Computationally efficient controller design for smart base-isolation systems: A reduced-order modal LQG approach

Abstract

Smart base isolation (SBI) is an advanced seismic protection technology for structures. LQG method is a mainstream choice for use in such systems. However, its engineering application is hindered by two critical bottlenecks: the excessively high controller order and the difficulty in determining optimal weighting matrices. For instance, an 8-story 3D base-isolated building alone requires handling 54 × 54 system matrices, and balancing multiple control objectives to obtain optimal control gains remains a formidable challenge. To address these issues, this study adopts a Hankel singular values (HSV)-based index formulated in modal coordinates. The index has an approximate closed-form expression, which takes the solutions of Riccati equations (and the derived controller/estimator gains) as variables and bears explicit physical significance in terms of modal reduction and pole shifting ratios. Leveraging these advantages, the index enables flexible manipulation of both control performance and controller order reduction. The method was applied to the aforementioned benchmark building equipped with MR dampers. The implementation procedure involves three core steps: first, determining optimal weighting matrices via pole allocation; second, calculating the HSV-based order index and deriving the reduced-order controller; third, assigning target damping forces to MR dampers based on real-time structural seismic responses. Further analysis is conducted on seismic performance under different estimator weighting combinations. Results demonstrate that, the method is efficient in that, the LQG order can be reduced from 27 modes to 18 or even 12 modes without sacrificing control efficacy; and optimal weightings can be obtained with minimum trials; the reduced- order controller effectively suppresses large isolation displacements dominated by lower modes without disturbing higher modes, achieving superior seismic control performance compared with passive control and nodal control strategies. Additionally, a 3-5 ratio between estimators and controllers is identified as the optimal matching criterion for enhanced control effects.