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摘要:
针对涡扇发动机过渡态多变量控制设计难的问题,提出了一种基于抽功法在过渡态加减速线上的准稳态工作点处提取线性模型的方法,并在此基础上提出了一种过渡态主控回路闭环控制律的优化设计方法。通过功率输入和功率提取解决过渡态动态特征提取难题,基于增益调度可作为非线性动态控制策略的基本原理,将稳态多变量控制规律的线性矩阵不等式(LMI)设计方法推广到涡扇发动机过渡态主控回路闭环控制的设计中,并通过最小化矩阵迹优化闭环极点配置。针对2种不同过渡态主控回路闭环控制策略,分别设计了最小化矩阵迹寻优的过渡态主控回路的多变量闭环控制律,并进行从慢车到中间状态的基于涡扇发动机非线性动态模型的双通道过渡态性能仿真验证,结果表明:方案1过渡态控制双通道
N 1、N 2的调节时间不大于5.0 s,超调量不大于0.8%;方案2过渡态控制双通道π T、N 2的调节时间不大于5.6 s,超调量不大于0.8%。-
关键词:
- 涡扇发动机 /
- 过渡态主控回路 /
- 增益调度 /
- 线性矩阵不等式(LMI) /
- 矩阵迹寻优
Abstract:In order to solve the problem that it is difficult to design transient multivariable control law for turbofan engines, a method of extracting linear model at quasi steady working point of transient acceleration and deceleration line based on power import and extraction is proposed. Based on this, a transient main closed-loop control optimal design method is proposed. It is extended from the steady multivariable control law's linear matrix inequality (LMI) design method to the design of transient main closed-loop control for turbofan engines because the gain-schedule can be used as nonlinear dynamic control method. Minimum matrix trace optimization closed-loop pole is configured to ensure the feasibility of the method. As demanded by two different transient main closed-loop control schedules, two different minimum matrix trace optimization transient multivariable main closed-loop control laws were designed respectively. Dual channels transient performance ground simulations based on a nonlinear turbofan engine model and containing the dynamic state between idle state and maximum power setting state were done. The results show that settling time of transient control dual channels
N 1 andN 2 is no more than 5.0 s and the maximum overshoot is 0.8% in case one. In case two, settling time of transient control dual channelsπ T andN 2 is no more than 5.6 s and the maximum overshoot is 0.8%. -
表 1 稳态点条件
Table 1. Conditions of steady state point
编号 n2cor SM 1 10 588 5 2 10 265 5 3 9 943 5 4 10 588 18 5 10 265 24 6 9 943 28 7 10 588 33 8 10 265 33 9 9 943 33 表 2 方案1基状态矩阵
Table 2. Basis state matrix in case 1
Ai a11 a21 a12 a22 A1 -6.36 -0.09 6.63 -4.18 A2 -9.10 0.13 5.75 -3.68 A3 -4.71 -0.16 3.82 -2.29 A4 -6.55 0.13 5.57 -3.72 A5 -5.29 -0.22 5.15 -3.54 A6 -2.90 -0.22 3.56 -2.17 A7 -5.81 0.47 3.56 -4.17 A8 -4.55 -0.34 4.60 -4.58 A9 -2.52 -0.32 3.80 -3.22 表 3 方案1基输入矩阵
Table 3. Basis input matrix in case 1
Bi b11 b21 b12 b22 B1 2.99 -0.10 0.31 0.67 B2 2.55 -0.14 0.46 0.68 B3 1.45 -0.02 0.72 0.67 B4 1.98 -0.01 0.48 0.66 B5 1.46 -0.04 0.64 0.70 B6 0.56 0 0.99 0.75 B7 0.42 0.02 0.92 1.00 B8 0.65 0.01 0.99 1.06 B9 0.36 0.01 1.00 1.15 表 4 方案1最优基控制参数KP
Table 4. Optimal basis control parameter KP in case 1
KPi, opt kP11 kP21 kP12 kP22 KP1, opt -0.47 -0.05 -0.06 -2.05 KP2, opt -0.56 -0.10 0.29 -2.09 KP3, opt -0.99 -0.08 0.71 -2.21 KP4, opt -0.72 -0.02 0.26 -2.12 KP5, opt -0.94 -0.11 0.65 -2.09 KP6, opt -2.40 -0.19 2.72 -2.23 KP7, opt -3.16 -0.03 2.78 -1.58 KP8, opt -2.06 -0.09 1.84 -1.52 KP9, opt -3.63 -0.23 3.03 -1.62 表 5 方案1最优基控制参数KI
Table 5. Optimal basis control parameter KI in case 1
KIi, opt kI11 kI21 kI12 kI22 KI1, opt -2.97 -0.59 3.41 -7.77 KI2, opt -4.95 -0.76 4.23 -6.73 KI3, opt -4.33 -0.68 5.23 -4.67 KI4, opt -4.62 0.05 5.12 -7.42 KI5, opt -4.65 -0.96 7.07 -6.52 KI6, opt -6.33 -0.83 14.32 -4.44 KI7, opt -19.44 0.62 22.69 -6.22 KI8, opt -8.69 -0.69 17.76 -6.21 KI9, opt -8.34 -0.86 23.52 -4.36 表 6 方案2基输出矩阵
Table 6. Basis output matrix in case 2
Ci c11 c21 c12 c22 C1 -0.64 0 1.18 1 C2 -1.13 0 1.27 1 C3 -0.55 0 1.21 1 C4 -0.88 0 1.14 1 C5 -0.64 0 1.28 1 C6 0.01 0 1.33 1 C7 -0.02 0 0.64 1 C8 -0.14 0 1.09 1 C9 0.25 0 1.27 1 表 7 方案2基前馈矩阵
Table 7. Basis feedforward matrix in case 2
Di d11 d21 d12 d22 D1 0.73 0 0 0 D2 0.75 0 0 0 D3 0.67 0 0 0 D4 0.74 0 0 0 D5 0.68 0 0 0 D6 0.37 0 0 0 D7 0.38 0 0 0 D8 0.45 0 0 0 D9 0.26 0 0 0 表 8 方案2最优基控制参数KP
Table 8. Optimal basis control parameter KP in case 2
KPi, opt kP11 kP21 kP12 kP22 KP1, opt -1.06 -0.29 0.40 -1.84 KP2, opt -0.86 -0.08 0.32 -2.01 KP3, opt -1.08 -0.35 0.78 -1.91 KP4, opt -0.85 0.10 0.11 -2.01 KP5, opt -1.02 -0.39 0.60 -1.69 KP6, opt 1.18 -0.18 -0.73 -1.84 KP7, opt 0.58 1.05 -0.06 -2.01 KP8, opt -0.30 -0.51 0.57 -1.02 KP9, opt -0.05 0.78 0.06 -2.43 表 9 方案2最优基控制参数KI
Table 9. Optimal basis control parameter KI in case 2
KIi, opt kI11 kI21 kI12 kI22 KI1, opt -6.99 -1.50 1.39 -7.98 KI2, opt -6.18 -0.68 1.80 -6.84 KI3, opt -5.98 -1.35 3.30 -4.52 KI4, opt -5.75 0.50 -0.23 -6.88 KI5, opt -5.78 -1.48 1.70 -6.83 KI6, opt -0.65 -1.31 2.95 -3.24 KI7, opt -2.45 2.22 2.64 -6.21 KI8, opt -3.98 -1.53 5.18 -5.63 KI9, opt -1.35 0.78 2.15 -6.24 表 10
过渡态控制器参数KP Table 10. Parameter KP of
transient controller KPi, opt kP11 kP21 kP12 kP22 KP1, opt -0.13 0 0 1.32 KP2, opt -0.16 0 0 1.64 KP3, opt -0.17 0 0 1.69 表 11
过渡态控制器参数KI Table 11. Parameter KI of
transient controller KIi, opt kI11 kI21 kI12 kI22 KI1, opt -7.23 0 0 72.3 KI2, opt -0.88 0 0 8.8 KI3, opt -1.34 0 0 13.4 -
[1] 赵连春, 杰克·马丁利. 飞机发动机控制: 设计、系统分析和健康监视[M]. 张新国, 等译. 北京: 航空工业出版社, 2012: 114-124.JAW L C, MATTINGLY J D. Aircraft engine controls: Design, system analysis, and health monitoring[M]. ZHANG X G, et al, translated. Beijing: Aviation Industry Press, 2012: 114-124(in Chinese). [2] SPANG H A, BROWN H. Control of jet engines[J]. Control Engineering Practice, 1999, 7(9): 1043-1059. doi: 10.1016/S0967-0661(99)00078-7 [3] GARG S. Propulsion controls and diagnostics research in support of NASA aeronautics and exploration mission programs: AIAA 2010-6747[R]. Reston: AIAA, 2010. [4] CSANK J, MAY D R, LITT S J, et al. Control design for a generic commercial aircraft engine: AIAA 2010-6629[R]. Reston: AIAA, 2010. [5] 苗浩洁, 王曦, 杨舒柏. 基于相似参数的加速供油规律反设计方法研究[J]. 推进技术, 2019, 40(3): 675-681. https://www.cnki.com.cn/Article/CJFDTOTAL-TJJS201903024.htmMIAO H J, WANG X, YANG S B. Reverse design method of fuel supply law for acceleration based on similarity parameters[J]. Journal of Propulsion Technology, 2019, 40(3): 675-681(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TJJS201903024.htm [6] YANG S B, WANG X. A comparative study on N-dot acceleration technique[C]//ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. New York: ASME, 2016: 1-9. [7] 西格德·斯科格斯特德, 伊恩·波斯尔思韦特. 多变量反馈控制分析与设计[M]. 韩崇昭, 张爱民, 刘晓风, 等译. 西安: 西安交通大学出版社, 2011: 57-99.SKOGESTAD S, POSTLETHWAITE I. Multivariable feedback control: Analysis and design[M]. HAN C Z, ZHANG A M, LIU X F, et al, translated. Xi'an: Xi'an Jiaotong University Press, 2011: 57-99(in Chinese). [8] RICHTER H. A multi-regulator sliding mode control strategy for output-constrained systems[J]. Automatica, 2011, 47(10): 2251-2259. doi: 10.1016/j.automatica.2011.08.003 [9] 理查特. 涡扇发动机先进控制[M]. 覃道亮, 王曦, 译. 北京: 国防工业出版社, 2013: 42-75.RICHTER H. Advanced control of turbofan engines[M]. QIN D L, WANG X, translated. Beijing: National Defense Industry Press, 2013: 42-75(in Chinese). [10] BOYD S P, CHAOUI E L. Method of centers for minimizing generalized eigenvalues[J]. Linear Algebra and its Applications, 1993, 188-189: 63-111. doi: 10.1016/0024-3795(93)90465-Z [11] GAHINET P. Explicit controller formulas for LMI-based H∞ synthesis[J]. Automatica, 1996, 32(7): 1007-1014. doi: 10.1016/0005-1098(96)00033-7 [12] BOYD S P, GHAOUI E L, FERON E, et al. Linear matrix inequalities in systems and control theory[M]. Philadelphia: SIAM, 1994: 7-27. [13] 高金凤, 俞立, 王春平. 线性矩阵不等式及其在控制工程中的应用[J]. 控制工程, 2003, 10(2): 145-148. doi: 10.3969/j.issn.1671-7848.2003.02.015GAO J F, YU L, WANG C P. Linear matrix inequality and its application in control engineering[J]. Control Engineering, 2003, 10(2): 145-148(in Chinese). doi: 10.3969/j.issn.1671-7848.2003.02.015 [14] 崔颖, 王曦. 涡扇发动机极点配置圆的多变量PI控制设计[J]. 航空发动机, 2019, 45(3): 31-38. https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201903006.htmCUI Y, WANG X. Multivariable PI control design for pole placing circle of turbofan engine[J]. Aeroengine, 2019, 45(3): 31-38(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HKFJ201903006.htm [15] 胡东, 陈文华, 周川. 基于LMI的一类LPV系统的自调整输出反馈极点配置[J]. 南京航空航天大学学报, 1998, 30(4): 388-393. https://www.cnki.com.cn/Article/CJFDTOTAL-NJHK804.005.htmHU D, CHEN W H, ZHOU C. Self-tuning output feedback pole placement for a class of LPV systems based on LMI[J]. Journal of Nanjing University of Aeronautics and Astronautics, 1998, 30(4): 388-393(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-NJHK804.005.htm [16] FENG Z, WANG Q G, LEE T H. On the design of multivariable PID controllers via LMI approach[J]. Automatica, 2002, 38(3): 517-526. doi: 10.1016/S0005-1098(01)00237-0 [17] SCHERER C, GAHINET P, CHILALI M. Multiobjective output-feedback control via LMI optimization[J]. IEEE Transactions on Atuomatic Control, 1997, 42(7): 896-910. doi: 10.1109/9.599969 [18] KANEV S, SCHERER C, VERHAEGEN M, et al. Robust output-feedback controller design via local BMI optimization[J]. Automatica, 2004, 40(7): 1115-1127. doi: 10.1016/j.automatica.2004.01.028 [19] WOLODKIN G, BAOAS G J, GARRARD W. Application of parameter-dependent robust control synthesis to turbofan engines[J]. Journal of Guidance, Control, and Dynamics, 1999, 22(6): 833-838. doi: 10.2514/2.4460 [20] PARSONS D A. N-dot schedules dynamic compensation system for gas turbines-inputs sum of speed and rate of change of speed of gas generator to schedule to output desired acceleration as function of generator speed: US, 5029441[P]. 1991-07-09. [21] 蔡常鹏, 郑前钢, 颜秋英, 等. 军用小涵道比涡扇发动机最大状态控制计划鲁棒性分析[J]. 推进技术, 2022, 43(5): 1-8. https://www.cnki.com.cn/Article/CJFDTOTAL-TJJS202205030.htmCAI C P, ZHENG Q G, YAN Q Y, et al. Robustness analysis of maximum state control plan for military small bypass ratio turbofan engine[J]. Journal of Porpulsion Technology, 2022, 43(5): 1-8(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-TJJS202205030.htm