Reduced order controllers for smart structural systems

The application of robust control theory, H₂ and H_∞ controls, on the active control of smart structural systems results in higher order controllers. The implementations of these controllers need complex hardware and more power and is difficult to embed in the stmcture. In this paper, we present two lower-order controller design methods, indirect and direct methods. For indirect method, using linear matrix inequalities (LMIs), the full order strictly proper controller with output limitations is first synthesized for given control objectives, bounded H₂ or H_∞ system norm. The full order controller is then reduced to a lower-order controller by a LMI based model reduction method for minimal H_∞ norm reduction error. For direct method, the fixed-order controller synthesis conditions are represented by LMIs with an additional nonconvex rank constraint. To utilize efficient computational tool for numerical solutions of convex LMIs, we relax the rank condition to a convex optimization. Although this relaxation can not fully solve the rank condition, in most cases, it gives a controller with lower-order. The proposed methods are tested on an experimental three-mass structure with PZT sensors and actuators. These two methods are compared based on the simulation and experimental results.