﻿ 基于输入成形的太阳能帆板自适应滑模控制<sup>*</sup>
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Adaptive sliding mode control of solar array with input shaping
ZHOU Tong, GUO Hong, XU Jinquan
School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2017-05-02; Accepted: 2017-08-01; Published online: 2017-09-25 10:01
Foundation item: Aeronautical Science Foundation of China (2016ZC51025)
Corresponding author. XU Jinquan, E-mail: xujinquan@buaa.edu.cn
Abstract: This paper proposes a control strategy which combines adaptive sliding mode control (ASMC) with input shaping technology for the solar array drive system (SADS) to improve the angular position control performance and suppress the flexible vibration. To improve the angular position control performance, ASMC is introduced, which is able to guarantee the uniform boundedness and uniform ultimate boundedness, regardless of the uncertainty. The command trajectory is planned by the input shaper (IS) based on the reference model, which suppresses the flexible vibration of solar array. The simulation results verify the validity of the proposed control strategy.
Key words: input shaping     adaptive sliding mode control (ASMC)     solar array     drive system     flexible vibration

1 太阳能帆板驱动系统数学建模

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 图 1 太阳能帆板驱动系统结构 Fig. 1 Structure of SADS

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2 控制系统设计

 图 2 基于本文控制策略的太阳能帆板驱动系统控制结构 Fig. 2 Control structure of SADS based on proposed control strategy

2.1 参考模型设计

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2.2 输入成形器设计

 图 3 输入成形器原理图 Fig. 3 Schematic diagram of IS

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2.3 自适应滑模控制设计

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1) 一致有界：对于任意τ > 0，存在z(τ) < ∞，使得当‖σ(t0)‖≤τ时，对于任意tt0，‖σ(t)‖≤z(τ)。

2) 渐进一致有界：对于任意τ > 0，‖σ(t0)‖≤τ，存在z > 0，使得对于任意z > z，当tt0+T(z, τ)，且T(z, τ) < ∞时，‖σ(t)‖≤z

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3 仿真结果

 参数 数值 定子电阻/Ω 28 定子电感/H 0.134 极对数 12 转矩常数/(N·m·A-1) 9.22 额定电流/A 1.4 额定功率/W 22 传动比 325 最大静摩擦力矩/(N·m) 404.54 第一阶模态耦合系数 188.7 第二阶模态耦合系数 30.1 第一阶模态阻尼比 0.01 第二阶模态阻尼比 0.01 第一阶模态角频率/(rad·s-1) 1.789 第二阶模态角频率/(rad·s-1) 11.21 转动惯量/(kg·m2) 1.7×106 滑动摩擦力矩/(N·m) 324.31

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 控制器 参数 数值 PID控制 比例系数(位置环) 0.075 积分系数(位置环) 0.000 8 微分系数(位置环) 2 比例系数(速度环) 33.3 积分系数(速度环) 0.1 微分系数(速度环) 0 比例系数(电流环) 500 积分系数(电流环) 6 000 微分系数(电流环) 0 ASMC KP 1 530 KD 89 760 k 3 κ 150 χ 3 IS A1 0.26 A2 0.25 A3 0.25 A4 0.24 t1/s 0 t2/s 0.28 t3/s 1.76 t4/s 2.03

 图 4 随机干扰力矩波形 Fig. 4 Random disturbance torque waveform

 图 5 角位置响应波形图及其局部放大图 Fig. 5 Oscillogram of time response of angular position and its partial enlarged views

 图 6 角速度响应波形图 Fig. 6 Oscillogram of time response of angular velocity

 图 7 振动能量波形图 Fig. 7 Oscillogram of vibration energy

 图 8 驱动力矩波形图 Fig. 8 Oscillogram of driving torque

4 结论

1) 为提高太阳能帆板驱动系统的角位置控制性能和抑制太阳能帆板的柔性振动，本文提出了一种自适应滑模控制与输入成形技术相结合的控制策略。

2) 理论分析表明，本文控制策略可以保证系统在不确定性影响下的一致有界性和渐进一致有界性。

3) 仿真结果表明，相比于PID控制，本文所提出的控制策略ASMC+IS在调节时间、超调量和跟踪误差方面具有更好的性能，并且降低了振动能量，有效抑制了柔性振动；相比于ASMC，ASMC+IS同样有效降低了振动能量，而其他性能基本相同。因此，ASMC+IS能在保证系统角位置控制性能的同时抑制太阳能帆板的柔性振动。

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#### 文章信息

ZHOU Tong, GUO Hong, XU Jinquan

Adaptive sliding mode control of solar array with input shaping

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(4): 737-745
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0276