Periodic H<inf>2</inf> synthesis for spacecraft attitude control with magnetorquers and reaction wheels

Abstract

Abstract-Particularly attractive for small satellites, the use of magnetic torquers for attitude control is still a difficult problem. Indeed, the problem is naturally time-varying and suffers from controllability issues. In this paper, a generic model, taking different kinds of pointing and different kinds of actuators into account, is proposed, linearized and then discretized. Recent studies demonstrate how combining magnetorquers and reaction wheels is attractive. Following the same line, latest LMI synthesis techniques for static periodic controller are applied in this paper to the attitude control problem of a spacecraft equipped with both actuation systems. Simulation results are provided, showing the performance of the obtained control law.

Recent advances in the active magnetic control of satellites

“…Однако для аппарата с двойным вращением сохраняется возможность быстрого разворота вокруг оси установки маховика. Поэтому в этой области при построении управления применяются оптимизационные методы, в частности, H 2 -управление [48] и H ∞ -управление [49; 50]. При этом уравнения движения линеаризуются и сводятся к уравнениям с периодическими коэффициентами, как и при построении линейно-квадратичного регулятора.…”

Reaction Wheels Desaturation Using Magnetorquers and Static Input Allocation

“…To assess the performance of the proposed controller in a more realistic environment, a disturbing torque T ext is injected in the dynamics and comparisons between the classical and the allocation schemes are given via a new set of simulations. Predominant for LEO, as in the Demeter example [28], gravity gradient disturbances, aerodynamic drag and magnetic torques disturbances caused by the interaction of the current loops with the magnetic field, can be modeled in the inertial frame by two periodic signals T 1 and T 2 , whose period is one and two times the orbital frequency ω 0 added to a secular term T 0 (see [7], [36]):…”

“…Simulations have been performed over 20 orbits using the aggressive attitude stabilizer previously introduced and are reported in Figures 15 and 16. For these simulations, according to [7], [36], the numerical parameteres in (27) have been selected as follows: Figure 14.…”

“…To prove (36), sinceã converges to zero, let us pick k = k δ sufficiently large to ensure |ã(2πk δ + ω)| < δ ∀ω ≥ 0. Then we have from (35) Moreover, we may easily compute:…”

Robust Stability of Periodic Systems with Memory: New Formulations, Analysis and Design Results

“…Bolzern and Colaneri [1988]. One can first recall the now classic examples of control of vibrations in helicopters studied by Bittanti and Lovera [1996] and Bittanti and Cuzzola [2002], as well as autonomous orbit control discussed in Schubert [2001], or the attitude control systems of satellites equipped with magnetorquers, the topic of Trégouët et al [2011b] and Wisniewski and Blanke [1999]. Surprisingly, few results exist in the robust control framework for this class of models.…”