Hierarchicalstructured robustadaptive attitude controller design for reusable launch vehicles

1.Schoolof Astronautics,Beihang University,Beijing 100191,China;

2.Beijing Institute of Astronautical Systems Engineering,Beijing 100076,China

1.Introduction

Hierarchicalstructured robustadaptive attitude controller design for reusable launch vehicles

Guangxue Yu1,2and Huifeng Li1,*

1.Schoolof Astronautics,Beihang University,Beijing 100191,China;

2.Beijing Institute of Astronautical Systems Engineering,Beijing 100076,China

Reentry attitude control for reusable launch vehicles (RLVs)is challenging due to the characters of fast nonlinear dynamics and large fl ight envelop.A hierarchical structured attitude controlsystem for an RLV is proposed and an unpowered RLV control model is developed.Then,the hierarchical structured control frame consisting of attitude controller,compound control strategy and controlallocation is presented.At the core of the design is a robust adaptive control(RAC)law based on dual loop time-scale separation.A radial basis function neural network(RBFNN)is implemented for compensation of uncertain modeldynamics and external disturbances in the inner loop.And then the robust optimization is applied in the outer loop to guarantee performance robustness.The overallcontroldesign frame retains the simplicity in design while simultaneously assuring the adaptive and robust performance.The hierarchical structured robust adaptive controller(HSRAC)incorporates fl exibility into the design with regard to controller versatility to various reentry mission requirements. Simulation results show thatthe improved tracking performance is achieved by means of RAC.

reusable launch vehicle(RLV),reentry,hierarchical structured,H∞optimization,neutralnetwork adaptive(NNA),attitude control.

1.Introduction

To reduce the operationalcostto access the space,reusable launch vehicles(RLVs)have received considerable research interests.Reentry control of RLVs is challenging due to the fast changes in the dynamics as the maneuver takes the vehicle over large fl ight envelope.The highly nonlinear couple characters and multiple control modes make the attitude controller design more dif fi cultthan that of an aircraft[1].

Moreover,there exist large of uncertainties and externaldisturbances in the reentry fl ightphase of RLVs,which in fl uence the control performance seriously.The reentry attitude controlof an RLV is operated by the reaction controlsystem(RCS)and aerosurfaces,which comes up with the control allocation issues[2-4].Thus it involves the compound control strategy coordinating multiple actuators,which brings dif fi culties and challenges for controller design.And the RLV fl ying qualities required in the reentry missions demand high levels ofperformance due to the constrains of aerodynamic heating,loading and dynamic pressure.

Due to the rapid changes in fl ight speed and altitude, the states of RLVs change rapidly bearing the serious coupling and nonlinearity dynamic characters.The design of attitude controller using small perturbation linearization method combining the gain scheduling controlis limited.This classical control method requires the intense analysis,gains scheduling and simulations whenever there are any changes in model or fl ight condition.There have been many advanced controlmethods used for RLV reentry attitude controller design[5],such as nonlinear dynamic inversion(NDI),sliding mode control(SMC),linear parameter varying(LPV),and trajectory linearization control(TLC).In addition,disturbance suppressing is an important research issue in attitude control.A variety of disturbance rejection controlmethods are used to estimate and compensate the disturbances and improve the control performance[6-8].The robust and adaptive ideas were applied to the control for RLVs in combination with advanced control methods[9-12].When the fl ight dynamics varies in a wide range,the use of robust control is dif fi cult to work for a good performance in the entire envelop and adaptive controlis the rightchoice forsuch cases [13-15].With the motivation that a controller which can adjust its parameters online could generate the improved performance over a fi xed-parameter counterpart,the adaptive control could deal with large uncertainties.A variety of disturbances existin the reentry phase of RLVs,such as unmodeled dynamics,disturbances of the wind,and mea-surement noises.These uncertainties could cause signi ficantperformance degradation in the behavior of vehicles. And the H∞controlis appropriate to achieve performance robustness design goals[16].

A hierarchical structured robust adaptive controller (HSRAC)design scheme is proposed.First,an RLV attitude control model is developed.Then the dual loop controlarchitecture is designed based on the time-scale separate theory.The robustadaptive control(RAC)consists of two cascade controllers,namely the inner loop controller and the outer loop controller.In the hierarchicalstructured control frame,the control strategy deals with the harmonization problem of the RCS and aerosurfaces.The control allocation maps the control moment commands into effectors'commands of the RCS and aerosurfaces.The radialbasis function neuralnetwork(RBFNN)adaptive control in the inner loop is designed in order to estimate the unknown disturbances.The estimation of the total disturbances is utilized to compensate for the in fl uence of the disturbances on the attitude controlsystem.The neuralnetwork adaptive(NNA)in the inner loop equalizes the uncertain dynamics throughout the fl ight envelope.This is importantfor the robustness design in outer loop as it can reduce the conservatism.After equalizing the dynamics of the vehicle via the nominal dynamic inversion and appropriate approximating in our hierarchicalstructured control frame,the robustoptimization is implemented in the outer loop to guarantee stability and robustness.Results show that the RAC meets the attitude tracking performance requirements.And the overall HSRAC scheme obtains the robustness of suppressing the uncertainties.

This paper is organized as follows.The nonlinear control model of the RLV unpowered reentry fl ight is set up in Section 2.Nextthe hierarchicalstructured attitude controlframe is discussed in Section 3.After thatthe RAC is explained in Section 4,followed by the simulation results obtained with the proposed HSRAC in Section 5.The paper ends with the conclusions in Section 6.

2.Reentry attitude controlmodel

As a typical lifting reentry,an RLV has to satisfy the maneuverability requirementofunpowered fl ightand landing. As shown in Fig.1(a),aerodynamic shape of the RLV is a combination con fi guration of the wing and lifting-body, equipped with the RCS and aerosurfaces.The aerodynamic controlsurfaces include two elevons,a rudder and a body fl ap.In order to complete the orbital maneuver task,the RCS is installed at the vehicle's front and tail sections. Reentry attitude control is completed by the tail RCS and aerosurfaces.Fig.1(b)is the con fi guration of thrusters at the tail section of the vehicle.There are two mounting surfaces S1 and S2.Each mounting surface is con fi gured with eightthrusters.The jetdirections of RCS thrusters are marked by the arrows.

Fig.1 RLV configuration

De fi neα,βandμas the angle of attack,sideslip angle and bank angle respectively;de fi ne p,q and r as the roll,pitch and yaw angular rates respectively.The kinematic and rotational dynamic equations are stated below [17]:

where L and Y are the aerodynamic lift and side force respectively de fi ned in the wind frame.γis the fl ight-pathangle,M is the mass,g is the acceleration of gravity.l, m and n are rolling,pitching and yawing momentrespectively in the body frame.Ixx,Iyyand Izzare the moments of the inertia for x,y,and z coordinates,respectively.And Izxis the product of the inertia for x and z coordinates in the baby frame.The momentexpressions acting on the vehicle are given by

where lA,mAand nAare aerodynamic moments.lR,mR, nRare moments due to the RCS.The equations of motion and aerodynamic modelare derived from[17].

The tracking control of the angle of attackαand the bank angleμis very important for reentry of the RLV. Tracking the angle of attack is used to controlthe aerodynamic heating and the energy managementof reentry.And tracking the bank angle is used to adjustthe downrange and the crossrange to ensure thatthe vehicle fl ies into the predetermined energy management window.Meanwhile,the sideslip angle should be suppressed to zero in orderto limit the heat fl ux of body surfaces and ensure the fl ightsafety.

3.Hierarchicalstructured controldesign

3.1 Dualloop controlarchitecture

In the reentry fl ight of the RLV,the motions of attitude angular rate are faster than the aerodynamic angle.Based on the principle of time-scale separation[18],the aerodynamic anglesα,βandμare divided into one group,denoted as the slow statesΩ;the attitude angular rates p,q and r are divided into another group,denoted as the fast statesω,speci fi cally as

These resultin the following setof simpli fi ed equations of motion,which is the mathematical model used for designing the attitude controller.We get

There existlarge of uncertain unmodeled dynamics and disturbances in the reentry phase of the RLV,which are re fl ected in(9)-(12).The measurement errors ofαand βwill affect the accuracy of gs.The inaccurate products of inertia will be re fl ected in ffand gf.Atmospheric disturbances will introduce disturbance forces and moments, which willdirectly affectthe slow and faststates dynamic (7)and(8).These disturbances affect the attitude control performance seriously,even induce controlthe failures.

From the enlightenment of the cascade control,which is mainly used to achieve fast rejection of disturbance before it propagates to the other parts of the plant,the RAC involves the inner and outer loop controllers design to achieve the tracking of aerodynamic angle commands. Firstly,the attitude angular rate commands are designed according to the slow states dynamic(7),referred to as the outerloop control.Secondly,the required controlmoments are designed according to the fast states dynamic(8),referred to as the innerloop control.The bandwidth ofthe inner loop should be atleast3-5 times than thatof the outer loop,for ensuring the time-scale separation.Thus the dynamic characteristics ofthe innerloop can be ignored when the outer loop is synthesized.Controller in the outer loop is the primary controllerthatregulates the aerodynamic angles by setting the set-pointofthe inner loop.Controller in the inner loop is the secondary controller that rejects disturbances locally before itpropagates to the vehicle.

To reduce the conservativeness,we introduce an RBFNNadaptive rule to estimate the modeling uncertainty and disturbance moments effectively in the innerloop.This procedure is to equalize the vehicle dynamics throughout the fl ight envelope via the dynamic inversion method and NNA.Then a robust control synthesis is applied inthe outer loop for the robustness and controlperformance. RBFNN via an online adaptive rule in the inner loop is implemented to estimate and compensate the total disturbances to ensure the attitude control performance.However it cannot solve all problems.When there are measurementerrors,the controlperformance willdecline.The inherent estimation errors of RBFNN will also affect the control performance.Adaptive control is also dif fi cult to solve the compromise problem balancing the control performance and the robustness of closed loop[19].For this reason,the design of robustcontrolto improve the overall performance ofthe controlsystem is valuable.On the basis of the NNA,robustcontroloptimization design is applied to ensure robustness for attitude control under the actual fl ightconditions.

To ensure that the RAC law can be ef fi ciently implemented,the controlstrategy is designed to coordinate the compound controlof the RCS and aerosurfaces.For the attitude control,the controlled variables are angle of attack, sideslip angle and bank angle.And the control variables are leftelevonδe,right elevonδa,rudderδr,body fl apδband the thrusts of RCS.So the controlsystem ofthe RLV is over-actuated.According to the fl ight mission and control ef fi ciency,the control allocation of planning the control modes of RCS and aerosurfaces should be designed carefully to meetthe controlconstraints.To simplify the fl ight control design,RLV reentry attitude control system is divided into control law design,compound control strategy and controlallocation.The hierarchical structured control system is shown as Fig.2. sive actuators and the RCS quits outfrom attitude control. Considering the RCS and aerosurfaces participate in controltogether,the weight coef fi cientis a linear function of dynamic pressure between RCS and aerosurfaces.

Fig.2 Hierarchical structured controlarchitecture

And k is the weightcoef fi cient,

The coordination of the RCS and aerosurfaces is based on the comprehensive consideration of the following factors,such as the vehicle's controlability,fl ightmechanics, reentry corridor,and reentry mission.For differentcontrol channels,the control ef fi ciencies of aerosurfaces are different.Thus,the dynamic interfacesshould be determined forroll,pitch and yaw controlchannels respectively.

To conclude,the RAClaw consists ofthe outerloop controller and the inner loop controller in cascade,mapping from the attitude angle commands into the control moments commands.The compound control strategy determines the transition interfaces between the RCS and aerosurfaces,coordinating the RCS and aerosurfaces.Control allocation maps the momentcommands into actualthrusts' commands and aerodynamic actuators'commands.There are two time scales in the dual loop control system.The outer loop is composed of the outer loop controller,inner loop controller,control allocation,and vehicle dynamic; the inner loop is composed of the inner loop controller, control allocation,and vehicle dynamic.The detailed robustadaptive controlalgorithm is designed in Section 4 of this paper.

3.2 Compound controlstrategy

The dynamic pressure is increasing gradually as the vehicle decreases from the orbit.When the dynamic pressure is small,the controlef fi ciency of aerosurfaces is low, and RCS is the exclusive actuator used to complete the attitude control.With the increasing of dynamic pressure, RCS gradually withdraws from attitude control.RCS and aerosurfaces complete the attitude control task together. When the fl ight altitude becomes lower,and the dynamic pressure is further increased,the aerosurfaces are exclu-

3.3 Controlallocation

Control allocation maps moment commands of the RCS and aerosurfaces into the thrusters'commands(open or close)and aerosurfaces'de fl ection commands.The independentdesign procedure of the controlallocation and the control law makes the attitude control design more easily.As to the controlallocation of aerosurfaces,we should map aerodynamic moment commandsinto the defl ecting commandsδcof aerosurfaces.The controlallocation for aerosurfaces can be converted into a mathematical programming problem,enabling the sequential quadratic programming(SQP)method to solve the optimal control allocation of the aerosurfaces[20].

The actualmoments MAgenerated by aerodynamic can be obtained from the expressions of aerodynamic moment coef fi cients,as shown in(15).

De fi ne the function

whereδ=[δeδaδrδf]T,then the control allocation problem is transformed into the following optimization problem.

The goalof optimization is

whereδminandδmaxare respectively the minimum and maximum de fl ection positions of the corresponding aero-

The optimization objective function is

RCS is a direct force control system.In order to make the control effect as close as possible to the effect of the given control law,and verify the fl ightcharacteristics,the single-axis controlallocation ofthe RCS is designed as follows.The thrusters of No.9○13○,10○14○(shown in Fig.1) are used for the roll channel control.The thrusters of No.1○2○,5○6○are used for the pitch channelcontrol.And the thrusters of No.3○4○11○12○,7○8○15○16○are used for the yaw channel control.For example,Fig.3 is the singleaxis control scheme for pitch channel.Each thruster is permanently assigned to roll,pitch and yaw channels respectively.Thus,the scheduling of the 16 thrusters does not exist coupling,which can simultaneously control the three channels.Each channelhas only one thrustlevel.Although the maximum available controlmomentcannotbe utilized in this single-axis control allocation,the dif fi culties of thruster logical choice arising by coupling control are avoided.

Fig.3 Single-axis controlallocation for pitch channel

According to the size and direction of the RCS control momentcommands,the switch commands ofeach thruster are determined by the modulator,such as pulse width and pulse frequency(PWPF)modulator.The PWPF modulatortransforms the momentcommands assigned to the RCS into a series of rectangular pulse,namely,the switch commands.After the corresponding switching commands are executed by the thrusts of roll,pitch and yaw channels,the desired controlmoments are obtained.

4.Robust adaptive controllaw

4.1 Baseline controller design

4.1.1 Outer loop baseline controller

For the slow states dynamic of aerodynamic angle(7),the uncertainties ofthe mass and aerodynamic force can be introduced into fs.Uncertainties such as measurementerrors of aerodynamic angle could be introduced into gs,which is determined by angle of attack and sideslip angle.As forthe outer loop,robustcontrolis bene fi cialto synthesis the controlperformance and the robustness with uncertainties attenuation.

Considering the slow states dynamic(7),the baseline controlleris designed based on the NDI technique.is the nominal value of fs.The NDI baseline controller(19)equalizes the dynamic of vehicle and eliminates the gain scheduling across the fl ightenvelop.And v is the robustcontrolquantity designed in Section 4.4.

Remark 1Itshould be noticed thatthe difference value betweenand fsis smallbecause of the large mass and fl ightvelocity.The measurementerrors ofαandβwillintroduce uncertainties in gs,so the robust controller in the outer loop should be able to compromise between the performance and uncertainties.

Remark 2To synthesize the outerloop,the dynamic of innerloop should be fastenough to be ignored.In addition, the NNA rule is introduced to shape the angular rate response with the perfectcancellation of various disturbance moments in the inner loop.

4.1.2 Inner loop baseline controller

For the faststates dynamic of attitude angular rate(8),the effects of the gravity center changing and aerodynamic moment uncertainties bring about notable effects on attitude control.The disturbances of the product of inertia could be introduced in ffand gf.And the disturbances of atmospheric will introduce external disturbance force and moment.Allthese willintroduce a notable disturbance moment d in the inner loop,which cannot be ignored for attitude control.Thus,we have to estimate the total disturbance moment d and compensate it in the inner loop to eliminate the adverse effects.The disturbance control modelof faststates dynamic is

De fi ne the error vectorΔffand the error matrixΔgfasare respectively the nominalvalues of ffand gf.

Considering the fast states dynamic(20),the baseline controlleris designed as Substituting the inner loop baseline controller(23)into (20),we obtain

where eω= ωc?ωis the errorvector of the angularrate.0 are the controlbandwidths in the innerloop forroll,pitch,and yaw channels respectively.

From(24),it can be seen that the error dynamic of the angular rate is induced by the error vectorΔff,the error matrixΔgfand the totaldisturbance momentvector d.

De fi ne the inner loop overalluncertain vector hfas

If we can estimate the overalluncertain term hf,and then add the estimation of hfto the baseline controller(23),we can get

Substituting(27)into(20),we obtain

That is to say,the inner loop dynamic obtains asymptotic convergence if we can effectively estimate the disturbance vector hfin the inner loop.An RBFNN is introduced to estimate this overalluncertain term hfin the nextsection.

Remark 3In(19),the singularity ofoccurs if the sideslip angleβequals±90°.However,this situation will not occur as the controller should keepβat 0°during the reentry.In(23),so the baseline controller Mcis valid.

Remark 4In(25),the vector hfcontains various uncertain disturbances.is the estimation of d.

4.2 Inner loop disturbance-rejection control

In the inner loop,the vector hfof total uncertain disturbances is unknown in practice.The RBFNN is implemented to generate the estimation ofthe disturbances.And then we can compensate it through the inner loop controller.

From(26),there exists an internal relationship hf= hf(eω)between the dynamics of eωand hf.The RBFNN is used to estimate the unknown function vector hf.From the outputof the RBFNN,we have

where the RBFNN output matrixR3×1.m is the node number of the RBFNN.is the Gaussian radial basis function.ciandσi(i=1,2,...,m)are respectively the center and width of the i th node.

For the continuous function,the RBFNN guarantees arbitrary precision approximation ability within the scope of the compact set.We make following two assumptions to match this condition[21].

Assumption 1The output of RBFNN is continuous, namely,?h(eω,W)is continuous.

Assumption 2There exists an idealoutputmatrix W?such that max

According to the assumptions above,forthe idealoutputobtains the optimal estimation of hf(eω). hf(eω)is bounded,and then W?is bounded.There exists a bounded wmax＞0 such that‖W?‖F(xiàn)?wmax.

De fi neηas the approximation error of the RBFNN,

andηis bounded,i.e.,there exists a constantη0＞0 such that

To compensate the disturbances hfin the inner loop,we design the innerloop controlleras

Substituting(33)into the fast states dynamic(20),we get

Substituting(21)and(22)into(35),we can obtain

From(25),we get

And we have

Lyapunov method will be used to design the NNA rule in the nextsection.

4.3 Neutralnetwork adaptive rule

Considerthe Lyapunov function candidate

From(39),we obtain

where Kfis the controlbandwidth matrix de fi ned before in the innerloop.Since Kfis a positive de fi nite symmetric matrix,there exists a positive de fi nite symmetric matrix P being the solution to the Lyapunov equation

where Q is a positive de fi nite matrix.

Differentiating(41),and using the expression

Substituting˙eωfrom(42)into(44),we get

Substituting(43)into(45),we get

Substituting(47)into(46),we obtain

Since W?is a constant in(40),we haveEquating the third term of(48)to zero,we get the following adaptive update rule:

where k1＞0 makes the output matrixbounded.γ1is used to tunnelthe tracking performance of the error between the RBFNN outputand the unknown true uncertain disturbance hf.And the larger the value ofγ1,the faster the tracking performance of the RBFNN converges.

Substituting(49)into(48),we get

According to the properties of the F-norm,we have

Exploiting the factthat

Equation(50)then becomes

The suf fi cientcondition of˙V?0 is

From the above inequality it can be seen that V?0 as long as

And from(53),we can getthe convergence radius of eωas follows:

This shows the stability in the sense of Lyapunov since V＞0 and˙V?0.and eωare bounded.

Remark 5From the convergence condition(55),we are able to conclude:the smaller upper boundedη0of the RBFNN modeling errorη,the smaller convergence radius of‖eω‖;and the smaller wmax,the smaller‖eω‖.From (43),the eigenvalues of P are smaller(hence‖eω‖)when the eigenvalues of Q are larger.

Remark 6We should initialize the node number,together with the center and width of each node.Only the outputmatrix of RBFNN is updated online in our adaptive rule.Thus,the RBFNN adaptive rule can match the realtime and fast requirementin practical fl ight control computer.

In conclusion,the RBFNN adaptive controller for the inner loop is constructed by(33)and(34).And the adaptive rule is(49),which makes the outputmatrix of RBFNN bounded.The convergence radius of the dynamic of fast states is(55).Based on the RBFNN,an adaptive control scheme has been derived in the inner loop for disturbance rejection.

4.4 Outer loop H∞synthesis

To synthesize the performance of response,uncertainties and robust stability,a robust outer loop controller is designed based on dynamic inversion and non-smooth H∞optimization.

The adaptive controller in the inner loop effectively equalizes the total disturbances across the fl ight envelop. According to the time-scale separation,the inner loop responds much fasterthan the outer loop.Based on the nominal NDI(19)and ignoring the dynamic of the inner loop, the feedback linearized model of the hierarchical structured controlsystem to be optimized is G.

The control input vector v in the NDI control frame (19)is the desired dynamic ofΩ.This intermediate controlquantity v can be decomposed into three independent control loops ofα,βandμrespectively.Since the three controllers have the same robust control structure,we introduce the general design process forα,βandμcontrol channels of the outer loop.It is noted that the desired closed loop dynamic for all three controllers is not the same.Thus,we should design differentweighting functions respectively for the three controlchannels.

In the robust control scheme,more information about the system is made available,the better are the chances of obtaining a high performance solution to address the controlproblem.An augmented modelconsisting of the plant model,reference model,performance weighting functions, inputweighting functions and fi lteris formed to design the outer loop robust controller.The robust control con fi guration for the outer loop and the corresponding synthesis interconnection are depicted in Fig.4.

Fig.4 Interconnection structure for robust synthesis

In Fig.4,we introduce the error of aerodynamic angle and its integral as the input of the robust controller K(s). Notice that u is one component of the vector v.r is one of aerodynamic angle commandsαc,βcandμc.d is the disturbance signalin the outer loop.We,Wp,Wuand Wnare weighting functions for the error of aerodynamic angle,the output of aerodynamic angle,the control input u and the measurementnoise n.

The inputcommand signal r is pre-fi ltered by a low-pass fi lter F to reduce high frequency excitations.R is the reference modelofthe idealresponse dynamic.Weand Wuare helpful to simultaneously optimize a performance criteria and restriction on the size of controlsignal.From the controlstructure shown in Fig.4,the transfer function form is obtained as follows:

Now,ze,zpand zuare selected so as to form the vector z of weighted outputs according to the performance criteria. r,d and n form the vector w of exogenous inputs.y1and y2form the measured outputvector y.Then,we get

These weighting functions,disturbance inputs and evaluated outputs are used for structuring the generalization plant P.We get the standard form of robust optimization shown as Fig.5.

Fig.5 Standard form ofrobust optimization

We partition P as

Then,the control problem is formulated into a linear fractionaltransformation(LFT).

The robustcontroldesign is to fi nd a stabilizing controller K(s)thatminimizes Tw→z,and could be solved via H∞optimization as follows:

The robust optimization problem is convex in the fullorder case.In that case,the order of the controller K(s) coincides with that of P.There are two mature methods to solve the optimization problem,the solution of coupled Riccatiequations[22]and the LMI-based formulation[23].However,these two methods do not allow to impose constrains neither on the order of controller nor its structure.In such cases,the optimization problem turns out to be non-convex.Thus,we apply the descent method proposed in[24]to solve the non-smooth optimization problem for the fi xed order controller K(s).

The weighting functions included in(60)give the optimization process more details on the frequency domain desired characteristics thatwillshape the closed loop control system.In our design procedure,control weighting function Wuis chosen as a constant.Measurement noise weighting function Wnis chosen as a high-pass fi lter.Output weighting function Wpand error weighting function Weare de fi ned as a high-pass fi lter a and low-pass fi lter, respectively.By the choices of weighting functions for robustcontroldesign,comprehensive performance speci fi cations are obtained in the outer loop.

5.Simulation results

Numericalsimulation is performed to verify the proposed HSRAC attitude controlsystem.The reentry phase begins about121 km altitude and ends atthe terminalarea energy management(TAEM)phase.And the guidance law is considered ideal,so the commanded aerodynamic angles are equalto the aerodynamic angles speci fi ed in the reference trajectory.

In order to have an effective HSRAC attitude control system,it is essential that the inner loop responds much fasterthan the outerloop.The bestpractice is to design the inner loop controller fi rst and then design the outer loop controllerwith the inner loop closed.

Fig.6-Fig.9 show the nominal performance of the HSRAC attitude control system.Fig.6 is the time histories of aerodynamic angle commandsα,βandμ.Fig.7 is the responses of aerodynamic angle under the proposed RAC.The errors of aerodynamic angle do not exceed 1°. Fig.8 is the time histories of the aerosurfaces'de fl ection. Fig.9 is the time histories of the thrusts'operation.In the early reentry phase,the angle of attack is maintained by operating the RCS to be 40°.

Fig.6 Aerodynamic angle command

Fig.7 Aerodynamic angle response

Fig.8 Aerosurfaces deflection

As the dynamic pressure gradually rises,the aerosurfaces begin to participate in the attitude control.When it comes aboutreversal of the bank angle,the left and right elevons differentially de fl ect,achieving the rollmaneuver. Meanwhile the rudderde fl ects togetherwith the elevons to ensure thatthe sideslip angle is zero.

Fig.9 Thrusts response of RCS pitch channel

In Fig.10-Fig.15,simulation results are presented to demonstrate the performance improvements of the RAC scheme when compared to a non-adaptive robust control design,i.e.,the case without the NNA in the inner loop of our HSRAC framework.For the integrated RAC law, the controller of the inner loop includes the NNA that is capable of overcoming the problem of uncertainties,such as aerodynamic modeluncertainties,controlforce/moment disturbances due to external atmosphere,disturbance moments introduced by center-of-gravity movement.In our simulation,we introduce the total uncertain disturbancesas sinusoidaldisturbance moments acting in the roll,pitch and yaw control channels respectively.The amplitude of the sinusoidal disturbance moment is 750 N·m,which is determined by the uncertain factors mentioned above.Fig. 10-Fig.12 are responses of the proposed HSRAC scheme withoutthe NNAcontrolin the innerloop.Fig.13-Fig.15 are responses of the HSRAC system under the same disturbance moments.Itcan be seen thatthe RACobtains improved control performance with NNA.Fig.16-Fig.18 are the RBFNN estimations of the disturbance moments in the HSRAC system.We can see thatthe NNA of the RAC can effectively estimate the uncertain disturbances.

Fig.10αresponse without NNA

Fig.11βresponse without NNA

Fig.12μresponse without NNA

Fig.13αresponse with RAC

Fig.14βresponse with RAC

Fig.15μresponse with RAC

Fig.16 NN estimation for rollaxis

Fig.17 NN estimation for pitch axis

Fig.18 NN estimation for yaw axis

The controller of the outer loop accommodates various uncertainties and constrains through robust optimization. And the compensation of the disturbances can improve the conservation of the robustcontrolin the outerloop and expand the operation domain of the HSRAC attitude control system.Fig.19-Fig.21 are the simulation results of the RAC law under turbulentwind(TW).The RAC works effectively against TW.This scenery tests the performance robustness of the HSRAC attitude controlsystem.

Fig.19αresponse under TW

Fig.20βresponse under TW

Fig.21μresponse under TW

6.Conclusions

This paper has focused on the design of attitude controller for the reentry of RLVs subjectto exogenous disturbances and uncertain dynamics.A hierarchical structured control system as wellas an RAC law has been designed simultaneously.The proposed HSRAC frame for RLV reentry is a unique combination of RAC law,compound controlstrategy and controlallocation.Controlallocation tackles with the redundantcontrolofthe vehicle.In accordance with the controlability of the RCS and aerosurfaces,the compound controlstrategy is executed according to the dynamic pressure,ensuring the attitude controllaw to be realized effectively.

The RAC law enables to overcome the conservatism of the pure robustcontroland enhances the robustness of the pure adaptive control.The adaptive controller based on the RBFNN is used to compensate for the effects of various disturbance moments in the inner loop.The robustcontrol in the outer loop is designed around the linearized closed attitude controlsystem to balance controlperformance and robustness objective.

The HSRAC provides a design reference of attitude control system for other entry vehicles or space planes. The HSRAC frame is applicable to attitude control systems having a structured design procedure,enables the assessment and comparison of competing control strategies or control allocation methods regardless of the control law.The further research directions are the control evaluation of RAC and the fault tolerant control for the RCS/aerosurfaces in the HSRAC frame.

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Biographies

Guangxue Yuwas born in 1986.He received his B.E.degree in Nanjing University of Aeronautics and Astronautics,in 2009.He is currently a Ph.D. candidate in Schoolof Astronautics,Beihang University.His research interests include control theory and applications,guidance,and controland dynamics.

E-mail:yuguangxue123@126.com

Huifeng Liwas born in 1970.She received her B.E. degree and Ph.D.degree in Xi'an Jiaotong University,in 1991 and 1998,respectively.She is now a professor in School of Astronautics,Beihang University.Her research interests include modeling and control methods of hypersonic vehicle,and guidance and control technology.

E-mail:lihuifeng@buaa.edu.cn

10.1109/JSEE.2015.00089

Manuscriptreceived July 30,2014.

*Corresponding author.

This work was supported by the National Natural Science Foundation of China(61174221).