Stability Evaluation of the SDRE Technique based on Java in a CubeSat Attitude and Orbit Control Subsystem

Abstract

In 2013, the STRaND (University of Surrey and Surrey Satellite Technology Ltd) and the PhoneSat (NASA) programs attracted the attention of the aerospace community applying commercial off-the-shelf smartphones in CubeSats. Both programs deployed CubeSats using smartphones based on Google's Android, in which application development is mainly based on Java programming language. Some of these CubeSats had actuators, e.g., STRaND-1 had three reaction wheels mounted in an orthogonal configuration to provide three-axis control, whereas PhoneSat 2.0 beta had magnetorquers to de-tumble the spacecraft. Taking into account a CubeSat that runs Android operating system (based on a smartphone), it is natural to evaluate the attitude and orbit control subsystem (AOCS) based on Java. Elsewhere, we shown State-Dependent Riccati Equation (SDRE) is a feasible non-linear control technique that can be applied in such CubeSats using Java. Moreover, we shown, through simulation using a Monte Carlo perturbation model, SDRE provides better performance than the PID controller, a linear control technique. In this paper, we tackle the next fundamental problem: stability. We evaluate stability from two perspectives: (1) parametric uncertainty of the inertia tensor and (2) a Monte Carlo perturbation model based on a uniform attitude probability distribution. Through the combination of these two perspectives, we grasp the stability properties of SDRE in a broader sense. In order to handle the uncertainty appropriately, we combine SDRE with H∞. The Nanosatellite Constellation for Environmental Data Collection (CONASAT), a CubeSat from the Brazilian National Institute for Space Research (INPE), provided the nominal parameters for the simulations. The initial results of the simulations shown that the SDRE controller is stable to ± 20% uncertainty in the inertia tensor for attitudes uniformly distributed and angular velocity up to 0.15 radians/second.