A new numerical algorithm for sub‐optimal control of earthquake excited linear structures

Abstract

SUMMARYExact optimal classical closed-open-loop control is not achievable for the buildings under seismic excitations since it requires the whole knowledge of earthquake in the control interval. In this study, a new numerical algorithm for the sub-optimal solution of the optimal closed-open-loop control is proposed based on the prediction of near-future earthquake excitation using the Taylor series method and the Kalman ÿltering technique. It is shown numerically that how the solution is related to the predicted earthquake acceleration values. Simulation results show that the proposed numerical algorithm are better than the closed-loop control and the instantaneous optimal control and proposed numerical solution will approach the exact optimal solution if the more distant future values of the earthquake excitation can be predicted more precisely. E ectiveness of the Kalman ÿltering technique is also conÿrmed by comparing the predicted and the observed time history of NS component of the 1940 El Centro earthquake.

Active Structural Control Based on the Prediction and Degree of Stability

“…where KGL [(SH\G)2SH\G] denotes the maximum eigenvalue of the matrix [(SH\G)2SH\G]) decreases sharply with the increasing i, including the near-future excitation in#uence in the solution gives a good approximation to optimal solution [18].…”

“…However, their near-future values can be predicted by using their known values in the past. Details of the prediction process are given in reference [18]. If the sound norm of the matrix SH\G ( j!i(0),…”

Robust H ∞ control for aseismic structures with uncertainties in model parameters

“…masts and long bridges, to reduce damage caused by earthquakes, wind or other environmental forces. Bakioglu and Aldemir (2001) proposed a numerical algorithm for the sub-optimal solution of optimal closedopen loop control based on the prediction of on-coming earthquake excitations, in which Taylor series and the Kalman fi ltering technique were both used; Akhiev et al (2002) proposed a multipoint instantaneous optimal control of structures; Wu and Yang (2000) applied the LQG control strategy to reduce the acceleration responses of a 310m TV tower subjected to strong winds with an active mass driver installed on the upper observation deck; and Song et al (2006) presented a precise integration strategy when using the LQG control strategy to avoid collision between adjacent tall buildings during earthquakes.…”

A Simple Active Control Algorithm for Earthquake Excited Structures

“…Owing to recent developments of digital control and measurement techniques, semiactive and active control techniques in the structural technology have received much attention (Bakioglu and Aldemir, 2001; Aldemir and Bakioglu, 2001; Aldemir, 2003, 2009; Saleh and Adeli, 1998b; Adeli and Saleh, 1998; Aldemir and Gavin, 2006; Alhan et al, 2006; Gavin and Aldemir, 2005). Active control methods are effective for a wide frequency range as well as for transient vibrations.…”

“…Therefore, it is almost impossible to find the optimal control exactly for the structures under earthquake forces. The researchers proposed various control algorithms to overcome this deficiency of the classical control algorithms (Yang et al, 1987; Xu et al, 2005; Zang et al, 2004; Bakioglu and Aldemir, 2001; Akhiev et al, 2002). An innovative and ground‐breaking work in this area is the work of Adeli and Kim (2004, 2009; Kim and Adeli, 2004) who developed a novel wavelet‐hybrid feedback–Linear Mean Square (LMS) algorithm for robust control of large civil structures.…”