Electromagnetic Formation Flight Progress Report: May 2003 Submitted to: Lt. Col. John Comtois Technical Scientific Officer National Reconnaissance Office Contract Number: NRO-000-02-C0387-CLIN0001 MIT WBS Element: 6893087 Submitted by: Prof. David W. Miller Space Systems Laboratory Massachusetts Institute of TechnologyOVERVIEW Description of the Effort The Massachusetts Institute of Technology Space Systems Lab (MIT SSL) and the Lockheed Martin Advanced Technology Center (ATC) are collaborating to explore the potential for an Electro-Magnetic Formation Flight (EMFF) system applicable to Earth-orbiting satellites flying in close formation. Progress Overview At MIT, work on EMFF has been pursued on two fronts: the MIT conceive, design, implement and operate (CDIO) class, and the MIT SSL research group. This report summarizes recent progress made in the MIT CDIO class with regards to system dynamic modeling, linear control design, and closed-loop control implementation on the electromagnetic formation flight testbed being designed and built in the class. First the testbed control requirements and experimental testing plan (“test cases”) are presented, and the linearized dynamic model of the testbed system is discussed. Then the linear control design methodology is reviewed, and the resulting control gains specific to each test case are presented. Finally, successful closed-loop dynamic results are presented for test cases 1a and 1b.EMFFORCE OPS MANUAL Space Systems Product Development – Spring 2003 Massachusetts Institute of Technology 1 Dept of Aeronautics and Astronautics A Control Algorithm Development A.1 Control Requirements Electromagnets and reaction wheels are used to provide the forces and torques necessary to control position and attitude of the vehicles. The interaction between electromagnets of different vehicles can be controlled to either attract or repel the vehicles. The reaction wheels can rotate either clockwise or counterclockwise, providing control to either accelerate or decelerate the vehicles rotationally. Varying the current through the magnets and changing the speed of the wheels control the actuators. Controlling these accurately allows for maneuvering the vehicles and disturbance rejection. The responsibility of the control team was to build a robust controller for the project that will command maneuvers and provide disturbance rejection. The controller is located on the avionics computer, and processes metrology inputs in order to calculate the necessary commands to send to the actuators. This is depicted in the block diagram in Figure A.1-A. Figure A.1-A: Block Diagram of Controller The control team designed controllers to meet the following requirements, derived from the requirements document. 1. Exhibit control in two modes a. Spin-up/spin-down b. Steady state 2. Build a robust controller for two types of maneuvering a. Trajectory following b. Disturbance rejection 3. Maximum allowable error in separation distance is 15 centimeters for a separation distance of 2 meters between vehicles +_ Controller PlantΣ SensorsActual TrajectoryPreprogrammed Trajectory Metrology Algorithm ActuatorsEMFFORCE OPS MANUAL Space Systems Product Development – Spring 2003 Massachusetts Institute of Technology 2 Dept of Aeronautics and Astronautics 4. Maximum allowable error in angular position is 5 degrees for each vehicle’s orientation 5. Rotation rate in steady state must be one revolution per minute The first requirement specifies the modes in which the test-bed operates. This is derived from the test case in which two vehicles are at rest, spin-up to steady state, and then spin-down to rest. Spin-up consists of controlling two vehicles initially at rest and positioned so that the electromagnet of the first vehicle is perpendicular to that of the second, as shown in Figure A.1-B. When the electromagnets are turned on, the vehicles rotate and shear in the directions of the arrows. By controlling the electromagnets and reaction wheels, thereby applying appropriate forces and torques on the vehicles, the vehicles will follow the trajectory specified in Figure A.2-C, where the arrows point to the “north pole” of the magnets. This path will guide the vehicles to the steady state configuration, in which the electromagnets are aligned along a common axis, as show Figure A.1-D, and spinning at a constant rate, Ω, about their common center. Finally, spin-down follows the same trajectory as spin-up but in reverse. In spin-down, as the magnets rotate in the opposite direction relative to the radial line between the electromagnets to align perpendicularly, the test-bed comes to rest. A controller has been designed for spin-up, but has not yet been tested. Figure A.1-B: Spin-up Mode Figure A.1-C: Spin-up Trajectory Figure A.1-D: Steady State Spin ModeEMFFORCE OPS MANUAL Space Systems Product Development – Spring 2003 Massachusetts Institute of Technology 3 Dept of Aeronautics and Astronautics To achieve a robust controller implies two responsibilities. The test-bed must both reject disturbances as well as have the control authority to reposition the vehicles. Rejecting disturbances implies both maintaining desired positions and desired angular rates, whether finite or zero in the presence of external disturbances. The controller was designed to demonstrate these capabilities in both the spin-up/spin-down as well as steady-state modes. Repositioning of the vehicles was to be used during the spin-up and spin-down maneuvers by following a user-supplied trajectory. Requirements three and four set the displacement and angular accuracies required for a successful controller. When the controller determines the desired displacement and angular position for each vehicle, they must reach these states with a set accuracy for the controller to work. These accuracies were derived from the accuracy of our system model. The model was obtained by adding a perturbation to the non-linear system dynamics and linearizing the equations of motion. In this process, higher order terms were neglected. To see when these higher order terms become negligible, further analysis was done by comparing the linearized model with the full non-linear model for different size perturbations. The electromagnetic forces on each vehicle due to the electromagnetic interaction between the vehicles were