Application of linear matrix inequalities in the control of smart structural systems

Sridhar Sana, Vittal S. Rao

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Natural frequency variations, unmodeled dynamics and control input constraints are some of the major problems in the design of controllers in smart structural systems. The performance and robustness of the closed-loop system are often constrained by the limited actuation force available from Lead Zirconate Titanate (PZT) actuators. Hence, it is desirable to design controllers to maximize the performance and robustness without violating the control input constraints. In this paper, we give a methodology for designing output feedback robust controllers for smart structural systems using Linear Matrix Inequalities (LMIs). A procedure is developed to incorporate the real parameter uncertainty resulting from natural frequency variations and complex uncertainty due to unmodeled dynamics in a Linear Fractional Representation (LFR) to be utilized in the design. The control input constraints are satisfied by finding an invariant ellipsoid of closed loop trajectories for a given set of initial condition disturbances. An iterative procedure is given to solve the optimization problem involving Bilinear Matrix Inequalities (BLMIs). The design procedure is applied on a smart structural test article and the effectiveness of the proposed method is verified by robustness analyses and experimental tests.

Original languageEnglish
Pages (from-to)311-323
Number of pages13
JournalJournal of Intelligent Material Systems and Structures
Issue number4
StatePublished - Apr 2000


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