Gyro-System for Guidance with Magnetically Suspended Gyroscope, Using Control Laws Based on Dynamic Inversion - Romulus Lungu; Constantin-Adrian Mihai; Alexandru-Nicolae Tudosie (Actuators)
The authors have designed a gyro-system for orientation (guidance) and stabilization, with two gimbals and a rotor in magnetic suspension (AMB—Active Magnetic Bearing) usable for self-guided rockets. The gyro-system (DGMSGG—double gimbal magnetic suspension gyro-system for guidance) orients and stabilizes the target coordinator’s axis (CT) and, at the same time, the AMB–rotor’s axis so that they overlap the guidance line (the target line). DGMSGG consists of two decoupled systems: one for canceling the AMB–rotor translations along the precession axes (induced by external disturbing forces), the other for canceling the AMB–rotor rotations relative to the CT-axis (induced by external disturbing moments) and, at the same time, for controlling the gimbals’ rotations, so that the AMB–rotor’s axis overlaps the guidance line. The nonlinear DGMSGG model is decomposed into two sub-models: one for the AMB–rotor’s translation, the other for the AMB–rotor’s and gimbals’ rotation. The second sub-model is described first by nonlinear state equations. This model is reduced to a second order nonlinear matrix—vector form with respect to the output vector. The output vector consists of the rotation angles of the AMB–rotor and the rotation angles of the gimbals. For this purpose, a differential geometry method, based on the use of the output vector’s gradient with respect to the nonlinear state functions, i.e., based on Lie derivatives, is used. This equation highlights the relative degree (equal to 2) with respect to the variables of the output vector and allows for the use of the dynamic inversion method in the design of stabilization and guidance controllers (of P.I.D.- and PD-types), as well as in the design of the related linear state observers. The controller of the subsystem intended for AMB–rotor’s translations control is chosen as P.I.D.-type, which leads to the cancellation of both its translations and its translation speeds. The theoretical results are validated through numerical simulations, using Simulink/Matlab models.