高速磁浮列车的悬浮控制稳定性是列车安全运行的关键问题，高速运行时的强气动载荷、轨道不平顺等外部扰动，以及控制系统的时滞等内部非线性因素都会对控制系统稳定性产生重要影响。传统的离线反馈控制方法通过感知悬浮系统响应后被动做出控制干预，在强气动冲击、时滞等条件下，其控制的反应速度和抗干扰能力无法应对悬浮系统的瞬时大扰动。强气动载荷作用下的悬浮控制的稳定性成为了制约列车安全的关键因素。本研究针对常导高速磁浮列车在高速运行过程中遇到的上述悬浮控制关键问题进行深入研究，综合运用理论分析、数值模型、半实物测试等手段，利用变结构滑模控制方法和模型预测控制方法，将人工智能神经网络技术融入控制策略，解决强气动载荷作用下常导高速磁浮车辆悬浮控制难题。

具体工作内容如下：

1 为适应气动载荷引起的不确定性，解决滑模控制器在应用时因时滞等因素引起的抖振问题，发展了考虑载荷干扰的变结构滑模控制器。进行了控制时滞和控制参数的敏感性分析，获得了控制时滞及控制参数的稳定域。基于分析结果，发展了可以有效抑制抖振的自适应拟滑模控制算法，算法会根据输入输出信息进行决策，以实时反馈调节控制参数。仿真和实验结果表明所设计的自适应变结构滑模控制器可以有效抑制扰动下电磁铁的振动。该算法应用于磁浮控制系统，其变结构特性可以使控制器跟随扰动而变化，这种自适应反馈优化特征提高了磁浮车辆的抗干扰能力。

2 为解决强气动载荷引起的悬浮间隙大幅波动及瞬态扰动问题，考虑高速气动载荷外部扰动、控制量饱和与电磁铁悬浮间隙物理有界的约束，开发了基于气动载荷观测器的扩展模型预测控制算法（AREMPC）。该算法通过结合高增益观测器和神经网络，构建了扰动观测器，实现了电磁铁悬浮间隙、悬浮间隙波动速度和气动载荷及其变化率的在线观测；将观测得到的速度、气动载荷和气动载荷变化率作为额外的状态输入，结合扰动状态扩展的动力学模型，构建了模型预测控制器，实现了磁浮系统状态预测。通过实时迭代优化，滚动计算当前时刻的最优控制序列，实现对额定悬浮间隙的准确跟踪。通过以上流程，建立了基于气动载荷观测器的扩展模型预测控制算法，该算法具有预测、优化和前馈控制特征，以快速和准确地抑制外部载荷导致的振动，提高了磁浮车辆高速运行时的稳定性。

3 虽然将气动载荷神经网络观测器引入控制方法，可以提升车辆状态的预测能力，抑制补偿气动载荷导致的振动。但是传统神经网络的训练需要大量实测数据支撑。为解决实际应用时缺乏训练样本的问题（难以进行高速实车测试，且实测样本噪音较大），设计了在线自学习径向基函数神经网络（ARBF）。在控制结束后，网络可以根据输入输出信息自适应调整网络结构。且面对复杂环境（例如高速会车场景），Lyapunov稳定性下的自适应律保证了在线学习的保守性。该网络具有在线自学习特征，脱离了对样本数据的需求。同时，Lyapunov稳定性理论保证了气动载荷神经网络观测器及模型预测控制器的安全性，设计的网络更适应磁浮列车的应用需求。

4 搭建了中低速单电磁铁悬浮实验台和高速磁浮磁轨耦合实验平台。高速磁浮磁轨耦合实验平台采用dSPACE构建控制系统，通过对轨道和等效车身的激励，实现轨道不平顺和气动载荷的加载。基于实验台，完成了自适应变结构滑模控制算法和基于气动载荷观测器的扩展模型预测控制算法（AREMPC）的实验验证。通过开展气动载荷加载、不平顺加载等实验，验证了本文所提控制方法的有效性和可靠性。

本文发展的优化方法提高了高速磁浮车辆的悬浮性能，研究成果不仅促进了磁浮车辆动力学与控制的理论发展，更为高速磁浮工程技术应用提供了实践参考。

The stability of suspension control in high-speed maglev trains is a critical issue for the safe operation of the train. Strong aerodynamic loads during high-speed operations, track irregularities, and other external disturbances, as well as internal nonlinear factors such as delays in the control system, significantly impact the stability of the control system. Traditional offline feedback control methods, which react passively by sensing responses from the suspension system, are unable to prevent transient large disturbances under conditions of strong aerodynamic impacts and system delays. The stability of suspension control under strong aerodynamic loads has become a key factor limiting train safety. This research delves into the critical issues of suspension control encountered by conventional high-speed maglev trains during high-speed operations. Through a comprehensive application of theoretical analysis, numerical modeling, and hardware-in-the-loop testing, this study employs variable structure sliding mode control and model predictive control methods, integrating artificial intelligence neural network techniques into the control strategy to address the challenges of suspension control in high-speed maglev vehicles under strong aerodynamic loads.

The specific tasks are outlined as follows:

1 To address the uncertainties caused by aerodynamic loads and the chattering issues in sliding mode controllers due to delays and other factors, a variable structure sliding mode controller considering load disturbances has been developed. Analyses of control delays and the sensitivity of control parameters were conducted to identify the stability domains for control delays and parameters. Based on these analyses, an adaptive pseudo-sliding mode control algorithm capable of effectively suppressing chattering was developed. This algorithm makes decisions based on input-output information to adjust control parameters in real-time. Both simulation and experimental results indicate that the designed adaptive variable structure sliding mode controller can effectively suppress vibrations of electromagnets under disturbances. When applied to maglev control systems, its variable structure characteristics allow the controller to adapt to disturbances, enhancing the disturbance resistance of maglev vehicles through adaptive feedback optimization.

2 To address the significant fluctuations in suspension gap and transient disturbances caused by strong aerodynamic loads, an extended model predictive control algorithm based on aerodynamic load observation correction (AREMPC) was developed. This algorithm integrates high-gain observers and neural networks to construct a disturbance observer that achieves online observation of the electromagnet suspension gap, the velocity of suspension gap fluctuations, and the aerodynamic load along with its rate of change. The observed velocities, aerodynamic loads, and their rates of change are incorporated as additional state inputs into a dynamics model expanded based on the disturbance state, thereby constructing a model predictive controller that facilitates state prediction of the maglev system. Through real-time iterative optimization, a rolling computation determines the optimal control sequence at the current moment, achieving accurate tracking of the designated suspension gap. This process establishes the AREMPC, which features predictive, optimizing, and feedforward control characteristics to swiftly and accurately mitigate vibrations caused by external loads, thereby enhancing the stability of maglev vehicles during high-speed operations.

3 Although the integration of a neural network observer for aerodynamic loads into control methodologies enhances the vehicle state prediction capabilities and mitigates vibrations caused by aerodynamic loads, traditional neural network training requires extensive empirical data support. To address the issue of a lack of training samples in practical applications (difficulty in conducting high-speed real vehicle tests and significant noise in empirical samples), an online self-learning radial basis function neural network (ARBF) has been designed. At the end of control operations, the network can adaptively adjust its structure based on input-output information. Furthermore, in complex environments (such as high-speed passing scenarios), the adaptive law under Lyapunov stability ensures the conservativeness of online learning. This network features online self-learning capabilities, liberating it from the dependence on sample data. Concurrently, Lyapunov stability theory ensures the safety of the aerodynamic load neural network observer and its corrected model predictive controller, making the designed network more suitable for the application requirements of maglev trains.

4 Experimental platforms for both medium-low speed single electromagnet suspension and high-speed maglev rail coupling have been established. The high-speed maglev rail coupling experimental platform utilizes a dSPACE-based control system to simulate track irregularities and aerodynamic loads by stimulating the track and an equivalent vehicle body. Based on the electromagnet suspension platform, experimental validation of the adaptive variable structure sliding mode control algorithm was completed. Similarly, experimental validation of the extended model predictive control algorithm based on aerodynamic load observation correction (AREMPC) was conducted using the high-speed maglev rail coupling experimental platform. Through experiments involving aerodynamic load application and uneven track loading, the effectiveness and reliability of the control methods proposed in this study were verified.

The optimization method developed in this paper improves the levitation performance of high-speed maglev vehicles, and the research results not only promote the theoretical development of the dynamics and control, but also provide a practical reference for the application of high-speed magnetic levitation engineering technology.