A Comprehensive Model of a Tracker System Based on Motion Equations of a Two Degree-of-Freedom Gimbal System
In this paper a comprehensive model of a tracker system including derive subsystem is presented. Since the main part of the under consideration system consists a two Degree-Of-Freedom (DOF) gimbal subsystem, at first, the model of a two-axis gimbal is considered. For this purpose, after introducing the coordinate systems and different transformation matrices, the related equations of pitch and yaw axes by considering the friction torques, mass unbalances and cable restraint torques are derived. Moreover, all disturbance terms and the methods for their reduction or elimination are investigated. Then, the derive system of the gimbal including a DC motor with a gear is modeled and governing overall equations of the whole system is obtained. In order to have a model with practical considerations, the model of rate gyro which is used for measuring the angular velocities is also included. Finally, the simulation results of the under consideration case study by using the derived comprehensive dynamical equations of this paper are provided. Analysis of these results are used to synthesis the behavior of the practical system and choosing the suitable control structure in order to achieve stabilization and tracking objectives.
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