航空涡轴发动机数学建模方法与控制规律研究
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摘要
本论文针对目前国内航空涡轴发动机非线性实时数学模型建模技术发展相对滞后的情况，通过研究某型航空涡轴发动机部件级数学模型，提取涡轴发动机的几条重要特性线，并基于这些特性线，采用特性线法建立起涡轴发动机数学模型。仿真研究表明，涡轴发动机特性线模型建模方法简单，实时性好，动稳态精度较高。
首先，论文介绍了涡轴发动机部件级数学模型的建模机理与思路，结合某型涡轴发动机，建立起该型涡轴发动机部件级数学模型，并仿真验证了数学模型的正确性和准确性。然后，根据涡轴发动机工作原理以及部件特性，结合某型涡轴发动机试验数据，提取出涡轴发动机的几条重要特性曲线，基于特性曲线，采用特性线法建立起该型涡轴发动机数学模型。仿真研究表明，该特性线数学模型动稳态特性与试验台试车数据吻合。
为研究特性线模型结构的适用性，论文将部件级模型作为真实发动机，以部件级模型仿真结果作为发动机真实信号，通过分析部件级模型仿真结果，提取出该型涡轴发动机的特性曲线，依照特性线模型建模步骤，建立该型涡轴发动机的特性线数学模型。在相同输入条件下，仿真比较两种建模方法得到的数学模型输出结果。仿真表明，两种建模方法得到的方针结果一致，动稳态过程吻合程度高。在模型的实时性方面，特性线模型更胜一筹，模型结构框架灵活，适用性好，且不需精确的部件特性数据，只需要涡轴发动机试车数据即可。建模过程更为简单易行。
文末针对涡轴发动机的控制规律，研究了两种涡轴发动机控制系统(分别为机械液压式燃油调节器和数字电子式控制器)的工作原理以及控制逻辑。在某软件平台上建立了某型涡轴发动机机械液压式燃油调节器的数学模型。对该燃油调节器数学模型的仿真研究表明，燃油调节器数学模型稳态特性符合该型燃油调节器试验台数据要求。并在仿真研究过程中得到了影响燃油调节器性能的关键结构参数。通过对某型涡轴发动机数字电子式控制器的分析，得到了涡轴发动机燃油控制系统中各种参数限制条件。并结合该数字电子式控制器正常控制模式，得
According to the low-development of turbo-shaft aero-engine modeling technology of real-time nonlinear mathematical model in China, the component-based model (CBM) of X turbo-shaft aero-engine is studied in this paper. Several important characteristic curves of the aero-engine are gained by analyzing the simulation results of the CBM. Then, based on the gained characteristic curves, a real-time characteristic-curve model (CCM) of the turbo-shaft aero-engine is developed. The simulation results of the CCM show that the CCM using the new modeling technology based on the characteristic curves is simple, real-time and accuracy both on steady state and transient process.
To start with, the turbo-shaft aero-engine modeling technology of CBM is introduced. Together with the component characteristic data of X turbo-shaft aero-engine, the CBM of X turbo-shaft aero-engine is set up. This model is validated by the simulation results. Then, by analyzing the data gathered from the test-bed of another turbo-shaft aero-engine, certain characteristic curves are obtained. Based on these curves, the CCM of this turbo-shaft aero-engine is established. The simulation results show the very similarity between the CCM and the test-bed data.
To study the adaptability of the CCM modeling technology, the CBM simulation is seemed as the real engine to produce the data in this paper. Then, the characteristic curves are gained by analyzing the simulation data, thus the CCM of the CBM is set up. The simulation shows the high accordance between the CCM and CBM both on steady state and transient process. The compared-simulation also shows the better performance of the CCM on real-time. Another advantage of CCM is that the CCM doesn't base on the explicit characteristic of the component. Furthermore, the CCM is adaptable, expandable and easy used in engine control system.
At the end of this paper, the control law of the turbo-shaft engine is studied. Two kinds controllers (one is hydro-mechanical and the other is digital-electronic) are analyzed. The mathematical model of the hydro-mechanical controller is established
首先，论文介绍了涡轴发动机部件级数学模型的建模机理与思路，结合某型涡轴发动机，建立起该型涡轴发动机部件级数学模型，并仿真验证了数学模型的正确性和准确性。然后，根据涡轴发动机工作原理以及部件特性，结合某型涡轴发动机试验数据，提取出涡轴发动机的几条重要特性曲线，基于特性曲线，采用特性线法建立起该型涡轴发动机数学模型。仿真研究表明，该特性线数学模型动稳态特性与试验台试车数据吻合。
为研究特性线模型结构的适用性，论文将部件级模型作为真实发动机，以部件级模型仿真结果作为发动机真实信号，通过分析部件级模型仿真结果，提取出该型涡轴发动机的特性曲线，依照特性线模型建模步骤，建立该型涡轴发动机的特性线数学模型。在相同输入条件下，仿真比较两种建模方法得到的数学模型输出结果。仿真表明，两种建模方法得到的方针结果一致，动稳态过程吻合程度高。在模型的实时性方面，特性线模型更胜一筹，模型结构框架灵活，适用性好，且不需精确的部件特性数据，只需要涡轴发动机试车数据即可。建模过程更为简单易行。
文末针对涡轴发动机的控制规律，研究了两种涡轴发动机控制系统(分别为机械液压式燃油调节器和数字电子式控制器)的工作原理以及控制逻辑。在某软件平台上建立了某型涡轴发动机机械液压式燃油调节器的数学模型。对该燃油调节器数学模型的仿真研究表明，燃油调节器数学模型稳态特性符合该型燃油调节器试验台数据要求。并在仿真研究过程中得到了影响燃油调节器性能的关键结构参数。通过对某型涡轴发动机数字电子式控制器的分析，得到了涡轴发动机燃油控制系统中各种参数限制条件。并结合该数字电子式控制器正常控制模式，得
According to the low-development of turbo-shaft aero-engine modeling technology of real-time nonlinear mathematical model in China, the component-based model (CBM) of X turbo-shaft aero-engine is studied in this paper. Several important characteristic curves of the aero-engine are gained by analyzing the simulation results of the CBM. Then, based on the gained characteristic curves, a real-time characteristic-curve model (CCM) of the turbo-shaft aero-engine is developed. The simulation results of the CCM show that the CCM using the new modeling technology based on the characteristic curves is simple, real-time and accuracy both on steady state and transient process.
To start with, the turbo-shaft aero-engine modeling technology of CBM is introduced. Together with the component characteristic data of X turbo-shaft aero-engine, the CBM of X turbo-shaft aero-engine is set up. This model is validated by the simulation results. Then, by analyzing the data gathered from the test-bed of another turbo-shaft aero-engine, certain characteristic curves are obtained. Based on these curves, the CCM of this turbo-shaft aero-engine is established. The simulation results show the very similarity between the CCM and the test-bed data.
To study the adaptability of the CCM modeling technology, the CBM simulation is seemed as the real engine to produce the data in this paper. Then, the characteristic curves are gained by analyzing the simulation data, thus the CCM of the CBM is set up. The simulation shows the high accordance between the CCM and CBM both on steady state and transient process. The compared-simulation also shows the better performance of the CCM on real-time. Another advantage of CCM is that the CCM doesn't base on the explicit characteristic of the component. Furthermore, the CCM is adaptable, expandable and easy used in engine control system.
At the end of this paper, the control law of the turbo-shaft engine is studied. Two kinds controllers (one is hydro-mechanical and the other is digital-electronic) are analyzed. The mathematical model of the hydro-mechanical controller is established
引文
[1] 侯志兴等编．世界航空发动机手册[M]．北京：航空工业出版社，1987-2．
[2] 樊思齐等编．航空推进系统控制[M]．西安：西北工业大学出版社，1995-12．
[3] 郭腊梅．涡轴发动机最优加速控制研究[D]．西安：西北工业大学硕士研究生论文，2003-3．
[4] Ballin, M.G. A High Fidelity Real-Time Simulation of a Small Turboshaft Engine [J]. NASA TM 100991, 1988.
[5] Ahmet Duyar. A Simplified Dynamic Model of the T700 Turboshaft Engine [J]. NASA TM 100991, 1992.
[6] 白书辉．涡轴发动机鲁棒控制器设计[D]．西安：西北工业大学硕士研究生论文，1995-3．
[7] Daniele C J, Krosel S M, Szueh J R. Digital computer program for generating dynamic turbofan engine models [J]. NASA TM-83446, Lewis Research Center, Ohio, 1983.
[8] Reed J A, Afjeh A A. Computational simulation of gas turbine: part Ⅰ-foundation of component-based models [J]. Journal of Engineering for Gas Turbines and Power, 2000-12.
[9] Xie Zhiwu, Yu Jun, Liu Jinyang. Applying UML to gas turbine engine simulation [C]. Proceedings of the IEEE International Conference on Technology of Object-Oriented Languages and Systems. 1999.
[10] 周文祥等．航空发动机简化实时模型仿真研究[J]．南京航空航天大学学报 2005-4．
[11] 彭泽琰，刘刚编．航空燃气轮机原理(上)[M]．北京：国防工业出版社，2000-9．
[12] 廉小纯，吴虎编．航空燃气轮机原理(下)[M]．北京：国防工业出版社，2001-8．
[13] 杨刚等．一种不需要迭代的发动机建模方法[C]．中国航空学会第十一届发动机自动控制学术研讨会论文集，温州，2002-8．
[14] 杨俊杰编．相似理论与结构模型试验[M]．武汉：武汉理工大学出版社，2006-6．
[15] 钟周威．航空涡轮轴发动机加速寻优控制研究[D]．西安：西北工业大学硕士研究生论文，2006-3．
[16] 曹源等．航空发动机系统级仿真研究的回顾与展望[J]．航空动力学报，2004-8．
[17] 和兴锁编，理论力学[M]．北京：科学出版社，2005-08．
[18] 王曦等．涡喷发动机多变量解耦控制系统设计[C]．中国航空学会第十三届发动机自动控制学术研讨会论文集，贵阳，2006-12．
[19] 高会生等译．MATLAB原理与工程应用(第二版) [M]．北京：电子工业出版社，2006-1．
[20] 范景乐等编．MATLAB仿真应用详解[M]．北京：人民邮电出版社，2001-7．
[21] 周雪芹等编．计算机控制系统[M]．西安：西北工业大学出版社，1998-1．
[22] [俄]涅恰耶夫．航空动力装置控制规律与特性[M]．单凤桐，程振海译．北京：国防工业出版社，1999．
[23] Martucci. A, Volponi. J. Fuzzy Fuel Flow Selection Logic for a Real Time Embedded Full Authority Digital Engine control [J]. Journal of Engineering for Gas Turbines and Power,2003, 125.
[24] 黄开明等．参数限制对涡轴发动机过渡态控制的影响[J]．航空动力学报，2006，21(02)．
[25] William H. Pfeil, Michael Athans, H. Austin Spang. Multi-Variable Control Of The GE-T700 Engine Using The LQG/LTR Design Methodology [C], Proceed of 1986 ACC, 1986-4.
[26] 刘昆等．考虑入口和出口容积效应的涡轮动力学模型[J]．国防科技大学学报 2001，23(03)．
[27] 方崇智等．过程辨识[M]．北京：清华大学出版社，1988．
[28] K. Seldner, J. R. Mihaloew, R. J. Blaba. Generalized simulation Technique for Turbojet Engine System [J]. NASA TN D-6670, 1972.
[29] R.W. Koening, L. H. Fishbach, GENENG-A Program for Calculating Design and off-design Performance for Turbojet and Turbofan Engines [J]. NASA TN D-6552, 1972.
[30] J.F. Sellers, C. J. Daniele. DTNGEN - A Program for Calculating steadt-state and Transient Performance of Turbojet and Turbofan Engines [J]. NASA TN D-7901, 1975.
[31] J.R. Palmer, GU Yong-gen. Turbo-Test-A computer Program for Rig Test Analysis of Arbitrary Gas Turbine Engine [J]. Intern Jour of Turbo and Jet Engines, 1985,Vol.2.
[32] J.S. Litt, J. C. Delaat, W. C. Merrill. A Microprocessor-Based Real-time Simulator of a Turbofan Engine [J]. NASA TM-100889, 1988.
[33] 孙春茹译．用于推进系统实时模拟的分段线性化状态变量技术[M]．株洲：1982．
[34] 沈伟．自由涡轮型涡轴发动机动态建模及仿真研究[D]．西安：西北工业大学硕士研究生论文，1994-3．
[35] 管彦深等．航空动力装置控制系统[M]．北京：国防工业出版社，1985．
[36] 李防战等．基于特性方程的燃气涡轮的建模与性能仿真[J]．中国动力工程学报，2005，25(01)．
[37] 黄开明等．基于无迭代解法的航空发动机实时模型[J]．航空发动机，2004，30(2)．
[38] 古列维奇，戈尔别格．航空燃气涡轮发动机的控制方法与燃气涡轮发动机动态特性的数学模拟．程心健等译．无锡：中国航空动力控制系统研究所，1998．
[39] 张世柽．航空发动机设计手册(第15册)[M]．北京：航空工业出版社，2002．
[40] 屈裕安等．某涡扇发动机过渡过程仿真研究[J]．航空动力学报，2003，18(04)．
[41] Wilson, C., Second-Law Characterization of Turboshaft Engine Performance [C], MS Thesis in Preparation, University of Missouri-Rolla, August 2002.
[42] Roth, B., A Work Potential Perspective of Engine Component Performance [C], AIAA,2001-3300, July 2001.
[43] Mark G. Ballin. A High Fidelity Real-Time Simulation of a Small Turboshaft Engine [J]. NASA-TM-100991,1988.
[2] 樊思齐等编．航空推进系统控制[M]．西安：西北工业大学出版社，1995-12．
[3] 郭腊梅．涡轴发动机最优加速控制研究[D]．西安：西北工业大学硕士研究生论文，2003-3．
[4] Ballin, M.G. A High Fidelity Real-Time Simulation of a Small Turboshaft Engine [J]. NASA TM 100991, 1988.
[5] Ahmet Duyar. A Simplified Dynamic Model of the T700 Turboshaft Engine [J]. NASA TM 100991, 1992.
[6] 白书辉．涡轴发动机鲁棒控制器设计[D]．西安：西北工业大学硕士研究生论文，1995-3．
[7] Daniele C J, Krosel S M, Szueh J R. Digital computer program for generating dynamic turbofan engine models [J]. NASA TM-83446, Lewis Research Center, Ohio, 1983.
[8] Reed J A, Afjeh A A. Computational simulation of gas turbine: part Ⅰ-foundation of component-based models [J]. Journal of Engineering for Gas Turbines and Power, 2000-12.
[9] Xie Zhiwu, Yu Jun, Liu Jinyang. Applying UML to gas turbine engine simulation [C]. Proceedings of the IEEE International Conference on Technology of Object-Oriented Languages and Systems. 1999.
[10] 周文祥等．航空发动机简化实时模型仿真研究[J]．南京航空航天大学学报 2005-4．
[11] 彭泽琰，刘刚编．航空燃气轮机原理(上)[M]．北京：国防工业出版社，2000-9．
[12] 廉小纯，吴虎编．航空燃气轮机原理(下)[M]．北京：国防工业出版社，2001-8．
[13] 杨刚等．一种不需要迭代的发动机建模方法[C]．中国航空学会第十一届发动机自动控制学术研讨会论文集，温州，2002-8．
[14] 杨俊杰编．相似理论与结构模型试验[M]．武汉：武汉理工大学出版社，2006-6．
[15] 钟周威．航空涡轮轴发动机加速寻优控制研究[D]．西安：西北工业大学硕士研究生论文，2006-3．
[16] 曹源等．航空发动机系统级仿真研究的回顾与展望[J]．航空动力学报，2004-8．
[17] 和兴锁编，理论力学[M]．北京：科学出版社，2005-08．
[18] 王曦等．涡喷发动机多变量解耦控制系统设计[C]．中国航空学会第十三届发动机自动控制学术研讨会论文集，贵阳，2006-12．
[19] 高会生等译．MATLAB原理与工程应用(第二版) [M]．北京：电子工业出版社，2006-1．
[20] 范景乐等编．MATLAB仿真应用详解[M]．北京：人民邮电出版社，2001-7．
[21] 周雪芹等编．计算机控制系统[M]．西安：西北工业大学出版社，1998-1．
[22] [俄]涅恰耶夫．航空动力装置控制规律与特性[M]．单凤桐，程振海译．北京：国防工业出版社，1999．
[23] Martucci. A, Volponi. J. Fuzzy Fuel Flow Selection Logic for a Real Time Embedded Full Authority Digital Engine control [J]. Journal of Engineering for Gas Turbines and Power,2003, 125.
[24] 黄开明等．参数限制对涡轴发动机过渡态控制的影响[J]．航空动力学报，2006，21(02)．
[25] William H. Pfeil, Michael Athans, H. Austin Spang. Multi-Variable Control Of The GE-T700 Engine Using The LQG/LTR Design Methodology [C], Proceed of 1986 ACC, 1986-4.
[26] 刘昆等．考虑入口和出口容积效应的涡轮动力学模型[J]．国防科技大学学报 2001，23(03)．
[27] 方崇智等．过程辨识[M]．北京：清华大学出版社，1988．
[28] K. Seldner, J. R. Mihaloew, R. J. Blaba. Generalized simulation Technique for Turbojet Engine System [J]. NASA TN D-6670, 1972.
[29] R.W. Koening, L. H. Fishbach, GENENG-A Program for Calculating Design and off-design Performance for Turbojet and Turbofan Engines [J]. NASA TN D-6552, 1972.
[30] J.F. Sellers, C. J. Daniele. DTNGEN - A Program for Calculating steadt-state and Transient Performance of Turbojet and Turbofan Engines [J]. NASA TN D-7901, 1975.
[31] J.R. Palmer, GU Yong-gen. Turbo-Test-A computer Program for Rig Test Analysis of Arbitrary Gas Turbine Engine [J]. Intern Jour of Turbo and Jet Engines, 1985,Vol.2.
[32] J.S. Litt, J. C. Delaat, W. C. Merrill. A Microprocessor-Based Real-time Simulator of a Turbofan Engine [J]. NASA TM-100889, 1988.
[33] 孙春茹译．用于推进系统实时模拟的分段线性化状态变量技术[M]．株洲：1982．
[34] 沈伟．自由涡轮型涡轴发动机动态建模及仿真研究[D]．西安：西北工业大学硕士研究生论文，1994-3．
[35] 管彦深等．航空动力装置控制系统[M]．北京：国防工业出版社，1985．
[36] 李防战等．基于特性方程的燃气涡轮的建模与性能仿真[J]．中国动力工程学报，2005，25(01)．
[37] 黄开明等．基于无迭代解法的航空发动机实时模型[J]．航空发动机，2004，30(2)．
[38] 古列维奇，戈尔别格．航空燃气涡轮发动机的控制方法与燃气涡轮发动机动态特性的数学模拟．程心健等译．无锡：中国航空动力控制系统研究所，1998．
[39] 张世柽．航空发动机设计手册(第15册)[M]．北京：航空工业出版社，2002．
[40] 屈裕安等．某涡扇发动机过渡过程仿真研究[J]．航空动力学报，2003，18(04)．
[41] Wilson, C., Second-Law Characterization of Turboshaft Engine Performance [C], MS Thesis in Preparation, University of Missouri-Rolla, August 2002.
[42] Roth, B., A Work Potential Perspective of Engine Component Performance [C], AIAA,2001-3300, July 2001.
[43] Mark G. Ballin. A High Fidelity Real-Time Simulation of a Small Turboshaft Engine [J]. NASA-TM-100991,1988.