Abstract
Time-delays of control force calculation, data acquisition, and actuator response will degrade the performance of Active Mass Damper (AMD) control systems. To reduce the influence, model reduction method is used to deal with the original controlled structure. However, during the procedure, the related hierarchy information of small eigenvalues will be directly discorded. As a result, the reduced-order model ignores the information of high-order mode, which will reduce the design accuracy of an AMD control system. In this paper, a new reduced-order controller based on the improved Balanced Truncation (BT) method is designed to reduce the calculation time and to retain the abandoned high-order modal information. It includes high-order natural frequency, damping ratio, and vibration modal information of the original structure. Then, a control gain design method based on Guaranteed Cost Control (GCC) algorithm is presented to eliminate the adverse effects of data acquisition and actuator response time-delays in the design process of the reduced-order controller. To verify its effectiveness, the proposed methodology is applied to a numerical example of a ten-storey frame and an experiment of a single-span four-storey steel frame. Both numerical and experimental results demonstrate that the reduced-order controller with GCC algorithm has an excellent control effect; meanwhile it can compensate time-delays effectively.
Highlights
Active Mass Damper (AMD) can be used to control the dynamic response of highly flexible building horizontally under strong wind or earthquake [1,2,3,4]
Regarding high-rise building structures, the excessive number of degrees of freedom causes the fact that the order of the designed controller based on the original model will be extremely large, and the long control force calculation time induces the fact that the control force is too difficult to fulfill the requirement of real-time control
A dynamic condensation method was proposed for high-rise buildings with Active Tuned Mass Damper (ATMD) control system; the analysis results showed the proposed method was efficient for the reduced-order modeling and reduced calculation time and workload [9]
Summary
Active Mass Damper (AMD) can be used to control the dynamic response of highly flexible building horizontally under strong wind or earthquake [1,2,3,4]. In order to implement GCC for a high-rise building, a key step is to solve a positive-definite solution of Riccati matrix equations This problem is based on the Riccati equation method, and several key parameters should be determined in advance. The time-delay compensation controller with GCC algorithm can be designed for high-rise buildings based on LMI approach. The design problem of a time-delay compensation control gain based on GGC algorithm can be expressed as a group of nonlinear matrix inequalities It can be further transformed into a group of linear matrix inequalities (LMIs) through variable substitution method [31]. A numerical example of ten-storey frame and an experiment of a single span four-storey steel frame will be presented to validate the effectiveness of the proposed method
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