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Modeling and distributed adaptive fault‐tolerant vibration control for bridge beam with single‐parameter adaptive neural network

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.