Collocated H∞ Control of a Cantilevered Beam using an Analytical Upper-bound Approach

This article examines the collocated H ^∞ control of vector second-order structural systems using an analytical upper-bound method. The structural system considered in this work is that of a cantilevered aluminum beam with a collocated pair of piezoceramic patches to serve as actuators and sensors. An explicit expression that bounds the H ^∞ norm of collocated structural systems is applied for analysis and control synthesis, resulting in significant computational advantages compared to standard H ^∞ analysis and control methods. The proposed approximation method is used to design a static output feedback controller that guarantees a closed-loop H ^∞ norm less than any user-defined value. This method is validated using a finite element representation of the beam, and then verified experimentally.