CN104950898B

CN104950898B - A kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle

Info

Publication number: CN104950898B
Application number: CN201510316506.8A
Authority: CN
Inventors: 盛永智; 金震; 刘向东
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2015-06-10
Filing date: 2015-06-10
Publication date: 2017-10-17
Anticipated expiration: 2035-06-10
Also published as: CN104950898A

Abstract

The full rank non-singular terminal Sliding Mode Attitude control method of a kind of reentry vehicle disclosed by the invention, is related to the full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle based on robust differentiator, belongs to flying vehicles control technical field.The present invention comprises the following steps：Generate the state vector of aircraft；Set up the mathematical modeling of reentry vehicle；Simplify reentry vehicle model with feedback linearization；Provide the command information y of attitude angle α, β, μ the progressive tracking system of aircraft when there are external disturbance and Parameter uncertainties in system_c=[α_c,β_c,μ_c]^T；Control distribution, obtains angle of rudder reflection instruction δ=[δ_e δ_a δ_r]^T；By obtained angle of rudder reflection instruction input aircraft, gesture stability is carried out to it.The invention can ensure that tracking error in Finite-time convergence to zero, and controller can be avoided to export singular problem, meanwhile, pass through and the measurement noise that estimation suppresses to introduce using conventional differential device carried out to error second dervative；By the buffeting for eliminating controlled quentity controlled variable with low-pass filtering technique using boundary layer simultaneously.

Description

A kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle

Technical field

Robust differentiator is based on the present invention relates to a kind of Sliding Mode Attitude control method of reentry vehicle, more particularly to one kind The full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle, belong to flying vehicles control technical field.

Background technology

Aircraft will be undergone during unpowered ablated configuration from supersonic flight condition to subsonic flight condition Change, and flying area is also larger, environmental disturbances are serious, each interchannel exist coupling, therefore the process can show it is more tight The nonlinear characteristic of weight.Moreover, the aerodynamic characteristic of aircraft can not be obtained accurately, and these factors have resulted in aircraft Gesture stability become complex.Therefore, design can, passage non-linear with suppression system coupling and systematic uncertainty Robust attitude controller is very crucial.

Sliding-mode control provides the solution of set of system for the control problem of implementation model uncertain system, this So that this method is widely used in aircraft manufacturing technology.Sliding formwork control technology possesses lot of advantages, for example：Parameter is become Change is insensitive, can resist external disturbance and fast dynamic response etc..However, traditional sliding formwork control only ensure that system gradually Enter stable, i.e., tracking error converges to zero in infinite time.In real-time control operation, Infinite Time convergence property is often not No more.

TSM control (Terminal Sliding Mode Control, TSMC) compared with traditional sliding mode controller, More superior characteristic can be provided, for example, faster convergence rate, higher control accuracy, more preferable interference rejection capability, And stronger robustness.However, TSM control method remains two subject matters.One is, terminal sliding mode control Singular problem occurs in device output processed.In order to overcome this defect, numerous experts and scholars are proposed corresponding solution, These methods can specifically be divided into two classes：One class is indirect method；It is another kind of to belong to direct method.These methods can not add Plus in the case of additional procedure singular problem is resolved.Terminal sliding mode another problem is that controller buffet, current side Interlayer technology and filter method are the buffeting suppressing methods being most widely used.In recent years, many scholars by artificial intelligence approach with TSM control method is combined, so that while TSM control method advantage is maintained so that buffeted existing As having obtained good suppression.It is therefore proposed that the full rank for reentry vehicle that is a kind of simple and easy to apply and tallying with the actual situation Non-singular terminal Sliding Mode Attitude control method is very important.

The content of the invention

Close coupling for aircraft reentry stage and it is non-linear the features such as, the technical problem to be solved in the present invention is to provide one Plant the full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle, it is ensured that tracking error is arrived in Finite-time convergence Zero, and controller can be avoided to export singular problem, meanwhile, for there are the special feelings of error second dervative in the sliding formwork equation of motion Condition, by carrying out the measurement noise that estimation suppresses to introduce using conventional differential device to error second dervative；By using side simultaneously Interlayer eliminates the buffeting of controlled quentity controlled variable with low-pass filtering technique.

The purpose of the present invention is achieved through the following technical solutions：

The full rank non-singular terminal Sliding Mode Attitude control method of a kind of reentry vehicle disclosed by the invention, including following step Suddenly,

Step 1, the state vector of aircraft is generated.

With reference to actual attitude angle Ω=[α, β, the μ] of aircraft^T, attitude angular velocity ω=[p, q, r]^T, constitute state vector x：X=[α β μ p q r]^T。

Step 2, the mathematical modeling of reentry vehicle is set up.

Set up the mathematical modeling such as formula (1) of reentry vehicle

y_i=h_i(x), i=1,2,3.

Wherein, state vector x=[α β μ p q r]^T, control moment u=[u₁,u₂,u₃]^T=[M_x,M_y,M_z]^T, output Vectorial y=[y₁,y₂,y₃]=h (x)=[α, β, μ]^T,

F (x)=[f₁(x) f₂(x) f₃(x) f₄(x) f₅(x) f₆(x)]^T。

f₁(x)=- pcos α tan β+q-rsin α tan β

f₂(x)=psin α-rcos α

f₃(x)=- pcos α cos β-qsin β-rsin α cos β

In formula (1), α, β, μ represents the angle of attack, yaw angle and angle of heel respectively；P, q, r represent rolling, pitching respectively And yaw rate；M=[M_x,M_y,M_z] represent control moment vector, M_x,M_y,M_zRolling, pitching and yaw forces are represented respectively Square；M_dIt is external disturbance torque vector；I_xx,I_yy,I_zz,I_xzIt is the rotary inertia and product of inertia on each reference axis respectively,Δ T represents to include the polymerization uncertainty such as Parameter Perturbation, external disturbance and Unmarried pregnancy, due to again Enter process medium velocity fast, atmospheric environment change is violent, and Δ T can not ignore.

Step 3, the reentry vehicle model that step 2 is set up is simplified with feedback linearization.

Using the method for expressing of Lie derivatives, then y in formula (1)_iDerivative can be expressed as formula (2)

Lie derivatives is defined as follows：

AndMeet following condition：

In formula, r₁,r₂,r₃It is the dummy vehicle Relative order in step 2.Only as the Relative order r=r of system₁+r₂+r₃ During=n, the system can just be fully converted to a linear system.

Shape feedback linearization processing is carried out to dummy vehicle, formula (3) can be obtained：

Wherein：

From calculating：Therefore controller is expressed as formula (4)：

U=E^-1(x)(-F(x)+v) (4)

It can be obtained by formula (3) and (4)：

In formula, v=[v₁,v₂,v₃] it is the auxiliary variable introduced, Δ v is the polymerization disturbance in system.Polymerization disturbance Δ v with And its first derivativeMeet following condition：

In formula, l_dmin, k_dminRepresenting matrix l_d,k_dIn nonzero element minimum value, l_d,k_dFor 3 × 3 diagonal matrix.

It is theoretical from previously described feedback linearization：Ask second derivative can by three outputs to system (2) To realize the purpose of linearisation, and the now Relative order r=2+2+2=6=n of system, therefore can realize to reentry vehicle The complete feedback linearization of model.

Step 4, for the gesture stability problem of reentry vehicle, provide full rank terminal and slide control method to ensure in system The command information y of attitude angle α, β, μ the progressive tracking system of middle aircraft when there are external disturbance and Parameter uncertainties_c= [α_c,β_c,μ_c]^T, i.e.,：

In formula,The tracking error of system, t_rFor the stabilization time of system.

Described full rank terminal slides control method, including step 4.1,4.2,

Step 4.1, in order to avoid the singular problem in ordinary terminal sliding formwork, the full rank terminal as shown in formula (7) is provided Sliding-mode surface：

In formula, S (t)=[s₁(t),s₂(t),s₃(t)]^T。

Step 4.2, full rank non-singular terminal sliding formwork control ratio is calculated：

Control law v is by nominal control law v_eqWith switching control v_nComposition, concrete form such as formula (8)：

V=v_eq+v_n

v_vss=-(k_d+k_T+η)sgn(S)

In formula, 0 ＜ θ ＜ 1；η=diag { η₁,η₂,η₃It is handoff gain matrix；k_dDefinition as shown in step 3；When T is Between constant, itself and k_TInequality k is met jointly_T≥Tl_d；S is the Integral Sliding Mode face designed in step 4.

Step 5, control distribution, obtains angle of rudder reflection instruction δ=[δ_e δ_a δ_r]^T。

Angle of rudder reflection instruction δ=[δ is obtained according to formula (9) and (10)_e δ_a δ_r]^T：

U=M=E^-1(x)(-F(x)+v) (9)

δ=G^-1u (10)

Distribution obtains δ=[δ to rudder face executing agency by formula (10)_e δ_a δ_r]^T, δ_e,δ_a,δ_rRespectively elevator, pair The drift angle of the wing, rudder.M=[M_x,M_y,M_z] it is that the gesture stability output v obtained in step 4.3 calculates obtained controling power Square, G is transition matrix, is determined by aerodynamic parameter.

Step 6, angle of rudder reflection instruction input aircraft step 5 obtained, gesture stability is carried out to it；Meanwhile, aircraft Export current flight device each state α, β, μ, p, q, r as gesture stability input, repeat step 1 to step 6 so that Obtain aircraft and realize actual attitude angle Ω=[α, β, μ]^TThe attitude angle instruction Ω that homing guidance system is provided_c=[α_c,β_c,μ_c]^T Purpose.

Beneficial effect：

1st, the nominal control law v that the present invention is provided_eqThe response of system is determined, when having uncertain, system is still It can realize and same corresponding of nominal system.

2nd, present system can realize finite time convergence control, tracking accuracy that can be higher with faster convergence rate, Effectively increase the performance of control system.

3rd, the present invention is by introducing full-order sliding mode face, it is to avoid controlled quentity controlled variable singular problem present in TSM control.

4th, the present invention using boundary layer and low-pass filtering technique by that can eliminate the buffeting of controlled quentity controlled variable simultaneously.

Brief description of the drawings

Fig. 1 is the flow chart of the full rank non-singular terminal Sliding Mode Attitude control method of the present invention；

Fig. 2 is reentry vehicle attitude control system structure chart of the invention；

When Fig. 3 is does not scramble dynamic in embodiment, respectively by full rank non-singular terminal sliding mode controller and original limit Posture response curve when time feedbacking controller is controlled；

When Fig. 4 is does not scramble dynamic in embodiment, control surface deflection during full rank non-singular terminal sliding mode controller control Angular curve；

When Fig. 5 is does not scramble dynamic in embodiment, control surface deflection angle is bent during former finite time feedback controller control Line；

When Fig. 6 is adds disturbance in embodiment, respectively by full rank non-singular terminal sliding mode controller and original limit Posture response curve when time feedbacking controller is controlled；

When Fig. 7 is adds disturbance in embodiment, only do not responded using rudder face when boundary layer technology and filtering technique Curve；

When Fig. 8 is adds disturbance in embodiment, only with rudder face response curve during the technology of boundary layer；

When Fig. 9 is adds disturbance in embodiment, not using rudder face response curve when boundary layer and filtering technique.

Embodiment

In order to better illustrate objects and advantages of the present invention, technical scheme is done further with example below in conjunction with the accompanying drawings Describe in detail.

Embodiment 1：

Hypersonic model using the NASA Winged-Cone configurations announced is emulation platform, for its ablated configuration mistake Cheng Jinhang numerical simulations.Simulated conditions are, elemental height 30km, and initial flight speed is 2800m/s, initial attitude angle y (0)= [0°,1°,0°]^T, the given instruction y of attitude angle_c=[3 °, 0 °, 5 °]^T, initial attitude angular speed p (0)=q (0)=r (0)= 0deg/s.Control surface deflection angle is limited in ± 30 °.

Due to reentry vehicle flying condition wide variation, and usually there is the uncertainties such as aerodynamic parameter perturbation, because This will not only examine the control performance under nominal case for the gesture stability problem of reentry vehicle, in addition it is also necessary to examine control Can device carry out robust, accurately control in the case where ambient parameter acute variation and system have relatively strong uncertainty.For Further robustness of the checking when disturbed, it is considered to atmospheric density perturbation -20%, rotary inertia perturbation -10%, and consider as follows The external disturbance torque of form：

By the way that a kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle disclosed in the present embodiment is provided The control result that is provided with finite time attitude feedback control method of control result contrasted, illustrate the beneficial effect of the present invention Really.

A kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle disclosed in the present embodiment, including following step Suddenly：

Step 1, the state vector of aircraft is generated.

Step 2, the mathematical modeling of reentry vehicle is set up.

Set up the mathematical modeling such as formula (1) of reentry vehicle

y_i=h_i(x), i=1,2,3.

Wherein, state vector x=[α β μ p q r]^T, control moment u=[u₁,u₂,u₃]^T=[M_x,M_y,M_z]^T, output Vectorial y=[y₁,y₂,y₃]=h (x)=[α, β, μ]^T, f (x)=[f₁(x) f₂(x) f₃(x) f₄(x) f₅(x) f₆(x)]^T。

f₁(x)=- pcos α tan β+q-rsin α tan β

f₂(x)=psin α-rcos α

f₃(x)=- pcos α cos β-qsin β-rsin α cos β

Lie derivatives is defined as follows：

AndMeet following condition：

Wherein：

From calculating：Therefore controller is expressed as formula (4)：

U=E^-1(x)(-F(x)+v) (4)

It can be obtained by formula (3) and (4)：

In formula, l_dmi,_nk_dmiTable_nShow matrix l_d,k_dIn nonzero element minimum value, and have matrix l_d=diag { l_d1, l_d2,l_d3, k_d=diag { k_d1,k_d2,k_d3}。

In formula,The tracking error of system, t_rFor the stabilization time of system..

Described full rank terminal slides control method, including step 4.1,4.2,

In formula, S (t)=[s₁(t),s₂(t),s₃(t)]^T。

V=v_eq+v_n

v_vss=-(k_d+k_T+η)sgn(S)

In formula, 0 ＜ θ ＜ 1；η=diag { η₁,η₂,η₃It is handoff gain matrix；k_dDefinition as shown in step 3；When T is Between constant, itself and k_TInequality k is met jointly_T≥Tl_d；S is the Integral Sliding Mode face designed in step 4.Ginseng in actual emulation Number is set, controller parameter：θ=0.6, d=20, T=1, η=3, k_d=k_T=1.

V points described of control law is two parts, and one is to make sliding formwork function be the zero equivalent control part v directly tried to achieve_eq；Two It is switching control part v_n, in order to weaken the buffeting problem of sliding mode controller inherently, we introduce single order in switching control Low pass filter is to reach the effect for disappearing and trembling, and T is the bandwidth of the wave filter.Further, to make the output of controller more smooth, Sign function in switching control is replaced using saturation function, then equivalent control term can be expressed as form again：

v_vss=-(k_d+k_T+η)sat(S)

In formula,It is boundary layer thickness, during emulation

Due to use the second dervative information of attitude angle when designing sliding-mode surface S (t), and attitude angle in systems in practice The information of second dervative cannot direct measurement obtain.Therefore, in order to realize the control method, and avoid directly to appearance The derivative information derivation at state angle introduces high-frequency noise, robust differentiator is introduced in steps of 5, to the second dervative information of attitude angle Estimated.

Step 5, super-twisting algorithm robust differentiator is introduced, it is ensured that evaluated error e is in Finite-time convergence to zero.

Levant proposes the aufbauprinciple of robust differentiator, and gives relative configurations process, below we drawn Enter into the controller of the present embodiment.

First, make

And have evaluated error

Then the derivative of evaluated error is

In order that observation error levels off to zero in finite time, the present embodiment provides following robust differentiator：

In formula, a ＞ 0, b ＞ 0 are supercoil gains.Z is the estimate of attitude angle second dervative.The robust in actual emulation Differentiator parameter is：A=2, b=4.

From pertinent literature, supercoil robust differentiator can ensure evaluated error e in Finite-time convergence to zero.

Step 6, control distribution, obtains angle of rudder reflection instruction δ=[δ_e δ_a δ_r]^T：

Angle of rudder reflection instruction δ=[δ is obtained according to formula (12) and (13)_e δ_a δ_r]^T：

U=M=E^-1(x)(-F(x)+v) (12)

δ=G^-1u (13)

Distribution obtains δ=[δ to rudder face executing agency by formula (12)_e δ_a δ_r]^T, δ_e,δ_a,δ_rRespectively elevator, pair The drift angle of the wing, rudder.M=[M_x,M_y,M_z] it is that the gesture stability output v obtained in step 4.3 calculates obtained controling power Square, G is transition matrix, is determined by aerodynamic parameter.

Step 7, angle of rudder reflection instruction input aircraft step 6 obtained, gesture stability is carried out to it；Meanwhile, aircraft Export current flight device each state α, β, μ, p, q, r as gesture stability input, repeat step 1 to step 7 so that Obtain aircraft and realize attitude angle Ω=[α, β, μ]^TThe attitude angle instruction Ω that homing guidance system is provided_c=[α_c,β_c,μ_c]^TMesh 's.

By the way that a kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle disclosed in the present embodiment is provided The control result that is provided with finite time attitude feedback control method of control result contrasted, illustrate the excellent of the present embodiment Point.

1. a kind of full rank non-singular terminal Sliding Mode Attitude control method (FONTSMC) of reentry vehicle of the present embodiment is verified System tracking error is enabled in Finite-time convergence.

A kind of reentry vehicle that Fig. 3 is given in no external disturbance and Parameter Perturbation respectively using the present embodiment is complete The attitude angle aircraft pursuit course of rank non-singular terminal Sliding Mode Attitude control method and former finite time controller simulation.From the figure 3, it may be seen that The control effect of the present embodiment is consistent with the response dynamics of former finite time feedback control, makes attitude error in finite time Zero is inside converged to, and ensure that tracking accuracy.

2. a kind of full rank non-singular terminal Sliding Mode Attitude control method (FONTSMC) of reentry vehicle of the present embodiment is verified With improvement of the former finite time feedback (FDC) in terms of robustness

Fig. 4,5 give is fed back using the present embodiment and former finite time respectively in no external disturbance and Parameter Perturbation The control surface deflection angular curve of controller simulation.From Fig. 4,5, control is not present without departing from saturation limiting in control rudder face Buffet in face.Fig. 6 gives when there is external disturbance and inner parameter perturbation uses the controller of the present embodiment and common respectively The attitude angle aircraft pursuit course that finite-time control device is emulated.It will be appreciated from fig. 6 that there is external disturbance and inner parameter perturbation When, the present embodiment has more preferable tracking effect and control accuracy.It is indicated above that the present embodiment has stronger robustness, And higher tracking accuracy.

3. subtracting used in a kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle of the present embodiment is verified The validity for the method that weak sliding mode controller output is buffeted

Fig. 7,8,9 are the l-G simulation test carried out under three kinds of different conditions respectively.

(1) switching control item uses sign function, and does not add wave filter (Fig. 7)；

(2) switching control item uses saturation function, and does not add wave filter (Fig. 8)；

(3) switching control item uses saturation function, and uses wave filter (Fig. 9).

From Fig. 8,9, when adding wave filter when switching control is using boundary layer technology, the output effect of rudder face is controlled most It is good, both in the absence of buffeting, there is more smooth control output again.During only with boundary layer technology, control effect is taken second place.Work as sliding formwork When switching control simply uses sign function, as shown in Figure 7, the output of control rudder face can have more violent buffeting, and There is controlled quentity controlled variable saltus step in the control starting stage.Therefore, the present embodiment uses the method that boundary layer technology is combined with wave filter Effectively inhibit and buffeted present in sliding formwork control, make the output of control rudder face more smooth.

The scope of the present invention is not only limited to embodiment, and embodiment is used to explaining the present invention, it is all with of the invention identical Change or modification under the conditions of principle and design is within protection domain disclosed by the invention.

Claims

1. a kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle, it is characterised in that：Comprise the following steps,

Step 1, the state vector of aircraft is generated；

With reference to actual attitude angle Ω=[α, β, the μ] of aircraft^T, attitude angular velocity ω=[p, q, r]^T, composition state vector x：x =[α β μ p q r]^T；

Step 2, the mathematical modeling of reentry vehicle is set up；

Set up the mathematical modeling such as formula (1) of reentry vehicle

<mrow> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>3</mn> </munderover> <msub> <mi>g</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>+</mo> <mi>&Delta;T</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

y_i=h_i(x), i=1,2,3.

Wherein, state vector x=[α β μ p q r]^T, control moment u=[u₁,u₂,u₃]^T=[M_x,M_y,M_z]^T, output vector y =[y₁,y₂,y₃]=h (x)=[α, β, μ]^T,

F (x)=[f₁(x) f₂(x) f₃(x) f₄(x) f₅(x) f₆(x)]^T；

f₁(x)=- p cos α tan β+q-r sin α tan β

f₂(x)=p sin α-r cos α

f₃(x)=- p cos α cos β-q sin β-r sin α cos β

In formula (1), α, β, μ represents the angle of attack, yaw angle and angle of heel respectively；P, q, r represent respectively rolling, pitching and partially Navigate angular speed；M=[M_x,M_y,M_z] represent control moment vector, M_x,M_y,M_zRolling, pitching and yawing are represented respectively；M_d It is external disturbance torque vector；I_xx,I_yy,I_zz,I_xzIt is the rotary inertia and product of inertia on each reference axis respectively,△ T represent to include the polymerization uncertainty such as Parameter Perturbation, external disturbance and Unmarried pregnancy, due to again Enter process medium velocity fast, atmospheric environment change is violent, and △ T can not ignore；

Step 3, the reentry vehicle model that step 2 is set up is simplified with feedback linearization；

Using the method for expressing of Lie derivatives, then y in formula (1)_iDerivative be expressed as formula (2)

<mrow> <msubsup> <mi>y</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>L</mi> <mi>f</mi> <mi>j</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mn>3</mn> </munderover> <msub> <mi>L</mi> <mi>gk</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>L</mi> <mi>f</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1,2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> 1

Shape feedback linearization processing is carried out to dummy vehicle, formula (3) is obtained：

<mrow> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mover> <mi>y</mi> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> </mover> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi>y</mi> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> </mover> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mover> <mi>y</mi> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> </mover> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>E</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mi>u</mi> <mo>+</mo> <mi>&Delta;v</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Wherein：

From calculating：Therefore controller is expressed as formula (4)：

U=E^-1(x)(-F(x)+v) (4)

It can be obtained by formula (3) and (4)：

<mrow> <mover> <mi>y</mi> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> </mover> <mo>=</mo> <mi>v</mi> <mo>+</mo> <mi>&Delta;v</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

In formula, v=[v₁,v₂,v₃] it is the auxiliary variable introduced, △ v are the polymerization disturbance in system；Polymerization disturbance △ v and it First derivativeMeet following condition：

<mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mi>&Delta;v</mi> <mo>|</mo> <mo>|</mo> </mrow> <mo>&infin;</mo> </msub> <mo>&le;</mo> <msub> <mi>l</mi> <mrow> <mi>d</mi> <mi>min</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mi>&Delta;</mi> <mover> <mi>v</mi> <mo>&CenterDot;</mo> </mover> <mo>|</mo> <mo>|</mo> </mrow> <mo>&infin;</mo> </msub> <mo>&le;</mo> <msub> <mi>k</mi> <mrow> <mi>d</mi> <mi>max</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

In formula, l_dmin,k_dminRepresenting matrix l_d,k_dIn nonzero element minimum value, and have matrix l_d=diag { l_d1,l_d2, l_d3, k_d=diag { k_d1,k_d2,k_d3}；

Step 4, for the gesture stability problem of reentry vehicle, provide full rank terminal and slide control method to ensure to deposit in systems The command information y of attitude angle α, β, μ the progressive tracking system of aircraft in external disturbance and Parameter uncertainties_c=[α_c,β_c, μ_c]^T, i.e.,：

<mrow> <munder> <mi>lim</mi> <mrow> <mi>t</mi> <mo>=</mo> <msub> <mi>t</mi> <mi>r</mi> </msub> </mrow> </munder> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>=</mo> <munder> <mi>lim</mi> <mrow> <mi>t</mi> <mo>=</mo> <msub> <mi>t</mi> <mi>r</mi> </msub> </mrow> </munder> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow>

In formula,The tracking error of system, t_rFor the stabilization time of system；

Step 5, control distribution, obtains angle of rudder reflection instruction δ=[δ_e δ_a δ_r]^T：

U=M=E^-1(x)(-F(x)+v) (9)

δ=G^-1u (10)

Distribution obtains δ=[δ to rudder face executing agency by formula (10)_e δ_a δ_r]^T, δ_e,δ_a,δ_rRespectively elevator, aileron, side To the drift angle of rudder；M=[M_x,M_y,M_z] it is that the gesture stability output v obtained in step 4 calculates obtained control moment, G is to turn Matrix is changed, is determined by aerodynamic parameter；

Step 6, angle of rudder reflection instruction input aircraft step 5 obtained, gesture stability is carried out to it；Meanwhile, aircraft output Each state α, β, μ, p, q, r of current flight device are as the input of gesture stability, and repeat step 1 is to step 6, so that flying Row device realizes actual attitude angle Ω=[α, β, μ]^TThe attitude angle instruction Ω that homing guidance system is provided_c=[α_c,β_c,μ_c]^TMesh 's.

2. a kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle as claimed in claim 1, its feature exists In：Described full rank terminal slides control method, including step 4.1,4.2,

Step 4.1, in order to avoid the singular problem in ordinary terminal sliding formwork, the full rank terminal sliding mode as shown in formula (7) is provided Face：

<mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>S</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> </mover> </mover> <mi>e</mi> </msub> <mo>+</mo> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>|</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>|</mo> </mrow> <mi>&theta;</mi> </msup> <mo>+</mo> <mi>sgn</mi> <mrow> <mo>(</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>|</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mfrac> <mi>&theta;</mi> <mrow> <mn>2</mn> <mo>-</mo> <mi>&theta;</mi> </mrow> </mfrac> </msup> <mo>)</mo> </mrow> <mo>,</mo> <mn>0</mn> <mo><</mo> <mi>&theta;</mi> <mo><</mo> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>&phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mo>-</mo> <mi>&theta;</mi> </mrow> </mfrac> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>|</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>|</mo> </mrow> <mrow> <mn>2</mn> <mo>-</mo> <mi>&theta;</mi> </mrow> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

In formula, S (t)=[s₁(t),s₂(t),s₃(t)]^T；

V=v_eq+v_n

<mrow> <msub> <mi>v</mi> <mi>eq</mi> </msub> <mo>=</mo> <mo>-</mo> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>|</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>|</mo> </mrow> <mi>&theta;</mi> </msup> <mo>-</mo> <mi>sgn</mi> <mrow> <mo>(</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <msup> <mrow> <mo>|</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>&Omega;</mi> <mo>~</mo> </mover> <mi>e</mi> </msub> <mo>,</mo> <msub> <mover> <mi>&Omega;</mi> <mover> <mo>~</mo> <mo>&CenterDot;</mo> </mover> </mover> <mi>e</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mfrac> <mi>&theta;</mi> <mrow> <mn>2</mn> <mo>-</mo> <mi>&theta;</mi> </mrow> </mfrac> </msup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mover> <mi>v</mi> <mo>&CenterDot;</mo> </mover> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>Tv</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>v</mi> <mi>vss</mi> </msub> </mrow>

v_vss=-(k_d+k_T+η)sgn(S)

In formula, 0<θ<1；η=diag { η₁,η₂,η₃It is handoff gain matrix；k_dDefinition as shown in step 3；T is time constant, Itself and k_TInequality k is met jointly_T≥Tl_d；S is the Integral Sliding Mode face provided in step 4.

3. a kind of full rank non-singular terminal Sliding Mode Attitude control method of reentry vehicle as claimed in claim 1 or 2, its feature It is：Also include introducing super-twisting algorithm robust differentiator between described step 4 and step 5, it is ensured that evaluated error e is having The step of zero being converged in limited time,

First, make

<mrow> <mover> <mi>&Omega;</mi> <mover> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> <mo>^</mo> </mover> </mover> <mo>=</mo> <mi>z</mi> </mrow>

And have evaluated error

<mrow> <mi>e</mi> <mo>=</mo> <mover> <mi>&Omega;</mi> <mo>&CenterDot;</mo> </mover> <mo>-</mo> <mover> <mi>&Omega;</mi> <mover> <mo>&CenterDot;</mo> <mo>^</mo> </mover> </mover> </mrow>

Then the derivative of evaluated error is

<mrow> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>&Omega;</mi> <mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> </mrow> </mover> <mo>-</mo> <mi>z</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

In order that observation error levels off to zero in finite time, following robust differentiator is provided,

<mrow> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mi>z</mi> <mo>=</mo> <mi>a</mi> <msup> <mrow> <mo>|</mo> <mi>e</mi> <mo>|</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mi>sgn</mi> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&omega;</mi> </mtd> </mtr> <mtr> <mtd> <mover> <mi>&omega;</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <mi>bsgn</mi> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

In formula, a>0,b>0 is supercoil gain；Z is the estimate of attitude angle second dervative.