Solar Pressure Variable Structure Model Reference Adaptive Spacecraft Attitude Control in Elliptic Orbits

Abstract

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-incontrol 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. NomenclatureA c , B c , h c , g g = Closed-loop system matrices a, e = Semi-major axis and eccentricity a mi , k m = Parameters of reference model S m B = Control input matrix A s , l p = Control surface area and the moment arm C s , C s = Solar parameter e 0 , e 0 , e 1 = Error signals f 0 , f 1 = Modulation functions g 0 , g a , g = Nonlinear functions I x , I y , I z = Moments of inertia of the satellite K = (I x − I y )/I z M g = Gravity gradient torque, M s , M d = Solar torque and disturbance torque i = Inclination of the orbital plane with ecliptic plane p = Solar radiation pressure, 4.65 × 10 −6 N m −2 y p , y m = Output signals * Professor, AIAA SciTech s = Laplace variable or differential operator v 0 , v 1 , v = Control input signals X b , Y b , Z b = Principal axes of the satellite α, α r = Pitch angle, reference pitch anglẽ α = Tracking error ξ i , χ i = Auxiliary signals X o , Y o , Z o = Orbital coordinates with X o along the local vertical, X o Y o defining the orbital plane δ i (i = 1, 2) = Control plate rotations θ = Orbital angle λ = Pitch attitude angle of the satellite with respect to orbital coordinates Λ f , λ i , b f = Regressor filter parameters ρ s = Reflectivity of the control surfaces φ = Location of the Sun from the line of nodes Ω = Mean orbital rate ω 1 , ω 2 , ω a = Regressor vectors θ i , Θ a , θ * i = Controller gains