H∞ State Feedback Controller Design for Flexible Spacecraft

doi:10.3969/j.issn.1009-086x.2024.02.009

Abstract

Abstract:

When flexible spacecraft operates， disturbances such as the swaying of liquid fuel and gravity gradients cause the spacecraft system to exhibit strong nonlinearity and coupling characteristics. Thus， controlling its attitude deflection has always been a challenging problem. To solve this issue， this paper designs a H_∞ state feedback controller. The integrated disturbance term in the dynamic model of the flexible spacecraft is redefined， and combined with the kinematic model， the mathematical expression of the flexible spacecraft is formulated. The mathematical model of the flexible spacecraft is transformed into an $H ∞$ state feedback control mathematical model. The theoretical applicability of the controller is demonstrated by mathematical theory. The mathematical model of the flexible spacecraft under $H ∞$ state feedback control is simulated by simulation software. The results show that the designed $H ∞$ state feedback controller can effectively achieve attitude stabilization and vibration suppression of flexible spacecraft， showing practical value.

Key words: flexible spacecraft, H_∞ control, mathematical model, state feedback, attitude control

摘要：

当柔性航天器工作时，由于液体燃料的晃动与重力梯度等外界环境干扰，导致航天器系统出现强非线性以及强耦合性等特点，因此如何控制其姿态偏转一直是极具难点的问题。为了解决此问题,设计了一种 $H ∞$ 状态反馈控制器，重新定义了柔性航天器的动力学模型中的综合扰动项，结合运动学模型描绘了柔性航天器的数学模型表达式。将柔性航天器的数学模型改写成了 $H ∞$ 状态反馈控制数学模型。使用数学理论验证了控制器理论可用性，通过仿真软件对处于 $H ∞$ 状态反馈控制律下的柔性航天器数学模型进行仿真。结果表明，设计的 $H ∞$ 状态反馈控制器可以有效地实现柔性航天器的姿态稳定，振动抑制，具有实际价值。

关键词: 柔性航天器, H_∞控制, 数学模型, 状态反馈, 姿态控制

CLC Number:

V448.2

Xinhua ZHAO, Kang WANG, Changsheng GAO. H_∞ State Feedback Controller Design for Flexible Spacecraft[J]. Modern Defense Technology, 2024, 52(2): 79-86.

赵新华, 汪康, 高长生. 柔性航天器的H_∞状态反馈控制器设计[J]. 现代防御技术, 2024, 52(2): 79-86.

Figures/Tables 10

Table 1 Flexible dynamics parameters

模态	频率	阻尼比
1阶	0.756 81	0.005 607
2阶	1.103 8	0.008 620
3阶	1.873 3	0.012 830
4阶	2.549 6	0.025 160

Fig. 1 Block diagram of H∞ state feedback control

Fig. 2 Variation curves of attitude angular velocity

Fig. 3 Variation curves of attitude angle

Fig. 4 Variation curves of vibration modal

Fig. 5 Variation curve of modal velocity

Fig. 6 Variation curves of control torque

Fig. 7 Comparison of attitude angle metrics

Fig. 8 Comparison of attitude angular velocity metrics

Fig. 9 Comparison of vibration modes

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