﻿ 基于非线性模型预测的绳系系统系绳摆振控制<sup>*</sup>
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Tether swing control of tethered system based on nonlinear model prediction
ZHANG Yujing, ZHONG Rui
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2018-01-02; Accepted: 2018-03-30; Published online: 2018-04-18 15:51
Foundation item: National Natural Science Foundation of China (11402009)
Corresponding author. ZHONG Rui, E-mail:zhongruia@163.com
Abstract: On the stability control of the rope system, a stability control method of tether swing for tethered system consisting of tether and tethered satellites during deorbitting is proposed in this paper. In this paper, a model of motion including satellite attitude motion is eatablished, and the dynamic equation of deorbit tethered system and the simplified equation that is convenient for controller design are proposed. According to the model prediction theory, the reference trajectory is designed by the optimization method, and then the stable tether swing nonlinear model predictive control method is designed based on the model predictive control method in this paper. Then, the feasibility of the designed controller and the reference trajectory are verified by the simulation of MATLAB software platform.
Keywords: tethered system     swing control     dynamics     orbit transfer     model predictive control

1 绳系系统动力学建模 1.1 建模假设和坐标系定义

 图 1 绳系系统坐标系示意图 Fig. 1 Schematic of coordinate system of tethered system
1.2 简化动力学方程

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2 基于最优化求参考轨迹

2.1 性能函数选取

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2.2 控制约束

1) 始末约束

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2) 过程约束

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3) 时间约束

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4) 推力约束

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2.3 最优问题求解

3 基于非线性模型预测控制律设计 3.1 模型离散化

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3.2 性能函数选取

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3.3 主星姿态和系绳摆角的预测

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3.4 控制约束

1) 始末约束

2) 过程约束

3) 推力约束

3.5 非线性模型预测控制律实现

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4 基于非线性模型预测控制方法仿真验证

 参数 数值 主星发动机推力/N 100 主星质量/kg 100 主星惯量/(kg·m2) 166.67 拖拽目标质量/kg 8 系绳未拉伸长度/m 200

 图 2 系绳面内摆角、系绳面内摆角速度、主星俯仰角、主星俯仰角速度和绳速的实际路径和最优路径 Fig. 2 Actual path and optimal path of tether's in-plane swing angle, tether's in-plane swing angular velocity, main satellite pitching angle, main satellite pitching angular velocity and tether speed
 图 3 系绳面内摆角、系绳面内摆角速度、主星俯仰角、主星俯仰角速度和绳速的跟踪路径和最优路径 Fig. 3 Tracking path and optimal path of tether's in-plane swing angle, tether's in-plane swing angular velocity, main satellite pitching angle, main satellite pitching angular velocity and tether speed

5 结论

1) 考虑主星姿态、系绳摆角稳定、系绳张力为正、系绳长度变化有限等约束，针对绳系系统拖拽离轨推力作用过程中系绳摆振的抑制问题，进行系统状态的最优轨迹求解，最优轨迹在满足变轨速度增量要求的同时实现了推力时间最短。

2) 仿真结果表明，所设计的非线性模型预测控制方法很好地跟踪了最优轨迹，并且满足控制约束条件；在变轨推力作用下主星姿态和系绳摆动稳定，且动态过程平滑。

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#### 文章信息

ZHANG Yujing, ZHONG Rui

Tether swing control of tethered system based on nonlinear model prediction

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(10): 2200-2207
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0810