TITLE:
H ∞ Control of Structural Vibration with Input Time Delay Based on CHsCTA Method
AUTHORS:
Yongfang Chen, Yuanguang Zheng
KEYWORDS:
Control, Building Structure, Input Time Delay, Chebyshev Collocation Points
JOURNAL NAME:
World Journal of Engineering and Technology,
Vol.14 No.4,
October
19,
2026
ABSTRACT: This study addresses the active control problem of structural vibration with input time delay. Taking the structural system equipped with an active mass damper (AMD) as the research object, an
H
∞
control scheme based on the Chebyshev spectral continuous-time approximation (CHsCTA) is proposed. Specifically, the CHsCTA method is first employed to approximate the closed-loop system with input time delay by a finite-dimensional delay-free augmented system, upon which the
H
∞
controller design is then carried out. To address the bilinear matrix inequality (BMI) constraints arising from the controller design process, the cone complementarity linearization (CCL) method is introduced to construct an iterative solving algorithm, thereby obtaining a controller that satisfies the prescribed
H
∞
performance index. Numerical simulation results demonstrate that the designed controller can effectively suppress structural vibration under the given input time delay. Under harmonic excitation, the peak vibration reduction rate of the primary structure is significantly improved. Under Gaussian white noise excitation, the average absolute value of the structural response is also markedly reduced, thereby verifying the effectiveness of the proposed control strategy.