The iterative linear matrix inequality suboptimal design of decentralized ∞ control

1999 ◽  
Vol 6 (2) ◽  
pp. 130-133
Author(s):  
Yongfang Xie ◽  
Weihua Gui ◽  
Xiaoying Liu ◽  
Min Wu
Keyword(s):  
Linear Matrix Inequality ◽  
Decentralized Control ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Suboptimal Design ◽  
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 Decentralized Control Strategies of Adjacent Building Structures Vibration under Earthquake Excitation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xiaofang Kang ◽  
Peipei Zhang ◽  
Yiwei Zhang ◽  
Dawei Man ◽  
Qinghu Xu ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
Decentralized Control ◽  
Control Algorithm ◽  
Control Method ◽  
Computational Cost ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Adjacent Buildings ◽  
Control Scheme

A decentralized control scheme can effectively solve the control problem of civil engineering structure vibration under earthquake. This paper takes a research into the decentralized control scheme of adjacent buildings when the earthquake happens. It combines overlapping decentralized control method and linear matrix inequality (LMI) with H ∞ control algorithm and puts forward the overlapping decentralized H ∞ control method. A simplified dynamical model of structural vibration control has been established considering the topology structural features of adjacent buildings. The H ∞ control algorithm is applied into each dynamically different subsystems and can be also served as the decentralized H ∞ controllers. Therefore, by contracting decentralized H ∞ controllers to original state space, overlapping decentralized H ∞ controllers are obtained. In this manner, the adjacent buildings’ structure model is analyzed in terms of simulation and calculation which provides a comprehensive insight into vibration control. The results show that the centralized control, the decentralized control, and the overlapping decentralized control, based on linear matrix inequality, can be nearly effective in cases above satisfactorily. Besides, it can also reduce the computational cost as well as increase the flexibility of controller design.

Iterative linear matrix inequality algorithms for fault detection with unknown inputs

2005 ◽  
Vol 219 (2) ◽  
pp. 161-172 ◽  
Author(s):  
H Wang ◽  
J Lam ◽  
S X Ding ◽  
M Zhong
Keyword(s):  
Fault Detection ◽  
Linear Matrix Inequality ◽  
Linear Time ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Unknown Inputs ◽  
Linear Time Invariant ◽  
Unknown Disturbances ◽  
Linear Time Invariant Systems ◽  
Iterative Linear Matrix Inequality

This paper deals with the fault detection problem for linear time-invariant systems with unknown disturbances. Two separate performance indices are presented to facilitate the design of desirable fault detection observers. Iterative linear matrix inequality (LMI) algorithms are proposed in order to design a fault detection observer that aims at enhancing the fault detection and attenuating the effects due to unknown inputs. Numerical examples are employed to demonstrate the effectiveness of the proposed methods.

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