Optimum control of one-dimensional structures with longitudinal periodic excitation

The damping of an one-dimensional structure's oscillations under the action of variable periodic excitation, which arises during the safety (emergency) braking of the mine carrier cable, is considered. The speed-in-action problem of an object's control described by the Mathieu equation is solved under conditions of limited longitudinal control action. A numerical method for calculating the switching times of piecewise constant control under conditions of a stable mode of the structure's oscillations is proposed. Numerical examples of damping of the oscillations of a skip hoist with different number of control stages and a different direction of the control action are presented.