Control of the compatible movement of the tank with the liquid based on the compensation of the force response of the liquid

Abstract

The combined motion of nonlinear dynamics of a cylindrical reservoir with liquid under non-periodic loading in the form of one or two periods of sine on below resonance frequency is studied. The high dimensionality of the system and its nonlinearity does not allow the application of commonly used mathematical methods of motion control problems. At the same time, problems of high precision maneuvering of structures with a liquid are urgent in modern engineering. We suggest the scheme of control based on the use of information about force interaction of a liquid with reservoir walls, obtained within the framework of the method, grounded on the Hamilton-Ostrogradskiy variational principle. For such approach, we succeeded to construct a mathematical model of the combined motion of the structure with a liquid, based on analytical methods of mathematical physics, variational and asymptotic methods of mechanics. The suggested model is the model of minimal dimensionality (its dimension is equal to the number of degrees of freedoms of the system), which creates preconditions for its successful numerical implementation. This model was successfully tested for transient and steady modes of motion of structures with a liquid for translational and angular motion of the structure. The testing of the model showed good qualitative concordance of results with known results of experimental research. The potential of obtaining forces of interaction of a liquid with the reservoir (liquid response) as a consequence of the use of the technique of varying is the specificity of application of the Hamilton-Ostrogradskiy variational principle. Using this information about the force interaction of the structure with a liquid we analyze the algorithm of motion control, which is based on the principle of compensation of liquid force response. The suggested algorithm enables the construction of control, which eliminates the effect of liquid mobility on the motion of a rigid body being extremely important for high precision performance of prescribed motion of structures with liquid. Such control is not optimal, but it enables getting the desired results for the relatively high dimensional and nonlinear problem. By the example of the system motion disturbance by one or two periods of action of harmonic forces we show efficiency of the suggested technique.