基于LMI的滑模控制在航空发动机中的应用

J4 ›› 2014, Vol. 36 ›› Issue (06): 1198-1203.

基于LMI的滑模控制在航空发动机中的应用

黄辉先，李燕，庄选，任科明

（湘潭大学信息工程学院，湖南湘潭 411105）

收稿日期:2013-01-14 修回日期:2013-04-27 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
国家部委预先研究基金资助项目（2011846）

Application of sliding mode control
in aero-engine based on LMI

HUANG Huixian，LI Yan，ZHUANG Xuan，REN Keming

(School of Information Engineering,Xiangtan University,Xiangtan 411105,China)

Received:2013-01-14 Revised:2013-04-27 Online:2014-06-25 Published:2014-06-25

摘要/Abstract

摘要：

针对航空发动机运行过程中存在不确定性和稳定性问题，运用状态空间模型理论与线性矩阵不等式LMI相结合的方法设计了控制器，改善了航空发动机的控制性能。以某型涡扇发动机为控制对象，基于LMI对普通终端滑模变结构控制进行了优化设计，在滑模超平面设计中引入了动态补偿器，采用改进的幂次趋近律，对该动态系统进行了性能仿真验证。结果表明，本文提出的方法较之普通终端滑模变结构控制对系统性能有较大改善，不仅使系统主供油量变化率、尾喷口面积变化率等的控制更为平稳，且保证了系统鲁棒性和稳定性。

关键词: 线性矩阵不等式, 航空发动机, 终端滑模控制, 动态补偿器

Abstract:

A new method,combined with the statespace model theory and the linear matrix inequality (LMI), is applied to design a controller to improve the control performance of the aeroengine for the sake of studying its uncertainty and instability during the actual operation. Taking the turbojet engine model as the control object, a dynamic compensator is introduced to improve the performance of aero-engine system through the optimal design of the terminal sliding mode control on the basis of the LMI. Furthermore, the improved power rate reaching law is used to validate the performance simulation of the dynamic system. It is shown that the proposed method not only smoothes the variance ratio of fuel and nozzle outlet area, but also holds the stable and robustness of the system. Our results based on LMI are better than the general terminal sliding mode control for the aero-engine.

Key words: linear matrix inequality;aero-engine;terminal sliding mode control;dynamic compensator

黄辉先，李燕，庄选，任科明. 基于LMI的滑模控制在航空发动机中的应用[J]. J4, 2014, 36(06): 1198-1203.

HUANG Huixian，LI Yan，ZHUANG Xuan，REN Keming. Application of sliding mode control
in aero-engine based on LMI [J]. J4, 2014, 36(06): 1198-1203.

参考文献

［1］Miao Zhuoguang, Xie Shousheng, Wu Yong,et al. Aeroengine state variable modeling based on the improved particle swarm optimization［J］. Journal of Propulsion Technology, 2012,33(1):7377.(in Chinese)
［2］Liu Ke,Ma Jing,Lu Peng.Robustness of adaptive backstepping control for aeroengine［J］. Science Technology and Engineering, 2012,12(1):102105.(in Chinese)
［3］Peng Jingbo, Xie Shousheng, Hu Jinhai. Improved genetic algorithm and application in a digital PID controller of turbofan engine［J］. Gas Turbine Experiment and Research, 2008,21(1):4750.(in Chinese)
［4］Li Shuqing, Zhan Jimin, Li Ming, et al. Robust PID design for turbofan engine［J］. Computer Simulation,2011,28(3):106109.(in Chinese)
［5］Liu Jinkun. MATLAB simulation for sliding mode control［M］. Beijing: Tsinghua University Press, 2005.(in Chinese)
［6］Liu Jinkun,Sun Fuchun.Research and development on theory and algorithms of sliding mode control［J］. Control Theory & Applications, 2007, 24(3):407418.(in Chinese)
［7］Yu Li. Robust controlLMI approach［M］. Beijing: Tsinghua University Press, 2002.(in Chinese)
［8］Gao Weibing. Theory and design method of variable structure control［M］. Beijing: Science Press, 1996.(in Chinese)
［9］Wang Hua, Han Zhengzhi, Xie Qiyue,et al. Sliding mode control for chaotic systems based on LMI［J］. Communications in Nonlinear Science and Numerical Simulation, 2009,14(4):14101417.
［10］Li Wenlin,Wang Hua.Robust slidingmode control for uncertain timedelay systems［J］. Dyn Contin Discr Impuls SystSer AMath Anal I, 2006,Part 1, Suppl(13):121125.
［11］Yao Yuxiang.Variable structure terminal sliding mode control’s application on aeroengine［D］.Xi’an:Northwestern Polytechnical University,2004.(in Chinese)
［12］Xue Dingyu. Computer aided control systems design using MATLAB language［M］. Beijing: Tsinghua University Press, 2011.(in Chinese)
附中文参考文献：
［1］苗卓广，谢寿生，吴勇,等. 基于改进粒子群算法的航空发动机状态变量建模［J］. 推进技术，2012, 33(1):7377.
［2］刘可，马静，鲁鹏. 航空发动机鲁棒自适应反演控制［J］.科学技术与工程，2012, 12(1):102105.
［3］彭靖波，谢寿生，胡金海. 基于遗传算法的某型涡扇发动机数字PID控制器设计［J］. 燃气涡轮试验与研究,2008,21(1):4750.
［4］李述清，詹济民，李明，等. 鲁棒PID设计在涡扇发动机中的应用［J］. 计算机仿真,2011, 28(3):106109.
［5］刘金琨.滑模变结构控制MATLAB仿真［M］. 北京:清华大学出版社，2005.
［6］刘金琨，孙富春. 滑模变结构控制理论及其算法研究与进展［J］. 控制理论与应用,2007, 24(3):407418.
［7］俞立. 鲁棒控制线性矩阵不等式的处理方法［M］. 北京:清华大学出版社,2002.
［8］高为炳. 变结构控制的理论及设计方法［M］. 北京:科学出版社, 1996.
［11］姚玉香. 变结构最终滑动模态控制在航空发动机中的应用研究［D］.西安：西北工业大学,2004.
［12］薛定宇. 控制系统计算机辅助设计——MATLAB语言及应用［M］.北京：清华大学出版社,2011.

[1]	惠俊军1,2，张合新1，孟飞1，张金生1，周鑫1. 具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据[J]. J4, 2014, 36(10): 2034-2040.
[2]	陈黎，武兆斌，王中许. 光电跟踪系统临界探测概率研究[J]. J4, 2012, 34(7): 182-189.
[3]	齐迹. 随机不确定网络控制系统的L2-L∞输出跟踪控制[J]. J4, 2011, 33(12): 22-26.
[4]	徐勇[1,2] 石陆魁[3] 李杰[4] 唐万生[1] 张建雄[1]. 基于S-Procedure的分段线性Delta算子系统的稳定性分析[J]. J4, 2008, 30(10): 98-99.
[5]	曾铭涛桂卫华唐朝晖. 一类变时滞中立型系统的全局指数稳定性研究[J]. J4, 2005, 27(10): 77-80.