Adaptive Fuzzy Sliding Mode Control for the Probe Soft Landing on the Asteroids with Weak Gravitational Field

Mathematical Problems in Engineering, May 2015

For the trajectory control of the probe soft landing on the asteroids with weak gravitational field, this paper presents a combined integral sliding mode control with an adaptive fuzzy logic system, named adaptive fuzzy sliding mode control (AFSMC) scheme. Considering the uncertainty of the orbit dynamics model in the small body fixed coordinate system, and the polyhedron modeling uncertainty in the gravitational potential, a fuzzy logic system is adopted to approximate the upper bound of the uncertainties. In addition, a robust control item is introduced to compensate for the approximation error of fuzzy logic system. The designed adaptive law and robust item make the closed-loop control stable and the tracking errors are convergent to zero. The controller not only guarantees the rapidity and accuracy of the desired trajectory tracking, but also enhances the robustness of the control system, improving the dynamic tracking performance for the probe soft landing on asteroids. Finally, the contrastive simulation results are presented to show the feasibility and effectiveness of the proposed control scheme.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

http://downloads.hindawi.com/journals/mpe/2015/582948.pdf

Adaptive Fuzzy Sliding Mode Control for the Probe Soft Landing on the Asteroids with Weak Gravitational Field

Adaptive Fuzzy Sliding Mode Control for the Probe Soft Landing on the Asteroids with Weak Gravitational Field Yuanchun Li,1 He Wang,1 Bo Zhao,2 and Keping Liu1 1Department of Control Engineering, Changchun University of Technology, Changchun 130012, China 2State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China Received 27 January 2015; Revised 7 May 2015; Accepted 7 May 2015 Academic Editor: Francesco Franco Copyright © 2015 Yuanchun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract For the trajectory control of the probe soft landing on the asteroids with weak gravitational field, this paper presents a combined integral sliding mode control with an adaptive fuzzy logic system, named adaptive fuzzy sliding mode control (AFSMC) scheme. Considering the uncertainty of the orbit dynamics model in the small body fixed coordinate system, and the polyhedron modeling uncertainty in the gravitational potential, a fuzzy logic system is adopted to approximate the upper bound of the uncertainties. In addition, a robust control item is introduced to compensate for the approximation error of fuzzy logic system. The designed adaptive law and robust item make the closed-loop control stable and the tracking errors are convergent to zero. The controller not only guarantees the rapidity and accuracy of the desired trajectory tracking, but also enhances the robustness of the control system, improving the dynamic tracking performance for the probe soft landing on asteroids. Finally, the contrastive simulation results are presented to show the feasibility and effectiveness of the proposed control scheme. 1. Introduction Soft landing on asteroids is one of the most complex tasks in deep space exploration. In the process of soft landing, the probe should not only achieve the most superior performance of the fuel in the decline stage, but also ensure the accuracy of soft landing. In order to guarantee the probe lands on asteroids safely and successfully, it is necessary to control and adjust the trajectory and velocity of the probe in real time. Many scholars domestically and overseas have done a lot of researches specific to the trajectory control for the probe soft landing, which is the most important link to achieve the exploration tasks successfully. Yang et al. [1] proposed a fuzzy sliding mode control scheme for the probe to achieve the soft landing according to the nominal trajectory by the means of utilizing fuzzy rules to adjust the sliding control gain as well as adopting adaptive law to compensate for the system uncertainty. Aimed at the declining and landing control of the probe, Cui et al. [2] decomposed the landing control into the velocity control and deceleration control and then designed a proportional guidance law with a terminal condition and a deceleration control law. Liu et al. [3] presented a continuous control scheme based on PD and nonsingular terminal sliding mode for the probe descending and safe landing. However, in the simulations of the methods mentioned above, the sine or cosine functions with the same frequency were taken as the uncertainty and disturbance, whose demonstrated results cannot verify the effectiveness of these strategies when the uncertainty and disturbance were in the form of different frequency and complex signal. Taking this problem into account, Cui et al. [4] developed a soft landing autonomous impulse maneuver control method to deal with the parameter uncertainty of the weak gravitational field of small body, and the robustness of the landing control was greatly improved. Zhang et al. [5] proposed a probe autonomous navigation strategy to achieve the fast tracking by adopting a sliding mode variable structure control method. Carson et al. [6] utilized a robust sliding mode predictive control for the trajectory tracking of the small body proximity operations. Many of these methods considered the uncertainty and disturbance; however, the strict stability proofs were not given in detail theoretically; thus they were not enough and impractical for real applications [7, 8]. Due to the strong robustness and autonomy to the model uncertainty and the disturbance, fuzzy sliding mode control has been employed widely in the fields such as robot, spacecraft attitude control. Liu and Sun [9] designed an adaptive fuzzy terminal sliding mode control for second-order nonlinear system to guarantee the output error convergence to zero in finite time. Nekoukar and Erfanian [10] combined the continuous nonsingular terminal sliding mode with the adaptive learning algorithm and the fuzzy logic system to estimate the uncertain MIMO nonlinear system model and guaranteed the closed-loop system stability. Boubakir et al. [11] pr (...truncated)


This is a preview of a remote PDF: http://downloads.hindawi.com/journals/mpe/2015/582948.pdf

Yuanchun Li, He Wang, Bo Zhao, Keping Liu. Adaptive Fuzzy Sliding Mode Control for the Probe Soft Landing on the Asteroids with Weak Gravitational Field, Mathematical Problems in Engineering, 2015, 2015, DOI: 10.1155/2015/582948