空空導彈自動駕駛儀設計

空空導彈自動駕駛儀設計,空空導彈,自動駕駛儀,設計 Article ID: 1004 - 0579( 2001) 04 -0364 - 06Model Reference Variable Structure Autopilot Designfor Homing MissileSONG Jian -mei( School of Mechano -Electronics Engineering, Beijing Institute of Technology, Beijing100081, China)Abstract: To design the control system for some homing missile so that the autopilot can trans -fer guidance command correctly and be robust to disturbances, such as the measurement noisesand parameter variation caused by areodynamic floating. The model reference adaptive controlwas combined with the variable structure control to design a model reference variable structure(MRVS) control system whose controlstructure is simple and can be realized easily. The simu -lation results indicate that MRVS can complete the task of transferring guidance command andsuppress the distrubances effectively.Key words: model reference variable structure; variable structure control; autopilotCLCnumber: TJ 765122 Document code: AReceived 2001 -07 - 12Biography SONG Jian - mei( 1968- ) , associate professor, doctor.T he tasks of missile control system are as follows1: the first one is to stabilize the missilebody and make the missile body have suitable damping; the second one is to transfer guidancecommand correctly which makes the rudder deflect and change its attitude. The final goal is tochange the magnitude and direction of the velocity and force the missile to hit the target accurately.However, during the missile flight, the model of missile body has some uncertainties becauseof the variation of missile mass, velocity, areodynamic and measurement noises. Furthermore themissile dynamics is in essence highly non -linear. The classical control theory and adaptive controltheory which is fit for linear plants could not give out robust design for missile autopilot.Variable structure control system theory 2is in essence a control theory for non -linear sys -tems, and it changes the structure of the system according to the variation of the system. s state.So it can get better control effects than the conventional control theory. Furthermore the slidingmode of variable structure control is more robust to the disturbance, many studies have showedthat the variable structure control method is suitable for missile control system design.T he model reference adaptive control system is a good control means for linear plant whoseparameters vary slowly. Since the performances of the controlled plant and the reference modelare compared directly, the speed of adaptation is high and the controller can be realized easily.But the model reference adaptive control is only fit for the continuous system whose model is)364)Journal of Beijing Institute of Technology , 2001, Vol. 10, No. 4certain, and may have unstable phenomenon when there are disturbance, noise and unmodelleddynamics.T he paper combined the model reference control with variable structure control and designedMRVS autopilot for some homing missiles.1 Model Reference Variable Structure System DesignT he paper only discusses the single input system because of the characteristics of rol- l stablemissile system.T he model of the controlled plant is assumed to bex= Ax+ Bu, x I Rn, u I R.( 1 )T he reference model isxm= Amxm+ Bmum, xmI Rn, umI R.( 2 )Define the error state ase( t) = xm( t)- x( t) , e( t)= xm( t )- x( t).( 3 )Select the sliding mode asS= Ge, G= c 1 ,( 4 )where c is a positive constant.T he control command for plant is assumed to be u and u= up+ um, where upis producedby variable structure controller.T hen the error state equation ise= xm- x= Amxm+ Bmum- Amx+ Amx- Ax- Bu=Ame+ ( Bm- B) um+ ( Am- A) x- Bup.( 5 )T ake derivative of Eq. ( 4) , thenS#= Ge= G Ame+ ( Bm- B) um+ ( Am- A) x- Bup .( 6 )According to the arriving condition of variable structure, thenS S# 0, G Ame+ ( Bm- B) um+ ( Am- A) x- Bup S 0.( 7 )Assuming the order of the linear model of the controlled plant is two, and assumingAm=a11ma12ma21ma22m, A=a11a12a21a22, Bm=0bm, B=0b,then Eq. ( 7) can be represented as ca11me1+ ca12me2+ a21me1+ a22me2+ c( a11m- a11)x1+ c( a12m- a12) x2+( a21m- a21) x1+ ( a22m- a22) x2+ ( bm- b) um- bup S 0.( 8 )Let uphave the control form as given below:up= k1| e1| + k2| e2| + k3| x1| + k4| x2| + km| um| .When the following inequalities hold, i. e.)365)SON G Jian-mei / Model Reference Variable Structure Autopilot Design f or Homing Missile ( ca11m+ a21m) e1- bk1| e1| S 0 ( ca12m+ a22m) e2- bk2| e2| S 0 ( ca11m- a11)+ ( a21m- a21) x1- bk3| x1| S 0 ( ca12m- a12)+ ( a22m- a22) x2- bk4| x2| S 0 ( bm- b) um- bkm| um| S 0,( 9 )then inequality ( 8) will hold, that is, upwil satisfy the arriving condition of variable structurecontrol.If b 0, ( c+ g/ V) 0,the equivalent system is convergent.3 SimulationT he simulation model of missile body is severely non -linear and time -varying, that is, themodel is formulated by the real wind tunnel data.Let the input of the reference model be a series of square wave.Firstly, white noise is added to the overload output according to the following pattern:overload= original overload* ( 1+ white noise) .When the standard deviation of the noise is 013, the curve of the overload controlled byMRVS is shown as Fig. 1. Fig. 2 is the curve of overload without MRVS. It indicates thatMRVS can suppress the measurement noises effectively.Secondly, let the aerodynamic coefficients vary according to the following pattern:aerodynamic coefficient of air dynamics= original aerodynamic coefficient of air dynamics*( 1+ white noise) .)367)SON G Jian-mei / Model Reference Variable Structure Autopilot Design f or Homing MissileFig. 1 The curve of overload ( MRVS and noise= 013)Fig. 2 T he curve of overload ( no MRVS and noise= 013)When the standard deviation of the noise is 011, the curves of overload and pitch angular rateare shown as Figs. 3- 6. It shows that MRVS makes the variation of output with noise inputmuch smaller. Especially for pitch angular rate, the decrease of variation is important to stabilizethe missile body.Fig. 3 The curve of overload ( no M RVS)Fig. 4 T he curve of overload ( MRVS)Fig. 5 T he curve of pitch angular rate( no MRVS)Fig. 6 The curve of pitch angular rate( MRVS)4 ConclusionT he model reference variable structure control system can make the autopilot transfer guid -ance command correctly and be robust to disturbances, such as the measurement noises and aero -dynamic coefficient variation. The control law can be realized easily and simulation results showedthat MRVS is effective for homing missile control system design.)368)Journal of Beijing Institute of Technology , 2001, Vol. 10, No. 4References: 1 Zhao Shanyou. Guidance and control system design for homing missile systems ( in Chinese) M.Beijing: Astronautic Publishing House, 1992. 2 Gao Weibing. Theory and design method of variable structure control ( in Chinese) M. Beijing:Science Press, 1996.一種尋的制導導彈模型參考變結構自動駕駛儀的設計宋 建 梅( 北京理工大學 機電工程學院, 北京 100081)摘 要: 設計某尋的導彈的自動駕駛儀回路, 使導彈控制系統在正確響應制導指令的同時, 對彈體氣動力參數變化、 量測噪聲等具有很好的抑制作用. 將模型參考自適應控制方法與變結構控制方法相結合, 為某型導彈設計了結構簡單、 實現方便的模型參考變結構控制系統. 仿真結構表明, 模型參考變結構自動駕駛儀不僅能準確傳遞制導指令, 而且具有很好的魯棒性, 能有效地抑制氣動力浮動、 量測噪聲等干擾因素.關鍵詞: 模型參考變結構; 變結構控制; 自動駕駛儀)369)SON G Jian-mei / Model Reference Variable Structure Autopilot Design f or Homing Missile