Development and Research of Mathematical Models of Deployment of Mobole Parts of Transformable Space Construction. Part I

The process of deployment elements of constructions and adjustment of the radio-reflecting network of large-sized transformable space-based reflector with the use of a cable-stayed form maintenance system is considered. The deployment process can be broken down into separate phases. At each stage, the movement is due to the impact on the design of the actuator — the element of the control system. Energy for the deployment of the reflector elements is produced by drives, in particular an electric machine. The use of this type of actuator allows you to control the process of disclosure. Due to the fact that currently achieved a huge process in computer technology that allows you to perform three-dimensional computing operations in a short time, it is particularly important to use optimal control algorithms. When deployment the reflector for two types of motion — rotational and translational — mathematical models based on Lagrange equations of the II-kind are obtained. These mathematical models take into account such parameters as dissipation, the presence of longitudinal and transverse deformation. The models provide for the presence of a stop and a lock, as an Executive element in the deployment selected brushless DC motor. All the observations made allow us to formulate a smooth statement disclose items on the stop with minimum oscillation of the structure. The developed models allow to analyze the n-th number of natural oscillation frequencies. Modeling with different parameters of the model is carried out. The parameters of the transition process of the spoke at the opening of the first link with the other links embedded in it and at the fully covered spoke are analyzed. It is shown that depending on the mass-dimensional parameters there is a significant change in the dynamics. For the spoke extension stage, the weight and size characteristics have little effect on the opening dynamics. The smaller the Young’s modulus and density of the material, the greater the damped longitudinal oscillations.. The simulation of this stage with a spoke made of different materials is carried out. Various methods are proposed to reduce the opening time at all stages and minimize transverse and longitudinal oscillations. The possibility of application of the developed mathematical models for a wide range of tasks is shown.

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