Modeling of Controlled Motions of an Elastic Rod by the Method of Integro-Differential Relations

摘要

The possibilities of controlling elastic systems with distributed parameters and constructing a solution corresponding to some given quality criteria are studied. The regular integro-differential approach to the construction of solutions for a wide class of boundary-value problems is developed and a quality criterion for the obtained solution is proposed. The case of the relay control, which induces substantial elastic oscillations in the system and results in significant computational difficulties when applying classic approaches, is considered for plane motions of the homogeneous straight rod. The problem parameters are chosen so that the period of the lower mode of oscillation is comparable with the interval on which the motions are studied. The results obtained by the variable separation method and the integro-differential approach are analyzed and compared.