A wave-based controller design for general flexible structures

This paper treats a travelling-wave approach to suppressing vibration of general flexible structures. This approach aims to minimize all of the reflective waves at actuator positions located at the structural boundaries. A variation of the transfer matrix method shows the property that the elastic motion is obtained by superposing the waves travelling in a flexible structure; this transfer matrix method is based on the finite element method for structural analysis. Moreover, the method gives the propagation and scattering relations of the waves in the structure. Since these relations are described by a complex-valued function with respect to Laplace variable, they are transformed into a real-valued form to design a controller by a lot of state-space methods. This transformation is given by diagonalizing the unity transfer matrix into a real-Jordan form. The problem is then formulated as an H-infinity optimization problem to find a compensator minimizing the reflective waves at the actuators. The designed compensator is based only on the scattering relations at the controller positions and on the sensor-input/controller-output relations. A multispan flexible beam is used to verify the validity of the present approach. It is numerically shown that the approach is able to achieve good damping improvement in the closed-loop system. (C) 1998 Academic Press.