Reduced order controllers for smart structural systems

Pengxiang Liu; Vittal S. Rao

doi:10.1117/12.475223

10 July 2002 Reduced order controllers for smart structural systems

Pengxiang Liu, Vittal S. Rao

Proceedings Volume 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control; (2002) https://doi.org/10.1117/12.475223
Event: SPIE's 9th Annual International Symposium on Smart Structures and Materials, 2002, San Diego, California, United States

Abstract

The application of robust control theory, H₂ and H_(infinity ) 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 structure. 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 H_(infinity ) or H₂ system norm. The full order controller is then reduced to a lower-order controller by a LMI based model reduction method for minimal H_(infinity ) 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.

Citation Download Citation

Pengxiang Liu and Vittal S. Rao "Reduced order controllers for smart structural systems", Proc. SPIE 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, (10 July 2002); https://doi.org/10.1117/12.475223

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