Application of Linear Matrix Inequalities in the Control of Smart Structural Systems

Abstract

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.

Design of a Control System using Linear Matrix Inequalities for the Active Vibration Control of a Plate

“…Limited work has been done on the use of LMI for active vibration control. Sana and Rao (2000) used LMI to design an output feedback controller to increase the damping in some modes of a cantilever beam. However, the resulting matrix inequalities involved bilinear matrix inequalities (BMI) in unknown variables, and hence it became a non-convex optimization problem.…”