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Mathematical Problems in Engineering
Volume 2014, Article ID 748237, 9 pages
http://dx.doi.org/10.1155/2014/748237
Research Article

Integrated Multiobjective Optimal Design for Active Control System Based on Genetic Algorithm

College of Civil Engineering, Southeast University, Nanjing 210096, China

Received 11 April 2014; Accepted 24 June 2014; Published 14 July 2014

Academic Editor: Haranath Kar

Copyright © 2014 Ma Yong-Quan and Qiu Hong-Xing. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The integrated multiobjective optimal design method for structural active control system is put forward based on improved Pareto multiobjective genetic algorithm, through which the position of actuator is synchronously optimized with active controller. External excitation is simulated by stationary filtered white noise. The root-mean-square (RMS) of structural response and active control force can be achieved by solving Lyapunov equation in the state space. The design of active controller adopts linear quadratic regulator (LQR) control algorithm. Minimum ratio of the maximum RMS of controlled structural displacement divided by the maximum RMS of uncontrolled structural displacement and minimum ratio of the maximum RMS of controlled structural shear divided by the maximum RMS of uncontrolled structural shear, together with minimization of the sum of RMS of active control force, are used as the three objective functions of multiobjective optimization. The optimization process takes the impact of structure and excitation parameter on the optimized results. An eight-storey six-span plane steel frame was used as an emulational example to demonstrate the validity of this optimization method. Results show that the proposed integrated multiobjective optimal design method is simple, efficient, and practical with good universality.