# Monitoring and control of satellite formations using its mutual magnetic interactions (PhD thesis)

**Project name:**Monitoring andcontrol ofsatelliteformationsusing its mutualmagneticinteractions(PhD thesis)

**Consignee:**The Faculty of Electronics and Information Technology, Warsaw University of Technology

**Author of the PhD thesis:**R. Wawrzaszek

**Supervisor:**Doc. dr hab. Marek Banaszkiewicz

**Timeframe of the Project:**

The aimof the project (which is a Ph.D. doctoral dissertation of Roman Wawrzaszek) was to determine the control system thetwo-andthree-object-complex formationwithmagneticallyinteractingsatellitesand testits effectivenessin the presence ofdisturbingforcesandwhen implementing simplereconfigurationmaneuvers.

SatelliteFormation is a group of artificial satellites remaining in a relatively small distance from each other and performing assigned tasks in the most organized and autonomous waypossible.

Such systems can perform many research and practical purposes, infeasible with the assistance of currently available solutions, e.g.: create optical and radio interferometers, create systems of telescopes with a split mirror and detector, to compose a large structures in space, etc.

The biggest problems related to thepractical use of satellite formation revolve around issues of control of the position and orientation of objects. Currently, the implementation of most of the maneuvers in space requires a certain amount of consumption of fuel. In the case oforbital motion, keeping constantthe relativepositionbetween the members ofthe formationrequires acontinuousexpenseof fuel.This considerably limitsthe duration ofthis type ofmissions.

As a solution tothe problems author had suggested formations updating the mutual arrangement of the satellites using magnetic interactions. The source of these interactions would be coils of electromagnets mounted on each of the satellites. Electric energy ispractically the only"fuel"that canbecontinuouslysuppliedto a satellitein spaceby means ofsolar batterieswhichcould theoreticallyallow foran infinite number ofmaneuvers.

In order to performthe analysis, the author constructed dynamics models of two-and three-bodies systems based on kinematic equations and equations describing the electromagnetic interactions. Starting from a model and a set of 45 equations describing the system of three-bodies, the part of thetheoretical work which consists of determining the stability of the system by analyzing the stability of the linearized system was finalized. Demonstrated instability justifies the need to find a controller to stabilize the system. It is designatedasthe feedbackfromthe state, byminimizing thequadraticcost functionforeach typeof formation considered in thework.

The secondpart of the project was the verification of the designated controllers carried out using developed simulator of magnetic formation. This simulator makes numerical integration of full (nonlinearized) equations of the dynamics of formation under different conditions, namely in an isolated free system, the orbital motion and in the disturbedorbital motion, taking into account thedisturbanceof theEarth's magnetic field.

The results of theanalysis and simulations show that there are near Earth orbits formations where the magnetic and gravitational disturbances do not cause the formation of a magnetic instability.This maybe importantfrom the viewpointof futurespace missions..