直升机阵风响应缓和控制律设计_英文_.pdf

DESIGN AND I M PLEM ENTATI ON OF GUST RESPONSEReceived date:2003-06-23;revision received date:2003-10-15ALLEVIATI ON CONTROL SYSTEM FOR HEL ICOPTERSGON G H ua2jun,YA N G Y i2dong(College of A utomation Engineering,NUAA29 Yudao Street,N anjing,210016,P.R.China)Abstract:Gust response alleviation is very i mportant forhelicopters which have strong coupling and vibration.Gust disturbance not only influences the ride quality andthe precision of the weapon delivery,but also affects tothe structural fatigue load and the strength.The methodof an opti mal control law to suppress the gust disturbancefor helicopters is presented.The opti m ization requires them ini m ization of the vertical overload at the pilots seat,the attitude variation and the control energy consumptionunder the gust disturbance.Based on the original controlsystem,the new system can be easily realized by adding avertical speed feedback passage.In order to develop thereal2ti me operational flight control system,the opti m izedcontrollawis w ritteninClanguage.Thehybridsi mulations prove that the performance of gust responsealleviationandtheefficiencyofdigitalizationaresatisfactory.Key words:helicopter;gust response;opti mal control;flight controlCLC number:V 24911Document code:AArticle I D:100521120(2004)0120013205INTRODUCTI ONInorderto meettheneedsincombatm issionsandimprovethesurvivability,helicopters generally fly at very lowaltitudeswherestrong atmospheric disturbances exist.The gust disturbancew ill aggregate the vibrationof helicopters which are unstable intrinsically inlow altitudes and poor in the ride quality.It alsomakes helicopters of strong coupling difficult tocontrol andcuts downthe precision oftheweapon delivery.From 1974,the control field of hilicoptersput forward many theories based on the activecontrolandtheelectricfeedbackofrotorvariablestosuppressthegustresponse1,2,because the rotor of a helicopter is the mostsensitive componenttothe gust disturbance.A zuma and Saito from Tokyo U niversity studiedrotor gustresponses by means ofthelocalmomentumtheory(LM T)3.Bir and Chopraresearched the gust response of the hingelesshelicopter rotor in cruising flight4.However,the gust response of the helicopter rotor is acomplex dynam ic phenomenon.It is very difficultto measure rotor variables directly to realize theelectric feedback.This paper presents a method of measuringflight state variables so as to keep the attitudesconstant as far as possible.M oreover,the ridequalityrequiresthem inim izationoftheaccelerationoverloadatthepilotsseat.Considering both the attitude and the overload,weavoidthedefectsofaccountingthestabilization of the attitude but neglecting theimprovement of ride quality and vice versa in theresearch ofthe gustresponse alleviation.Inorder to realize the digitalization of the flightcontrol system,the optim ized control lawisw ritten in C language.It is proved by hybridsimulationthatthemethodsforoptim izingcontrol law and digitizing are all feasible.M ar.2004T ransactions of N anjing U niversity of A eronautics&A stronauticsVol.21 No.11MOTI ON EQUATI ON OF HE-L ICOPTERUNDERVER-TICAL GUST D ISTURBANCEInfluences of the vertical gustWverin theshort2period motion of helicopters are discussedin this paper.A ssume that a helicopter is in levelflight w ith the body axis close to a horizontalline,andthedirection ofthevertical gustcoincidentw iththeverticalaxisofthehelicopter.Supposing that the upward verticalgust is positive,we have the follow ing short2period small perturbation equation defined in theleft2hand coordinate system5.(FZvZS-FZvZ)vZ-FZ+FZ=FZWYWY+FZvZWver(MYvZS-MYvZ)vz-MY+(MYS+MY)=MZWYWY+MYvZWver(1)whereSis the differential operator,vZandvZare the increments of the vertical speed and thevertical acceleration,respectively.andarethe increments of the pitch angle and the pitchangular velocity,WYis the longitudinal controlinput,FZvZ,FZvZ,FZ,FZandFZWYareaerodynam ic coefficients along the vertical axisZ,MYvZetc.aretheaerodynam ic momentcoefficients about the horizontal axisYandWveris the gust disturbance.In order to realize thefeedback of the state variables,vZ,andare taken to be state variables.The matrix equation of Eq.(1)can bew ritten as follow sHX=FX+MU+EWver(2)whereH=FZvZ00MYvZ0MY010F=FZvZFZ-FZMYvZMY-MY001M=FZWYMYWY0TE=FZvZMZvZ0TX=vZ TU=WYWveris the gust model selected to be a discretegust model(1-cos)from M I L28785B.Thestandard form of Eq.(2)may be expressed asX=AX+BU+GWver(3)whereA=H-1F,B=H-1M,G=H-1EThe state equation w ithout the gust distur2bance isX=AX+BU(4)2DESIGN OF CONTROL LAWIn order to apply the modern control theoryto m inim izing the acceleration overload under thegustdisturbance,wemustfirstw ritetheincremental equation of the overload at the pilots seat located at a distanceLfrom the centre ofgravity of the helicopternZ=aZ?g=(vZ+v0+L)?g(5)wherev0istheflightspeed.W hentheincrementofattackangularvelocityapproaches zero,i.e.v0v0,v0may betaken as the vertical acceleration as the helicopterflies w ith the flight path angular velocity.Lis the vertical acceleration as the helicopterflies w ith angular accelerationL.U sing the state variables from Eq.(3),Eq.(5)may be expressed asnZ=CX+DU(6)whereCandDare constant matrices related tothe aerodynam ic coefficients,control inputs andg,v0,L.From Eq.(6)we know thatnZhassomething to do w ith the state vectorXand canbe controlled w ith input vectorU.In order to realize the system and obtain thelinear control law of the optim ized system,thequadratic performance index is defined asJ=0(nZ2+XTQ1X+UTR1U)dt(7)whereQ1andR1are the given positive definitesymmetric matrices.The optimal control lawwhich m inim izes the performance indexJw illm inim ize the acceleration overload,the attitude41T ransactions of N anjing U niversity of A eronautics&A stronauticsVol.21variations and the control energy consumption atthe same time.Substituting Eq.(6)into Eq.(7)yieldsJ=0(XTQX+2XTSU+UTRU)dt(8)whereQ=Q1+CTCS=CTDR=R1+DTD(9)It is necessary to change Eq.(8)into astandard quadratic form to get the control law,so the cross term 2XTSUshould be elim inated.J=0(XTQMX+UMTRUM)dt(10)whereUM=U+R-1STX(11)QM=Q-SR-1ST(12)To apply the performance index,the stateequation must be w ritten w ith the state vectorXand the control vectorUM.Substituting Eq.(11)into Eq.(4)yieldsX=AMX+BUM(13)whereAM=A-BR-1ST(14)Applying the optimal control theory,theoptimalcontrollawwhichm inim izestheperformance indexJis determ ined byUM=-KMX(15)KMis the feedback gain matrixKM=R-1BTP(16)where the positive definite symmetric matrixPisthe solution of the R iccatimatrix equationPAM+AMTP-PBR-1BP=-QM(17)From Eqs.(11,14,16),we have the optimalcontrol lawUdefined by Eq.(4)U=-R-1(BTP+ST)X=KX(18)whereK=-R-1(BTP+ST)(19)By simulation,a set of the best weightfactor matricesR1,Q1andthe correspondingfeedback gain matrixKcan be obtained.3SI M ULATI ON RESULTS ANDSYSTEM REAL IZATI ONDolphinhelicopter of SF I MCompanyinFrance flies at a speed of 22 m?s and an altitudeof 1 000 m.Its longitudinal short2period andsmall perturbation equation under a vertical gustis described in Ref.10.vZ=-01528 5-01005 0901387 5001-11058 3-01001 82-21758 6vZ+01086 30-51590 2u+-01528 50-11058 3Wver(20)N eglecting the disturbance term in Eq.(20)and substituting it into Eq.(6),we have thevertical overload at the pilots seat which is 118m from the centre of gravitynZ=CX+DUwhereC=-01248 3-01000 9411768 6D=-11017 98By selecting a set of weight factor matricesR1andQ1,the feedback gain matrixKcan becalculated.Simulation results show that ifR1=1Q1=D iag111thesystemw illhavetheidealoverallperformance.This means that it is the mostsuitable forthe vertical overloadnZ,statevariables and the control termuto have thesame weight factors.The solution of R iccati equation is01949 8-01124 801007 03-01124 821674 001253 401007 0301253 401169 1A nd the optimal feedback gain matrix isK=01145-01701-11348The gust model is the discrete gust(1-cost)selected from M I L28785BWver=0vm1-cos(t?tm)?20t 00 t 2tmwherevm=20 m?s,andtm=015 s.Fig.1 show sthe responses of the gust alleviationsystem.51No.1GON G Hua2jun,et al.Design and I mplementation of Gust ResponseCompared w ith responses of the original systemunder the gust disturbance(dotted line in Fig.1),we w illseethatthe peakof overloadresponsesis only one2fourthofthe originalsystem and the peaks of pitch angle and pitchangular velocity are 1?3 and 1?4 of the originalsystem,respectively.Fig.1Responses ofnZ,andvZunder gust disturbanceSimulation of long2periodmotion also show sthatthegustalleviationresponsesaresatisfactoryifthelong2periodmotionisconsidered.Basedontheoriginalattitudecontrolsystem of the helicopter,the gust alleviationcontrol system(Fig.2)can be easily realized byadding a vertical speed feedback passage.It isproved by theoretical analyses and simulationthat zero assigned byKS+Kis reasonable tothe attitude control system.Hence,the attitudecontrol system and the gust alleviation systemare compatible w ith each other.Fig.2Block diagram of hybrid si mulationThe hybrid simulation(Fig.3)show s thatdynam ic responses of the gust alleviation arevery close to the digital simulation.This provesthat the development and the realization of thecontroller are both very effective.4CONCLUSI ONThe quadratic and optimal control methodpresented in this paper effectively provides agust response alleviation control for helicopters.Thecontrolleris veryeasyforengineeringrealization and due considerations are given tovertical overload,attitude variations and controlenergy consumption.The digitalization methodof in flight control system programmed in Clanguage has been proved to be feasible.61T ransactions of N anjing U niversity of A eronautics&A stronauticsVol.21Fig.3Responses of hybrid si mulationReferences:1Taylor R B,Zw icke P E,Gold P,et al.A nalyticaldesign and evaluation of active control system forhelicopter vibration reduction and gust responsealleviationR.NA SA CR 152377,1980.2Chen R T N,L ebacqz J V,A iken E W,et al.He2licopter mathematical modelsandcontrollawdevelopment for handling qualities research R.NA SA2CR22495,1988.3A zuma A,Saito S.Study of rotor gust response bymeans of the local momentum theory J.Journalof the American Helicopter Society.1982,27(1):3136.4Bir G S,Chopra I.Gust response of hingeless ro2torsA.The 41st A nnual Forum of the AmericanHelicopter SocietyC.FortWorth,Texas,1985.923928.5Gong Huajun.Design and i mplementation of gustalleviationcontrolsystemforhelicopter D.N anjing:N anjing U niversity of A eronautics andA stronautics,1990.6Sarathy S,M urthy U R.A n advanced rotorcraftflight si mulation model:parallel i mplementationand performance analysisR.A I AA293235502CP,1993.7Woods2V edeler J A,Pototzky A S,Hoadley S T.Rolling maneuverloadalleviationusingactivecontrolJ.Journal of A ircraft.1995,32(1):6876.8Xiao Yelun,Jin Changjiang.Flight principle in at2mospheric disturbances M.Beijing:N ationalDefence Industry Press,1992.9Norman D C,Hynes R J,Gaangsas D.A n integr2ated maneuver enhancement and gust alleviationmode for the A FT I?F2111 MAWaircraft R.A I AA 18322217,1992.391403.10 Yang Yidong,Gao L ixin.The development of thedigital flight control system operational softwareusingClanguage J.JournalofN anjingU niversity of A eronautics and A stronautics,1990,22(4):106110(in Chinese).直升机阵风响应缓和控制律设计龚华军,杨一栋(南京航空航天大学自动化学院,南京,210016)摘要:阵风响应缓和研究对于具有强耦合和振动的直升机非常重要,阵风扰动不仅影响直升机的乘座品质和武器投放精度,而且影响直升机的疲劳载荷和强度。本文提出直升机抑制阵风扰动的最优控制律设计方法。优化性能指标要求在阵风扰动下驾驶员处法向过载、飞机姿态变化以及控制信号能量损耗最小。最终所综合的系统工程实现简便,只需在直升机姿态控制系统基础上增加垂直升降速率反馈通道即可。最后使用C语言实现控制律并进行半物理仿真,仿真结果表明,控制律优化及数字化实现的效果是令人满意的。关键词:直升机;阵风响应;最优控制;飞行控制中图分类号:V 2491171No.1GON G Hua2jun,et al.Design and I mplementation of Gust Response