基于多项式平方和规划的航空发动机鲁棒LPV/PI控制

吴斌; 黄金泉; 姜锐

doi:10.13224/j.cnki.jasp.2016.03.022

基于多项式平方和规划的航空发动机鲁棒LPV/PI控制

doi: 10.13224/j.cnki.jasp.2016.03.022

吴斌^1,3,
黄金泉^1,2,
姜锐¹

1. 南京航空航天大学能源与动力学院江苏省航空动力系统重点实验室, 南京 210016;
2. 先进航空发动机协同创新中心, 北京 100191;
3. 中国航空工业集团公司航空动力控制系统研究所, 江苏无锡 214063

基金项目:

江苏省普通高校研究生科研创新计划(CXZZ12_0166)

江苏省航空动力系统重点实验室开放课题(NJ20130029)

中央高校基本科研业务费专项资金(NP2012504)

详细信息

作者简介:
吴斌(1985-),男,江苏大丰人,博士生,主要从事航空发动机控制研究.

中图分类号: V233.7
计量
- 文章访问数: 939
- HTML浏览量: 3
- PDF量: 423
- 被引次数: 0
出版历程
- 收稿日期: 2014-07-06
- 刊出日期: 2016-03-28

Robust LPV/PI control for aero-engine based on polynomial sum of squares programming

1. Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Collaborative Innovation Center for Advanced Aero-engine, Beijing 100191, China;
3. Aviation Motor Control System Institute, Aviation Industry Corporation of China, Wuxi Jiangsu 214063, China

摘要

摘要: 针对航空发动机常规(proportion integration,PI)控制器设计过程中难以保证鲁棒性及参数适应性差等问题,提出了一种基于线性变参数(linear parameter varying,LPV)模型及多项式平方和(sum of squares,SOS)规划的控制器设计方法.结合传递函数模型下的鲁棒稳定条件及弱对偶定理给出了多项式描述的LPV模型鲁棒稳定条件,并转化为便于求解的SOS规划问题.根据发动机非线性模型获取不同转速下的传递函数模型,并利用多项式拟合的方法建立发动机LPV模型.根据所提出的定理构造出SOS规划问题,并求解得出LPV/PI控制器.最终以某型双轴涡扇发动机为被控对象,在包线内不同点进行了阶跃仿真,结果表明:高压转子转速控制系统的稳态误差为0,调节时间小于3s.
- 航空发动机 /
- LPV模型 /
- 平方和(SOS)规划 /
- 鲁棒控制 /
- 多项式 /
- PI控制
Abstract: A controller design method based on the model and polynomial sum of squares(SOS) programming was put forward for the conventional PI controller of aero-engine featuring poor adaptability and difficulty to guarantee robustness. Combining the robust stability conditions of transfer function model and the weak duality theorem, the robust stability conditions of linear parameter varying(LPV) model depicted by polynomial were proposed. Using the frequency response method, a family of transfer function models was obtained from non-linear model. And then these transfer functions were used to get LPV model by polynomial fitting method. With the proposed theorem and the LPV model, the controller design problem could be transformed into SOS programming problem, which was solved to obtain the linear parameter varying/proportion integration(LPV/PI) controller. Finally the controller was applied to a turbofan engine model. And step simulation results show that the settling time of this high pressure rotor speed control system is less than 3 seconds, and the steady state error is zero.
- aero-engine /
- linear parameter varying model /
- sum of squares programming /
- robust control /
- polynomial /
- proportion integration control

HTML

参考文献(23)

[1]	黄金泉,仇小杰,鲁峰,等.航空发动机性能恢复控制方法[J].航空动力学报,2012,27(7):1595-1604. HUANG Jinquan,QIU Xiaojie,LU Feng,et al.Per-formance recovery control method for aircraft engine[J].Journal of Aerospace Power,2012,27(7):1595-1604.(in Chinese)
[2]	樊思齐,李华聪,樊丁,等.航空发动机控制:下册[M].西安:西北工业大学出版社,2008.
[3]	王曦,林永霖,吴永康.H_∞控制在飞行/推进综合控制系统中的应用[J].航空动力学报,2004,19(5):695-702. WANG Xi,LIN Yonglin,WU Yongkang.H_∞ control applied in integrated flight and propulsion control systems[J].Journal of Aerospace Power,2004,19(5):695-702.(in Chinese)
[4]	吴君凤,郭迎清.发动机稳态与过渡态控制集成设计仿真验证[J].航空动力学报,2013,28(6):1436-1440. WU Junfeng,GUO Yingqing.Design and simulation of aero-engine steady-state and transient-state control integration[J].Journal of Aerospace Power,2013,28(6):1436-1440.(in Chinese)
[5]	Lu B,Wu F,Kim S W.Switching LPV control for high performance tactical aircraft[R].AIAA-2010-7903,2010.
[6]	LI Shuqing,ZHANG Shengxiu.A modified LPV modeling technique for turbofan engine control system[R].Taiyuan:International Conference on Computer Application and System Modeling(ICCASM),2010.
[7]	Giarre L,Bauso D,Falugi P,et al.LPV model identification for gain scheduling control:an application to rotating stall and surge control[J].Control Engineering Practice,2006,14(4):351-361.
[8]	Wu F,Packard A,Gary B.Systemmatic gain-scheduling control design:a missile autopilot example[J].Asian Journal of Control,2002,4(3):341-347.
[9]	Jean B L.Global optimization with polynomials and the problem of moments[J].Society for Industrial and Applied Mathematics,2001,11(3):796-817.
[10]	Scherer C W.LMI relaxation in robust control[J].European Journal of Control,2006,12(1):3-29.
[11]	Anirudha M,Amir A A,Russ T.Control design along trajectories with sums of squares programming[R].Karlsruhe:IEEE International Conference on Robotics and Automation,2013.
[12]	Kazuo T,Hiroto Y,Hiroshi O,et al.A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems[J].IEEE Transactions on Fuzzy Systems,2009,17(4):911-922.
[13]	Gatermann K,Parrilo A P.Symmetry groups,semidefinite programs and sums of squares[J].Journal of Pure and Applied Algebra,2002,192(1/2/3):95-128.
[14]	吴勇,谢寿生,唐奇,等.基于支持向量机的航空发动机PID解耦控制[J].航空动力学报,2009,24(10):2349-2355. WU Yong,XIE Shousheng,TANG Qi,et al.PID decoupling controller for aero-engine based on support vector machines[J].Journal of Aerospace Power,2009,24(10):2349-2355.(in Chinese)
[15]	潘慕绚,黄金泉,殷石.航空发动机神经网络反步控制方法[J].航空动力学报,2009,24(10):2344-2348. PAN Muxuan,HUANG Jinquan,YIN Shi.Backstepping control strategy for aero-engine using neural networks[J].Journal of Aerospace Power,2009,24(10):2344-2348.(in Chinese)
[16]	Ceri E,David R,Antoni B.Identification of aircraft gas turbine dynamics using frequency-domain techniques[J].Control Engineering Practice,2000,8(2):457-467.
[17]	Wilfried G,Didier H,Jacques B,et al.Polynomial LPV synthesis applied to turbofan engines[J].Control Engineering Practice,2010,18(9):1077-1083.
[18]	Didier H,Denis A,Dimitri P.Positive polynomial matrices and improved LMI robustness conditions[J].Automatica,2003,39(8):1479-1485.
[19]	Ufuk T,Andrew P,Peter S,et al.Stability region analysis using simulations and sum-of-squares programming[C]//Proceedings of the 2007 American Control Conference.New York:IEEE,2007:6009-6014.
[20]	Bertsekas D P.Nonlinear programming[M].Massachusetts:Athena Scientific,1999.
[21]	LIU Nan,HUANG Jinquan,LU Feng.Multivariable PID parameters tuning method based on model matching on frequency domain for aero-engine[R].Wollongong:IEEE/ASME International Conference on Advanced Intelligent Mechatronics,2013.
[22]	Astrom K.Limitations on control system performance[J].European Journal of Control,2000,6(1):2-20.
[23]	仇小杰,黄金泉,鲁峰,等.航空发动机多路模糊切换控制系统设计[J].南京航空航天大学学报,2011,43(4):439-445. QIU Xiaojie,HUANG Jinquan,LU Feng,et al.Multi-loop fuzzy switching control system design for air-craft engines[J].Journal of Nanjing University of Aeronautics and Astronautics,2011,43(4):439-445.(in Chinese)