Closed‐form solution for seismic response of adjacent buildings with linear quadratic Gaussian controllers

Closed‐form solution for seismic response of adjacent buildings connected by hydraulic actuators with linear quadratic Gaussian (LQG) controllers is presented in this paper. The equations of motion of actively controlled adjacent buildings against earthquake are first established. The complex modal superposition method is then used to determine dynamic characteristics, including modal damping ratio, of actively controlled adjacent buildings. The closed‐form solution for seismic response of the system is finally derived in terms of the complex dynamic characteristics, the pseudo‐excitation method and the residue theorem. By using the closed‐form solution, extensive parametric studies can be carried out for the system of many degrees of freedom. The beneficial parameters of LQG controllers for achieving the maximum response reduction of both buildings using reasonable control forces can be identified. The effectiveness of LQG controllers for this particular application is evaluated in this study. The results show that for the adjacent buildings of different dynamic properties, if the parameters of LQG controllers are selected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[2]  Jann N. Yang,et al.  New Optimal Control Algorithms for Structural Control , 1987 .

[3]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[4]  Billie F. Spencer,et al.  Feedback-feedforward control of structures under seismic excitation☆ , 1990 .

[5]  B. F. Spencer,et al.  Active Structural Control: Theory and Practice , 1992 .

[6]  Zexiang Li,et al.  Closure of "Control of Hysteretic System Using Velocity and Acceleration Feedbacks" , 1992 .

[7]  Billie F. Spencer,et al.  Frequency domain optimal control strategies for aseismic protection , 1994 .

[8]  E. Vanmarcke,et al.  Seismic Random‐Vibration Analysis of Multisupport‐Structural Systems , 1994 .

[9]  Jiahao Lin,et al.  Structural responses to arbitrarily coherent stationary random excitations , 1994 .

[10]  Shirley J. Dyke,et al.  Role of Control-Structure Interaction in Protective System Design , 1995 .

[11]  Guanrong Chen,et al.  Linear Stochastic Control Systems , 1995 .

[12]  T. T. Soong,et al.  Acceleration Feedback Control of MDOF Structures , 1996 .

[13]  T. T. Soong,et al.  STRUCTURAL CONTROL: PAST, PRESENT, AND FUTURE , 1997 .

[14]  Billie F. Spencer,et al.  Controlling buildings: a new frontier in feedback , 1997 .

[15]  J. Enrique Luco,et al.  Optimal damping between two adjacent elastic structures , 1998 .

[16]  Yl L. Xu,et al.  Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers , 1999 .

[17]  Yl L. Xu,et al.  Dynamic response of damper-connected adjacent buildings under earthquake excitation , 1999 .