NONLINEAR ANALYSIS AND ATTITUDE CONTROL OF A GYROSTAT SATELLITE WITH CHAOTIC DYNAMICS USING DISCRETE-TIME LQR-OGY

Quasi-periodic and chaotic behavior, along with the control of chaos for a Gyrostat satellite (GS), is investigated in thiswork. The quaternion-based dynamical model of the GS is first derived, and then the influences of the reaction wheels in the GS structure, under the gravity gradient perturbation that causes a route to chaos through quasi-periodicity mechanism, is investigated. For the suppression of chaos in the system, a chaos control system with the quaternion feedback is designed for the GS based on the extension of the Ott-Grebogi-Yorke (OGY) method using the linearization of the Poincare map. In the extended OGY controller, the Poincare map is estimated using the Least Square Support Vector Machine (LSSVM) technique. After linearization of the Poincare map, the Discrete-time Linear Quadratic Regulator (DLQR) is applied on the linearized Poincare map, making the DLQR-OGY controller for chaos. The DLQR-OGY control system stabilizes the orbits to the fixed points providing a small control input signal, which leads to a decrease in the control effort and energy consumption in the GS system.