Robust optimal H-infinity control for irregular buildings with AMD via LMI approach

Sheliang Wang,Zhijun Li

doi:10.15388/na.2014.2.8

Abstract

In view of the numerous uncertainties of seismic disturbances and structural parameters, the irregular building structure is uncertain. In this paper, a new robust optimal H∞ controller for irregular buildings is designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties. Such a control method can provide a convenient design procedure for active controllers to facilitate practical implementations of control systems through the use of a quadratic performance index and an efficient solution procedure based on linear matrix inequality (LMI). To verify the effectiveness of the control method, a MDOF (multipledegree-of-freedom) eccentric building structure with two active mass damper (AMD) systems on the orthogonal direction of the top storey subjected to bi-directional ground motions is analyzed. In the simulation, the active control forces of the AMD systems are designed by the robust optimal H∞ control algorithm, and the structural system uncertainties are assumed in the system and input matrices. The simulation results obtained from the proposed control method are compared with those obtained from traditional H∞ control method, which shows preliminarily that the performance of robust optimal H∞ controllers is remarkable and robust. Therefore, the robust optimal H∞ control method is quite promising for practical implementations of active control systems on seismically excited irregular buildings.

Highlights

As tall building and long-span bridges become lighter and more flexible, they are more susceptible to the effects of vibration
In research studies and practical applications, various active control algorithms have been investigated in designing controllers, such as linear quadratic regulator (LQR) [4, 5], linear quadratic Gaussian (LQG) [6], sliding mode control (SMC) [7, 8], and H∞ control [4, 9]
Active mass damper (AMD) systems have been a popular area of research in recent decades and significant progress has been made in this area over these years [18,19,20,21]

Summary

Introduction

As tall building and long-span bridges become lighter and more flexible, they are more susceptible to the effects of vibration. H∞ control strategy is useful in designing the robust controller because these robustness criteria in a way can be interpreted as the H∞ norm of a transfer function to be smaller than a given value. The results from both numerical simulations and experimental tests indicate that H∞ control is effective [9]. In [14,15,16,17], the LMI-based solution approach had been used to design robust H∞ control for a given H∞-norm bound. The comparisons with the numerical results using the traditional H∞ control are made for demonstration of its control performance

Equations of motion of structural systems

H NΓT Π2

Numerical results

Conclusions