Modeling and vibration control of a bridge beam system are considered in this article. The beam bridge with both ends fixed can be regarded as an Euler‐Bernoulli beam, which is a typical distributed parameter system. First, the partial differential equations (PDE) model of the bridge was established according to the Hamilton principle. Then, a reasonable distributed control law was designed on the PDE model to eliminate the elastic deformation and suppress the vibration of the bridge. At the same time, uncertainties related to system status were considered during the design of the closed‐loop system. In addition, the possible actuator and sensor faults in the control system were analyzed. Single‐parameter adaptive neural networks were used to estimate the effects of coupling terms for uncertainties and faults. The parameter estimation adaptive law was designed to replace the adjustment of neural network weights, which simplifies the algorithm and facilitates practical engineering applications. Finally, the feasibility of the control system was verified by simulation.

中文翻译：

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单参数自适应神经网络的桥梁梁建模与分布式自适应容错振动控制

本文考虑了桥梁梁系统的建模和振动控制。两端固定的梁桥可以看作是典型的分布式参数系统欧拉-伯努利梁。首先，根据汉密尔顿原理建立了桥梁的偏微分方程（PDE）模型。然后，在PDE模型上设计了合理的分布控制律，以消除弹性变形并抑制桥梁的振动。同时，在闭环系统的设计中考虑了与系统状态有关的不确定性。此外，分析了控制系统中可能的执行器和传感器故障。单参数自适应神经网络用于估计不确定性和故障的耦合项的影响。设计参数估计自适应律来代替神经网络权重的调整，从而简化了算法并方便了实际工程应用。最后，通过仿真验证了控制系统的可行性。