Simple Nonlinear Proportional-Derivative Control for Global Finite-Time Stabilization of Spacecraft

Abstract

S TABILIZATION of a rigid body has attracted a considerable amount of interest in the control of rigid spacecraft and aircraft. Several control techniques that stabilize the arbitrary attitude motion of a spacecraft can be found in the literature. For example, Egeland and Godhavn [1] established the passivity between the angular velocity vector and the Euler parameter vector, and they proposed an adaptive stabilization control. Lizarralde and Wen [2] developed velocity-free controllers. The results in [1,2] were later extended by Tsiotras [3]. The attitude stabilization of a rigid body, using the unit quaternion and the angular velocity in the feedback control law, has been investigated by many researchers (see, for instance, [4–6]). Due to its inherent robustness with respect to external disturbances and uncertainties, various optimal attitude stabilization control schemes have been proposed [7,8]. The efforts that stabilize the spacecraft with actuator constraints can be found in [9–13] and the references within. For progress on stabilization of rigid spacecraft under other varieties of actuator constraints, such as underactuation or control singularity, see [14–16] and the references therein. The aforementioned works achieved asymptotic stability, implying that the system trajectories converge to the origin as time goes to infinity. It is known that finite-time stabilization of dynamical systemsmay give rise to fast transient, high-precision, and robustness performances besides finite-time convergence [17–20]. Recognizing these advantages, several finite-time stabilization control schemes for rigid spacecraft have been proposed. In particular, Zhu et al. [21] exploited the advantages of sliding-mode control and the adaptive method, and they proposed a robust attitude stabilization control with finite-time convergence. Li et al. [22] developed a continuous finitetime attitude control law. Recently, Du and Li [23] constructed a globally saturated finite-time stabilizing controller. The aforementioned controls are developed based on the quaternion description of spacecraft. Ding and Li [24] designed a finite-time stabilizing controller by combining the terminal sliding-mode control and adding a power integrator, in terms of the Rodrigues parameters. This Note presents an improved design for global finite-time stabilization of spacecraft. Specifically, two very simple finite-time proportional-derivative (FPD) controllers are proposed. The contribution of this Note is twofold. Compared with the work presented in [3], the proposed controls ensure global finite-time stabilization featuring fast transient and high-precision performances. In comparison with the finite-time control [24], the proposed controllers do not refer to the modeling parameter and are much simpler and more intuitive; thus, they are readily implemented. It is proven that spacecraft can be globally finite-time stabilized via the proposed FPD controls in agreementwithLyapunov’s stability theory and geometric homogeneity technique. Simulations are presented to demonstrate the effectiveness and improved performances of the proposed approach.