Sun–Earth L2 point formation control using polynomial eigenstructure assignment |
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| Institution: | 1. School of Automation, Central South University, Changsha, Hunan 410083, China;2. College of Electrical Engineering, Henan University of Technology, Zhengzhou, Henan 450001, China;3. School of Electronic Engineering and Intelligent Manufacturing, Anqing Normal University, Anqing, Anhui 246011, China;4. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China;1. Federal University of Minas Gerais, Graduate Program in Electrical Engineering, Brazil;2. Federal University of São João del-Rei, Department of Electrical Engineering, Brazil;3. Federal University of Minas Gerais, Department of Electronics Engineering, Brazil |
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| Abstract: | A nonlinear controller based on polynomial eigenstructure assignment (PEA) is presented for the control of Sun–Earth L2 point formation flying. The relative motion dynamics is formulated as a nonlinear equation and rewritten as a Quasi-Linear Time-Varying (QLTV) model. Using a coprime factorization of the desired closed-loop transfer function, the PEA controller structure is calculated by representing the controller gains as polynomials. During the implementation of spacecraft formation flying, the PEA method is extended from Linear Time-Invariant (LTI) and Linear Parameter-Varying (LPV) models to a QLTV model to produce a closed-loop system with invariant performance over a wide range of conditions. To ensure system performance, the analytic stability analysis of the closed-loop system is developed and a position keeping controller for MIMO formation flying is designed using a decoupling method to achieve the desired performance. Finally, a simulation is carried out to validate the controller performance for the formation flying. |
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