Dissipativity and performance analysis of smart dampers via LMI synthesis

Johnson E. A., Erkus B.

STRUCTURAL CONTROL & HEALTH MONITORING, vol.14, no.3, pp.471-496, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1002/stc.169
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.471-496
  • Istanbul Technical University Affiliated: No


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 (c) 2006 John Wiley & Sons, Ltd.