Abstract
In this paper, an instantaneous optimal control performance index for active control of structures under seismic excitation is analytically proposed. Absolute velocity and absolute displacement terms are implemented to the conventional state vector terms and eventually to the resulting performance index expression. The seismic response reduction effectiveness of the proposed performance index is compared with the linear quadratic regulator control (LQR). For numerical verification of the performance index, an eight‐story shear building with a fully active tendon controller system under unidirectional earthquake is considered as the first example. For a more complex model, a three‐dimensional tier building under the effect of bidirectional earthquakes is selected as second numerical example. Unidirectional near fault and bidirectional near fault earthquakes are used in the simulations. The control energy demand of each control method is also considered in the comparison. It is obtained from numerical simulations that the proposed performance index is as effective as LQR in attenuating structural vibrations. However, the resulting performance index does not require a priori knowledge of the seismic excitation like the LQR. The nonlinear Riccati matrix equation solution of the LQR is not required in the proposed performance index as well.
Highlights
Active control has been an interesting topic of research for seismic mitigation of structures since smart control devices into structures were first implemented by Yao [1]
For N-S direction, the uncontrolled absolute acceleration reduction percentages range from 14% to 34% in INS-ABS. e control energy consumption in INS-ABS case is found to be extremely smaller than Linear Quadratic Regulator (LQR) for Northridge earthquake
Numerically tested in this paper. e major distinction of this performance index from LQR is, as the nonlinear matrix Riccati equation of LQR is obtained by ignoring the earthquake excitation term, LQR is approximately optimal and does not satisfy the optimality condition
Summary
Active control has been an interesting topic of research for seismic mitigation of structures since smart control devices into structures were first implemented by Yao [1]. It was stated by Yang et al [13] that LQR controllers are known to be ineffective for systems suffering from variation of parameters and excitations which are broadband It has been mentioned by Aldemir and Bakioglu [14] that only classical closed-loop control is applicable to structural control problems, and the Riccati equation is derived by not considering the seismic excitation term. It has been shown by Etedali and Tavakoli [15] that LQR did not show good performance in mitigating the seismic responses of an 11-story structure incorporating active tuned mass damper (ATMD) under strong seismic excitations.
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