CLASSICAL vs MODERN MAGNETIC ATTITUDE CONTROL DESIGN: A CASE STUDY

Electromagnetic actuators are a particularly effective and reliable technology for attitude control of small satellites. As is well known, the main difficulty in the design of attitude control laws based on such actuators is related to the fact that magnetic torques are instantaneously constrained to lie in the plane orthogonal to the local direction of the geomagnetic field vector. Controllability of attitude dynamics is ensured for a wide range of orbit altitudes and inclinations in spite of this constraint, thanks to the variability of the geomagnetic field. However, this implies that the attitude control engineer has to deal with a time-varying model in the control design process. A considerable effort has been devoted to the analysis of this control problem; in particular, as far as the linear attitude regulation problem is concerned, two main lines of work can be identified in the literature. Classical methods are based on the use of averaged models, i.e., on the idea of replacing the actual time-varying dynamics of the magnetically actuated spacecraft with an approximate time-invariant model obtained using averaging techniques. Clearly, the advantage of this approach is that the control problem becomes time-invariant, however the designer is left with the burden of verifying a posteriori that the designed controller actually stabilises the original timevarying dynamics and achieves a satisfactory performance level. This averaging approach, originally proposed in [1], was further developed in [2] to deal with the stabilisation problem for the coupled roll/yaw dynamics of a momentum biased spacecraft using a magnetic torquer aligned with the pitch axis. More recently, design methods based on full periodic models have been proposed. As the variability of the geomagnetic field is almost time-periodic, most of the recent work on the linear magnetic attitude control problem has focused on the use of optimal and robust periodic control theory for the design of state and output feedback regulators. While periodic control design methods have the significant advantage of guaranteeing closed loop stability a priori, they unfortunately lead to the synthesis of time-periodic regulators, which would be extremely impractical to implement and operate. Therefore, the main current research efforts in this area aim at developing sound design methods leading to constant gain controllers (see, e.g., [3, 4] and the recent survey paper [5]) while ensuring closed loop stability and some specified level of performance. In the light of the above discussion, the aim of the paper is compare the results obtained in the design of magnetic attitude control systems using classical (i.e., based on averaging) and modern (i.e., based on periodic models) methods for the tuning of the control algorithms. Specific reference will be made to the case of roll/yaw stabilization for a momentum bias LEO spacecraft. More precisely, classical methods such as the ones reported in [2] are compared with the approach of [4] to the design of digital attitude controllers for spacecraft equipped with magnetic actuators. This approach allows the design of periodic control laws (of the so-called ”projection based” class, an architecture widely used in the practice of magnetic attitude control) parameterised via constant gains with guaranteed nominal stability and LQ performance, using an optimisation-based method.