Semi-active reduction of vibrations in the mechanical system driven by an electric motor.

*(English)*Zbl 1386.49057Summary: In this paper, a semi-active damping approach is used for reduction of vibrations in a laboratory drivetrain system. The considered drivetrain system is powered by an electric, asynchronous motor at the one side and loaded with a harmonically varying torque on the other side. Here, an influence of electromechanical interaction, i.e., an electromechanical coupling, between the electric motor and the mechanical system has been taken into consideration. The harmonic load signal induces torsional vibrations in the system, which in the steady-state phase of motion become periodic. The aim of the work is to determine the optimal control function for a semi-active damping element, leading to vibration reduction and considering only the steady-state phase of system motion. The optimal control is derived by using a semi-analytical approach based on the optimal control theory aided with supplementary numerical computations. The proposed methodology is fully general, and it can be directly applied to any type of a periodically oscillating system.

##### MSC:

49N90 | Applications of optimal control and differential games |

74H45 | Vibrations in dynamical problems in solid mechanics |

93A30 | Mathematical modelling of systems (MSC2010) |

34H05 | Control problems involving ordinary differential equations |