Optimal Discrete-Time Design of Three-Axis Magnetic Attitude Control Laws

Abstract

The problem of designing discrete-time attitude controllers for three-axis stabilization of magnetically actuated spacecraft is considered. Several methods are discussed and an approach to the tuning of various classes of projection-based controllers is proposed relying on periodic optimal output feedback control techniques. The main advantages of the proposed methods are discussed and illustrated in a simulation study.

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

“…This formulation encompasses those proposed in [13], [17] and [20] established in the particular case of a geocentric pointing taking into account the gravity gradient torque.…”

“…Furthermore, derivation of discrete-time model is very briefly documented, see e.g. [17] and [21]. Therefore, this paper contributes to the modelling effort by proposing a unifying model including, on the first hand, different choices of pointing, inertial or geocentric, traditionally associated with star and Earth observation missions, and, on the other hand, different choices of actuation, magnetorquers and/or reaction wheels.…”

Distributed Model Predictive Control of satellite attitude using hybrid reaction wheels and magnetic actuators

“…However, they are only capable of producing torques perpendicular to the geomagnetic plane and are subjected to loss of controllability. Several methods of magnetic actuation such as time-periodic optimal control that exploits the quasi-periodic nature of the geomagnetic field have been proposed [11] as well as orthogonal projection methods [12][13][14]. Optimal periodic control can provide a guaranteed level of performance but are difficult to implement due to the storage required for a fully time-periodic gain, accurate time synchronization as well as variations in geomagnetic field due to drifting of the satellite orbit over time [12].…”

Optimal periodic output feedback control: a continuous-time approach and a case study

“…In particular, in the practice of control engineering there is a lot of interest in linear time-periodic (LTP) systems since many challenging applications can be naturally described as continuous-time LTP systems, particularly in aerospace and mechanical engineering: high-order helicopter rotor dynamics (see e.g. Lovera, Colaneri, Malpica, and Celi (2006)), satellite attitude and orbit dynamics (Wisniewski 2000;Schubert 2001;Silani and Lovera 2005;Pulecchi, Lovera, and Varga 2005), wind turbines (Stol and Balas 2001), etc.…”

“…In Calise, Wasikowski, and Schrage (1992), a Floquet-transformed LQ cost-function, penalising the response and control envelopes rather than the actual time histories, was considered. A different approach has been proposed in Varga and Pieters (1998) for discrete-time LTP systems (see also Pulecchi et al (2005) for an application to magnetic satellite attitude control): the LQ performance index is minimised computing the analytical gradient and exploiting gradient descent optimisation algorithms; reliable numerical functions for Matlab environment have also been developed (Varga 2005a). A similar approach has been proposed in Aliev, Arcasoy, Larin, and Safarova (2005), where the cost function for the discrete-time case is minimised using a gradient-free method which is suitable also for open-loop unstable systems.…”