In this paper we consider the problem of keeping a nanosatellite near the nominal inspection ellipse, which is the Hill ellipse. The source of the disturbing effect, leading to the deformation of the nominal trajectory, is the drag of the atmosphere and the nonlinearity of the central attraction field. Using the traditional approach to finding the control law in the form of a linear-quadratic controller does not always meet the specified requirements, since it is based on the formation of a control law based on a linearized model of motion dynamics. The method of control law synthesis in the form of a linear-quadratic controller, using a quasilinear model of motion (SDRE-method), allows to increase the accuracy of the implementation of the inspection motion. In this work, a study was carried out to select the parameters of the quadratic quality criterion from the conditions to provide the requirements for energy costs and the quality of implementation of the inspection motion.