Analysis and Optimization of Rotation of an Elastic Loaded Link with an Electric Drive

Plane rotations of an elastic link, which is controlled by an electric driver at one end and loaded by a point mass at the other, are studied. An optimal control problem is considered to turn the link into the desired state with damping elastic vibrations by the voltage supplied to the motor winding. According to the method of integro-differential relations, a generalized statement of the control problem is given for the dynamical system with distributed and lumped parameters, and consistent approximations for unknown lateral displacements, momentum density, and bending moment are proposed. The procedure minimizing the cost function and regularizing the numerical error is discussed.