An iterative linear matrix inequality controller-design strategy for H ∞ structural vibration control

2019 ◽  
pp. 49-54
Author(s):  
F. Palacios-Quiñonero ◽  
J. Rubió-Massegú ◽  
J.M. Rossell ◽  
H.R. Karimi
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
Controller Design ◽  
Design Strategy ◽  
Structural Vibration ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Structural Vibration Control ◽  
Iterative Linear Matrix Inequality

scholarly journals A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

2020 ◽  
Vol 10 (17) ◽  
pp. 5859
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
State Feedback ◽  
Optimization Problems ◽  
Seismic Protection ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Static State ◽  
Fluid Viscous Dampers ◽  
Iterative Linear Matrix Inequality

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.

scholarly journals TLCD Parametric Optimization for the Vibration Control of Building Structures Based on Linear Matrix Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Linsheng Huo ◽  
Chunxu Qu ◽  
Hongnan Li
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Structural Vibration ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lumped Mass ◽  
Mass Model ◽  
Liquid Dampers

Passive liquid dampers have been used to effectively reduce the dynamic response of civil infrastructures subjected to earthquakes or strong winds. The design of liquid dampers for structural vibration control involves the determination of the optimal parameters. This paper presents an optimal design methodology for tuned liquid column dampers (TLCDs) based on theH∞control theory. A practical structure, Dalian Xinghai Financial Business Building, is used to illustrate the feasibility of the optimal procedure. The model of structure is built by the finite element method and simplified to the lumped mass model. To facilitate the design of TLCDs, the TLCD parametric optimization problem is transferred to the feedback controller design problem. Through the bounded real lemma, an optimization problem with bilinear matrix inequality (BMI) constraints is constructed to design a static output feedbackH∞controller. Iterative linear matrix inequality method is employed and it added some value range constraints to solve the BMI problem. After the TLCD parameters are optimized, the responses of displacement and acceleration in frequency domain and time domain are compared for the structure with and without TLCD. It is validated that the TLCD with the optimized parameters can make the structure satisfy the need for safety and comfort.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

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