Robust H ∞ control for aseismic structures with uncertainties in model parameters

Abstract

This paper presents a robust H ∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LMI toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H ∞ strategy, a six-story building was subjected both to the 1940 El Centro earthquake record and to a suddenly applied Kanai-Tajimi fi ltered white noise random excitation. The results show that the proposed robust H ∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.

μ-Synthesis Controller Design for Seismic Alleviation of Structures with Parametric Uncertainties

“…However, LQG and LQR are only applicable to structures with known system parameters, limited bandwidth and they are sensitive to spillover [30]. Another optimal control theory used in the control of civil structures is H 2 and H ∞ [31][32][33][34][35][36][37][38][39]. The procedure consists of finding a causal controller which stabilizes the system and minimizes the quadratic performance index.…”

Active Vibration Control of Container Cranes against Earthquake by the Use of LMI Based MixedH2/H∞State-Feedback Controller

“…Because of the modeling errors, variation in material properties, and changing disturbance excitations, the description of structures inevitably contains uncertainties in different natures and levels. Since these uncertainties can affect both the stability and performance of control systems, many robust control methods are offered for the active control of structural systems [16,17]. This paper is a basic study on reducing structural vibration of cranes against seismic effects.…”

Fault Tolerant Vibration-Attenuation Controller Design for Uncertain Linear Structural Systems with Input Time-Delay and Saturation

“…Therefore, research on the active vibration control of linear structural systems has received increasing attention in the recent years. Many scholars have applied themselves to the research of active vibration control strategies and many control techniques have been utilized, such as, classical H ∞ theories [1,2], Finite frequency H ∞ control [3], sliding mode control [4,5], neural networks [6], optimal control [7], bang-bang control [8,9], Semiactive -passive control [10], Semi-decentralized Control [11], mixed H 2 /H ∞ output-feedback control [12], etc., have been developed with the goal of protecting structures subjected to external disturbance excitation. Accompanied with the development of structural control strategies, some active control devices were designed for applying those control algorithms, for example, active brace system (ABS) [13,14], active mass damper (AMD) [15], etc.…”