This paper presents a sample control design for the base‐isolated benchmark building with bilinear hysteretic bearings (e.g. lead–rubber bearings). Since there is no well‐defined control strategy for nonlinear structures, and available linear strategies are well‐known among the civil engineering community, a linear quadratic Gaussian (LQG) controller is selected for this purpose. To utilize an LQG controller, a linearized model of the nonlinear structure is required. A good linearized model, however, should be able to represent the nonlinear structure responses when both are controlled. It is shown that design problems of an equivalent linear model and an LQG controller are not, in fact, independent and require one for the other. In this study, the LQG controller is designed based on some parametric studies, and an iterative method is proposed for the development of an equivalent linear model. In the iterative method, the equivalent linear model is formed by replacing the nonlinear isolation elements that have bilinear stiffness and zero damping in the benchmark structure with a linear stiffness and a linear damping. Here, the linear stiffness is determined in the iterative method such that the RMS force of the bilinear isolation elements in the controlled (nonlinear) benchmark structure is equivalent to that of the corresponding isolation elements in the equivalent linear model. The overall approach is applied to the benchmark structure for seven historical earthquake ground acceleration data, and both an LQG controller and an equivalent linear model are obtained. The numerical simulations show that the equivalent linear model successfully replicates the nonlinear response, and the controller is able to improve the overall performance. As the final designs are not intended to be competitive, the method proposed can be improved in several ways to obtain better results. While the equivalent linear model developed herein may be used as a starting point in studying this benchmark problem, because of the strong interaction between controller and equivalent linear model, the participants of the base isolation benchmark problem are strongly encouraged to develop their own controller‐specific equivalent linear models. Copyright © 2005 John Wiley & Sons, Ltd.
This paper investigates the dissipativity and performance of semiactive systems with smart dampers via linear matrix inequality (LMI) synthesis. For this purpose, a dissipativity index is proposed to modify a standard linear quadratic regulator (LQR) using the techniques available in LMI‐based multiobjective convex programming for better semiactive performance. First, a review of available dissipativity indices is given, and two new dissipativity indices are defined based on the concept of energy dissipation rate. Second, an LQR problem is defined in terms of a linear objective function and several LMI constraints. Then, for each dissipativity index, a dissipativity inequality constraint is defined. It is observed that only one of the dissipativity constraints can be represented in terms of LMIs and implemented in the LQR problem. A modified LMI‐based LQR controller is obtained by attaching the dissipativity constraint in its weak form. The dissipativity indices and the proposed controller are employed for two numerical examples to investigate the dissipativity and performance of semiactive systems. The first example is a 2DOF building with an ideal damper attached in the first storey, and an LQR controller is selected such that it has high dissipativity levels. The second example is a 2DOF model of a highway bridge where a realistic magnetorheological (MR) fluid damper is attached at the bearing location resulting in an LQR controller with low dissipativity levels. Comprehensive parametric studies are carried out for both examples using the modified LQR with various dissipativity constraint values and the standard LQR. For the first example, it is found that the indices are very useful to identify the dissipative nature and semiactive performance relations. Also, the proposed method is able to improve the dissipative nature of the controller improving the semiactive performance. On the other hand, for the second example, although the proposed method is able to improve the dissipativity, the overall semiactive performance does not show a major improvement due to drastically lowered dissipativity levels caused by the realistic damper model. Copyright © 2006 John Wiley & Sons, Ltd.
This paper investigates the dissipativity and performance characteristics of the semiactive control of the base isolated benchmark structure with magnetorheological (MR) fluid dampers. Previously, the authors introduced the concepts of dissipativity and dissipativity indices in the semiactive control of structures with smart dampers and studied the dissipativity characteristics of simple structures with idealized dampers. To investigate the effects of semiactive controller dissipativity characteristics on the overall performance of the base isolated benchmark building, a clipped optimal control strategy with a linear quadratic Gaussian (LQG) controller and a 20 ton MR fluid damper model is used. A cumulative index is proposed for quantifying the overall dissipativity of a control system with multiple control devices. Two control designs with different dissipativity and performance characteristics are considered as the primary controller in clipped optimal control. Numerical simulations reveal that the dissipativity indices can be classified into two groups that exhibit distinct patterns. It is shown that the dissipativity indices identify primary controllers that are more suitable for application with MR dampers and provide useful information in the semiactive design process that complements other performance indices. The computational efficiency of the proposed dissipativity indices is verified by comparing computation times.
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