针对飞机初步设计阶段其放宽静稳定度（RSS）与电传飞控系统时间延迟边界之间的定量关系求解问题，以战斗机纵向短周期方程为基础，分析了飞控系统中的时间延迟因素，描述了放宽静稳定度与方程参数间的关系。并以等效输入延迟的形式构建了含飞控系统时间延迟的闭环系统特征方程，通过根轨迹趋势理论和数值计算方法确定了放宽静稳定度与飞控系统时间延迟边界的定量数值关系，同时探讨了舵效与动导的参数不确定性对所求时间延迟边界的影响。本文方法对飞机初步设计阶段飞控系统时间延迟指标和可放宽静稳定度边界的确定具有一定的工程实践意义。
The problem of quantitative determination between Relaxed Static Stability (RSS) and time delay boundary of the fly-by-wire control system during the preliminary design stage of aircraft is studied. Based on the longitudinal short-period equation of the combat aircraft, the time delay factor in the flight control system and the relationship between parameters in short period equation and RSS is analyzed. A characteristic equation of closed-loop system with time delay of flight control system is constructed in the form of equivalent input delay. The quantitative numerical relationship between the RSS and the time delay boundary of the flight control system is determined by the root tendency theory and the numerical calculation method. Moreover, the influence of the parameter uncertainty of control surface efficiency and dynamic derivative on the time delay boundary is also discussed. The method of this paper has certain engineering practical significance for determining the time delay boundary of the flight control system and the RSS of the aircraft in the preliminary stage of aircraft design.
[1] 李力, 白俊强, 郭同彪, 等. 考虑放宽静稳定度的民用客机气动优化设计[J]. 航空学报,2017, 38(9):121112. LI L, BAI J Q, GUO T B, et al. Aerodynamic optimization design for civil aircraft considering relaxed static stability[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(9):121112(in Chinese).
[2] ANDERSON B C, BERGER R L, HESS J R. Maneuver load control and relaxed static stability applied to a contemporary fighter aircraft[J]. Journal of Aircraft, 1973, 10(2):112-120.
[3] BIEZAD D, BOLE K. Using eigenspace analysis to determine aircraft flying qualities[C]//AIAA Atmospheric Flight Mechanics Conference and Exhibit.Reston:AIAA, 2001:4198.
[4] 马超, 李林, 王立新. 小展弦比飞翼布局作战飞机可控性设计方法[J]. 航空学报, 2008, 29(4):788-794. MA C, LI L, WANG L X. Design method of controllability of low aspect-ratio flying wing configuration combat aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(4):788-794(in Chinese).
[5] 范丽, 史忠科. 具有时滞的非线性纵向飞行模型稳定性和分支分析[J]. 控制与决策, 2013, 28(7):985-990. FAN L, SHI Z K. Stability and bifurcation analysis of nonlinear model for longitudinal motion with time delay[J]. Control and Decision, 2013, 28(7):985-990(in Chinese).
[6] 李清东, 张孝功, 任章. FADS压力传感器延迟补偿[J].航天控制, 2008, 26(6):12-15. LI Q D, ZHANG X G, REN Z. The time delay compensation for the pressure sensors of FADS[J]. Aerospace Control, 2008, 26(6):12-15(in Chinese).
[7] 付永领, 韩旭, 杨荣荣, 等. 电动静液作动器设计方法综述[J]. 北京航空航天大学学报, 2017, 43(10):1939-1952. FU Y L, HAN X, YANG R R, et al. Review on design method of electro-hydrostatic actuator[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(10):1939-1952(in Chinese).
[8] HOU C, WANG S, WANG Q, et al. Performance analysis of high-speed MIL-STD-1553 bus system using DMT technology[C]//2013 8th International Conference on Computer Science & Education, 2013:533-536.
[9] 米宁, 周海涛, 朱纪洪. 基于光纤通道的光传飞行控制系统通信方案[J]. 清华大学学报:自然科学版, 2005, 45(7):969-972. MI N, ZHOU H T, ZHU J H. Communication scheme of fly-by-light flight control system based on fibre channel[J]. Journal of Tsinghua University (Science and Technology), 2005, 45(7):969-972(in Chinese).
[10] ZAYCHIK L E, GRINEV K N, YASHIN Y P, et al. Effect of feel system characteristics on pilot model parameters[J]. IFAC-PapersOnLine, 2016, 49(32):165-170.
[11] 许舒婷, 谭文倩, 孙立国, 等. 主动侧杆引导下的Ⅱ型驾驶员诱发振荡抑制[J]. 航空学报, 2018, 39(8):121861. XU S T, TAN W Q, SUN L G, et al. Using active side-stick to prevent Ⅱ category pilot-induced oscillations[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(8):121861(in Chinese).
[12] ETKIN B. Dynamics of atmospheric flight[M]. Chicago:Courier Corporation, 2012.
[13] COOK M V. Flight dynamics principles:a linear systems approach to aircraft stability and control[M]. Oxford:Butterworth-Heinemann, 2012.
[14] RUSSELL R S. Nonlinear F-16 simulation using Simulink and Matlab[R]. 2003.
[15] 桂敬玲, 姜兵, 李建平, 等. 基于EA方法的飞行控制律设计与仿真[J]. 计算机仿真, 2013, 30(6):72-76. GUI J L, JIANG B, LI J P, et al. Design and simulation of flight control laws based on EA method[J]. Computer Simulation, 2013, 30(6):72-76(in Chinese).
[16] OLGAC N, SIPAHI R. An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems[J]. IEEE Transactions on Automatic Control, 2002, 47(5):793-797.
[17] REKASIUS Z V. A stability test for systems with delays[C]//Joint Automatic Control Conference, 1980:39.
[18] COLLINS G E. The calculation of multivariate polynomial resultants[C]//Proceedings of the Second ACM Symposium on Symbolic and Algebraic Manipulation, 1971:212-222
[19] PAKZAD M A, PAKZAD S, NEKOUI M A. Exact method for the stability analysis of time delayed linear-time invariant fractional-order systems[J]. IET Control Theory & Applications, 2015, 9(16):2357-2368.
[20] VYHLIDAL T, PAVEL Z. Quasipolynomial mapping based rootfinder for analysis of time delay systems[C]//4th IFAC Workshop on Time Delay Systems, 2003:227-232.
[21] VYHLIDAL T, PAVEL Z. QPmR-quasi-polynomial root-finder:Algorithm update and examples[M]. 2014:299-312.
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