Fabio Celani

Robust Three-axis Attitude Stabilization for Inertial Pointing Spacecraft Using Magnetorquers

Abstract In this work feedback control laws are designed for achieving three-axis attitude stabilization of inertial pointing spacecraft using only magnetic torquers. The designs are based on an almost periodic model of geomagnetic field along the spacecraft׳s orbit. Both attitude plus attitude rate feedback and attitude only feedback are proposed. Both feedback laws achieve local exponential stability robustly with respect to large uncertainties in the spacecraft׳s inertia matrix. The latter properties are proved using general averaging and Lyapunov stability. Simulations are included to validate the effectiveness of the proposed control algorithms.

Output Stabilization of Strongly Minimum-phase Systems

Abstract In this work it is shown that adapting the notions of relative degree and strong minimum-phaseness introduced in Liberzon et al. IEEE Trans. Automat. Control 47 (3) 2002, it is possible to obtain global stabilization results via output feedback. The notions in question are coordinate-free; consequently, it is not required that the system is transformed into normal form. The stabilization methods are based on small-gain arguments and provide global results.

Certainty Equivalence in Nonlinear Output Regulation with Unmeasurable Regulated Error

Abstract In the present paper we consider a general nonlinear output regulation problem in which the regulated error is unmeasurable. It is assumed that the interconnection of the controlled plant with the exosystem observed through the measured output satisfies some appropriate observability conditions that allow the design of an asymptotic observer. Then, the contribution of this paper consists in showing that in the latter scenario, a design based on certainty equivalence is effective for determining a controller that achieves semiglobal output regulation.

A Robust Optimization Approach for Magnetic Spacecraft Attitude Stabilization

Attitude stabilization of spacecraft using magnetorquers can be achieved by a proportional–derivative-like control algorithm. The gains of this algorithm are usually determined by using a trial-and-error approach within the large search space of the possible values of the gains. However, when finding the gains in this manner, only a small portion of the search space is actually explored. We propose here an innovative and systematic approach for finding the gains: they should be those that minimize the settling time of the attitude error. However, the settling time depends also on initial conditions. Consequently, gains that minimize the settling time for specific initial conditions cannot guarantee the minimum settling time under different initial conditions. Initial conditions are not known in advance. We overcome this obstacle by formulating a min–max problem whose solution provides robust gains, which are gains that minimize the settling time under the worst initial conditions, thus producing good average behavior. An additional difficulty is that the settling time cannot be expressed in analytical form as a function of gains and initial conditions. Hence, our approach uses some derivative-free optimization algorithms as building blocks. These algorithms work without the need to write the objective function analytically: they only need to compute it at a number of points. Results obtained in a case study are very promising.

Determining optimal parameters in magnetic spacecraft stabilization via attitude feedback

The attitude control of a spacecraft using magnetorquers can be achieved by a feedback control law which has four design parameters. However, the practical determination of appropriate values for these parameters is a critical open issue. We propose here an innovative systematic approach for finding these values: they should be those that minimize the convergence time to the desired attitude. This a particularly diffcult optimization problem, for several reasons: 1) such time cannot be expressed in analytical form as a function of parameters and initial conditions; 2) design parameters may range over very wide intervals; 3) convergence time depends also on the initial conditions of the spacecraft, which are not known in advance. To overcome these diffculties, we present a solution approach based on derivative-free optimization. These algorithms do not need to write analytically the objective function: they only need to compute it in a number of points. We also propose a fast probing technique to identify ...

Spacecraft attitude stabilization with piecewise-constant magnetic dipole moment

In actual implementations of magnetic control laws for spacecraft attitude stabilization, the time in which Earth magnetic field is measured must be separated from the time in which magnetic dipole moment is generated. The latter separation translates into the constraint of being able to genere only piecewise-constant magnetic dipole moment. In this work we present attitude stabilization laws using only magnetic actuators that take into account of the latter aspect. Both a state feedback and an output feedback are presented, and it is shown that the proposed design allows for a systematic selection of the sampling period.