基于控制结构优化的航空发动机多变量鲁棒控制研究
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摘要
多变量鲁棒控制是航空发动机控制发展的趋势,随着航空发动机控制量和被控制量的增多,如何从发动机的众多输出参数中选择合适的被控制量以及设计合适的控制结构成为航空发动机多变量控制中必须解决的问题。本文围绕航空发动机多变量鲁棒控制这一主题,开展了航空发动机建模、输出选择和控制结构设计、多变量鲁棒控制器设计及工程化实现研究。首先研究建立航空动机非线性部件级模型方法,在原有模型基础上,添加了导叶角对发动机影响的功能模块,完善了航空发动机非线性部件级模型;并研究了航空发动机自适应模型的建立方法,提出了基于误差反馈控制的航空发动机自适应模型建立方法,为今后进一步研究基于模型的航空发动机智能控制奠定了一定的基础。
然后在此模型基础上,开展了航空发动机输出量选择和和控制结构设计研究,采用基于鲁棒稳定性和条件数(RSCN)方法分别对该型发动机进行了三变量、四变量输出选择,再采用相对矩阵增益(RGA)、块相对增益(BRG)方法和基于相互作用分解(RID)方法分别对它们进行了控制结构分析,确定了它们的控制结构;
研究了增广LQR(ALQR)控制器设计方法与基于线性矩阵不等式(LMI)的航空发动机H_2/H_∞解耦控制器设计方法;采用遗传算法优化基于线性矩阵不等式的H_2/H_∞控制器的动态性能;通过将被控对象回路之间的耦合看成扰动信号并转化成H_∞性能指标,提出了基于线性矩阵不等式的H_2/H_∞解耦控制器设计方法;进行仿真验证了控制器设计方法的有效性;研究了航空发动机控制器工程化实现方法,包括抗积分饱和方法、加力扰动抑制方法和控制器整形化方法;
Multivariable robust control is the developing trend of aero-engine control. Along with the increasing of the number of engine’s adjustable variables and controlled variables, how to select the better controlled variables and how to design the control configuaration of the engine have become crucial problems in engine’s control. This dissertation decomposed the aero-engine control system designing into three steps: controlled variables selection and control configuration design, multivariable robust controller design, and engineering implement of the controller. And this dissertation also studied the method of building aero-engine’s adaptive model.
The research of this dissertation begins with the component-level modeling of areo-engine. In the basis of the existing component-level model, this dissertation added a new module which can reflect the influence of guide vane to the aero-engine. And adaptive modeling method also studied in this dissertation. A new adaptive modeling method which modeling the adaptive model based on err-feedback control was presented.
And then, the controlled variabes selection and control structure design was studied based on the aero-engine model. The controlled variables of aero-engine’s three-variable control systes and four-variable control systes were selected by controlled variables selection method which is called RSCN (Robust Stability & Conditon Number). And then design the control structure by two methods: Relative Gain Array (RGA) & Block Relative Gain (BRG) and Relative Interaction Decomposition (RID).
In chaper 4, Augmented LQR (ALQR) controller design method and H_2/H_∞controller design methed based on Linear Matrix Inequality (LMI) were studied; The dynamic performance of H_2/H_∞controller based on LMI was optimized by genetic algorithm. By converting the loop coupling of the controlled plant to H_∞performance index, a new controller design method,H_2/H_∞decoupling controller design methed based on LMI, was presented. And then, engineering implement of the controller was researched, includes anti-windup, anti-afterburner disturbance and transform the float controller to integer controller. And simulations were conducted to verify these methods.
然后在此模型基础上,开展了航空发动机输出量选择和和控制结构设计研究,采用基于鲁棒稳定性和条件数(RSCN)方法分别对该型发动机进行了三变量、四变量输出选择,再采用相对矩阵增益(RGA)、块相对增益(BRG)方法和基于相互作用分解(RID)方法分别对它们进行了控制结构分析,确定了它们的控制结构;
研究了增广LQR(ALQR)控制器设计方法与基于线性矩阵不等式(LMI)的航空发动机H_2/H_∞解耦控制器设计方法;采用遗传算法优化基于线性矩阵不等式的H_2/H_∞控制器的动态性能;通过将被控对象回路之间的耦合看成扰动信号并转化成H_∞性能指标,提出了基于线性矩阵不等式的H_2/H_∞解耦控制器设计方法;进行仿真验证了控制器设计方法的有效性;研究了航空发动机控制器工程化实现方法,包括抗积分饱和方法、加力扰动抑制方法和控制器整形化方法;
Multivariable robust control is the developing trend of aero-engine control. Along with the increasing of the number of engine’s adjustable variables and controlled variables, how to select the better controlled variables and how to design the control configuaration of the engine have become crucial problems in engine’s control. This dissertation decomposed the aero-engine control system designing into three steps: controlled variables selection and control configuration design, multivariable robust controller design, and engineering implement of the controller. And this dissertation also studied the method of building aero-engine’s adaptive model.
The research of this dissertation begins with the component-level modeling of areo-engine. In the basis of the existing component-level model, this dissertation added a new module which can reflect the influence of guide vane to the aero-engine. And adaptive modeling method also studied in this dissertation. A new adaptive modeling method which modeling the adaptive model based on err-feedback control was presented.
And then, the controlled variabes selection and control structure design was studied based on the aero-engine model. The controlled variables of aero-engine’s three-variable control systes and four-variable control systes were selected by controlled variables selection method which is called RSCN (Robust Stability & Conditon Number). And then design the control structure by two methods: Relative Gain Array (RGA) & Block Relative Gain (BRG) and Relative Interaction Decomposition (RID).
In chaper 4, Augmented LQR (ALQR) controller design method and H_2/H_∞controller design methed based on Linear Matrix Inequality (LMI) were studied; The dynamic performance of H_2/H_∞controller based on LMI was optimized by genetic algorithm. By converting the loop coupling of the controlled plant to H_∞performance index, a new controller design method,H_2/H_∞decoupling controller design methed based on LMI, was presented. And then, engineering implement of the controller was researched, includes anti-windup, anti-afterburner disturbance and transform the float controller to integer controller. And simulations were conducted to verify these methods.
引文
[1]孙健国.现代航空动力装置控制.北京:航空工业出版社, 2009: 1~15
[2]樊思齐.航空发动机控制(下册).西安:西北工业大学出版社, 2008:1~53
[3]孙健国. 21世纪航空动力控制展望.航空动力学报, 2001, 16(2): 97-102
[4]樊思齐,徐芸华.推进系统控制.西安:西北工业大学出版社, 1995: 5~12
[5] Sun Jianguo;V. Vasilyev; B. Ilyasov. Advanced multivariable control systems of aeroengines.北京:北京航空航天大学出版社, 2005: 1~57
[6] McKinnet; John S. Simulation of turbofan engine part I: Description of method and balancing technique. AFAPL-TR-67-125, 1967
[7] Viars; Philip, R.; The impact of IHPTET on the engine/aircraft system. AIAA89-2137, 1989
[8] Adibhatla; Shrider; Lewis; Timothy J. Model-based intelligent digital engine control. AIAA 97-3192, 1997
[9]黄春风.航空智能发动机的研究发展.中国航空学会,大型飞机关键技术高层论坛暨中国航空学会2007年学术年会论文集,北京:中国航空学会, 2007: 1-14.
[10]金茂贤.航空发动机先进控制概念及最新进展.航空科学技术, 2005(1): 24-27.
[11]苗卓广,何秀然,魏永志.基于模糊RBF神经网络整定的航空发动机多变量解耦控制.空军工程大学学报:自然科学版. 2009, 10(2): 10-13
[12]孙护国,李华聪,樊思齐等.航空发动机固定阶混合μ控制器设计方法的研究.西北工业大学学报, 2004, 22(6): 769-773
[13]李秋红,孙健国.航空发动机控制器降阶方法.南京航空航天大学学报, 2008, 40(3): 284-287
[14]黄金泉.发动机神经网络自适应控制, [博士学位论文].南京:南京航空航天大学, 1995
[15] H. Melker. Control Structure Design Methods Applied to a Jet Engine. Proceedings of the 1999 IEEE International Conference on Control Applications, 1999(1): 45-50.
[16] M. van de Wal; B. de Jager. Control Structure Design: A Survey. Proceedings of the 1995 American Control Conference, 1995, 1(1): 225-229.
[17] M. van der War; B. de Jager. A review of methods for input/output selection. Automatica, 2001, vol. 37: 487-510.
[18] D.E. Reeves. A Comprehensive Approach to Control Configuration Design for Complex Systems, [ Ph. D. Thesis]. Georgia: Georgia Institute of Technology, 1991.
[19] J.H. Lee; M. Morari. Robust Control Structure Selection and Control System Design Methods Applied to Distillation Column Control. Proceedings of the 29th IEEE Conference on Decision and Control, 1990, 4: 2041-2046.
[20] A.G.Shutler. Control configuration design for the aircraft gas turbine engine. Computing & Control engineering Journal ,1995, 6(1):22-28
[21] W.F. Dellinger; A.T. Alouani. Application of linear multivariable control design for the GE-21 turbofan jet engine. The Twenty-First Southeastern Symposium on System Theory. Washington, DC, USA: IEEE Comput. Soc. Press , 1989
[22] Bristol, E. H. On a new measure of interactions for multivariable process control. IEEE Trans. Autom. Control, 1966, 11, 133-134
[23] V. Manousiouthakis; R. Savage; Y. Arkun. Synthesis of decentralized process control structures using the concept of block relative gain. AICHe Journal, 1986, Vol.32(6), 991-1003
[24] P. Grosdidier; M. Morari. Interaction measures for systems under decentralized control. Automatica, 1986, vol. 22(3), 309-319,
[25] A. Conley; M. E. Salgado. Gramian based interaction measure. Sydney, Australia: In proceedings of the 39th IEEE conference on decision and control, 2000, pages 5020-5022
[26] B. Wittenmark; M. E. Salgado. Hankel-norm based interaction measure for input-output pairing. Barcelona, Spain: In Proc. of the 2002 IFAC World Congress, 2002.
[27]周克敏; Doyle J. C.; Glover, K.鲁棒与最优控制.北京:国防工业出版社,2002.
[28]姜长生,孙隆和,吴庆宪等.系统理论与鲁棒控制.北京:航空工业出版社,1998。
[29] Daniel E. M.; etc. Simultaneous stabilization with near optimal LQR performance, Proceedings of the 38th IEEE conference on Decision and Control, 1999, Vol. 3, 2300-2305.
[30] Garg, S.; Athans, M. The LQG/LTR procedure for multivariable feedback control design. IEEE Trans. Automatic Control, 1987, Vol. 32(2), 105-128
[31] Doyle, J.; Stein, G. Multivariable feedback design: concepts for a classical / modern synthesis. IEEE Trans. On Automatic Control, 1981, Vol. 26(1), 4-16
[32] Athans, M.; Petros, K.; Efthimios, K. etc. Linear quadratic gaussian with loop transfer recovery methodology for the F-100 Engine. Journal of Guidance, 1986, Vol. 9(1), 45-52.
[33] McFarlane, D.; Glover, K. A loop shaping design procedure using H∞synthesis. IEEE Trans. Automatic Control, Vol. AC-37, No. 6, 1992, pages: 759-769.
[34] Masami, S. H∞/LTR procedure with specified degree of recovery. Automatica, Vol. 28, No. 3, 1992, pages: 509-517,
[35] Saberi, A.; Stoorvogel A.A.; Sannuti P. etc. On optimal output regulation for linear systems. International Journal of Control, Vol. 76, No. 4, 2003, pages:319-333
[36]杨刚,孙键国,李秋红.航空发动机控制系统中的增广LQR方法,航空动力学报, 2004, 19(1):153-158。
[37] Sugiyama, N. Derivation of ABCD system matrices from nonlinear dynamic simulation of jet engines. AIAA 92-3319
[38]冯正平,孙健国,黄金泉等.一种建立航空发动机状态变量模型的新方法[J].航空动力学报, 1998, 13(4):435-438.
[39] R. H. Luppold; J. R. Roman; G. W. Gallops etal. Estimating in-flight performance variation using Kalman filter concepts. AIAA 89-2584, 1989.
[40] Dan Simon. Aircraft turbofan engine health estimation using constrained Kalman filtering. NASA/TM 2003-212528, 2003
[41] Takahisa Kobayashi. Application of a constant gain extended Kalman filter for in-flight estimation of aircraft engine performance parameters. NASA/TM 2005-213865,2005
[42] Takahisa Kobayashi. Hybrid Kalman filter: a new approach for aircraft engine in-flight diagnostics. NASA/TM 2006-214491,2006
[43] G. Gilyard; J. Orme. Subsonic flight test evaluation of a performance seeking control algorithm on an F-15 airplane. AIAA 92-3743, 1992.
[44] K. Lietzau; A. Kreiner. Model based control concepts for jet engines. Proceedings of ASME TURBO EXPO 2001, new Orleans, louisian, USA, ASME, New York, NY, United States, june 4-7, 2001.
[45] Frank W. Burcham; Jr. Glenn B. Gilyard; Lawrence P. Myers. Propulsion system/flight control integration and optimization. NASA Technical Memorandum 4207, 1990
[46] E. Nemeth; R. Anderson; J. Maram; A.Norman. An advanced intelligent control system framework. AIAA-92-3162.
[47] Sanjay Garg. Controls and health management technologies for intelligent aerospace propulsion systems. NASA/TM-2004-212915.
[48]袁春飞,姚华,杨刚.航空发动机机载自适应模型研究.航空学报, 2006, 27(4): 561-564.
[49] M. J. He, W. J. Cai, B. F. Wu, Block control structure selection based on reletive interaction decomposition. ICARCV '06. 9th International Conference on Control, Automation, Robotics and Vision, 2006,pages:1-6.
[50] Niederlinski, A. A heuristic approach to the design of linear multivariable interacting subsystems.Automatica, 1971, 7: 691-701
[51] He M.-J; Cai W.-J. New criterion for control loop configuration of multivariable prcesses. Ind. Eng. Chem. Res. 2004(43):7057-7064
[52] C. Scherer; P. Gahinet; M. Chilali. Multiobjective output-feedback control via LMI optimization. IEEE Trans Auto Control, 1997, AC-42(7):896-911
[53]王曦,陈华荣.不确定性系统鲁棒H∞/H2混合控制在航空发动机中的应用.航空动力学报, 2002, 17(2): 250-254
[54]谢光华,曾庆福.基于LMI的航空发动机混合H2/H∞输出反馈控制.推进技术. 2000, 21(6): (28-31)
[55]俞立.鲁棒控制——线性矩阵不等式处理方法.北京:清华大学出版社, 2002,12
[56]杨刚,姚华.实用航空发动机LQR权阵选取方法.南京航空航天大学学报, 2006.8, 38(4): 403-407
[57] Li S. L.; Sun J. G. Application of genetic algorithm to solving nonlinear model of aero-engines. Chinese Journal of Aeronautics, 2003, 16(2): 69-72.
[58]张明君,张化光.基于遗传算法优化的神经网络PID控制器.吉林大学学报(工学版), 2005, 35(1): 69-72
[59]李秋红,孙健国.航空发动机解耦控制器设计.航空学报, 2006, 27(6): 1046-1050
[60]蒋平国,孙健国.航空发动机数控系统抗积分饱和算法研究.推进技术, 2006, 27(6):532-535.
[61]陶永华.新型PID控制及其应用.北京:国防科技大学出版社, 1999
[62]杨刚.多变量鲁棒控制在涡扇发动机中的应用研究与实验验证, [博士学位论文].南京:南京航空航天大学, 2004。
[2]樊思齐.航空发动机控制(下册).西安:西北工业大学出版社, 2008:1~53
[3]孙健国. 21世纪航空动力控制展望.航空动力学报, 2001, 16(2): 97-102
[4]樊思齐,徐芸华.推进系统控制.西安:西北工业大学出版社, 1995: 5~12
[5] Sun Jianguo;V. Vasilyev; B. Ilyasov. Advanced multivariable control systems of aeroengines.北京:北京航空航天大学出版社, 2005: 1~57
[6] McKinnet; John S. Simulation of turbofan engine part I: Description of method and balancing technique. AFAPL-TR-67-125, 1967
[7] Viars; Philip, R.; The impact of IHPTET on the engine/aircraft system. AIAA89-2137, 1989
[8] Adibhatla; Shrider; Lewis; Timothy J. Model-based intelligent digital engine control. AIAA 97-3192, 1997
[9]黄春风.航空智能发动机的研究发展.中国航空学会,大型飞机关键技术高层论坛暨中国航空学会2007年学术年会论文集,北京:中国航空学会, 2007: 1-14.
[10]金茂贤.航空发动机先进控制概念及最新进展.航空科学技术, 2005(1): 24-27.
[11]苗卓广,何秀然,魏永志.基于模糊RBF神经网络整定的航空发动机多变量解耦控制.空军工程大学学报:自然科学版. 2009, 10(2): 10-13
[12]孙护国,李华聪,樊思齐等.航空发动机固定阶混合μ控制器设计方法的研究.西北工业大学学报, 2004, 22(6): 769-773
[13]李秋红,孙健国.航空发动机控制器降阶方法.南京航空航天大学学报, 2008, 40(3): 284-287
[14]黄金泉.发动机神经网络自适应控制, [博士学位论文].南京:南京航空航天大学, 1995
[15] H. Melker. Control Structure Design Methods Applied to a Jet Engine. Proceedings of the 1999 IEEE International Conference on Control Applications, 1999(1): 45-50.
[16] M. van de Wal; B. de Jager. Control Structure Design: A Survey. Proceedings of the 1995 American Control Conference, 1995, 1(1): 225-229.
[17] M. van der War; B. de Jager. A review of methods for input/output selection. Automatica, 2001, vol. 37: 487-510.
[18] D.E. Reeves. A Comprehensive Approach to Control Configuration Design for Complex Systems, [ Ph. D. Thesis]. Georgia: Georgia Institute of Technology, 1991.
[19] J.H. Lee; M. Morari. Robust Control Structure Selection and Control System Design Methods Applied to Distillation Column Control. Proceedings of the 29th IEEE Conference on Decision and Control, 1990, 4: 2041-2046.
[20] A.G.Shutler. Control configuration design for the aircraft gas turbine engine. Computing & Control engineering Journal ,1995, 6(1):22-28
[21] W.F. Dellinger; A.T. Alouani. Application of linear multivariable control design for the GE-21 turbofan jet engine. The Twenty-First Southeastern Symposium on System Theory. Washington, DC, USA: IEEE Comput. Soc. Press , 1989
[22] Bristol, E. H. On a new measure of interactions for multivariable process control. IEEE Trans. Autom. Control, 1966, 11, 133-134
[23] V. Manousiouthakis; R. Savage; Y. Arkun. Synthesis of decentralized process control structures using the concept of block relative gain. AICHe Journal, 1986, Vol.32(6), 991-1003
[24] P. Grosdidier; M. Morari. Interaction measures for systems under decentralized control. Automatica, 1986, vol. 22(3), 309-319,
[25] A. Conley; M. E. Salgado. Gramian based interaction measure. Sydney, Australia: In proceedings of the 39th IEEE conference on decision and control, 2000, pages 5020-5022
[26] B. Wittenmark; M. E. Salgado. Hankel-norm based interaction measure for input-output pairing. Barcelona, Spain: In Proc. of the 2002 IFAC World Congress, 2002.
[27]周克敏; Doyle J. C.; Glover, K.鲁棒与最优控制.北京:国防工业出版社,2002.
[28]姜长生,孙隆和,吴庆宪等.系统理论与鲁棒控制.北京:航空工业出版社,1998。
[29] Daniel E. M.; etc. Simultaneous stabilization with near optimal LQR performance, Proceedings of the 38th IEEE conference on Decision and Control, 1999, Vol. 3, 2300-2305.
[30] Garg, S.; Athans, M. The LQG/LTR procedure for multivariable feedback control design. IEEE Trans. Automatic Control, 1987, Vol. 32(2), 105-128
[31] Doyle, J.; Stein, G. Multivariable feedback design: concepts for a classical / modern synthesis. IEEE Trans. On Automatic Control, 1981, Vol. 26(1), 4-16
[32] Athans, M.; Petros, K.; Efthimios, K. etc. Linear quadratic gaussian with loop transfer recovery methodology for the F-100 Engine. Journal of Guidance, 1986, Vol. 9(1), 45-52.
[33] McFarlane, D.; Glover, K. A loop shaping design procedure using H∞synthesis. IEEE Trans. Automatic Control, Vol. AC-37, No. 6, 1992, pages: 759-769.
[34] Masami, S. H∞/LTR procedure with specified degree of recovery. Automatica, Vol. 28, No. 3, 1992, pages: 509-517,
[35] Saberi, A.; Stoorvogel A.A.; Sannuti P. etc. On optimal output regulation for linear systems. International Journal of Control, Vol. 76, No. 4, 2003, pages:319-333
[36]杨刚,孙键国,李秋红.航空发动机控制系统中的增广LQR方法,航空动力学报, 2004, 19(1):153-158。
[37] Sugiyama, N. Derivation of ABCD system matrices from nonlinear dynamic simulation of jet engines. AIAA 92-3319
[38]冯正平,孙健国,黄金泉等.一种建立航空发动机状态变量模型的新方法[J].航空动力学报, 1998, 13(4):435-438.
[39] R. H. Luppold; J. R. Roman; G. W. Gallops etal. Estimating in-flight performance variation using Kalman filter concepts. AIAA 89-2584, 1989.
[40] Dan Simon. Aircraft turbofan engine health estimation using constrained Kalman filtering. NASA/TM 2003-212528, 2003
[41] Takahisa Kobayashi. Application of a constant gain extended Kalman filter for in-flight estimation of aircraft engine performance parameters. NASA/TM 2005-213865,2005
[42] Takahisa Kobayashi. Hybrid Kalman filter: a new approach for aircraft engine in-flight diagnostics. NASA/TM 2006-214491,2006
[43] G. Gilyard; J. Orme. Subsonic flight test evaluation of a performance seeking control algorithm on an F-15 airplane. AIAA 92-3743, 1992.
[44] K. Lietzau; A. Kreiner. Model based control concepts for jet engines. Proceedings of ASME TURBO EXPO 2001, new Orleans, louisian, USA, ASME, New York, NY, United States, june 4-7, 2001.
[45] Frank W. Burcham; Jr. Glenn B. Gilyard; Lawrence P. Myers. Propulsion system/flight control integration and optimization. NASA Technical Memorandum 4207, 1990
[46] E. Nemeth; R. Anderson; J. Maram; A.Norman. An advanced intelligent control system framework. AIAA-92-3162.
[47] Sanjay Garg. Controls and health management technologies for intelligent aerospace propulsion systems. NASA/TM-2004-212915.
[48]袁春飞,姚华,杨刚.航空发动机机载自适应模型研究.航空学报, 2006, 27(4): 561-564.
[49] M. J. He, W. J. Cai, B. F. Wu, Block control structure selection based on reletive interaction decomposition. ICARCV '06. 9th International Conference on Control, Automation, Robotics and Vision, 2006,pages:1-6.
[50] Niederlinski, A. A heuristic approach to the design of linear multivariable interacting subsystems.Automatica, 1971, 7: 691-701
[51] He M.-J; Cai W.-J. New criterion for control loop configuration of multivariable prcesses. Ind. Eng. Chem. Res. 2004(43):7057-7064
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