Based on the variable structure model reference adaptive control (VS-MRAC) theory, a new adaptive control system for the attitude control of satellites in elliptic orbits with uncertain dynamics, using solar radiation pressure (SRP), is derived. The nonaffine-in-control nonlinear spacecraft model includes the gravity gradient torque, the control torque produced by two solar flaps, and external time-varying disturbance torque. The objective here is to derive a control law for the pitch attitude control using the pitch angle and pitch rate feedback. For the trajectory tracking of the pitch angle, a variable structure model reference adaptive attitude control system, including two relays and linear filters, is designed. Although, the modulation functions of the relays are functions of certain auxiliary signals, for simplicity in implementation, these functions are assigned constant values. Simulation results are presented which show that the simplified VS-MRAC law accomplishes precise attitude control of the spacecraft, despite unmodelled (unstructured) nonlinearities, parameter uncertainty and external disturbance torque in the model.
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