On Math Modeling of Solid Body’s Motion Control with an Excess Number of Rope Propulsion Devices

Abstract

A design scheme and a mathematical model of the dynamics of the translational motion of a solid body, which simulate the movement of an underwater platform using anchor-cable propulsion devices, are proposed, and examples of the use of such platforms during the mining and exploration of new hydrocarbon deposits on the continental shelf are given. A diagram of the underwater platform with anchor-cable propulsion devices, as well as the method of its movement. The peculiarity of the mathematical model of the process of moving a platform with this type of propulsion devices is in the dependence of the developed efforts on the position of the cables relative to the moving body and the excess of the number of control actions over the number of degrees of freedom of the mechanical system. The mathematical model describing the movement of the platform is based on geometric equations with simultaneous operation of propulsion drives on the one hand, and on the equation of the dynamics of the translational motion of the body on the other. It is shown that the task of the control system in this process is to provide the necessary balance of forces in the cables going to the propulsion anchor. As drives, DC motors and stepper motors are considered due to their ability to operate from an independent power source, such as batteries. The features of control of DC motors and stepper motors as part of anchor-cable drives drives are established. To resolve dynamic uncertainty, the necessity of introducing an additional equation into a mathematical model has been proved. In accordance with the developed mathematical model, the laws of changes in time of control actions are obtained, in particular, such as the voltage applied to the armatures of DC motors and the switching frequency of the windings when using stepping motors. A method for controlling the movement of a solid body under the influence of two drives has been developed. It can be used to study the translational movement of an underwater platform with anchor-cable propulsion devices. The features of control of DC motors and stepper motors are considered to change the length of cable drives according to a given law.