Adaptive boundary control and vibration suppression of a flexible satellite system with input saturation

Abstract

In this paper, the vibration suppression problem of a flexible satellite system is addressed. The dynamic model of the flexible satellite system is expressed by a set of non-homogeneous partial differential equations (PDEs). By using the theory of systems with uniform ultimate bounded (UUB) solutions and adaptive techniques, adaptive boundary control is presented to suppress the vibration of the flexible satellite with parametric uncertainties. A disturbance adaptive law is constructed to compensate for the effect of the boundary disturbance, and an auxiliary system is considered to mitigate the effect of input saturation. The well-posedness of the closed-loop system is discussed, and UUB stability can be ensured through a rigorous Lyapunov-like analysis. Numerical simulation results show the effectiveness of the proposed control scheme.

Observer-based multi-objective parametric design for spacecraft with super flexible netted antennas

“…(1) Different from many existing control methods that is proposed for a single objective (e.g., [2][3][4][5][6][7][8], [11][12][13][14][15][16][17][18][19][20][21]), this paper considers multi-objective design issues, and it aims to make the closed-loop system have simultaneously lower eigenvalue sensitivity, and also it aims a smaller control gain and a stronger tolerance for high-order unmodeled dynamics and disturbances.…”

“…For example, in 1958 the satellite named "Explorer-1" caused the energy dissipation in the system owing to the flexible vibration of the four whip antennas that eventually led to the attitude roll [1]. Therefore, vibration suppression and attitude control of spacecraft with large flexible attachments is a critical problem and it has received lots of attention [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Sliding mode control (SMC) and backstepping control are commonly used control methods in order to solve this problem.…”

“…The problems of robust H ∞ controller design with input constraints are considered in [11,12]. In addition to SMC, backstepping, and robust H ∞ control, many other control methods are also applied to the vibration suppression and attitude control of flexible satellites, such as disturbance observer-based control [13][14][15], adaptive control [16][17][18][19][20], and finite-time control [16,18,21]. Many of the current control methods are proposed for a single control target (e.g., [2][3][4][5][6][7][8][11][12][13][14][15][16][17][18][19][20][21]) to provide flexible spacecraft control.…”

General Planar Motion Modeling and Control of a Smart Rigid-Flexible Satellite Considering Large Deformations

“… Investigation of the vibrations of flexible appendages [1,2].  Investigation of the attitude maneuver of the satellite along with vibrations of its flexible appendages [3,4].…”

“…In order to design a controller for flexible satellites, two approaches can be taken: (i) controller design based on the coupled ordinary-partial differential equations (ODE_PDEs) of motion [1][2][3][4]7] or (ii) controller design based on the coupled ordinary differential equations (ODEs) of motion [5,6]. Of course, ODEs of motion can be obtained directly (e.g., the Rayleigh-Ritz method) or ODE-PDEs can be obtained first and then they can be discretized and converted to a set of ODEs (e.g., the Galerkin method) [16].…”