Attitude Control by Means of Explicit Model Predictive Control, via Multi-parametric Quadratic Programming Master Thesis Spring 2004 Ntnu Fakultet for Informasjonsteknologi, Norges Teknisk-naturvitenskapelige Matematikk Og Elektroteknikk Universitet Institutt for Teknisk Kybernetikk Masteroppgave

The topic of this thesis is attitude control of a micro-satellite. Due to their physical size, microsatellites have fairly limited power supply, data storage, and computational resources, hence making it crucial to have a simple and reliable control system. A reasonable approach is to evaluate the controller off-line, and consequently reducing the need for CPU speed drastically as real-time effort in space can be restricted to a table-lookup. In many circumstances it may also be desirable to prevent the different components from operating near their thresholds, either the design focus is to keep power consumption within some limits or to keep the rate of wear as low as possible. It is shown in this thesis that all these concerns can be dealt with by formulating a Model Predictive Control problem (MPC). It is shown that explicit solutions to constrained linear MPC problems can be computed by solving multi-parametric quadratic programs (mpQP), where the parameters are the components of the state vector. The solution to the mpQP is a piecewise affine (PWA) function, which can be evaluated at each sample to obtain the optimal control law. In addition to reducing the on-line effort, the controller can be implemented on inexpensive hardware as fixed-point arithmetics can be used. A simple second order system is included to illustrate the procedure. An explicit MPC (eMPC) controller is derived for the SSETI/ESEO micro-satellite, initiated by the European Space Agency (esa). The structural data is based on the the latter, and the spacecraft is modelled as an ideal rigid body. Various topics within spacecraft and astrodynamics are included to provide a thorough insight in how the model is derived. To represent its attitude, the well known Euler parameters are utilized, while the dynamic equations are based on the Newton-Euler formulation. An important thing to keep in mind is that the thrusters on the satellite are on-off by nature. An attempt to solve this problem is done using a preliminary bang-bang modulation scheme. The controller is connected in closed-loop with the nonlinear plant, and the effectiveness is demonstrated through simulations. With purpose of comparing the performance to other control schemes, we also derive and simulate PD-control and stationary LQR. As familiar to the author, the eMPC approach has not yet been applied for attitude control of satellites. A paper based on the work in this thesis is to be submitted to the American Control Conference (ACC) 2005. A preprint is given in the appendix.