Nonlinear Dynamics and Adaptive Control Using the Dynamic Inversion Concept and Neural Networks for a Guidance Gyrosystem (Gg) With One Gyroscope and Two Suspension Gimbals (Gar) Part 1.obtaining the Nonlinear Dynamic Model

This paper series presents a study on the nonlinear dynamics and adaptive control of the guidance (GG) with a fast astatic gyroscope in external gimbal suspension (GAR), using the concept of dynamic inversion and neural networks. In part 1, a new nonlinear dynamic model is derived for the GG placed on an aircraft (rocket), which expresses the GG dynamics relative to the absolute trihedron; generalized Euler equations are used for its dynamic elements (rotor- inner gimbal assembly and outer gimbal). The absolute angular velocities of the GG's dynamic elements have as components their angular velocities relative to the trihedron linked to the guidance line, and the perturbing angular velocities induced by the rocket's angular velocities around its axes. The obtained nonlinear equations are then expressed in equivalent forms, where the new variables are the angular rotation velocities of the guidance line (the target coordinator axis, i.e., the gyroscope's proper angular momentum axis). The angular rotation velocities of the guidance line are chosen as the output variables of the GG, with respect to which the relative degrees of the equations are equal to 2. The input variables of the nonlinear dynamic model are the command currents applied to the command coils of the motors located in the axes of the two gyroscopic gimbals, which create, by gyroscopic effect, correction angular velocities the orientation of the target coordinator axis (guidance line) in the direction of the target line. The obtained equations contain terms that are functions of the input and output variables, as well as terms that are functions of the transport angular velocities of the guidance line and perturbing terms (functions of the rocket's angular velocities).