Copyright © IFAC Control Applications of Optimization Ho.i fo. . Isro. cl. 1995 THREE-AXIS SATELLITE ATTITUDE CONTROL BASED ON MAGNETIC TORQUING - LINEAR OPTIMAL APPROACH* Rafal Wisniewski Aalborg University, Department of Control Engineering, Frederik Bajers Vej 7, DK-9220 Aalborg 0, Denmark. raf@control.auc.dk Abstract: Recently small satellite missions have gained considerable interest due to low-cost launch opportunities and technological improvement of micro-electronics. This paper discusses an attitude controller for a low earth orbit satellite actuated by a set of mutually perpendicular electromagnetic coils. Magnetic torquing is cheap, lightweight, and power efficient. The actuation principle is to use the interaction between the Earth's magnetic field and the magnetic field generated by the coils. Design of the attitude controller is based on linear approach since the satellite trajec- tory remains in a neighbourhood of a reference, due to influence of conservative forces of the gravity gradient and the gyro-effect owing to rotation of the satellite around the Earth. Limited computer capacity and restrictions on power consumption demand computational simplicity and power optimality of the attitude control system. Design of a quasi optimal attitude controller with time varying gain for an earth pointing satellite is a subject of considerations in this paper. Keywords: Attitude control, periodic systems, receding horizon control, Riccati Equation. 1 INTRODUCTION Several attitude control methods for three-axis stabilization of satellites have been developed over the past years. Generally speaking all those meth- ods may be classified as active or passive. Active methods are used for missions where pointing ac- curacy is vital. The 3-axis active stabilization using magnetic torquing only for a gravity gradient stabilized satellite is considered in this paper . The complex- ity of the magnetic control is due to the magnetic control torque lies always perpendicular to the ge- omagnetic field vector. Thus the system would not be three-axis controllable if the geomagnetic field were fixed at any instant in time. The obser- ·Work supported by the 0rsted Satellite Project . 91 vation, that the geomagnetic field is time depen- dent in an orbit fixed coordinate system, will be used in the paper. There is rich literature covering satellite attitude control. Nevertheless most of the algorithms pre- sented assume application of jet actuators or re- action wheels. The problem of three-axis mag- netic control was addressed in Musser and Ward (1989). The local stabilization of the satellite was achieved via implementation of the infinite time horizon linear quadratic regulator. Another lin- ear approach was given in Martel et al. (Septem- ber 1988), where the linearized time varying satel- lite motion model was approximated by a linear time invariant counterpart. Three-axis stabiliza- tion with use of magnetic torquing of a satellite without appendages was treated in Wisniewski