Adaptive Model Reference Sliding Mode Control of Structural Nonlinear Vibration

In this paper, an active mass damper (AMD) with adaptive control design is used to mitigate the vibrations of a multi-degree-of-freedom (MDOF) nonlinear structure under earthquake excitation. In the adaptive control design, a modified unscented Kalman filter (UKF) is developed to identify the unknown states and parameters adaptively. Based on the identified states and parameters, model reference sliding model control (MRSMC) is proposed for structural nonlinear vibration control. In the design of MRSMC, the structure with tuned mass damper (TMD) is used as a reference model. In the control process, the parameters and states needed to obtain the control forces are updated adaptively through UKF. A numerical example of a three-story shear-type model with an active mass damper (AMD) mounted on the top story is used to study the proposed controller. The interstory shear restoring forces are simulated by the Bouc–Wen model. This model could simulate the hinge effect of the yielding joints in steel structures or the performance of the hysteretic energy dissipation devices. The simulation results demonstrated that, with the help of the modified UKF method and the reference model, the vibration of the structure is effectively mitigated under the proposed MRSMC.