Application of Generalized Butterworth Polynomials for Stabilization of the Equilibrium Position of a Space Station

The problem of searching for and holding the International Space Station in a position of dynamic equilibrium is considered. The equilibrium orientation of the International Space Station (ISS) is determined by the superposition of gravitational, gyroscopic, and aerodynamic moments acting on it. The system of powered gyroscopes installed on the space station plays the role of effectors in this task. Using this example as an example, we consider the possibility of applying the method of the sequential closure of the modes of motion to synthesize the multi-input multi-output (MIMO) control law, a multidimensional multiply connected dynamic system. It is proposed to use the generalized Butterworth polynomial as the reference polynomial determining the location of the poles of the closed system. Using the mathematical modeling of the control system in the search mode and maintaining the dynamic equilibrium, the advantage of using the generalized Butterworth polynomials in comparison with the classical Butterworth polynomials is demonstrated.