ОПТИМАЛЬНОЕ ГАШЕНИЕ ПОПЕРЕЧНЫХ КОЛЕБАНИЙ КОНСОЛЬНОЙ БАЛКИ

Abstract

The multicriteria problem of transverse vibrations damping of a console beam is colved by the active and passive damping methods. The mathematical model of beam is provided by Bernoulli-Euler's hypotheses with the linear viscosity. Perturbation acting on the beam belongs to a class L2 of functions. The beam mode is described by Krylov functions. The normal form method is used to convert to the main coordinates. A model of active vibration isolation applied along the entire length of the console beam and a model connected to a vertical base at one point were constructed. The task of transverse vibrations damping is a state feedback control problem with two controlled outputs. Two criteria are introduced: the level of the control force and the maximum deflection of the beam. The generalized H2-norm is used as a measure of functional evaluation in the synthesis of optimal regulators. The search for optimal feedback is based on the use of linear matrix inequalities and efficient algorithms for solving, implemented in the MATLAB package. Synthesis of Pareto optimal control is implemented on the basis of Germeyer convolution. The optimal values of the functional under distributed and concentrated vibration isolations are given with respect to two criteria for active and passive damping methods. The paper includes a comparison of vibration isolation for different damping methods.