Solution of the filtration problem with the optimal adjustment of the radio-reflecting net of a transformable reflector

In this paper, we consider the solution of the filtering problem using the Kalman filter with the optimal tuning of the radio-reflecting net. A large-sized transformable space-based reflector is considered. In the process of placing in orbit this structure, it is possible that the real form of the radio-reflecting net can deviate the desired one. To ensure point-to-point adjustment of the active part of the mesh, a cable-cable system is used. The nodal points of the radio-reflecting surface are connected to the back side of the net through cables. They have built-in actuators that allow you to change the length of the cables. A piezo actuator was selected as a control device. By point-by-point adjustment of the piezo actuators, the net is stretched to the required shape. This allows you to provide a high-quality radiation pattern and a high signal level when receiving and transmitting data. Specific values of the disturbing influences are given. To measure the supply voltage on the piezo actuator and the cable length, a voltage converter and a laser scanner are used. Possible deviations from the calculated initial position are determined. In accordance with the principle of separation, the estimation problem is solved first, then the control problem. The estimation problem is solved using the Kalman filter. The control problem is solved using the optimal control algorithm according to the hierarchy of target criteria. The results of numerical simulation are presented. The successful solution of the problem is shown with variable values of measurement noise and disturbing influences. Comparison with trajectories obtained using various optimal control algorithms is given.