Optimal Sensor Placement in Structural Control Systems

Due to the accuracy requirements of system performance and suppressing the cost of monitoring associated with the physical constraints, many researchers has focused on the design of optimal sensor systems along with the requirement to perform a specific observation extensively. It is obvious that the optimal sensor allocation is a required tool in enhancing performance qualities from structural control problems. Measures of optimality often include the quality of controllability, the observability and information matrix. The problem of optimal sensor placement for decentralized discrete-time systems was investigated in the literature, and that work is based on optimizing the observation matrices with constraints. The observation matrices with constraints can be considered as a natural optimality measure, since the coefficients of these matrices are a valid evidence to measure state variables by the controller. Therefore, a smaller number of output variables can be achieved by optimally allocating a linear combination of these measurements. In this paper, we extend this idea to the decentralized unified regulator problem using output feedback. For application, structural systems having natural frequency can be considered, where sensors can be located in a finite number of positions. To verify the validity and effectiveness, numerical results are presented. Introduction In recent years, innovative means of enhancing structural functionality and safety against natural and man-made hazards have been researched for maintenance system[1]. In order to keep structural stability from excitation, a concept of active structural control system is introduced as a maintenance system of structure[2]. But, in terms of practicality and economy, the number of sensors and controller will be limited for real structure. Hence, owing to the accuracy requirements of control performance, the design of optimal sensor placement systems has been studied extensively[3]. The optimal sensor placement problem for decentralized continuous system was first considered by El-Sayed, and is based on optimazing the constrained observation matrices[4]. And, these concepts were extended to the decentralized discrete time control problem by Oloomi and Sawan[5]. In this paper, in order to design a stable control system, we applied the unified control system for optimal sensor placement using output feedback. Also, this proposed algorithm was applied to the four degree-of-freedom structural system. It is also proved to be useful to choose the best sensor location for controllability and observability of the structural system. Description of Control Algorithm Unified Control System for Decentralized System. Let us consider the following description of linear time-invariant system which cover discrete and continuous times cases simultaneously[6]: Key Engineering Materials Online: 2004-08-15 ISSN: 1662-9795, Vols. 270-273, pp 1454-1459 doi:10.4028/www.scientific. net/KEM.270-273.1454 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-13/03/20,17:38:07) Title of Publication (to be inserted by the publisher) 0 0 ( ) ( ) [ ( )], (0) ( ) ( ), 1, 2, . , k i i i i x A x S B u x x y C x i N ρ ρ ρ ρ τ τ τ τ τ = + = = = (1)