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Vibration control of hysteretic systems via neural network adaptive backstepping

In this paper, an intelligent control methodology is proposed to mitigate earthquake vibrations in a building. The structure object of study is a 10-story building whose base is isolated by means of a passive actuator and an MR damper. The system has uncertain parameters and nonmeasurable variables that must be accounted for in order to gain good control performance. Besides, the system is subject to unknown perturbations (incoming earthquakes). An adaptive backstepping controller is designed to generate the actuator control signal based on the base velocity and displacement measurements as well as on the dynamics of the base isolation system. Uncertainty in structure stiffness and damping coefficients are compensated by parameter adaptation. The MR damper can be modeled by the well known Bouc-Wen model. However, this model contains an unmeasurable variable, z, that describes the hysteretic behavior, so it must be estimated. A neural network approximator is proposed to estimate the unmeasurable variable. This way, the hysteresis effect is modeled by the neural network. The control performance is verified by simulations performed in MATLAB/Simulink using common earthquakes such as those of El Centro and Taft.