2023年第九届数维杯国际大学生数学建模挑战赛于日正式开赛啦！开赛时间为北京时间2023年11月16日08:00至北京时间2023年11月20日08:00，共计四天。学长第一时间把新鲜出炉的赛题拿出来与大家一起分享，题目难度如何？大家速来围观吧！另外还整理了本次赛题的思路和参考文献，后面也会持续更新代码以及论文资料，有需要的可以关注一下~A题2023“ShuWei Cup”ProblemA:Modeling and Optimization Control Issues of Compound HelicopterA.Problem BackgroundHelicopters possess flight capabilities such as vertical takeoff andlanding,making them widely applicable in fields such as reconnaissance and transportation.The configuration of traditional helicopters causes the rotor blades to be affected by shock waves during high-speed flight, making stable flight difficult.In order to retain the flexible flying capability of helicopters while developing their high-speed flight capability,the design of compound helicopters,which combine fixed wings with rotors,has become an essential direction for development. Coaxial helicopters are a typical type of compound helicopter.This configuration mainly consists of four power components:coaxial rigid rotors,propeller thrusters,and horizontal and vertical tails.The centers of the propeller thrusters and horizontal and vertical tails are all located on the flying machine fuselage’s symmetry plane.The flying machine’s attitude angles refer to the roll angle o,pitch angle 0,and yaw angle y during flight,and the corresponding moments are known as roll moment, pitch moment,and yaw moment (as shown in Figure 1).The influences of the four power components on the flying machine’s attitude angles are as follows:1)The aerodynamic moment generated by the coaxial rigid rotors can be approximated as a function proportional to the air density p, rotor disc area,and rotor blade tip velocity,the positive scale factor is called the rotor moment factor.2)The propeller thrusters generate thrust and rotational moment through rotation.3)The horizontal tails are equipped with elevator control devices,which adjust the relative angle of the horizontal tails to provide pitch moment.This moment is proportional to dynamic pressure,horizontal tail area,and the lateral distance between the horizontal tail and the center of mass,with the proportionality coefficient known as the horizontal tail moment coefficient.4)Similar to the horizontal tails,the vertical tails provide yaw/roll moment by adjusting the relative angle by installing a rudder control device.This moment is proportional to dynamic pressure,vertical tail area,and the lateral/longitudinal distance between the vertical tail and the center of mass,with the proportionality coefficient known as the vertical tail moment coefficient.The maneuverable parts of a composite helicopter are as follows:(1) Coaxial rotor overall distance ue,(2)Coaxial rotor differential total distance ucd,(3)Coaxial rotor longitudinal cycle pitch ue,(4)Coaxial rotor lateral cycle pitch u(5)Propeller thruster operating capacity ut,(6) Elevator deflection values ueh,(7)Rudder deflection values uav. Depending on the helicopter’s flight speed,in the low-speed mode (generally referring to speeds below 85 meters/second),attitude angle control is realized mainly by coaxial rotor and propeller thrusters.In the high-speed mode (generally referring to speeds above 100 meters/second), attitude angle control is mainly realized through propeller thrusters, elevators,and rudder.An example of a coaxial composite helicopter prototype is available, and some of the aerodynamic coefficients and airframe parameters of this vehicle have been obtained through wind tunnel experiments,as shown in Appendix I.Fig.I.Coaxial helicopter configuration and roll,yaw,pitch schematic diagramB.Title DataRefer to Appendix I.C.Issues To Be Addressed1.Considering the given parameters,establish the expression for the pitch moment of the compound helicopter and develop a model for pitch angle variation.Please provide the attitude angles of the flying machine at 5s,10s,and 20s initial flight altitude of 3000 meters,flight speed forward component 80 m/s,vertical ascent component 2 m/s,ue =0 degree、ued=-2.1552 degree、ue=-3.4817 degree、ua=-2.0743 degree、4=0 degree、ueh=-9.0772×10-7 degree、uar=4.1869× 10-7 degree)2.Based on the title given parameters,establish the expressions forthe compound helicopter’s roll,pitch,and yaw moments and develop a model for the variation of attitude angles.Please provide the attitude angles of the flying machine at 5s,10s,and 20s (initial flight altitude of 3000 meters,flight speed forward component 80 m/s,vertical ascent component 0.2 m/s,uc 0 degree ucd =-2.1552 degree,ue =3.4817 degree、ua=-2.0743 degree、w=0 degree、ueh=-9.0772×10-7 degree、uam=4.1869×10-7 degree)3.Based on the maneuvering characteristics of helicopters during low-speed and high-speed flight,designing the magnitude of the maneuvers of each component to satisfy the vehicle’s level-flying mission (zero attitude angle)for the aircraft (initial flight altitude of 3000 meters, flight speed forward component of 80 meters/second,vertical ascent component of 0.2 meters/second;initial flight altitude of 3000 meters, flight speed forward component of 180 meters/second,vertical ascent component of 0.2 meters/second).4.Considering the helicopter’s acceleration maneuver task,where the flight speed forward component increases uniformly from 80 meters/second to 180 meters/second within 20 seconds (assuming the forward acceleration is provided solely by the propeller booster),please design the dynamic values of each control input to achieve both forward acceleration and level flight (zero attitude angle)for the aircraft,taking into account the maneuvering characteristics of the helicopter during low-speed and high-speed flight (initial flight altitude of 3000 meters,flight vertical ascent component rate of 0.2 meters/second).D.Online Resources and References Related to The Question[1]何伟，陈燕云，杨杰等基于H∞回路成形的高速直升机控制器).兵工自动化，2020,39(09)：74-79[2]孔卫红，陈仁良.反流区对复合高速直升机旋翼气动特性的影响) 航空学报，2011,32(02)223-230[3]黄明其，徐栋霞，何龙等常规旋翼构型复合式高速直升机发展概况及关键技术U】航空动力学报，2021,36(06)：1156-1168.D01:10.13224 cnki.jasp.2021.06.004[4]Ye Y,Thomson D,Renliang C,et al.Heading control strategyassessment for coaxial compound helicopters[J].Chinese Journal of Aeronautics,2019,32(9):2037-2046[5]Floros M W,Johnson W.Stability and Control Analysis of theSlowed-Rotor Compound Helicopter Configuration[J].Journal of the American Helicopter Society,2007,52(3):239-253[6)邓柏海，徐锦法.复合式无人直升机姿态自抗扰控制J/OL].北京航空航天大学学报：1-10.htps:/doi.org/10.13700j.bh.1001-5965.2021.788[刀范欣林，王立峰，钟伦超.复合式共轴无人直升机低速飞行的姿态控制研究J.电子测量技术，2020,43(12)：12-17.D0:10.19651j.cnki.emt 2004302[8]Zheng F,Xiong B,Zhang J,et al.Improved neural network adaptive control for compound helicopter with uncertain cross-coupling in multimodal maneuver[J].Nonlinear Dynamics,2022,108(4):3505-3528.[9]Phelps A E,Mineck R E.Aerodynamic characteristics of a counter-rotating,coaxial,hingeless rotor helicopter model with auxiliary propulsion[R].1978.[10]曹燕.复合式高速直升机飞行动力学建模与控制技术研究D引南京航空航天大学，2018Title Statement:The questions are only used by the contestants of the 9th “ShuWei Cup” International Competition in 2023,and any form of tampering.editing and other purposes is strictly prohibited without the authorization of the Organizing Committee of the”ShuWei Cup”.Once found,it shall bear the relevant responsibility.
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