Schoolof Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China

BTT autopilotdesign for agile missiles with aerodynamic uncertainty

Yueyue Ma,Jie Guo*,and Shengjing Tang

Schoolof Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China

The approach to the synthesis ofautopilotwith aerodynamic uncertainty is investigated in order to achieve large maneuverability of agile missiles.The dynamics of the agile missile with reaction-jet control system(RCS)are presented.Subsequently, the cascade control scheme based on the bank-to-turn(BTT) steering technique is described.To address the aerodynamic uncertainties encountered by the control system,the active disturbance rejection control(ADRC)method is introduced in the autopilot design.Furthermore,a compound controller,using extended state observer(ESO)to online estimate system uncertainties and calculate derivative of command signals,is designed based on dynamic surface control(DSC).Nonlinear simulation results show the feasibility of the proposed approach and validate the robustness ofthe controller with severe unmodeled dynamics.

agile missile,autopilot,high angle ofattack,active disturbance rejection control(ADRC),dynamic surface control(DSC), extended state observer(ESO).

1.Introduction

Due to the growing ability of high off-boresightlaunching for the shortrange air-to-air missiles,the omni-directional attack for the fi ghter carrier has attracted broad attention. The omni-directionalattack enables the missile to engage the target in the rear hemisphere of the launch platform, implicating a rapid change in attitude during the fast maneuvering after launching,which is called the agile turn. Such maneuver requires the agile missile to operate at high angle of attack(AoA)to possess needed superagility. Due to the ineffectiveness of aerodynamic control at high AoA,however,the missile needs alternative actuators such as reaction-jetcontrol system(RCS)or thrust vector control(TVC)to achieve controllability during stall.Additionally,the missile dynamics are characterized by fast timevarying,nonlinearity and uncertainty.The considerable system uncertainties induced by uncertain aerodynamic characteristics at high AoA result in a dif fi culty to effectively predict the aerodynamic coef fi cients in advance. Consequently,research of the missile autopilot for agile turn has adopted various nonlinear and robust control approaches instead of those traditionaldesign methods.

Taking the missile dynamic uncertainties at high AoA into account,the variable structure control(VSC)which is robust to system disturbances has been applied in autopilotdesign for agile turn.An approach based on the sliding mode control(SMC)was proposed to perform a maneuverof a 180°heading reversalwith the help of RCS in[1]. Other research shows that neural networks are capable of enhancing the performance of approximate dynamic inversion for controlof uncertain nonlinear systems.As a consequence,a neural-adaptive method described in[2]was specialized in the control of agile missile.In[2],the numericalsimulation presenting a typicalengagementgeometry for the head-on merge scenario was performed.In addition,other various controlmethods,such as H∞control [3],pole-placement[4]and back-stepping[5],were also suitable for autopilot design of agile missiles.Recently,a novelapproach based on purely aerodynamic controlwas proposed in[6]foragile turn and furtherinvestigated in[7] with simulation results.In the above research works,autopilots were synthesized under the precondition that the aerodynamic data had been obtained with the method of engineering estimation or wind tunneltest.Because of the severe aerodynamic uncertainties,nevertheless,the actual aerodynamic characteristics athigh AoAare highly unpredictable,which means the predictions ofaerodynamic data are extremely unreliable.As a result,the direct use of the aerodynamic coef fi cients in the control scheme for high AoA fl ightshould be avoided[8].

The agile turn is usually implemented under an extremely high AoA fl ightthatfollows a 90°AoA command[2]or 180 AoAcommand[6,7].The uncertainties ofsystem dynamics are greatly dominated by the aerodynamic properties athigh AoAregimes.However,mostresearches deal with uncertainties of plant dynamics by the robustness of the control system itself,resulting in a conservative property and high energy consumption ofthe designed controller.Among the latest studies of agile turn,the controllaws proposed in[8]did notrequire precise knowledge of aerodynamic data by regarding the aerodynamic relevant terms in the system dynamics equations as unknown quantities.Two proposed control laws were based on the integrator backstepping and H∞-norm minimization respectively.Unfortunately,the pitching moment given in [8]was assumed to vary according to a sinusoidal function whose amplitude was smallwhen considering the realworld conditions.The time-delay adaption scheme used in [9]was able to online estimate the unmodeled dynamics containing aerodynamic uncertainties,and compensate the uncertainties by introducing approximations into the control law.The time-delayed information,however,was obtained from the single-lag system,which consequentially brought time-delay characteristics to the control system. Furthermore,only small AoA fl ight(α＜35°)was simulated in this literature.

In this paper,autopilot design for agile missiles considering high Ao A maneuvering is investigated.Regarding the aerodynamic characteristics as uncertainties for the controlsystem,any aerodynamic data is unavailable to the autopilot implementation.Based on this idea,the active disturbance rejection control(ADRC)method is adopted to synthesize the control system for the plant with strong uncertainties.As the key technique of ADRC,the extended state observer(ESO)is capable of estimating the totaldisturbances of the system dynamics in real time.Such ability of online estimation enables the controlsystem to possess the disturbance rejection mechanism which is used to compensate the system uncertainties.

The outline of the paper is as follows.The dynamics model of the agile missile equipped with RCS is established in Section 2.In this section,the aerodynamicsmodel involving high AoA domain is also described for the sake of subsequenttrajectory simulation.The process ofthe autopilot synthesis is discussed in Section 3.First,the baseline control scheme using ADRC method based on the bank-to-turn(BTT)steering technology is presented for agile turn.Second,an improved method by combining dynamic surface control(DSC)with ESO is employed to design another autopilot structure.In Section 4,a numericalsimulation for the agile missile demonstrates the effectiveness ofthe proposed approach.Finally,conclusions are summarized in Section 5.

2.Agile missile dynamics

In this section,the dynamics model of the agile missile is discussed for the purpose of autopilotdesign on post stall maneuver.The agile missile takes a wingless con fi guration shown in Fig.1,which is bene fi cial to increase the available range of AoA and reduce aerodynamic uncertainty. Assume that it is able to provide the control moments in roll,pitch and yaw channelseparately,the RCS in the forebody of the missile is in charge of the fl ight control particularly for angles of attack much higher than stall.For unstalled state,the aerodynamic controldepending on the tailrudders can make contribution to the missile controlas well as RCS.In this paper,however,the RCS is the only actuatorforthe designed controlsystem due to the unavailability of the aerodynamic controlathigh AoA regimes.

Fig.1 Sketch map ofthe agile missile

The dynamics models of angle of attack and sideslip angle are needed when considering the missile dynamics characteristics for high AoA maneuver,which are described as

whereαis the angle ofattack,βis the sideslip angle,p,q,r are missile angular velocities,m is the missile mass,V is the missile velocity,T is the main engine thrust,X,Y,Z are aerodynamic forces in missile body coordinate system, g is the acceleration of gravity,θ,φare missile pitch angle and roll angle,and uy,uzare controlforces produced by RCS thrusters in the ybodyand zbodydirection respectively.To simplify the rollcontrolin BTT fl ight,an aerodynamic bank angleμaboutthe velocity vectoris introduced[2]as follows:

The momentequations of the missile are shown as

where L,M,N are aerodynamic moments in the body coordinate system,Ix,Iy,Izare rolling,pitching and yawing moments of inertia,lRis the distance between the point of RCS action and the mass center,and uxis the control momentproduced by RCS thrusters in the xbodydirection.

Aerodynamic modeling is signi fi cantbutdif fi cultforautopilot design at high AoA fl ight.In terms of the aircraft with high slenderness ratio,the asymmetric vortex shedding occurs on the body leeside when the AoA increases to a certain degree,near 30°to 60°,which induces undesirable random out-of-plane moment[10].Accordingly,it is impossible to predictthe aerodynamic data precisely in advance due to the aerodynamic uncertainties athigh AoA.

To setup an aerodynamic modelfor simulation,a compromise scheme employing both engineering approximation and arti fi cial disturbance is proposed.For the engineering approximation,the missile aerodynamic data are calculated by the Missile DATCOM code,which is capable of approximating the aerodynamic data at high AoA domain.Compared with the experiment data from wind tunneltest,the calculations of the Missile DATCOM code generally accord with the actualsteady aerodynamic forces and moments at high AoA,which is veri fi ed by investigations in[11,12].For the reference velocity Ma=0.6,the computed aerodynamic coef fi cients of the agile missile for AoA form 0°to 90°are shown in Fig.2.Cland Cdin the fi gure denote lift coef fi cient and drag coef fi cient respectively.Furthermore,the actual aerodynamic randomness at high AoA cannot be re fl ected in calculations by Missile DATCOM code.Therefore arti fi cial functions can be used to characterize the aerodynamic uncertainties which are practically impossible to predict[8].It is noted that, duo to the asymmetric vortices at high AoA,the out-ofplane moment(yawing moment)is larger than the in-plane moment(pitching moment)[13].As a consequence,the main concern in the aerodynamic uncertainties is the lateral aerodynamic load.The rolling and yawing moments of the missile are described as

whereρis the atmospheric density,S is the reference area, D is the reference length,CLis the rolling momentcoeffi cient and CNis the yawing moment coef fi cient.In this paper,the speci fi c expressional forms of the moment coef fi cients CLand CNare speci fi ed arti fi cially,while the pitching moment M is calculated by the Missile DATCOM code.

Fig.2 Aerodynamic forces versus AoA

3.Autopilotdesign

3.1 BTT controlpolicy for agile turn

In this section,the missile autopilot for agile turn is designed.For the scenario of engaging targets in the rear hemisphere,the missile fl ightfrom launching to hitting the targetcan be separated into differentmission phases such as separation,agile turn,midcourse and endgame.With regard to the agile turn phase that we are concerned about, the directional control of the missile's velocity vector relative to the missile body is desired[13],which equates to commanding AoA and regulating sideslip angle to zero. Therefore the agile turn should be implemented by an autopilotemploying BTT steering policy.Regular BTT control depends on controlling AoAα,sideslip angleβand roll angleφ.Considering the second equation of(1),the rollmotion of the missile plays a decisive role in controlling sideslip angle if AoA increases to as much as 90°which is common for agile turn.This leads to a logical contradiction in stabilizing the sideslip angle and rollangle simultaneously.To simplify the rollcontrolof BTT fl ight, the control of the velocity bank angleμis adopted in the autopilotdesign exactly as the autopilotapplication in[2], while the rollangleφis outof control.

Equations(1)to(3)can be rewritten in the vector form as

where

In(5),fxand fωdenote the known terms in the dynamics system,based on the assumption that x andωare measurable,and dxand dωdenote the unknown terms,i.e. system uncertainties,which are mainly caused by aerodynamic characteristics at high AoA.This needs to be emphasized thatallaerodynamic information are unknown to the control system according to the expression of(5).umis regarded as the virtualcontrol in(5).Accordingly,it is necessary to con fi rm the relationship betweenωand umfor the control implementation,which is presented by a transform matrix as follows:

A cascade controlscheme is appropriate for the autopilotin consideration ofcharacteristics of(5)and(6).Forthe system(5),as the command of the virtualcontrol,umcis generated by the command signal xc.Then the command inputωccan be derived through a transition described as

Ultimately the actualcontrolinput u can be determined.

3.2 ADRC method

With respect to the systems(5)and(6)that need to be addressed in this work,disturbance rejection is essential for improving the autopilotperformance.The method proposed in this section employs ADRC method to estimate and compensate the system uncertainties.

ADRC was originally proposed by Han[14-16],then explained and analyzed detailedly by Gao etal.[17,18]in recent years.As the most crucial mechanism in ADRC, ESO is able to estimate the system uncertainties in real time,which provides the autopilot with a new way to overcome the plant uncertainties.ADRC has great practical value in engineering practices,proven by related researches[19,20],including works for agile missiles[21].

In order to design an ADRC controller dedicated to the cascade system(5),fi rstly an ESO is constructed for the fi rstequation(outer controlloop)as the following:

where

and a1,a2,a3are constantpower exponents.For the ESO system(8),x and umare inputs.The output?dxwillbe incorporated into the controllaw which needs to be designed.

Then a nonlinear state error feedback is adopted in the controller,shown as

where Kx=diag[Kα,Kβ,Kμ]is a positive coef fi cient matrix.As a function vector,fal(ex,cx,δx)is described as

where cx=[cα,cβ,cμ]T,δx=[δα,δβ,δμ]T,they are parameter vectors needed to be determined.f al(ei,ci,δi)(i denotesα,βorμ)is a continuous power function with a linear segmentnear origin:

Playing an important role in ADRC,f al function sometimes provides surprisingly better results in practice.Details about f al function are discussed in[16].Eventually the virtualcontrolinput umccan be constructed aswhich means ESO can estimate the uncertainties accurately,the outercontrolloop willbe linearized with the resultin the form of

For the second equation(inner control loop)of the system(5),the design approach described above is also adopted to achieve linearization.Another ESO is given by

where Gω1=diag[g14,g15,g16],Gω2=diag[g24,g25,they are matrices composed of constant coef fi cients.Then the nonlinear feedback is constructed by introducing

where Kω=diag[Kp,Kq,Kr],cω=[cp,cq,cr]T,δω= [δp,δq,δr]T,they are parameter vectors needed to be determined.The controlinputis written as follows:

Similarly,when the conditionis met,the inner controlloop can be linearized,resulting in

Using ESO to online estimate and compensate the system uncertainties,the ADRC method discussed above transforms nonlinear inner and outer controlloop into linear systems.This process of compensation is referred to as dynamic linearization.In this case,those common error feedback approaches can be utilized to redesign the control system after linearization.In this section,a nonlinear error feedback using f al function has been employed in the control law.Fig.3 illustrates the structure framework of the missile controlsystem based on ADRC.

Fig.3 Structure diagram of ADRC

The ability to online estimation ofthe system uncertainties is the key to decide whether the ADRC controller is ef fi cient or not.The convergence of ESO(8)and(14)has been proved in[22].If ESOs are expressed in scalar form, instead of vector form described above,the actual ADRC controller needs six independent ESO systems to estimate the system uncertainties in both inner and outer control loops.Thus a great deal of undetermined parameters of these ESOs will greatly affect actual observation performance.According to the currentstate of the artofthe ESO theory,parameters selecting,to a greatextent,depends on the experiences,which often results in degradation of the ESO performance and large estimation errors.In the next section,an improved ESO-based control approach whichprovides a mechanism to weaken the effect of ESO estimation errors on the controlperformance is proposed.

3.3 Compound controlbased on DSC and ESO

In this section,a compound controlmethod based on DSC and ESO is applied to the agile missile autopilot.DSC provides an effective methodology when designing robust controllers for uncertain nonlinear systems.Sample applications have been provided to demonstrate how DSC can be effectively used to solve design problems in the automotive fi eld[23].Bene fi ting from the compensation mechanism in ESO,the proposed compound method possesses superior robustness.

For the systems(5)and(6),the design approach of the proposed compound controller is presented as follows.In accordance with DSC,the design process can be divided into two steps.The fi rst step is to get the virtual control signal,followed by the second step for generating the actualcontrolinput.

Step 1A sliding surface function is de fi ned as

Taking the time derivative of S1and using(5)gives

To achieve the reaching ofsliding surface in fi nite time,the reaching law for S1is de fi ned as

whereΔx=diag[Δα,Δβ,Δμ],sgn(S1)=[sgn(α?αc),sgn(β?βc),sgn(μ?μc)]T,andΔxis a matrix composed of positive constantgains.

Considering(19)and(20),the virtual control input is obtained as

This needs to be stressed thatwhich is the approximation of uncertainty dx,is calculated by ESO(8)and incorporated into the virtual control(21).It is assumed that˙xcis regarded as a known quantity to controldesign.

Step 2De fi ne anothersliding surface function as

whereωcis determined by(7).Using the system(5),the time derivative of S2is rewritten as In the same way as Step 1,S2is driven to zero under the reaching law:

whereΔω=diag[Δp,Δq,Δr],sgn(S2)=[sgn(p?pc),sgn(q?qc),sgn(r?rc)]T.Considering(23)and(24), the actualcontrolinputcan be designed as

denotes the approximation of˙ωc.

In DSC,the derivative of command signal is indirectly calculated by the introduction of the fi rst-order low-pass fi lter[23].In this paper,however,˙ωcis treated as the uncertainty.Based on this idea,the derivative ofsignalcan be online calculated by ESOwhich is used as an outputtracking differentiator,rather than a state observer for estimating the real disturbances.Compared with the fi lter-based indirect calculation,the ESO-based calculation of derivative of signal can not only improve the accuracy,but also maximize the excellent effect of estimating uncertainties of ESO.Thus the dynamics to be processed for ESO is modeled as

where dωcdenotes the uncertainty,i.e.a quantity needed to be observed.An ESO is designed for the system(26)as

So far we have designed a compound controller based on DSC and ESO.In the control system,ESOs are employed not only to estimate the system uncertainties,but to calculate derivatives of signals needed for control implementation.For convenience,all ESOs used in the proposed approach are integrated into a system described in the vector form of

where X1=[x,ω,ωc]T,X2=[dx,dω,˙ωc]T, fESO=[fx,fω,0]T,uESO=[um,bu,0]T.In(28), vectors composed in design parameters include G1= diag[g11,g12,...,g1n],G2=diag[g21,g22,...,g2n],where n=9.

Theorem 1With the sliding surface given by(18)and (22),ESO obtained by(28),the trajectory of the closedloop systems(5)and(6)can be driven onto the sliding surface in fi nite time with the control law(25)and evoles in a neighborhood around the sliding surface.Finally,itconverges into a residualsetof the reference trajectory.

ProofFirstly,the observation errors of ESOare de fi ned.Subtracting(28)from (5)and(26),the observer error dynamics are obtained as

where˙X2denotes the derivative of uncertainty X2.The observations of ESO will converge to a small neighborhood of observed quantities in fi nite time under certain conditions.The convergence of ESO has been mathematically proved by Theorem 2.2 in[22].When ESO is stable, we get˙e1=0 and˙e2=0,thus the observation errors can be written as

Considering a vector Y=[y1,y2,...,yn]T,two functions in(30)are de fi ned as

It is seen that the errors of estimation are determined by G1,G2,εand a.Via tuning these parameters appropriately,the estimation errors of the observercan be forced smallenough such thatthe uncertainty X2can be observed by ESO effectively.Particularly,an appropriateεcan be selected small enough such that|e1|and|e2|are small enough despite˙X2is unknown.Therefore?X1and?X2will converge into a neighborhood ofthe realstatus X1and X2respectively.

For convenience,the observation errors for the system uncertainty are denoted by

Taking the derivative of(31)and making use of the control law(25)gives

where KωiandΔωiare the i th componentof main diagonalof KωandΔωrespectively,S2i,e22iand e23iare the i th componentof S2,e22and e23respectively.Evidently, we get˙VS2＜0 when VS2is out of a certain bounded region which contains the equilibriumpoint.Decreasing VS2eventually drivesthe system trajectory into a neighborhood around the sliding surface S2=0.Hence,the trajectory of the system is ultimately bounded in the region

Therefore,S2is uniformly ultimately bounded,by which ωtracking the referenceωcis guaranteed.

In order to illustrate the reference state tracking of x, the Lyapunov function is chosen as follows:

The time derivative of(33)with the virtualcontrol(21)and state-transition equations(6)and(7)is computed as

where KxiandΔxiare the i th componentofmain diagonal of KxandΔxrespectively,S1iand e21iare the i th componentof S1and e21respectively,T?1(x)ijis the component of matrix T?1(x)at row i and column j.Similarly, we have˙VS1＜0 if VS1is outof a certain bounded region which contains zero.Making use of(32),it can be seenthat the trajectory of the system is ultimately bounded in the region

Eventually,it is guaranteed that the state x can track the reference state xc.?

Remark 1If the design parametersΔxandΔωmeet the condition as follows:

VS1and VS2will converge to zero absolutely,indicating that the system states can be guaranteed to reach the sliding surface S1=0 and S2=0 in fi nite time and fi nally converge to the origin.For practical situation,however,it is dif fi cult to meet the condition(35)all the time,since the upper bounds of|e21i|,|e22i|and|e23i|are almostimpossible to estimate.The value selection ofΔxandΔωis related to the estimation error of ESO,whose steady state error is affected byεto a large extent.In this case,the value ofΔxandΔωcan be roughly determined according to the order of magnitude ofε.Certainly,the value ofΔxandΔωshould be smallas far as possible in orderto avoid serious chattering of control input.Therefore the asymptotic stability is lost and only the bounded motion about the sliding surface is guaranteed in the practical tracking control.

The structure diagram of the proposed compound controlsystem is shown in Fig.4.Contrasting the ADRC laws (12)and(16)with the compound control laws(21)and (25),it can be seen that the compound method has better performances on rate ofconvergence and steady state error compared with ADRC method.

Fig.4 Structure diagram of compound scheme

4.Simulation results

Six-degree-of-freedomsimulations ofthe proposed autopilots foragile turn are performed in this section.In the simulations,the local vertical plane is selected as the missile expected maneuvering plane,resulting in a simpli fi cation that the missile need not perform a roll motion before the high Ao A maneuvering.Under the large angle maneuver controlthatwe need to turn the missile quickly,the Euler angle coordinate system is unsuitable for modeling the rotation motion of the missile due to the singular problem of kinematicalequations.Consequently,the quaternion algorithm is employed to modelthe kinematics ofagile missile foraddressing the problem ofattitude angle degradation of high maneuvering.

Parameters used in simulations are chosen as follows. The initial fl ight altitude is 5 km,the initial velocity is Ma=0.8,the main engine thrust is 15 000 N and the maximum steady thrust of RCS is 2 000 N.Parameters used in controllaws are summarized in Table 1 and Table 2. As a constantvalue,the simulation time is chosen as 5 s.In the simulations,the missile conducts the turning maneuver according to the commands generated by the ADRC and compound method respectively.

Table 1 Design parameters of ESOs

Table 2 Design parameters offeedback controllaws

As described in Section 2,the rolling moment coef ficient CLand yawing moment coef fi cient CNare arti ficially chosen in advance.Here CLand CNvary according to sinusoidalfunctions only for high AoA fl ight,as shown in Fig.5.When AoA is less than 30°,CLand CNare assigned with zero due to the lack of obvious uncertainty of the missile aerodynamics atsmall AoA.

Fig.6 illustrates two typical engagement trajectories which are generated by ADRC method and compound method respectively.In the simulation,the missile is stipulated to fl y straight after turning maneuver.As shown in the fi gure,the missile trajectory under the compound method possesses a smaller turning radius compared with the traditional ADRC method.The time histories of themissile velocity throughout the maneuver are plotted in Fig.7.For AoA 90°fl ight,huge drag and unavailability of the main engine thrust in velocity direction lead to a distinct drop in velocity magnitude.The missile velocity, however,increases rapidly with the action of the main engine thrustafter the large angle turning.Atthe end of simulation(t=5 s),the missile velocity under the compound method is largerthan thatunder the ADRC method.

Fig.5 Time histories ofrolling and yawing moment coefficients

Fig.6 Trajectories

Fig.7 Velocity curves

The missile responses in AoAα,sideslip angleβand velocity bank angleμare given in Fig.8.A AoA 90°command[2,13]is used in the simulation,since the missile can bene fi tfrom the maximalnormaloverload provided by the engine thrustwhich is absolutely used in the normaldirection.The simulation results illustrate that AoA under the compound method can track the command more quickly than that under ADRC method.For sideslip angle and velocity bank angle,desired commands are zero signals.The sideslip angle and velocity bank angle will deviate from the equilibrium position inevitably under lateral aerodynamic disturbances.Under this circumstance,the amplitudes of variation underthe compound method are smaller as shown in Fig.8.

Fig.8 Time histories of controlled angles

Fig.9-Fig.11 illustrate the online estimation of ESO of the compound controller.The observation errors of the uncertainty dxare plotted in Fig.9.Actually,the value of each componentof dxis so small that can be ignored. Thus,it is unnecessary to use ESO to estimate dx,which can reduce the computation burden of the control system. The online estimations of uncertainty dωand˙ωchave achieved good results,shown in Fig.10 and Fig.11 respectively.Actually,itis unnecessary to be strictin the control accuracy for the missile agile turn,since the top priority of this phase is to make the missile turn around roughly,and the missile attitude willbe adjusted by guidance command in the subsequentcontrolphase.

Fig.9 Estimation errors of dxvia ESO

Fig.11 Estimations of˙ωcvia ESO

Atthe end,in orderto demonstrate the effectof ESO in disturbance rejection,Fig.12 illustrates the time histories of responses under the compound controlwhen the contribution of ESO to the control system is arti fi cially reduced by replacingin control laws.Comparing with the simulation results shown in Fig.8,it is seen that the controlled angles with low performance ESO can not track the command signals in a satisfactory level.

Fig.12 Time histories of responses with low performance ESO

5.Conclusions

In this work,the BTT autopilot of agile missile has been designed to achieve the large maneuvering turn.After the modeling of missile dynamics,the BTT steering policy for agile turn is discussed and corresponding cascade control structure is determined.To overcome the unpredictability of aerodynamic data at high AoA,ADRC method is employed to synthesize the autopilot.ESO used in ADRC is capable of online estimating the system uncertainty including aerodynamic disturbances,which is helpfulto achieve dynamic linearization of uncertain nonlinear system.Subsequently,a compound method based on DSC and ESO is applied in design in order to improve the performance ofautopilot.Nonlinearnumericalsimulations forattacking the targetin rear hemisphere are performed to validate the feasibility and robustness of the proposed autopilotunder system uncertainty.Simulation results show that the compound method has better performance on convergentrate and controlaccuracy compared with the traditionalADRC method.Therefore the proposed method based on active disturbance rejection mechanism is available to the design and implementation of missile control system with severe unmodeled dynamics.

Fig.10 Estimations of dωvia ESO

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Biographies

Yueyue Mawas born in 1988.He received his B.S.degree from Beijing Institute of Technology in 2010.He is currently a doctoral student in School of Aerospace Engineering,Beijing Institute of Technology.His main research interests include fl ight vehicle design,fl ight dynamics and control.

E-mail:mayy@bit.edu.cn

Jie Guowas born in 1981.He received his Ph.D. degree from Beijing Institute of Technology in 2010. He is currently a lecturer in Schoolof Aerospace Engineering,Beijing Institute of Technology.His main research interests include fl ightvehicle design,fl ight dynamics and control.

E-mail:guojie1981@bit.edu.cn

Shengjing Tangwas born in 1959.He received his Ph.D.degree from Technical University Munich in 2002.He is currently a professor and a vice-dean in School of Aerospace Engineering,Beijing Institute of Technology.His main research interests include fl ightvehicle design,fl ightdynamics and control. E-mail:tangsj@bit.edu.cn

10.1109/JSEE.2015.00088

Manuscriptreceived August19,2014.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(11202024).