Motion Control for Structure with Liquid Based on Compensation of the Liquid Hydrodynamic Response

摘要

The problem of dynamics of structures with a free surface liquid is considered for the mode of motion with the manifestation of nonlinear properties of the interaction of a reservoir with a liquid. The method of solving is based on the previously developed model of the combined motion of a structure with the free surface liquid aimed at studying transient processes. Using the formulation of the problem in the form of the Hamilton variational principle and using the Kantorovich method of mathematical physics, we reduce the initial problem of continuum mechanics to a system of ordinary differential equations relative to amplitudes of excitation of normal modes of a liquid free surface and parameters of motion of the structure, considered as the absolutely rigid body. This model was verified on different problems of nonlinear dynamics and takes into account a great number of normal modes of oscillations. For the implementation of high-precision maneuvering, we suggest the algorithm of control of motion of structures with liquid, based on the compensation of force interaction of a liquid with reservoir walls (the so-called liquid response). The efficiency of such an approach for the construction of motion control laws is shown by the examples of impulsive disturbance (acceleration and braking) and the problem of vibration disturbance of the system motion. The suggested approach is based on the analytical properties of the initial nonlinear model of the combined motion of the structure with a liquid and is used for the nonlinear dynamical model of high dimensionality, where the application of traditional approaches to control problems solving is awkward. This approach can be used for the perfection of control of structures with liquid with a free surface, used in transport and energy systems. At the same time, the results of this article show that the basic experiment in studying the resonant modes of oscillations of liquid with a free surface in a reservoir should be revised from the point of view of providing good quality of implementation of the prescribed motion of a carrying body according to the sinusoidal law. The obtained results can be easily extended for problems with other modes of motion of the carrying body, including the case of the rotational motion of the reservoir and for reservoirs of non-cylindrical shape.