Reaction-Wheel Momentum Dumping by Hybrid Control of Magnetorquers and Thrusters

Abstract

Magnetorquers and thrusters are usually employed independently to dump the accumulated momentum of reaction wheels installed in a satellite to control the spacecraft attitude. Momentum dumping using magnetorquers can be slow and restricted by Earth magnetic field strength. Hybrid use of thrusters and magnetorquers brings the benefit of minimizing the thruster fuel dissipation and maintaining the required dumping cycle. This paper focuses on investigating and analyzing hybrid control strategies of onboard thrusters and magnetorquers for dumping reaction wheel momentum on a 3-axis stabilized Earthpointing satellite. Both one-phase and two phase combined algorithms are established. Based on optimal dumping torque profile from an optimal dumping controller by using PWM thrusters only, two sub-optimal combined dumping algorithms based on instantaneous cost function minimization on energy and fuel at each sampling interval are explored and derived. In addition, the boundary constraints due to actuator control limits for practical application concerns are analyzed and their impacts on control algorithms are discussed. Extensive simulation demonstrations revealed that a large mount of thruster propellant can be saved through hybrid control for momentum dumping. Those hybrid dumping methods do not rely on complex geomagnetic field model and can be practically implemented onboard satellites. NomenclatureA = 3×3 attitude matrix I = Moment of inertia tensor h = 3-axis reaction-wheel momentum vector I B ω = Inertially referenced body angular rate vector O B ω = Orbit-referenced angular rate vector N GG = Gravity-gradient torque M N = Torque vector generated by 3-axis magnetorquers N T = Torque vector generated by 3-axis PWM thrusters × = Cross product of two vectors ω o = Orbital angular rate vector 2 0 ω = Mean orbital angular rate M = Magnetic control dipole vector of magnetorquers Q = A matrix related to magnetic field vector B o = Geomagnetic field vector in the local orbital coordinates W = A constant matrix in RW momentum dumping model N W −max = RW maximum torque vector z W y W x W N N N − − − − − − max max max = 3-axis RW maximum torque components t min = Minimum time of RW momentum dumping by thrusters z y x t t t − − − min min min = Minimum time of 3-axis RW momentum dumping J = A cost function H = A Hamiltonian function f t = Integration final time N( ) k = Required combined torque vector at each sampling interval ) ( ) ( ) ( k N k N k N z y x = Required combined torque components D( ) k = A matrix for optimal combined RW momentum dumping N MT k ( ) = Combined control vector of magnetorquers and thrusters S = A 6-by-6 diagonal positive weighting matrix λ = A 3-by-1 vector of Lagrange multiplier a, b = Positive weighting scalars J TF = A cost function to minimize thruster fuel consumption m K = A scalar gain for the common cross-product law ME J = Control energy cost function for magnetic control moment d p k k , = Positive PD gain scalars e q = The vector formed by the first three components of quaternion error det...