Dissipativity and performance analysis of smart dampers via LMI synthesis
Dissipativity and performance analysis of smart dampers via LMI synthesis
复制标题
DOI：
10.1002/stc.169
复制
发表时间：
2007-04
影响因子：
5.4
通讯作者：
E. A. Johnson;B. Erkus
中科院分区：
文献类型：
--
作者：
E. A. Johnson;B. Erkus
利用线性矩阵不等式（LMI）综合方法研究了具有智能阻尼器的半主动系统的耗散率和性能。为此，利用基于LMI的多目标凸规划中可用的技术，提出了一个耗散指数来修改标准线性二次型调节器（LQR），以获得更好的半主动性能。首先对现有的耗散率指标进行了综述，并基于能量耗散率的概念定义了两个新的耗散率指标。其次，用线性目标函数和若干LMI约束来定义LQR问题。然后，对于每个耗散指数，定义一个耗散不等式约束。观察到只有一个耗散性约束可以用lmi表示并在LQR问题中实现。通过附加弱形式的耗散约束，得到了一种改进的LMI - based LQR控制器。通过两个数值算例研究了半主动系统的耗散率和性能。第一个例子是一个2自由度的建筑，理想的阻尼器附在第一层，并选择一个LQR控制器，使其具有高耗散率水平。第二个例子是公路桥的2DOF模型，其中在轴承位置附加了一个真实的磁流变（MR）流体阻尼器，从而产生一个具有低耗散率水平的LQR控制器。采用具有不同耗散约束值的改进LQR和标准LQR对这两个例子进行了全面的参数研究。对于第一个例子，我们发现这些指标对于识别耗散性质和半主动性能关系是非常有用的。此外，该方法还能改善控制器的耗散特性，提高半主动性能。另一方面，对于第二个例子，尽管所提出的方法能够提高耗散率，但由于实际阻尼器模型导致耗散率水平大幅降低，因此总体半主动性能并未显示出重大改善。版权所有©2006约翰威利父子有限公司
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.