A comparison of approaches to specifying the modal matrices in the modal control of elastic systems with and without observers

The implementation of modal control of distributed elastic objects involves the use of modal matrices: a mode analyzer and a mode synthesizer specifying the linear transformation of vectors of measured and control signals in order to separate the eigenmodes of the object in the control system. The standard method for calculating the modal matrices is the inversion of the influence matrices. The article proposes an alternative method: transposing the influence matrices with normalization of the action on different modes. As an example, the problem of suppression of forced vibrations of a thin metal beam using piezoelectric sensors and actuators has been solved numerically, and different combinations of the above methods and different variants of normalization have been tested. Two types of control systems were considered, the former being based on modal and frequency filters and the latter being based on modal observers. The best control result was shown to be achieved with the combined use of the above methods for both types of control systems considered.