Electromagnetic Formation Flight NRO-000-02-C0387-CLIN0001MIT Space Systems Laboratory 1Electromagnetic Formation FlightProgress Report: May 2002Submitted to: Lt. Col. John ComtoisTechnical Scientific OfficerNational Reconnaissance OfficeContract Number: NRO-000-02-C0387-CLIN0001MIT WBS Element: 6893087Submitted by: Prof. David W. MillerSpace Systems LaboratoryMassachusetts Institute of TechnologyElectromagnetic Formation Flight NRO-000-02-C0387-CLIN0001MIT Space Systems Laboratory 2DESCRIPTION OF THE EFFORTThe Massachusetts Institute of Technology Space Systems Lab (SSL) and the LockheedMartin Advanced Technology Center (ATC) are collaborating to explore the potential for aElectro-Magnetic Formation Flight (EMFF) system applicable to Earth-orbiting satellites flyingin close formation.PROGRESS OVERVIEWAt MIT, work on electro-magnetic formation flight (EMFF) has been pursued on twofronts: the MIT conceive, design, implement and operate (CDIO) class, and the MIT SpaceSystems Lab research group, as described in the April 2002 progress report.The CDIO class has just completed its first semester performing trades on andpreliminary design of a six-degree-of-freedom electromagnetic formation flight testbed, called“ElectroMagnetic Formation Flight of Rotating Clustered Entities,” or “EMFFORCE.”EMFFORCE will utilize electromagnets to control the size and attitude of a cluster of bodies.The MIT Space Systems Lab research staff is supporting the CDIO class with both hardware andsoftware analysis and design.Recent work has focused on the design and analysis of a control system for theEMFFORCE testbed. Specifically, three testbed modes have been considered:• Spin-up of multiple bodies from rest• Steady-state spin of multiple bodies, ensuring:- Operation at a fixed cluster radius- Disturbance rejection• Spin-down of multiple bodies from steady-state spin.Analysis shows the steady-state spin mode to be unstable, yet controllable with eithersimple PID control or more optimal state-space control methods. Further, a one-degree-of-freedom air-track system is identified to have unstable dynamics almost identical to thedynamics of a spinning cluster; hence demonstrating control on the air track system will beconsidered a positive step toward demonstrating control on the spinning system.The following report summarizes recent progress on the control analysis and designfor the first two configurations. The third configuration will be treated similarly to the first,but with a “reversed” algorithm.Electromagnetic Formation Flight NRO-000-02-C0387-CLIN0001MIT Space Systems Laboratory 3Preliminary Control Design For the “ElectromagneticFormation Flight of Rotating Clustered Entities” (EMFFORCE)Testbed in the MIT Space Systems Laboratory1 Subsystem OverviewFigure 1.1 Control Subsystem Flow ChartThe control subsystem, a computer program located within the avionics processor, takes state inputsfrom the metrology subsystem and compares the current state with the desired state. It then outputscommands, in the form of an output voltage, to the actuators to adjust the current state to match thedesired one. The output voltages are fed through the power system, which powers the actuators.Figure 1.2 Feedback SystemThere are two different actuators to control the system, the electromagnets and the reaction wheels. Theelectromagnets can provide forces and torques along the three degrees of freedom in which the vehiclesoperate (x, y, and θ). Unfortunately, since the forces produced by the electromagnet cannot beindependently controlled, there is also need for a reaction wheel. The reaction wheel produces a torqueElectromagnetAvionicsControllerMetrologySensor DataPowerReactionWheelController PlantPreprogrammedTrajectory+MetrologySensor DataOutput VoltageElectromagnetic Formation Flight NRO-000-02-C0387-CLIN0001MIT Space Systems Laboratory 4about the θ axis and it provides the opportunity to place the electromagnet’s magnetic poles. It is withthese two actuators that all controlling forces will be produced.The requirements for the controller are derived from the requirements document. The main requirementis to create a robust controller. This implies both rejecting any disturbance force that the formation mayencounter and having enough control authority to reposition satellites within the formation.To demonstrate a robust controller, the system must execute three maneuvers: spin-up, steady state spin,and spin-down. The spin-up maneuver consists of controlling three vehicles initially at rest in a straightline with perpendicular magnetic fields (See Figure 1.3) to follow a specified trajectory to the steadystate configuration. In steady state spin the cluster is spinning about the center vehicle with an angularrotation rate of at least 1 RPM. This configuration has all three magnetic fields lined up along acommon axis. Spin-down follows the same trajectory as spin-up in reverse. From the steady state thesystem will gradually cause its magnetic fields to be perpendicular so as to stop the clusters motion.These maneuvers are further developed in Sections 2 and 3.Figure 1.3 Three Vehicle Spin-Up Figure 1.4 Three Vehicle Steady StateThe last requirement determines the control tolerance. Derived from the accuracy of our analysis, themaximum displacement error allowed is one tenth of the separation distance between two adjacentvehicles. For the specified maneuver, the maximum displacement error should not exceed 20 cm.2 Steady State Mode2.1 Definition of Steady State ModeAfter the vehicles have completed the spin-up maneuver, they should complete three revolutions insteady state mode. The steady state mode defines the control algorithm for this system maneuver. Thesteady state mode will seek to decrease the error between the desired separation distance and the actualseparation distance. Since the purpose of the steady state mode is to keep the vehicles in configuration,this controller will mostly reject disturbances. To design a controller, the system must first be analyzed.Since the force from the electromagnets is axial then it is necessary to analyze the axial dynamics of thesystem.Electromagnetic Formation Flight NRO-000-02-C0387-CLIN0001MIT Space Systems Laboratory 5First, a system model must be developed. Force balance and perturbation analyses are used to find thedominant poles of the system. In this mode, the forces acting on the system are the electromagneticforces from each electromagnet,