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

The process of deployment elements of constructions and adjustment of the radio-reflecting network of large-sized transformable space-based reflector is considered. The reflector consists of a frontal network, which is stretched on the power frame, cables, with which the front network is pulled to the rear network to set the desired shape of the reflecting surface. The problem of setting and determining the shape of the radio-reflective network is solved both in one plane and in three planes. In general, the task of adjusting the form of a radio reflecting reticle is solved by affecting the design of the actuators — the element of the control system. For the correct functioning of the reflector in orbit, it is necessary to control the shape of the reflecting surface by stretching the frontal network. For the formation and maintenance of the shape of the reflector, the frontal and rear networks are connecte d by cable-stayed reinforcements (tie rods). The cable connect the opposite network nodes. The cable system is the basis for building a sub-system. Miniature mechatronic modules can be located on each of the adju stable guys. To adjust the shape in one plane, the technique of flexible threads is applied. The possibility of changing the surface by simultaneous action of one or more actuators is sho wn. To adjust the shape in space, the membrane method described by the Laplace equation is used. The piezo actuator, DC motor and servomotor are considered as actuators for setting t he shape. As a mathematical model of the piezoactuator, the model of A. A. Nikolsky is considered. The system is solved taking into account rigid fixation of the reflector response. A comparison of the use of PID-controller and optimal controller. The structure of optimal control is revealed from the maximum principle. The arising two-point boundary value problem is solved by the methods of the steepest descent and Newton. It is shown that the use of optimal control can reduce the time of the transition process. A similar problem was solved for DC motor and servo motor. The advantage of using optim al control methods is shown for all actuators. The solution of the problem with the help of algorithm with correction of parameters of control structure is offered.

mathematical model, rotational motion, translational motion, deployment, modeling, large-sized transformable reflector

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