火箭发动机燃烧过程的鲁棒非脆弱<i>H</i><sub>∞</sub>控制

吴玉彬; 张合新; 朱开锐; 李国梁; 惠俊军

doi:10.11883/bzycj-2017-0231

火箭发动机燃烧过程的鲁棒非脆弱H_∞控制

doi: 10.11883/bzycj-2017-0231

1.
火箭军工程大学控制工程系，陕西西安 710025
2.
中国人民解放军陆军重庆军代局，重庆 400060
3.
中国人民解放军96037部队，陕西宝鸡 721013

基金项目: 国家自然科学基金（61374120）

详细信息

作者简介:
吴玉彬（1984－　），男，博士，工程师， wuyubinxa@126.com

通讯作者:
张合新（1965－　），男，博士，教授，博导，59153220@qq.com

中图分类号: O381; TP13
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- 被引次数: 0
出版历程
- 收稿日期: 2017-06-30
- 修回日期: 2017-09-08
- 网络出版日期: 2019-03-25
- 刊出日期: 2019-03-01

The robust non-fragile H_∞ control for the combustion process in rocket motor

1.
Department of Control and Engineering, Rocket Force University of Engineering, Xi’an 710025, Shaanxi, China
2.
Chongqing Military Agency of the Army, Chongqing 400060, China
3.
Chinese People’s Liberation Army 96037, Baoji 721013, Shaanxi, China

摘要

摘要: 针对某液体火箭发动机燃烧室的燃烧过程,设计了鲁棒非脆弱 H_∞ 状态反馈控制器。首先，基于一种新型的时滞分割法和交互式凸组合技术，借助于构造一个包含四重积分项的Lyapunov-Krasovskii泛函(LKF)，并利用新的积分不等式方法给出了LMI形式的时滞相关有界实判据；其次，在有界实判据的基础上，采用矩阵的合同变换以及变量替代技巧将燃烧过程非线性矩阵不等式线性化，通过求解线性矩阵不等式得到相应的非脆弱H_∞控制器的可行解。模拟结果验证了本文设计方法的有效性。
- 非脆弱 /
- 交互式凸组合技术 /
- Lyapunov-Krasovskii泛函(LKF) /
- 火箭发动机 /
- 四重积分
Abstract: In this study we dealt with the robust non-fragile H_∞ controller for the combustion process in liquid propellant rocket motor chambers. In developing a less conservative H_∞ performance analysis criterion, we introduced a Lyapunov-Krasovskii functional comprising quadruple-integral term. Then, based on a new delay-partitioning method, the reciprocally convex combination technique and the integral inequality approach (IIA), we formulated the bounded real criterion in terms of linear matrix inequalities (LMIs). Furthermore, based on this bounded real criterion, we translated the nonlinear matrix inequality into the linear matrix inequality by using the matrix congruent transformation and the variable substitution technique, and obtained the parameter expression of non-fragile H_∞ controller by solving the feasible linear matrix inequality. The numerical examples we provided showed the effectiveness of the proposed theoretical results.
- non-fragile /
- reciprocally convex combination /
- Lyapunov-Krasovskii functional (LKF) /
- rocket motors /
- quadruple-integral term

HTML全文

图 1 燃烧室燃烧过程的自由运动曲线

Figure 1. Free motion of combustion in chambers

下载: 全尺寸图片幻灯片

图 2 非脆弱H_∞控制器作用下系统的状态响应

Figure 2. Response of system under non-fragile H_∞ controller

下载: 全尺寸图片幻灯片

图 3 不同控制器作用下系统状态${x_2}(t)$的响应

Figure 3. Response of ${x_2}(t)$ under different controller

下载: 全尺寸图片幻灯片

图 4 控制器对时滞参数$\delta $的鲁棒性

Figure 4. Robust performance of controller to variation of $\delta $

下载: 全尺寸图片幻灯片

表 1 不同的H_{${_\infty }$}性能指标ρ，模拟给出的MADB值h_M

Table 1. The maximum allowable delay bound h_M for a given ρ

来源	h_M
来源	ρ=2.0	ρ=2.5	ρ=3.0	ρ=3.5	ρ=4.0
文献[16]	0.405 7	0.466 0	0.504 7	0.531 6	0.551 5
文献[17]	0.405 7	0.466 0	0.504 6	0.531 6	0.551 5
文献[18]	0.420 3	0.477 9	0.514 6	0.540 1	0.558 9
文献[4]	0.473 4	0.523 7	0.554 5	0.575 4	0.590 4
文献[19]	0.662 0	0.704 0	0.730 0	0.747 0	0.759 5
定理1	0.957 1	1.013 6	1.056 5	1.081 2	1.092 7

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表 2 不同的MADB值h_M，仿真给出的MAPI值ρ

Table 2. The minimum allowable performance index ρ for a given h_M

来源			ρ
来源	h_M=0.1	h_M=0.2	h_M=0.3	h_M=0.4	h_M=0.5
文献[16]	1.071 4	1.242 6	1.506 7	1.963 4	2.298 1
文献[17]	1.071 4	1.242 5	1.506 7	1.963 4	2.298 1
文献[18]	1.057 7	1.211 2	1.451 5	1.873 3	2.775 7
文献[19]	0.933 1	0.952 5	1.021 6	1.120 4	1.284 3
定理1	0.815 6	0.853 2	0.924 5	1.042 8	1.123 9

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