Mathematical Problems in Engineering
Volume 6 (2001), Issue 6, Pages 557-598

Mixed H2/H control of flexible structures

D. P. De Farias, M. C. De Oliveira, and J. C. Geromel

LAC-DT/School of Electrical and Computer Engineering, UNICAMP, C.P. 6101, Campinas 13081-970, SP, Brazil

Received 18 January 2000

Copyright © 2001 D. P. De Farias et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses the design of full order linear dynamic output feedback controllers for flexible structures. Unstructured H uncertainty models are introduced for systems in modal coordinates and in reduced order form. Then a controller is designed in order to minimize a given H2 performance function while keeping the maximum supported H perturbation below some appropriate level. To solve this problem we develop an algorithm able to provide local optimal solutions to optimization problems with convex constraints and non-convex but differentiable objective functions. A controller design procedure based on a trade-off curve is proposed and a simple example is solved, providing a comparison between the proposed method and the usual minimization of an upper bound H2 to the norm. The method is applied to two different flexible structure theoretical models and the properties of the resulting controllers are shown in several simulations.