Nonlinear controller design based on cascade adaptive sliding mode control for PEM fuel cell air supply systems

Optimized robust control for proton exchange membrane (PEM) fuel cell air supply systems is now a hot topic in improving the performance of oxygen excess ratio (OER) and the net power. In this paper, a cascade adaptive sliding mode control method is proposed to regulate oxygen excess ratio (OER) for proton exchange membrane (PEM) fuel cell air supply systems. Based on a simplified sixth-order nonlinear dynamic model, which takes parametric uncertainties, external disturbances and measurement noises into consideration, the nonlinear controller based on cascade adaptive sliding mode (NC-ASM) control is proposed. The method combines the nonlinear terms of super twisting algorithm and two added linear terms, and the modified second order sliding mode (SOSM) algorithm based on an observer is employed to form a cascade structure. Besides, an adaptive law is also utilized to regulate the parameters of the NC-ASM controller online. The performance of the controller is implemented on a real-time emulator. The results show that the proposed strategy performs better than the conventional constant sliding mode (CSM) control and PID method. Though during large range of load current and in the presence of various uncertainties, disturbances and noises, the NC-ASM controller can always converge rapidly, the feasibility and effectiveness are validated.     

Oxygen excess ratio control for proton exchange membrane fuel cell using model reference adaptive control

Optimized robust oxygen excess ratio (OER) control for proton exchange membrane fuel cells (PEMFCs) is now a critical issue for improving their economic efficiency and performance. In general, it is very difficult to control the OER due to modeling errors, parameter uncertainties, and disturbances. To address these issues, we propose a control system based on model reference adaptive control (MRAC) various difficulties inherent air supply systems.We utilize an adaptive law to address uncertainties implementation of the MRAC and nominal feedback controllers on a nonlinear model of fuel cell system is presented for illustration of the proposed system's robustness with various operating conditions. In addition, the control performance of MRAC is compared with nominal feedback control. The results show that the presented MRAC strategy performs better than the nominal feedback control method with less wear and less control effort on the compressor. The proposed MRAC algorithm can increase the compressor efficiency by using the adaptive law even with uncertainties.     

基于模型预测的电辅助涡轮增压柴油机空气系统优化控制研究

针对配备电辅助涡轮增压器(electrically assisted turbocharger,eTurbo)和高压废气再循环(exhaust gas recirculation,EGR)的发动机的油耗和电耗最低、进气氧浓度跟踪误差最小等多目标优化问题,提出了一种eTurbo在线优化控制算法:根据目标进气氧浓度和增压压力,采用自抗扰方法调节EGR阀的开度和压气机需求功率;然后采用模型预测控制(model predictive control,MPC)算法,在线将压气机的需求功率分配给涡轮机和电机,以实现发动机油耗、电能消耗和进气氧浓度跟踪误差的最佳折中。在GT-SUITE/Simulink平台上的仿真结果表明:在FTP-75驾驶循环下,相比于传统增压柴油机,eTurbo柴油机在该优化算法控制下,增压压力的跟踪误差减小87.20%,进气氧浓度的跟踪误差增加1.93%,发动机等效比油耗改善0.82%,验证了该方法的有效性。     

An adaptive sliding mode observer based near-optimal OER tracking control approach for PEMFC under dynamic operation condition

Tracking control of oxygen excess ratio (OER) is crucial for dynamic performance and operating efficiency of the proton exchange membrane fuel cell (PEMFC). OER tracking errors and overshoots under dynamic load limit the PEMFC output power performance, and also could lead oxygen starvation which seriously affect the life of PEMFC. To solve this problem, an adaptive sliding mode observer based near-optimal OER tracking control approach is proposed in this paper. According to real time load demand, a dynamic OER optimization strategy is designed to obtain an optimal OER. A nonlinear system model based near-optimal controller is designed to minimize the OER tracking error under variable operation condition of PEMFC. An adaptive sliding mode observer is utilized to estimate the uncertain parameters of the PEMFC air supply system and update parameters in near-optimal controller. The proposed control approach is implemented in OER tracking experiments based on air supply system of a 5 kW PEMFC test platform. The experiment results are analyzed and demonstrate the efficacy of the proposed control approach under load changes, external disturbances and parameter uncertainties of PEFMC system.     

Nonlinear model predictive control for efficient and robust airpath management in fuel cell vehicles

The fuel cell airpath multivariable control problem of optimally coordinating the electric compressor motor and the back-pressure valve to achieve efficient and safe conditions, for both steady state and transient operation, has not been completely addressed in the literature. This paper proposes a nonlinear model predictive control strategy, implemented via the Garrett Motion proprietary NMPC toolbox, to regulate the oxygen stoichiometry and the cathode pressure of an automotive fuel cell airpath system, while avoiding compressor surge and air starvation. The controller set-points are optimized, using the nonlinear model, to achieve the maximum system power as a function of the operating stack condition. The effectiveness and robustness of the proposed control strategy have been validated by means of a simulated World harmonized Light-duty vehicles Test Cycle (WLTC), under both state feedback and model parameters uncertainties.     

Weighted fusion control for proton exchange membrane fuel cell system

Oxygen excess ratio (OER) is closely correlated with the power generation efficiency and dynamic performance of proton exchange membrane fuel cell (PEMFC) system. As OER changes with varying load, it is prone to oxygen starvation and slow response to OER reference value, and great challenges to OER control technology are brought. To this end, a dual closed-loop weighted fusion control for PEMFC system is proposed. The outer loop is utilized to obtain the optimal OER reference value, and the inner loop is utilized to track the OER reference value. This inner loop combines the merits of active disturbance rejection control (ADRC) algorithm and fuzzy self-tuned PID (FSTPID) method. Simulation results reveal that the proposed approach is superior to the other three methods in reducing the overshoot, settling time and avoiding oxygen starvation issues, and also in improving several key performance indices, such as integrated absolute error, settling time, etc.     

Modeling and control of air stream and hydrogen flow with recirculation in a PEM fuel cell system—II. Linear and adaptive nonlinear control

In this part of the paper, linear and nonlinear multivariable controllers are designed for the air stream and hydrogen flow with recirculation in a proton exchange membrane (PEM) fuel cell system. The focus of the model is to obtain the desired transient performance of air stoichiometric ratio, cathode inlet pressure, and pressure difference between the anode and the cathode. Based on linearization of the nonlinear dynamic model in the first part of this paper, the coupling between control inputs and performance is analyzed first. The phase relationship between the stack voltage and water transport in frequency domain is meaningful to the future humidity estimation and active purge operation. Then, linear quadratic Gaussian (LQG) algorithm based on observer feedback is used for set-point tracking, and a model-predictive controller (MPC) with an on-line neural network identifier is also designed to improve robustness. Compared with decentralized PI controllers, the multivariable controllers improve the transient response and shows better disturbance rejection capability.     

Data driven NARMAX modeling for PEMFC air compressor

Air compressor of proton exchange membrane fuel cell (PEMFC) system is usually nonlinear and strong coupled. It is difficult to establish a online optimization oriented model. In order to solve this problem, this paper proposed a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model for air compressor of PEMFC system. The NARMAX model is an equivalent time-varying linear model, and the time-varying parameters are identified by recurrent neural network (RNN). Simulation results show that the proposed method has small fitting error, the error of air flow and pressure ratio approximate zero, while the mean square error (MSE) of air flow and pressure ratio are 1.5171e-07 and 6.3767e-05, respectively. Therefore, the established air compressor model is accurate and effective.     

Feedback-Linearization-Based Nonlinear Control for PEM Fuel Cells

This paper presents a dynamic nonlinear model for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on the proposed model to prolong the stack life of the PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. A dynamic PEM fuel cell model is proposed as a nonlinear, multiple-input multiple-output system so that feedback linearization can be directly utilized. During the control design, hydrogen and oxygen inlet flow rates are defined as the control variables, and the pressures of hydrogen and oxygen are appropriately defined as the control objectives. The details of the design of the control scheme are provided in the paper. The proposed dynamic model was tested by comparing the simulation results with the experimental data previously published. The simulation results show that PEMFCs equipped with the proposed nonlinear controls have better transient performances than those with linear controls.     

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.     

Adaptive maximum power point tracking control of fuel cell power plants

A fuel cell's output power depends nonlinearly on the applied current or voltage, and there exists a unique maximum power point (MPP). This paper reports a first attempt to trace MPPs by an extremum seeking controller. The locus of MPPs varies nonlinearly with the unpredictable variations in the fuel cell's operation conditions. Thus, a maximum power point tracking (MPPT) controller is needed to continuously deliver the highest possible power to the load when variations in operation conditions occur. A two-loop cascade controller with an intermediate converter is designed to operate fuel cell power plants at their MPPs. The outer loop uses an adaptive extremum seeking algorithm to estimate the real-time MPP, and then gives the estimated value to the inner loop as the set-point, at which the inner loop forces the fuel cell to operate. The proposed MPPT control system provides a simple and robust control law that can keep the fuel cell working at MPPs in real time. Simulation shows that this control approach can yield satisfactory results in terms of robustness toward variations in fuel cell operation conditions.     

A control architecture to coordinate energy management with trajectory tracking control for fuel cell/battery hybrid unmanned aerial vehicles

Fuel cell/battery hybrid energy storage system (HESS) powered unmanned aerial vehicle (UAV) has the outstanding advantage of long endurance time. Trajectory tracking motion is a commonly used task execution mode of UAVs, especially in autonomous UAVs. This study aims at developing a control architecture to coordinate energy management with trajectory tracking control for fuel cell/battery hybrid UAVs. Its position tracking control adopts model predictive control (MPC) and an extended state observer to eliminate the modeling errors and effect of interference. The attitude tracking control adopts an auto-disturbance rejection controller having a quick response. The obtained control parameters are given as an input to the energy management block. Energy management strategies (EMSs) based on online dynamic programming and hierarchical MPC have been proposed. The results obtained from a simulation show that the proposed trajectory tracking control architecture can track the target trajectory stably with a small tracking error. The tracking performance is stable under interference. Experimental results show that dynamic programming is solved online with good control performance. Compared to ordinary EMSs, dynamic programming and hierarchical MPC can increase endurance time by 2.69% and 1.27%, respectively. The proposed control architecture verifies the coordination of energy management and trajectory tracking control, and prospected the advantages of the combination of fuel cell and autonomous driving for long endurance UAVs in the future.     

燃油温度的多变量模糊预测函数控制

燃油供给温度的精确控制是一个具有非线性特性的流体加热供给多变量控制问题,实际测试表明,现有的单回路PID控制很难实现对燃油供给温度的动态跟踪控制,影响燃油的充分喷射、雾化及其与空气的混合,使部分燃油得不到充分燃烧,造成了能源浪费和环境污染.基于粒子群优化模糊预测函数控制(PSO-F-MPFC)的油料燃烧供给温度多变量解耦控制方法,通过与PID控制方法的比较,以及在阳极焙烧炉重油燃烧供给温度的动态跟踪控制应用表明,该方法优于原有燃油燃烧系统的PID控制,实现了燃油供给温度的动态跟踪精确控制.     

The dynamics analysis and controller design for the PEM fuel cell under gas flowrate constraints

This paper is on the dynamics analysis and controller design for the PEM fuel cell under the flowrate constraints of the supplied hydrogen and oxygen. By linearization around the equilibrium trajectories defined by the quantities of hydrogen and oxygen input flowrate, the nonlinear dynamics of the PEM fuel cell can be expressed as a linear parameter varying system with the output current and temperature as the system parameters. The state-feedback controller design is performed based on the linear time-invariant model obtained from the derived linear parameter varying system evaluated at the half load operation condition. The control objective is to achieve a maximized relative stability or equivalently the maximum decay rate under the specified magnitude constraints on the input flowrate of hydrogen and oxygen. The convex linear matrix inequality algorithm is utilized for numerical construction of the state-feedback control law. Under the fixed load resistance corresponding to the half load condition, the time response simulations are conducted for both the cases of initial condition regulation and external command tracking. For the simulation of regulation, the initial deviation of state variables diminishes quickly that agrees with the obtained large delay rate during controller design. In the case of command tracking for the same amount of state variables, the controlled system can follow the issued command in the right direction but leave large tracking error, which is due to the weak controllability of the gas flowrates on the activation overvoltage for the PEM fuel cell system dynamics.     

On-line implementation of model free controller for oxygen stoichiometry and pressure difference control of polymer electrolyte fuel cell

This paper proposes and validates a model free controller to improve the real time operating conditions of Proton Exchange Membrane Fuel Cells (PEMFC). This approach is based on an ultra-local model that does not depend on a precise knowledge of the system. It is perfectly adapted to a complex system such as the fuel cell, while benefiting from the ease of online implementation and low computational cost. The designed controller is used to regulate both the oxygen stoichiometry and the membrane inlet pressure, which are crucial operating conditions for the fuel cell's lifetime. The objectives of the proposed control strategy are twofold: preventing the starvation failure, and limiting the potential for mechanical degradation of the membrane during a large pressure difference. The performance of the proposed control strategy is initially evaluated by a simulation environment for both oxygen stoichiometry and inlet pressure difference control of fuel cell stack. An online validation on 1.2 KW fuel cell stack is conducted to control the membrane pressure drop. Two case studies are comprehensively investigated in relation to stoichiometry control: set point tracking and rejection of unmeasured disturbances caused by current variations. Simulations and experimental results reveal that the proposed controller provides significantly better performance in terms of fast trajectory tracking, and ensures less overshoot compared to the Fuzzy PID and PID controller. This efficiency is proven using the Integral Absolute Error (IAE), Integral Squared Error (ISE) and Integral of the Square input (ISU) performance indexes.     

High-potential control for durability improvement of the vehicle fuel cell system based on oxygen partial pressure regulation under low-load conditions

In the state-of-the-art high-power self-humidifying proton exchange membrane fuel cell (PEMFC) systems for vehicles, the high potential and low water production at idle or low load conditions strongly cause corrosion and decay of key materials and thus reduce durability. Therefore, the control technology of system-level durability requires an innovative design. Cathode recirculation is beneficial in alleviating the above unfavorable factors from the perspective of regulating oxygen and vapor partial pressure. This paper presents a pioneering study on the dynamics and control of cathode recirculation in vehicle high-power self-humidifying PEMFC system under low load conditions. First, a control-oriented dynamic model of the vehicle PEMFC system with a cathode recirculation loop is developed and the steady-state and dynamic performance is verified with experimental data from a 120 kW system. Active control of the intake component is achieved by re-feeding the reacted cathode gas to the air compressor outlet through a recirculation pump. On this basis, a high-potential controller based on oxygen partial pressure regulation is designed in combination with the dynamics of cathode recirculation. Results show that the designed dynamic fuzzy logic segmented proportional integral derivative controller with feedforward compensation achieves the optimal high-potential control effect by managing the oxygen partial pressure under variable low load conditions. It not only has excellent anti-disturbance ability but also effectively reduces the dynamic response time, transient overshoot, and steady-state error to satisfy the rapid and stable voltage output. Finally, the concomitant effect of humidification brought by the implementation of the optimal high-potential controller is analyzed, and the results show that the proton membrane is completely humidified.     

Study of nonlinear control schemes for an automotive traction PEM fuel cell system

To be practical in automotive traction applications, fuel cell systems must provide power output levels of performance that rival that of typical internal combustion engines. In so doing, transient behavior is one of the keys for success of fuel cell systems in vehicles. The focus of this paper is on the air/fuel supply subsystem in tracking an optimum variable pressurization and air flow for maximum system efficiency during load transients. The control-oriented model developed for this study considers electrochemistry, thermodynamics, and fluid flow principles for a 13-state, nonlinear model of a pressurized fuel cell system. For control purposes, a model reduction is performed, and several multi-variable control designs are examined. The first technique uses an observer-based linear optimum control which combines a feed-forward approach based on the steady-state plant inverse response, coupled to a multi-variable LQR feedback control. An extension of that approach, for control in the full nonlinear range of operation, leads to the second technique, nonlinear gain-scheduled control. Some enhancements were applied to overcome the fast variations in the scheduling variable. Finally, a rule-based, output feedback control, implemented with fuzzy logic, is coupled with a nonlinear feed-forward approach, and is examined under the same conditions applied to the first two techniques. The control designs developed are compared in simulation studies to investigate robustness to disturbance, time delay, and actuator limitations.     

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.     

Output-feedback voltage tracking control for input-constrained PEM fuel cell systems

An output-feedback voltage control system for nonlinear PEM fuel cells is presented. For voltage tracking around equilibrium operating points, the controller design minimizes the energy ratio between tracking error and normalized command while hydrogen and oxygen flowrates satisfy specified magnitude constraints and closed-loop poles meet desired placement constraints. Time response simulations based on Ballard 5 kW PEM fuel cell system parameters verify the design. Simulated controllers constructed numerically via the linear matrix inequality algorithm elaborate relationships between designed input flowrate and voltage tracking error. With controller design based on the same nominal input flowrate constraints, the achieved voltage tracking capability is comparable to our published state-feedback design study. To reduce voltage tracking error under fixed external resistance, gas flowrate magnitude constraints must be relaxed, requiring more fuel energy to manipulate the system variables for operation away from equilibrium conditions. Whereas state-feedback designs depend on internal state variables which are not always measurable, output-feedback control using only voltage tracking error as measurement simplifies practical implementation.     

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.