faults of solid oxide fuel cell (SOFC) systems can affect the characteristics of the stack and inhibit SOFC system commercialization. It has been found that the temperature fluctuation of the burner caused by fluctuation of steam flow rate would greatly affect the temperature of SOFC system and even exceed the safe operation range. Firstly, this paper introduces a mathematical model for the process of steam and natural gas reforming in a real SOFC system. Secondly, the cause of the burner temperature fluctuation is analyzed, and the model to simulate this faulty situation is established. Then, the Bayesian regularization neural network is used for fault diagnosis and good test results are obtained. Finally, fuzzy fault-tolerant control strategy is designed for the thermal safety problem of SOFC system. The simulation results validate the effectiveness of the proposed fault-tolerant control strategy.     

循环流化床锅炉主汽温的模糊预测函数控制

循环流化床锅炉主汽温具有大惯性、大滞后和非线性的特性,在特定工况下可以等效为一个具有可测扰动的一阶惯性加纯滞后对象.针对这一典型对象,考虑扰动通道和控制通道纯滞后时间相对大小,基于Smith预估补偿思想,提出了一种可测扰动前馈补偿的预测函数控制算法,结合锅炉负荷调度的T-S模糊模型,设计了循环流化床锅炉主汽温模糊预测函数控制器.仿真结果表明,在不同工况下,模糊预测函数控制器具有良好的设定值跟踪能力和调节性能.该控制方法应用模型简单,计算量小,具有较高的实际应用价值.     

Dynamic temperature modeling of an SOFC using least squares support vector machines

Cell temperature control plays a crucial role in SOFC operation. In order to design effective temperature control strategies by model-based control methods, a dynamic temperature model of an SOFC is presented in this paper using least squares support vector machines (LS-SVMs). The nonlinear temperature dynamics of the SOFC is represented by a nonlinear autoregressive with exogenous inputs (NARXs) model that is implemented using an LS-SVM regression model. Issues concerning the development of the LS-SVM temperature model are discussed in detail, including variable selection, training set construction and tuning of the LS-SVM parameters (usually referred to as hyperparameters). Comprehensive validation tests demonstrate that the developed LS-SVM model is sufficiently accurate to be used independently from the SOFC process, emulating its temperature response from the only process input information over a relatively wide operating range. The powerful ability of the LS-SVM temperature model benefits from the approaches of constructing the training set and tuning hyperparameters automatically by the genetic algorithm (GA), besides the modeling method itself. The proposed LS-SVM temperature model can be conveniently employed to design temperature control strategies of the SOFC.     

Parameter identification of an SOFC model with an efficient,adaptive differential evolution algorithm

An efficient, adaptive differential evolution (DE) algorithm is proposed in which DE parameter adaptation is implemented. A ranking-based vector selection and crossover rate repairing technique are also presented. The method is referred to as IJADE (Improved Jingqiao Adaptive DE). To verify the performance of IJADE, the parameters of a simple SOFC electrochemical model that is used to control the output performance of an SOFC stack are identified and optimized. The SOFC electrochemical model is built to provide the simulated data. The results indicate that the proposed method is able to efficiently identify and optimize model parameters while showing good agreement with both simulated and experimental data. Additionally, when compared to other DE variants and other evolutionary algorithms, IJADE obtained better results in terms of the quality of the final solutions, robustness, and convergence speed.     

Optimization of a solid oxide fuel cell and micro gas turbine hybrid system

For a solid oxide fuel cell (SOFC) and micro gas turbine (MGT) hybrid system, optimal control of load changes requires optimal dynamic scheduling of set points for the system's controllers. Thus, this paper proposes an improved iterative particle swarm optimization (PSO) algorithm to optimize the operating parameters under various loads. This method combines the iteration method and the PSO algorithm together, which can execute the discrete PSO iteratively until the control profile would converge to an optimal one. In MATLAB environment, the simulation results show that the SOFC/MGT hybrid model with the optimized parameters can effectively track the output power with high efficiency. Hence, the improved iterative PSO algorithm can be helpful for system analysis, optimization design, and real‐time control of the SOFC/MGT hybrid system. Copyright © 2011 John Wiley & Sons, Ltd.