Study of the influence of external forces on the performance of discrete modal filters

Abstract

Discrete modal filters are built as a weighted summation of signals from sensors installed on a flexible structure. The positions of the sensors are relevant for the filter performance, particularly when the number of sensors is lower than the numbers of the considered system modes. In this work, a new methodology to design discrete modal filters is presented that finds the position of the sensors and the position of the external force that improves the performance. First, for each candidate position of the external force, the proposed methodology determines the positions of a given number of accelerometers and their gains so that the filter can best isolate the vibration modes in each of its outputs. For this, a minimum error criterion is implemented, using the L2 norm, between the nominal system output signal and the desired output, for each of the possible configuration. After this, a performance index is implemented that allows comparing the effectiveness of the filter for different numbers of accelerometers. This methodology was implemented and evaluated through simulations in the design of a discrete modal filter on a slender flexible beam in a free-fixed end configuration. The results corresponding to the best performance of the filter are presented for 1, 3 and 5 accelerometers, showing that it is possible to design a modal filter with fewer accelerometers than the number of vibration modes, considering the position of the external force as a design variable.