Numerical evaluation for optimal design of number and positions of controllers in 2D frames under earthquake and wind loadings using different active control algorithms

Abstract

Structures which are designed in accordance with previously used design codes are usually weak to sustain dynamic loading and therefore they shall be rehabilitated. One approach for rehabilitation is to use active control. In this study, active tendon is used as a structural device control. Various arrangements of controllers can be used to limit the response of the structure but it is desired to find an arrangement at which the cost of the placement will be minimized. The aim of this thesis is to find the best placement of active tendons on a frame such that the placement satisfies two general restrictions; namely structural response and control forces. Genetic algorithm is applied to the 2D frames in order to optimize the controllers. Four control Algorithms including Classic, Instantaneous, modal and pole assignment in optimal manner are considered for linear behavior and Classic algorithm is used for nonlinear behavior. Effect of time delay is considered in the linear control algorithms. Two dynamic loadings consisting of earthquake and wind loadings are applied to the frames. Earthquake loadings include from seven records which are scaled in accordance with INBC code (2800) and the wind loading is produced in accordance with ASCE7-05 and Davenport density spectrum. Two three-bay-eight-story frames are used to consider linear and nonlinear behavior. Results show that under defined restrictions, for a special frame, special dynamic loading, special control algorithm and both linear and nonlinear behavior without calculations and with acceptable precision, the optimal number and placement of controllers can be guessed. The results also show that non-shear frame could be analyzed as the shear frame with negligible error in the final results and the time of computation greatly reduced. Also if the permissible control force is less than saturation limit, instantaneous algorithm will have the best results and therefore nonlinear frames have more control cost than linear; however the structural cost should be considered for estimating the overall cost.