Under strongly non-stationary excitations such as earthquakes, high-rise buildings are susceptible to amplified floor accelerations and cumulative displacements. In practical applications, the performance of Active Tuned Mass Dampers may deteriorate due to measurement noise, model uncertainties, and unknown disturbances. To address these challenges, this study proposes a Kalman-filter-based disturbance estimation model predictive control strategy. First, a coupled structural–ATMD dynamic model is formulated and discretised to obtain a discrete-time state-space representation suitable for receding-horizon optimisation. Second, a Kalman filter is employed under noisy measurement conditions to perform online recursive state estimation; simultaneously, it is used for online state reconstruction and lumped disturbance estimation. In the estimator, seismic ground acceleration is retained as an explicit exogenous input, while slowly varying model mismatches and unmodelled effects are represented through an augmented disturbance state. Subsequently, within the MPC framework, a quadratic cost function is constructed to balance structural response mitigation against control effort, while explicitly incorporating engineering constraints such as actuator saturation, thereby casting the online control law synthesis as a quadratic programming problem. Finally, comparative simulations are conducted using the El Centro, Taft, Kobe, and an artificial ground motion as inputs, with quantitative evaluation performed via six benchmark performance indices and a weighted composite index. The results indicate that, under all four ground motions, the proposed KF-MPC achieves more stable vibration mitigation within the prescribed constraints, reducing the composite performance index by approximately 36%–56% relative to the uncontrolled case and outperforming conventional MPC and LQR overall. Moreover, in terms of peak and root-mean-square metrics of floor acceleration and relative displacement with respect to the ground, KF-MPC provides more pronounced suppression across the majority of floors, demonstrating its effectiveness in enhancing prediction accuracy and closed-loop robustness in the presence of noise and uncertainties.
Xiaojing et al. (Fri,) studied this question.