Chaotic attitude analysis of a satellite via Lyapunov exponents and its robust nonlinear control subject to disturbances and uncertainties

Abstract

This article investigates chaotic attitude maneuvers in a satellite for a range of parameters via Lyapunov exponents (LEs) and designs an appropriate robust nonlinear controller to ensure chaos suppression and achieve desired performance. Since the dynamic equations of satellite are described as a nonlinear nonautonomous system, an improved technique for calculating the LEs of such systems as a measure of chaos phenomenon is presented. Using the proposed algorithm, the chaotic behavior of satellite is proved within a range of its parameters. Then, by converting dynamic equations to canonical form, a robust nonlinear control is proposed using back-stepping sliding mode method. The stability of closed-loop system and its robustness against disturbances and uncertainties are guaranteed by proving a theorem. Moreover, by converting the system description into a compatible form with the conditions of the Melnikov theorem, an analytical approach is presented to ensure chaos suppression in the controlled system. Finally, the simulation results for different operational conditions of a three-axis stabilized satellite are provided to show the effectiveness of the proposed analyses and syntheses.

Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle

“…e extremal points of the Casimir function of the QUAV attitude system are determined by setting _ C � 0 in equation (20); the triaxle ellipsoid equation then becomes…”

“…Kuang et al [19] gave a chaotic analysis of the attitude of the satellite under small disturbances of its moments. Faramin and Ataei [20] analyzed the chaos of the satellite attitude via the Lyapunov exponents (LEs), designed a nonlinear robust control to suppress chaos, and confirmed its suppression using Melnikov's analysis. Generally, the Melnikov method affords the necessary conditions for the existence of chaotic motion [31][32][33][34].…”

“…Angles are evaluated and measured but do not necessarily undergo chaotic behavior if the angular velocities behave chaotically. According to the studies reported in [19][20][21], angular velocities usually display chaotic modes for a forceddissipative rigid body, the description of which is given by the Kolmogorov model. e literature studies concerning the dynamic analysis of the attitude of the QUAV are scant; therefore, we can refer to the research of many other physical forced-dissipative rigid or generalized rigid systems exhibiting chaotic motion under some parameter configurations or disturbances, for instance, the chaotic system of a brushless DC motor (BLDCM) [22] and the chaos and bifurcation of a permanent magnet synchronous motor (PMSM) [23].…”

Modeling of a Chaotic Gyrostat System and Mechanism Analysis of Dynamics Using Force and Energy

“…It is designed to analyze the changes in Casimir energy in the system trajectory [ Figure 4(c)], from which we may find the maxima and minima of the Casimir energy (32). The orbit of the chaotic attractor of system (4) intersects the hyperboloid with a change in Casimir energy [ Figure 4(c)].…”

“…The dynamics of different structural satellites, including the dual-spin satellite and the three-axis stabilized satellite, have received great attention in many studies. Based on the research of three-axis stabilized satellites [10,32], we present a gyrostat system with a three-axis rotor. Thus, a mathematical model of the gyrostat system with the three-axis stabilized satellites as background is developed and is transformed into a Kolmogorov model.…”