CN102880060A - Self-adaptive index time varying slip form posture control method of reentry flight vehicle - Google Patents

Abstract

The invention relates to a self-adaptive index time varying slip form posture control method of a reentry flight vehicle, belonging to the technical field of flight vehicles. The method comprises the steps of firstly establishing a posture motion equation in a mode that a powerless reentry flight vehicle model is used as an object; secondly modifying the equation into the mode of an MIMO (Multiple Input Multiple Output) affine non-linear system, further applying a feedback linearization principle to carry out linearization processing so as to obtain a three-channel linearization model of pitching, rolling and yawing; aiming at the obtained linearization system, designing a modified self-adaptive index time varying slip form controller; and subsequently obtaining a control moment instruction for the posture control of the reentry flight vehicle, and inputting the control moment instruction into the reentry flight vehicle so as to control the posture. By combining the index time varying slip form control with a self-adaptive method, the problem of excessive adaptation of switch gain in the self-adaptive slip form control is solved to a certain extent, the uncertainty of system parameters and the influence of external disturbance can be suppressed effectively, and the precise posture control is realized.

Description

Reentry vehicle self-adaptive index time-varying sliding mode attitude control method

Technical Field

The invention relates to a reentry vehicle self-adaptive index time-varying sliding mode attitude control method, and belongs to the technical field of vehicle control.

Background

For a reentry aircraft, the flight conditions (airspace and speed domain) change in a large range in the reentry process, the coupling among channels is serious, and the reentry aircraft presents strong nonlinear dynamic characteristics. In addition, the presence of various uncertain external disturbances and the aerodynamic characteristics of the aircraft are not precisely known, making its attitude control extremely complex. The key problem to be solved by reentry aircraft control system design is to suppress the above-mentioned non-linearities, strong coupling and uncertainty effects on system performance.

Although various advanced nonlinear control methods (such as dynamic inverse, feedback linearization, trajectory linearization, backstepping method, adaptive control method and the like) are widely applied to the design of attitude control systems of reentry vehicles, the sliding mode variable structure control method is still the primary choice for processing bounded disturbance/uncertainty and unmodeled dynamics in system models. The sliding mode variable structure is used as a nonlinear control method, and has strong robustness on uncertainty and disturbance of matching parameters existing in the system. However, the conventional sliding mode natural control has the defects that: 1) the arrival section has no robustness; 2) the problem of buffeting; 3) the selection of the switching gain in the control law.

In order to solve the problem that an arrival section does not have robustness and achieve the purpose of global robustness, A.Bartoszewicz [ A.Bartoszewicz, Time-varying sliding modes for second-order systems, IEE Proceedings of Control Theory Application,143(5),1996:455-462 ] adopts a Time-varying sliding mode surface to replace a Time-invariant sliding mode surface, so that the system state is on the sliding mode surface at the initial Time, the Time-invariant sliding mode surface determined in advance is approached along with Time in a rotating or translating mode, and the problem that the sliding mode Control quantity is not smooth still exists. The buffeting problem of the sliding mode variable structure control is taken as an inherent characteristic and can be weakened but not completely eliminated, and a plurality of methods can be used for processing the buffeting problem, such as: boundary layer methods [ J.J.Slosine, Sliding mode controller design for nonlinear system, International Journal of control,40(2),1984: 421-; sliding sector method [ K.Furuta, Y.Pan, Variable structured with sliding sector, Automatica,36 (2); 2000: 211-; a high-order Sliding mode Control method [ A.Levant, Sliding order and Sliding access in Sliding mode Control, International journal of Control,58(6),1993:1247 and 1263 ]. Generally, the switching gain in sliding mode control is determined based on a previously known upper bound of uncertainty in the system. However, for reentry vehicles, the reentry process is complex and variable, and these upper bounds of uncertainty are not easily obtained. If the switching gain value is too large, the robustness of the system is strong, but the buffeting is serious, and the high-frequency unmodeled dynamic state of the system is easy to be excited to cause the instability of the system; if the switching gain value is too small, the buffeting is small, but the anti-interference capability of the system is weak, and the robustness is poor. For this reason, an adaptive method is required to calculate the switching gain of the sliding mode control on line.

Disclosure of Invention

The invention aims to provide a high-precision global robust attitude control method for a reentry vehicle with uncertain pneumatic parameters and external disturbance moment by combining an exponential time-varying sliding mode and a self-adaptive control method aiming at the characteristics of fast time variation, strong coupling and high nonlinearity of the reentry vehicle.

The purpose of the invention is realized by the following technical scheme:

step 1, establishing an attitude motion equation by taking an x-O-y plane symmetric unpowered reentry aircraft model as an object, wherein the x-O-y plane symmetric unpowered reentry aircraft model is related to an aircraft coordinate system (the origin O of the coordinate system is taken at the center of mass of the aircraft, the axis Ox is coincident with the longitudinal axis of the aircraft, the pointing head is positive, the axis Oy is positioned in the longitudinal symmetry plane of the aircraft and is vertical to the axis Ox, the pointing direction is positive, the axis Oz is vertical to the plane Oxy, and the direction is determined according to a right-hand rectangular coordinate:

$\stackrel{\·}{\mathrm{\α}}={\mathrm{\ω}}_z$

$\stackrel{\·}{\mathrm{\β}}={\mathrm{\ω}}_x\sin \mathrm{\α}+{\mathrm{\ω}}_y\cos \mathrm{\α}$

$\stackrel{\·}{\mathrm{\μ}}={\mathrm{\ω}}_x\cos \mathrm{\α}-{\mathrm{\ω}}_y\sin \mathrm{\α}$

${\stackrel{\·}{\mathrm{\ω}}}_x=\frac{I_{\mathrm{yy}}}{I^{*}}{M}_x+\frac{I_{\mathrm{xy}}}{I^{*}}{M}_y-\frac{I_{\mathrm{yy}}(I_{\mathrm{zz}}-I_{\mathrm{yy}})-I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\ω}}_y{\mathrm{\ω}}_z-\frac{I_{\mathrm{xy}}(I_{\mathrm{yy}}+I_{\mathrm{xx}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\ω}}_x{\mathrm{\ω}}_z---\left(1\right)$

${\stackrel{\·}{\mathrm{\ω}}}_y=\frac{I_{\mathrm{xy}}}{I^{*}}{M}_x+\frac{I_{\mathrm{xx}}}{I^{*}}{M}_y-\frac{I_{\mathrm{xx}}(I_{\mathrm{xx}}-I_{\mathrm{zz}})+I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\ω}}_x{\mathrm{\ω}}_z+\frac{I_{\mathrm{xy}}(I_{\mathrm{xx}}+I_{\mathrm{yy}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\ω}}_y{\mathrm{\ω}}_z$

${\stackrel{\·}{\mathrm{\ω}}}_z=\frac{1}{I_{\mathrm{zz}}}{M}_z-\frac{I_{\mathrm{yy}}-I_{\mathrm{xx}}}{I_{\mathrm{zz}}}{\mathrm{\ω}}_x{\mathrm{\ω}}_y-\frac{I_{\mathrm{xy}}}{I_{\mathrm{zz}}}({\mathrm{\ω}}_y^2-{\mathrm{\ω}}_x^2)$

in the formula, alpha, beta and mu are respectively an attack angle, a sideslip angle and a roll angle; omega_x,ω_y，ω_zRoll, yaw and pitch velocities, respectively; i is_xx,I_yy,I_zz,I_xyRespectively, the moment of inertia and the inertia product I about the x, y and z axes under the body coordinate system_xz=I_yz=0，

M_x,M_y,M_zRespectively, the aerodynamic moment under the coordinate system of the body. Wherein, the aerodynamic moment is:

$M_i=\hat{q}\mathrm{Sl}{C}_{\mathrm{mi}}(\mathrm{\α},\mathrm{\β},\mathrm{Ma},{\mathrm{\δ}}_x,{\mathrm{\δ}}_y,{\mathrm{\δ}}_z),i=x,y,z---\left(2\right)$

in the formula:

the pressure is dynamic pressure, rho is atmospheric density, and V is the flying speed of the aircraft; s, l is the reference area and the reference length of the aircraft respectively; delta_x，δ_y，δ_zRespectively an aileron, a rudder and an elevator; c_mx,C_my,C_mzRoll, yaw and pitch moment coefficients, respectively, with respect to α, β, δ_x，δ_y,δ_zAnd mach number Ma.

Since the earth rotation angular velocity is much slower than the rotational motion of the aircraft, and the rotational motion of the aircraft is much faster than the displacement motion, the effects of the earth rotation angular velocity and the displacement motion of the aircraft in the rotational motion equation are ignored. And BTT control is adopted in the reentry process, the sideslip angle is maintained near a zero value, sin beta is approximately equal to 0, tan beta is approximately equal to 0, and cos beta is approximately equal to 1.

Step 2, rewriting the reentry aircraft model established in the step 1 into a MIMO affine nonlinear system form:

$\stackrel{\·}{x}=f\left(x\right)+g\left(x\right)u---\left(3\right)$

Ω=h(x)

wherein x = [ α β μ ω =_x ω_y ω_z]^TIs the state vector, Ω = [ α β μ =]^TIs a system output variable, u = [ M = [)_x M_y M_z]^TIs calculated aerodynamic moment and rudder surface deflectionAngle instruction [ delta ]_x,δ_y,δ_z]^TObtained by the inversion calculation of the formula (2). f (x) = [ f₁(x)…f₆(x)]^TIs a 6 × 1 dimensional matrix, g (x) = [ g [)₁(x) g₂(x) g₃(x)]^TIs a 6 × 3 dimensional matrix, h (x) = [ h%₁(x) h₂(x) h₃(x)]^TIs a 3 x 1 dimensional matrix. Wherein,

$\left\{\begin{array}{c}{f}_1\left(x\right)={\mathrm{\ω}}_z\\ f_2\left(x\right)={\mathrm{\ω}}_x\sin \mathrm{\α}+{\mathrm{\ω}}_y\cos \mathrm{\α}\\ f_3\left(x\right)={\mathrm{\ω}}_x\cos \mathrm{\α}-{\mathrm{\ω}}_y\sin \mathrm{\α}\\ f_4\left(x\right)=-\frac{I_{\mathrm{yy}}(I_{\mathrm{zz}}-I_{\mathrm{yy}})-I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\ω}}_y{\mathrm{\ω}}_z-\frac{I_{\mathrm{xy}}(I_{\mathrm{yy}}+I_{\mathrm{xx}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\ω}}_x{\mathrm{\ω}}_z\\ f_5\left(x\right)=-\frac{I_{\mathrm{xx}}(I_{\mathrm{xx}}-I_{\mathrm{yy}})+I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\ω}}_x{\mathrm{\ω}}_z+\frac{I_{\mathrm{xy}}(I_{\mathrm{xx}}+I_{\mathrm{yy}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\ω}}_y{\mathrm{\ω}}_z\\ f_6\left(x\right)=-\frac{I_{\mathrm{yy}}-I_{\mathrm{xx}}}{I_{\mathrm{zz}}}{\mathrm{\ω}}_x{\mathrm{\ω}}_y-\frac{I_{\mathrm{xy}}}{I_{\mathrm{zz}}}({\mathrm{\ω}}_y^2-{\mathrm{\ω}}_x^2)\end{array}\right.,$

$\left\{\begin{array}{c}{g}_1\left(x\right)={\left[\begin{array}{cccccc}0& 0& 0& \frac{I_{\mathrm{yy}}}{I^{*}}& \frac{I_{\mathrm{xy}}}{I^{*}}& 0\end{array}\right]}^T\\ g_2\left(x\right)={\left[\begin{array}{cccccc}0& 0& 0& \frac{I_{\mathrm{xy}}}{I^{*}}& \frac{I_{\mathrm{xx}}}{I^{*}}& 0\end{array}\right]}^T\\ g_3\left(x\right)={\left[\begin{array}{cccccc}0& 0& 0& 0& 0& \frac{1}{I_{\mathrm{zz}}}\end{array}\right]}^T\end{array}\right..$

and 3, aiming at the affine nonlinear system obtained in the step 2, applying a feedback linearization theory to carry out linearization treatment to obtain a three-channel linearization model of pitching, rolling and yawing:

$\stackrel{\·\·}{\mathrm{\Ω}}=F\left(x\right)+E\left(x\right)U---\left(4\right)$

in the formula,

$F\left(x\right)=\left[\begin{array}{c}{f}_3\left(x\right)\\ \sin \mathrm{\α}\·f_1\left(x\right)+\cos \mathrm{\α}\·f_2\left(x\right)+({\mathrm{\ω}}_x\cos \mathrm{\α}-{\mathrm{\ω}}_y\sin \mathrm{\α})\·{\mathrm{\ω}}_z\\ \cos \mathrm{\α}\·f_1\left(x\right)-\sin \mathrm{\α}\·f_2\left(x\right)-({\mathrm{\ω}}_x\sin \mathrm{\α}+{\mathrm{\ω}}_y\cos \mathrm{\α})\·{\mathrm{\ω}}_z\end{array}\right],$

$E\left(x\right)=\left[\begin{array}{ccc}0& 0& \frac{1}{I_{\mathrm{zz}}}\\ \frac{I_{\mathrm{yy}}\sin \mathrm{\α}}{I^{*}}+\frac{I_{\mathrm{xy}}\cos \mathrm{\α}}{I^{*}}& \frac{I_{\mathrm{xy}}\sin \mathrm{\α}}{I^{*}}+\frac{I_{\mathrm{xx}}\cos \mathrm{\α}}{I^{*}}& 0\\ \frac{I_{\mathrm{yy}}\cos \mathrm{\α}}{I^{*}}-\frac{I_{\mathrm{xy}}\sin \mathrm{\α}}{I^{*}}& \frac{I_{\mathrm{xy}}\cos \mathrm{\α}}{I^{*}}-\frac{I_{\mathrm{xx}}\sin \mathrm{\α}}{I^{*}}& 0\end{array}\right],$

U＝[u₁ u₂ u₃]^T=[M_x M_y M_z]^T。

calculating to obtain: det (e (x) ═ -1/(I)^*I_zz) Not equal to 0, so E (x) is reversible. The control law form is therefore chosen to be:

U＝E^-1(v-F)（5）

wherein v = [ v =₁ v₂ v₃]^TIs the assist control amount.

Substituting the control law into the linearized model yields the decoupled integrator form:

$\stackrel{\·\·}{\mathrm{\Ω}}=v---\left(6\right)$

when there is parameter uncertainty and external disturbances in the affine nonlinear system of the reentry aircraft model, the feedback linearized system model is represented as:

$\stackrel{\·\·}{\mathrm{\Ω}}=F+\mathrm{\ΔF}+(E+\mathrm{\ΔE})U---\left(7\right)$

with Δ v = [ ]₁ Δv₂ Δv₃]^TRepresenting the polymerization perturbation in the above formula: Δ v = Δ F + Δ EU. And the uncertainty perturbation is bounded, i.e. Δ v is present_1max,Δv_2max,Δv_3maxSo that | Δ v₁|≤Δv_1max，|Δv₂|≤Δv_2max，|Δv₃|≤Δv_3max。

Substituting the selected control law form (5) and the aggregate disturbance expression Δ v into the feedback linearized system model formula (7), the reentry aircraft feedback linearized system considering parameter uncertainty and disturbance is:

$\stackrel{\·\·}{\mathrm{\Ω}}=v+\mathrm{\Δv}---\left(8\right)$

and 4, designing a self-adaptive exponential time-varying sliding mode controller for the linearized system obtained in the step 3.

Firstly, selecting an exponential time-varying sliding mode surface:

$S\left(t\right)=\stackrel{\·}{\widetilde{\mathrm{\Ω}}}+\mathrm{\Λ}\widetilde{\mathrm{\Ω}}+A{e}^{-\mathrm{at}}---\left(9\right)$

in the formula,

is the system tracking error, Ω_c=[α_c β_c μ_c]^TIs an attitude command given by the guidance ring, S (t) = [ s = [ ()_α(t) s_β(t) s_μ(t)]^T∈R³Is a sliding mode surface function vector, and A belongs to R³Is a parameter matrix related to the initial value of the system state, Λ = diag { λ }₁,λ₂,λ₃}∈R^3×3Representing the slope of the slip form surface, a ∈ R⁺Determining the approaching speed of the time-varying slip form surface to the time-invariant slip form surface, and controlling the lambda value₁=λ₂=λ₃= a = λ. According to the time-varying sliding mode theory, the system state requirement is required to be on the sliding mode surface from the initial moment, namely, the following requirements are met: s (0) =0_3×1Then the value of a is:

$A=-\stackrel{\·}{\widetilde{\mathrm{\Ω}}}\left(0\right)-\mathrm{\Λ}\widetilde{\mathrm{\Ω}}\left(0\right)=-\mathrm{\Λ}\widetilde{\mathrm{\Ω}}\left(0\right)---\left(10\right)$

then, designing a modified adaptive exponential time-varying sliding mode controller in the form of:

$v=v_{\mathrm{eq}}+v_{\mathrm{sw}}={\stackrel{\·\·}{\mathrm{\Ω}}}_c-\mathrm{\Λ}\stackrel{\·}{\widetilde{\mathrm{\Ω}}}+\mathrm{A\λ}{e}^{-\mathrm{\λt}}-\mathrm{\ηsat}\left(S\left(t\right)\right)---\left(11\right)$

in the formula,

denotes equivalent control, v_sw= η sat (s (t)) indicates that the switching control (saturation function sat () is used to reduce the chattering), η = diag { η ·)_α,η_β,η_μAnd the multiplication is the switching gain of sliding mode control. The saturation function sat (-) and the handover gain adaptation algorithm are respectively expressed as:

${\stackrel{\·}{\mathrm{\η}}}_j=\frac{1}{k_j}(-{\mathrm{\σ}}_j{\mathrm{\η}}_j+|s_j\left(t\right)\left|\right),j=\mathrm{\α},\mathrm{\β},\mathrm{\μ}---\left(13\right)$

wherein,

denotes the boundary layer thickness, σ_jIs a small positive constant, k_j>0 is the adaptation rate. Eta_jAdaptive speed of (k)_jBy selecting the appropriate k_jIt is possible to effectively avoid the high-frequency vibration of the phase-up controlled quantity. Without loss of generality, the invention will k_jIs set to be constant, and k_α=k_β=k_μ=k。

Step 5, obtaining a control moment instruction of attitude control of the reentry vehicle according to the step 4:

U＝E^-1(v-F)（14）

then distributing the control torque to the aerodynamic control surface according to the aerodynamic torque expression (2), and calculating to obtain a control surface deflection angle instruction [ delta ] required by attitude control_x δ_y δ_z]^T。

Step 6, the control surface deflection angle instruction [ delta ] obtained in the step 5 is processed_x δ_y δ_z]^TInputting the attitude data into the reentry vehicle to control the attitude. At the same time, the aircraft control system outputs real-time flight states (α, β, μ, ω)_x,ω_y,ω_z) And inputting the feedback state into the attitude control system, and repeating the steps 2 to 6.

Therefore, under the condition that parameter uncertainty and external disturbance exist in the system, the control surface deflection angle [ delta ] is controlled_x δ_y δ_z]^TAnd realizing the attitude command omega given to the guidance ring_c=[α_c β_c μ_c]^TEfficient tracking of.

Advantageous effects

Compared with the prior art, the invention has the advantages that:

1) the method combines the characteristics of the reentry vehicle, provides a model simplification method, analyzes the uncertainty of the model, and applies a feedback linearization method to carry out linearization processing on the nonlinear dynamic equation of the reentry vehicle. Aiming at a reentry vehicle dynamic equation decoupled after linearization, a design method of an index time-varying sliding mode attitude controller is provided, the problem that the conventional sliding mode control arrival section does not have robustness is effectively solved, the robustness of a control system is improved, and the response effect of the system is effectively improved;

2) the switching gain self-adaptive adjustment algorithm introduced by the invention effectively solves the problem of blind adjustment of sliding mode control switching gain, and can effectively improve the adaptability of the system;

3) the invention combines the exponential time-varying sliding mode control with the self-adaptive method, and solves the problem of excessive adaptation of the switching gain of the existing self-adaptive sliding mode control to a certain extent.

The invention can effectively inhibit the influence of system parameter uncertainty and external disturbance and realize accurate attitude control.

Drawings

FIG. 1 is a structural diagram of a control method of an adaptive index time-varying sliding mode according to the present invention;

FIG. 2 is a block diagram of a reentry vehicle adaptive index time-varying sliding mode control system in an implementation;

fig. 3 is a response curve of adaptive index time-varying sliding mode control and adaptive normal sliding mode control when the reentry vehicle attitude control system tracks a given attitude angle command in specific implementation, where (a) is an attack angle response curve and (b) is a sideslip angle response curve; (c) a roll angle response curve is shown;

FIG. 4 is a re-entrant aircraft attitude control system attitude angular velocity response curve in an implementation. The left graph is a response curve when the adaptive exponential time-varying sliding mode controller is adopted, and the right graph is a response curve when the adaptive ordinary sliding mode controller is adopted;

FIG. 5 is a control plane deflection angle response curve of a reentry aircraft attitude control system in an implementation. The left graph is a response curve when the adaptive exponential time-varying sliding mode controller is adopted, and the right graph is a response curve when the adaptive ordinary sliding mode controller is adopted;

FIG. 6 is a graph illustrating adaptive handoff gain response of a reentry vehicle attitude control system in an implementation. The left graph is a response curve when the adaptive exponential time-varying sliding mode controller is adopted, and the right graph is a response curve when the adaptive ordinary sliding mode controller is adopted;

fig. 7 is a sliding mode surface response curve of the reentry vehicle attitude control system in an implementation. The left graph is a response curve when the adaptive exponential time-varying sliding mode controller is adopted, and the right graph is a response curve when the adaptive ordinary sliding mode controller is adopted.

Detailed Description

For better illustrating the objects and advantages of the present invention, the following description is further provided in conjunction with the accompanying drawings and examples.

The structure diagram of the reentry vehicle adaptive index time-varying sliding mode controller implemented by the invention is shown in fig. 2, and the attitude angle command omega is realized by using the adaptive index time-varying sliding mode attitude control system provided by the invention_c=[α_c β_c μ_c]^TEfficient tracking of.

Generally, an adaptive exponential time-varying sliding mode controller is designed in the form of:

$v=v_{\mathrm{eq}}+v_{\mathrm{sw}}={\stackrel{\·\·}{\mathrm{\Ω}}}_c-\mathrm{\Λ}\stackrel{\·}{\widetilde{\mathrm{\Ω}}}+\mathrm{A\λ}{e}^{-\mathrm{\λt}}-\mathrm{\ηsgn}\left(S\left(t\right)\right)---\left(15\right)$

in the formula,

representing equivalent control, in the case of a nominal model, according to

Deducing to obtain; v. of_sw= - η sgn (s (t)) for switching control in order to counteract uncertainties and disturbances in the model. Wherein, eta = diag { eta }_α,η_β,η_μThe method is characterized in that the method is a sliding mode control switching gain, and an online self-adaptive updating algorithm comprises the following steps:

${\stackrel{\·}{\mathrm{\η}}}_j=\frac{1}{k_j}\left|s_j\left(t\right)\right|,j=\mathrm{\α},\mathrm{\β},\mathrm{\μ}---\left(16\right)$

in the formula, k_j>0, j = α, β, μ is the adaptation rate. Eta_jAdaptive speed of (k)_jBy selecting the appropriate k_jIt is possible to effectively avoid the high-frequency vibration of the phase-up controlled quantity. Without loss of generality, the invention will k_jIs set to be constant, and k_α=k_β=k_μ=k。

And correcting the self-adaptive index time-varying sliding mode controller.

Due to the presence of the sign function sgn (-) in the control law (15), the system state is discontinuous when traversing the sliding mode plane. This can cause unnecessary buffeting and seriously affect the life and response characteristics of the aircraft steering engine. In addition, s (t) cannot be limited to 0 precisely due to the influence of measurement noise, model mismatch, and limited switching frequency in practical applications. In this case, the adaptive switching gain η increases infinitely to unbounded according to equation (16). In order to overcome the defects, a continuous adaptive index time-varying sliding mode control law modified as follows is adopted:

$v=v_{\mathrm{eq}}+v_{\mathrm{sw}}={\stackrel{\·\·}{\mathrm{\Ω}}}_c-\mathrm{\Λ}\stackrel{\·}{\widetilde{\mathrm{\Ω}}}+\mathrm{A\λ}{e}^{-\mathrm{\λt}}-\mathrm{\ηsat}\left(S\left(t\right)\right)---\left(17\right)$

in the formula, the saturation function sat (-) and the modified switching gain adaptive algorithm are respectively expressed as:

${\stackrel{\·}{\mathrm{\η}}}_j=\frac{1}{k_j}(-{\mathrm{\σ}}_j{\mathrm{\η}}_j+|s_j\left(t\right)\left|\right),j=\mathrm{\α},\mathrm{\β},\mathrm{\μ}---\left(19\right)$

wherein,

denotes the boundary layer thickness, σ_jIs a smaller positive constant.

And (3) stability analysis:

for the reentry vehicle nonlinear system (8) which considers uncertainty, the whole reentry vehicle closed-loop attitude control system is gradually stable by adopting an exponential time-varying sliding mode control law shown in an equation (15) and a corresponding switching gain adaptive algorithm (16).

First, an adaptive error is defined: $\widetilde{\mathrm{\&eta;}}={[{\mathrm{\&eta;}}_1-\mathrm{\&Delta;}{v}_{1\max }{\mathrm{\&eta;}}_2-\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00002306734600013.png"\; state="\{\{state\}\}">v</figure-callout>}}_{2\max }{\mathrm{\&eta;}}_3-\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA00002306734600013.png,HDA00002306734600041.png"\; state="\{\{state\}\}">v</figure-callout>}}_{3\max }]}^T.$

the positive definite Lyapunov function was chosen as:

$V=\frac{1}{2}{S}^T\left(t\right)S\left(t\right)+\frac{1}{2}k{\widetilde{\mathrm{\&eta;}}}^T\widetilde{\mathrm{\&eta;}}---\left(20\right)$

the derivative with respect to time of the formula (20) is obtained

$\stackrel{\&CenterDot;}{V}=S^T\left(t\right)\stackrel{\&CenterDot;}{S}\left(t\right)+k{\widetilde{\mathrm{\&eta;}}}^T\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&eta;}}}$

$=S^T\left(t\right)\mathrm{\&Delta;v}+\left[\begin{array}{ccc}-{\mathrm{\&Delta;v}}_{1\max }& -{\mathrm{\&Delta;<figure-callout\; id="2"\; label="v"\; filenames="HDA00002306734600013.png"\; state="\{\{state\}\}">v</figure-callout>}}_{2\max }& -{\mathrm{\&Delta;<figure-callout\; id="3"\; label="v"\; filenames="HDA00002306734600013.png,HDA00002306734600041.png"\; state="\{\{state\}\}">v</figure-callout>}}_{3\max }\end{array}\right]\left|S\left(t\right)\right|\&le;0---\left(21\right)$

As can be seen from the formula (21),

is semi-negative, meaning that V is non-growing and bounded, i.e., V (t). ltoreq.V (0). Thus, the available s (t) and the adaptive gain η are bounded. Further, let

And is integrated from time 0 → t to obtain

${\&Integral;}_0^t\mathrm{\&Xi;}\left(t\right)\mathrm{d\&tau;}=V\left(0\right)-V\left(t\right)---\left(22\right)$

Since both V (0) and V (t) are bounded, it is easy to obtain:

${\&Integral;}_0^t\mathrm{\&Xi;}\left(t\right)\mathrm{d\&tau;}\&le;V\left(0\right)\&le;\&infin;---\left(23\right)$

therefore, according to the Barbalt theorem,

this indicates that: when t → ∞, s (t) → 0. Visually see, by

Can not deduceHowever, the progressive stability of the reentry aircraft attitude control closed loop system may be explained as follows:

as can be seen from the adaptive law expression (16), if s (t) ≠ 0, the switching gain η increases all the time. Therefore, there must be a time t_F>0, η is increased to a value large enough to satisfy the reach condition of the sliding mode (e.g., η)_j>Δv_imaxJ = α, β, μ) such that a sliding mode is established, i.e. present

Thus according to s (t) = 0:

$\widetilde{\mathrm{\&Omega;}}\left(t\right)=e^{-\mathrm{\&lambda;t}}(\mathrm{\&Lambda;t}+I_{3\&times;3})\widetilde{\mathrm{\&Omega;}}\left(0\right)---\left(24\right)$

as can be seen from the formula (24),

i.e. the closed loop attitude control system is asymptotically stable.

In the case of adopting a modified continuous adaptive exponential time-varying sliding mode control law (17) and an adaptive gain algorithm (19), the closed-loop system is consistent and stable in a bounded mode.

Examples

1) Establishing a reentry vehicle six-degree-of-freedom twelve-state equation as a controlled object model, and using a kinematic equation of three airflow attitude angles (an attack angle alpha, a sideslip angle beta and a roll angle mu) related in the equation and three angular velocities (a roll angular velocity omega) rotating around a body axis_xYaw rate ω_yPitch angle velocity ω_zEquation of dynamics) written in affine nonlinear form (3)）；

2) Performing feedback linearization processing on the affine nonlinear system to obtain a decoupled reentry aircraft three-channel mathematical model;

3) and constructing an exponential time-varying sliding mode function formula (9) and a corresponding control law (11), wherein the switching gain in the control law is calculated on line through a formula (13).

4) And calculating according to the formula (14) to obtain a control torque command. Because the control moment can not be directly applied to the reentry flight model, corresponding inverse operation is required to be carried out according to the fitting expression (2) of the aerodynamic moment to obtain the real control surface deflection angle instruction [ delta ]_x δ_y δ_z]^T。

5) And inputting the control surface deflection angle instruction obtained in the last step into the reentry aircraft for attitude control.

In order to verify the superiority of the method in the attitude control of the reentry vehicle, the method is compared with the control effect of a self-adaptive common sliding mode controller.

The general slip surface definition is:

$S\left(t\right)=\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}+\mathrm{\&Lambda;}\widetilde{\mathrm{\&Omega;}}---\left(25\right)$

correspondingly, the sliding mode attitude control law is as follows:

$v={\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c-\mathrm{\&Lambda;}\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}-\mathrm{\&eta;sat}\left(S\left(t\right)\right)---\left(26\right)$

wherein, the adaptive algorithm of the switching gain is consistent with the adaptive exponential time-varying sliding mode, and an expression (13) is adopted.

The invention carries out simulation verification in the Matlab2009a environment. The initial state of flight is as follows: the initial height was 28km, the speed was 2000m/s, and the initial values of attitude angles were [1 °,1 ° ]]^TThe rudder surface deflection angle is limited to ± 20 °. The attitude angle given instruction is: [ alpha ] to_c,β_c,μ_c]^T=[4°,0°,20°]^TFurther, to verify the robustness of the designed control law, consider-30% atmospheric density pull bias and high frequency external disturbances (directly applied to the three-axis control moments) as follows:

d=[100sin(t) 100sin(t) 100sin(t)]^TN·m。

selecting parameters of a controller: the parameters of the common sliding mode surface are the same as those of the index time-varying sliding mode surface, the slope of the sliding mode surface is lambda =4, and the thickness of a boundary layer

The adaptation parameter k = 0.0005.

The reentry vehicle attitude angle response curve when the adaptive exponential time-varying sliding mode controller and the adaptive common sliding mode controller are applied is shown in fig. 3. As can be seen from the figure, both can realize stable tracking control of the attitude angle. In addition, when the common sliding mode control is adopted, the attitude angle response speed is high, because the common sliding mode control has an obvious arrival stage, and the control quantity is large at the beginning.

Fig. 4 shows the response comparison curves of the attitude angular velocity when the adaptive exponential time-varying sliding mode controller and the adaptive normal sliding mode controller are respectively adopted. It can be seen from the figure that when adaptive common sliding mode control is adopted in the initial stage, the attitude angular velocity is large, and the saturation of the control quantity is easily caused.

FIG. 5 shows control surface deflection angle response contrast curves when an adaptive index time-varying sliding mode controller and an adaptive common sliding mode controller are respectively adopted. It can be seen from the figure that the deflection angle of the control surface can be saturated at the beginning stage when the common sliding mode control is adopted, which is caused by the larger self-adaptive switching gain; and when the index time-varying sliding mode control is adopted, the deflection angle of the control surface is not saturated, and the instruction of the deflection angle of the control surface is smooth. This is an advantage of combining exponential time-varying sliding mode control with an adaptive algorithm.

Fig. 6 shows adaptive switching gain comparison curves when an adaptive exponential time-varying sliding mode controller and an adaptive normal sliding mode controller are respectively adopted. It can be seen from the figure that the value of the switching gain of the adaptive normal sliding mode control is obviously larger than that of the adaptive exponential time-varying sliding mode control. The main reason is that the initial stage deviates far from the sliding mode surface when the common sliding mode control is adopted, and according to the formula (13), the switching gain can be rapidly increased to a larger value (far larger than the actual disturbance of the system); and when the index time-varying sliding mode is controlled, the initial moment is on the sliding mode surface, so that the rapid increase of the self-adaptive switching gain cannot be caused.

Fig. 7 shows the sliding mode surface response contrast curves when the adaptive index time-varying sliding mode controller and the adaptive normal sliding mode controller are respectively adopted, and it can be seen that an obvious arrival stage exists when the normal sliding mode controller is adopted.

Claims (3)

1. The attitude control method of the reentry vehicle self-adaptive index time-varying sliding mode is characterized by comprising the following steps: the method comprises the following steps:

step 1, taking an unpowered reentry aircraft model which is symmetrical about an x-O-y plane of a body coordinate system as an object, establishing an attitude motion equation:

$\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}={\mathrm{\&omega;}}_z$

$\stackrel{\&CenterDot;}{\mathrm{\&beta;}}={\mathrm{\&omega;}}_x\sin \mathrm{\&alpha;}+{\mathrm{\&omega;}}_y\cos \mathrm{\&alpha;}$

$\stackrel{\&CenterDot;}{\mathrm{\&mu;}}={\mathrm{\&omega;}}_x\cos \mathrm{\&alpha;}-{\mathrm{\&omega;}}_y\sin \mathrm{\&alpha;}$

${\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_x=\frac{I_{\mathrm{yy}}}{I^{*}}{M}_x+\frac{I_{\mathrm{xy}}}{I^{*}}{M}_y-\frac{I_{\mathrm{yy}}(I_{\mathrm{zz}}-I_{\mathrm{yy}})-I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z-\frac{I_{\mathrm{xy}}(I_{\mathrm{yy}}+I_{\mathrm{xx}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z---\left(1\right)$

${\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_y=\frac{I_{\mathrm{xy}}}{I^{*}}{M}_x+\frac{I_{\mathrm{xx}}}{I^{*}}{M}_y-\frac{I_{\mathrm{xx}}(I_{\mathrm{xx}}-I_{\mathrm{zz}})+I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+\frac{I_{\mathrm{xy}}(I_{\mathrm{xx}}+I_{\mathrm{yy}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z$

${\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z=\frac{1}{I_{\mathrm{zz}}}{M}_z-\frac{I_{\mathrm{yy}}-I_{\mathrm{xx}}}{I_{\mathrm{zz}}}{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_y-\frac{I_{\mathrm{xy}}}{I_{\mathrm{zz}}}({\mathrm{\&omega;}}_y^2-{\mathrm{\&omega;}}_x^2)$

in the formula, alpha, beta and mu are respectively an attack angle, a sideslip angle and a roll angle; omega_x,ω_y,ω_zRoll, yaw and pitch velocities, respectively; i is_xx,I_yy,I_zz,I_xyRespectively, the moment of inertia and the inertia product I about the x, y and z axes under the body coordinate system_xz=I_yz=0，

M_x,M_y,M_zRespectively are aerodynamic moment under a coordinate system of the machine body; wherein, the aerodynamic moment is:

$M_i=\hat{q}\mathrm{Sl}{C}_{\mathrm{mi}}(\mathrm{\&alpha;},\mathrm{\&beta;},\mathrm{Ma},{\mathrm{\&delta;}}_x,{\mathrm{\&delta;}}_y,{\mathrm{\&delta;}}_z),i=x,y,z---\left(2\right)$

in the formula:

the pressure is dynamic pressure, rho is atmospheric density, and V is the flying speed of the aircraft; s, l is the reference area and the reference length of the aircraft respectively; delta_x,δ_y，δ_zRespectively an aileron, a rudder and an elevator; c_mx,C_my,C_mzRoll, yaw and pitch moment coefficients, respectively, with respect to α, β, δ_x,δ_y,δ_zAnd mach number Ma;

in the reentry process, BTT control is adopted, the sideslip angle is maintained near a zero value, sin beta is approximately equal to 0, tan beta is approximately equal to 0, and cos beta is approximately equal to 1;

step 2, rewriting the reentry aircraft model established in the step 1 into a MIMO affine nonlinear system form:

$\stackrel{\&CenterDot;}{x}=f\left(x\right)+g\left(x\right)u---\left(3\right)$

Ω=h(x)

wherein x = [ α β μ ω =_x ω_y ω_z]^TIs the state vector, Ω = [ α β μ =]^TIs a system output variable, u = [ M = [)_x M_y M_z]^TIs the calculated aerodynamic moment and control surface deflection angle instruction [ delta ]_x,δ_y,δ_z]^TCalculated by inverting the aerodynamic momentTo; f (x) = [ f₁(x)…f₆(x)]^TIs a 6 × 1 dimensional matrix, g (x) = [ g [)₁(x) g₂(x) g₃(x)]^TIs a 6 × 3 dimensional matrix, h (x) = [ h%₁(x) h₂(x) h₃(x)]^TIs a 3 x 1 dimensional matrix; wherein,

$\left\{\begin{array}{c}{f}_1\left(x\right)={\mathrm{\&omega;}}_z\\ f_2\left(x\right)={\mathrm{\&omega;}}_x\sin \mathrm{\&alpha;}+{\mathrm{\&omega;}}_y\cos \mathrm{\&alpha;}\\ f_3\left(x\right)={\mathrm{\&omega;}}_x\cos \mathrm{\&alpha;}-{\mathrm{\&omega;}}_y\sin \mathrm{\&alpha;}\\ f_4\left(x\right)=-\frac{I_{\mathrm{yy}}(I_{\mathrm{zz}}-I_{\mathrm{yy}})-I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z-\frac{I_{\mathrm{xy}}(I_{\mathrm{yy}}+I_{\mathrm{xx}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z\\ f_5\left(x\right)=-\frac{I_{\mathrm{xx}}(I_{\mathrm{xx}}-I_{\mathrm{zz}})+I_{\mathrm{xy}}^2}{I^{*}}{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+\frac{I_{\mathrm{xy}}(I_{\mathrm{xx}}+I_{\mathrm{yy}}-I_{\mathrm{zz}})}{I^{*}}{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z\\ f_6\left(x\right)=-\frac{I_{\mathrm{yy}}-I_{\mathrm{xx}}}{I_{\mathrm{zz}}}{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_y-\frac{I_{\mathrm{xy}}}{I_{\mathrm{zz}}}({\mathrm{\&omega;}}_y^2-{\mathrm{\&omega;}}_x^2)\end{array}\right.,$

$\left\{\begin{array}{c}{g}_1\left(x\right)={\left[\begin{array}{cccccc}0& 0& 0& \frac{I_{\mathrm{yy}}}{I^{*}}& \frac{I_{\mathrm{xy}}}{I^{*}}& 0\end{array}\right]}^T\\ g_2\left(x\right)={\left[\begin{array}{cccccc}0& 0& 0& \frac{I_{\mathrm{xy}}}{I^{*}}& \frac{I_{\mathrm{xx}}}{I^{*}}& 0\end{array}\right]}^T\\ g_3\left(x\right)={\left[\begin{array}{cccccc}0& 0& 0& 0& 0& \frac{1}{I_{\mathrm{zz}}}\end{array}\right]}^T\end{array}\right.;$

and 3, aiming at the affine nonlinear system obtained in the step 2, applying a feedback linearization theory to carry out linearization treatment to obtain a three-channel linearization model of pitching, rolling and yawing:

$\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}=F\left(x\right)+E\left(x\right)U---\left(4\right)$

in the formula,

$F\left(x\right)=\left[\begin{array}{c}{f}_3\left(x\right)\\ \sin \mathrm{\&alpha;}\&CenterDot;f_1\left(x\right)+\cos \mathrm{\&alpha;}\&CenterDot;f_2\left(x\right)+({\mathrm{\&omega;}}_x\cos \mathrm{\&alpha;}-{\mathrm{\&omega;}}_y\sin \mathrm{\&alpha;})\&CenterDot;{\mathrm{\&omega;}}_z\\ \cos \mathrm{\&alpha;}\&CenterDot;f_1\left(x\right)-\sin \mathrm{\&alpha;}\&CenterDot;f_2\left(x\right)-({\mathrm{\&omega;}}_x\sin \mathrm{\&alpha;}+{\mathrm{\&omega;}}_y\cos \mathrm{\&alpha;})\&CenterDot;{\mathrm{\&omega;}}_z\end{array}\right],$

$E\left(x\right)=\left[\begin{array}{ccc}0& 0& \frac{1}{I_{\mathrm{zz}}}\\ \frac{I_{\mathrm{yy}}\sin \mathrm{\&alpha;}}{I^{*}}+\frac{I_{\mathrm{xy}}\cos \mathrm{\&alpha;}}{I^{*}}& \frac{I_{\mathrm{xy}}\sin \mathrm{\&alpha;}}{I^{*}}+\frac{I_{\mathrm{xx}}\cos \mathrm{\&alpha;}}{I^{*}}& 0\\ \frac{I_{\mathrm{yy}}\cos \mathrm{\&alpha;}}{I^{*}}-\frac{I_{\mathrm{xy}}\sin \mathrm{\&alpha;}}{I^{*}}& \frac{I_{\mathrm{xy}}\cos \mathrm{\&alpha;}}{I^{*}}-\frac{I_{\mathrm{xx}}\sin \mathrm{\&alpha;}}{I^{*}}& 0\end{array}\right],$

U=[u₁ u₂ u₃]^T=[M_x M_y M_z]^T；

the selected control law form is:

U=E^-1(v-F)（5）

wherein v = [ v =₁ v₂ v₃]^TIs an auxiliary control amount;

substituting the control law into the linearization model to obtain a decoupled integrator in the form of:

$\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}=v---\left(6\right)$

when there is parameter uncertainty and external disturbances in the affine nonlinear system of the reentry aircraft model, the feedback linearized system model is represented as:

$\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}=F+\mathrm{\&Delta;F}+(E+\mathrm{\&Delta;E})U---\left(7\right)$

Δv=[Δv₁ Δv₂ Δv₃]^Trepresents the polymerization disturbance: Δ v = Δ F + Δ EU; and Δ v is present_1max,Δv_2max,Δv_3maxSo that | Δ v₁|≤Δv_1max，|Δv₂|≤Δv_2max，|Δv₃|≤Δv_3max；

Substituting the selected control law form and the aggregate disturbance delta v into the system model subjected to feedback linearization to obtain a reentry aircraft feedback linearization system considering parameter uncertainty and disturbance, wherein the reentry aircraft feedback linearization system comprises the following steps:

$\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}=v+\mathrm{\&Delta;v}---\left(8\right)$

step 4, designing a self-adaptive index time-varying sliding mode controller aiming at the linearization system obtained in the step 3;

firstly, selecting an exponential time-varying sliding mode surface:

$S\left(t\right)=\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}+\mathrm{\&Lambda;}\widetilde{\mathrm{\&Omega;}}+A{e}^{-\mathrm{at}}---\left(9\right)$

in the formula,

for systematic tracking error, Ω_c=[α_c β_c μ_c]^TAttitude command given for guidance loop, s (t) = [ s ]_α(t)s_β(t)s_μ(t)]^T∈R³Is a sliding mode surface function vector, A belongs to R³For the parameter matrix related to the initial value of the system state, Λ = diag { λ }₁,λ₂,λ₃}∈R^3×3Representing the slope of the slip form surface, a ∈ R⁺Represents the approaching speed, lambda, of the time-varying slip form surface to the time-invariant slip form surface₁=λ₂=λ₃=a=λ；S(0)=0_3×1The value of A is:

$A=-\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}\left(0\right)-\mathrm{\&Lambda;}\widetilde{\mathrm{\&Omega;}}\left(0\right)=-\mathrm{\&Lambda;}\widetilde{\mathrm{\&Omega;}}\left(0\right)---\left(10\right)$

then, designing a modified adaptive exponential time-varying sliding mode controller in the form of:

$v=v_{\mathrm{eq}}+v_{\mathrm{sw}}={\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&Omega;}}}_c-\mathrm{\&Lambda;}\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&Omega;}}}+\mathrm{A\&lambda;}{e}^{-\mathrm{\&lambda;t}}-\mathrm{\&eta;sat}\left(S\left(t\right)\right)---\left(11\right)$

in the formula,

denotes equivalent control, v_sw= η sat (s (t))) indicates switching control, η = diag { η =_α,η_β,η_μThe gain is the switching gain of sliding mode control; the saturation function sat (-) and the handover gain adaptation algorithm are respectively expressed as:

${\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_j=\frac{1}{k_j}(-{\mathrm{\&sigma;}}_j{\mathrm{\&eta;}}_j+|s_j\left(t\right)\left|\right),j=\mathrm{\&alpha;},\mathrm{\&beta;},\mathrm{\&mu;}---\left(13\right)$

wherein,

denotes the boundary layer thickness, σ_jIs a small positive constant, k_j>0 is the adaptive rate; eta_jAdaptive speed of (k)_jControl of (2);

step 5, obtaining a control moment instruction of attitude control of the reentry vehicle according to the step 4:

U＝E^-1(v-F)（14）

then, the control moment is distributed to the pneumatic control surface by combining the pneumatic moment to obtain a control surface deflection angle instruction [ delta ] required by attitude control_x δ_y δ_z]^T；

Step 6, the control surface deflection angle instruction [ delta ] obtained in the step 5 is processed_x δ_y δ_z]^TInputting the attitude data into a reentry vehicle to control the attitude; at the same time, the aircraft control system outputs real-time flight states (α, β, μ, ω)_x,ω_y，ω_z) And input to the attitude control system as a feedback state; repeating the steps 2-6, thereby realizing the existence of the systemUnder the condition of parameter uncertainty and external disturbance, the deflection angle [ delta ] of the control surface is controlled_x δ_y δ_z]^TAttitude command Ω given to guidance ring_c=[α_c β_c μ_c]^TAnd (6) tracking.

2. The reentry vehicle adaptive index time-varying sliding mode attitude control method according to claim 1, characterized in that: the origin O of the aircraft body coordinate system is taken at the mass center of the aircraft, the axis Ox is coincident with the longitudinal axis of the aircraft body, and the pointing head is positive; the Oy axis is positioned in the longitudinal symmetry plane of the machine body and is vertical to the Ox axis, and the pointing direction is positive; the Oz axis is perpendicular to the Oxy plane, and the direction is determined according to a right-hand rectangular coordinate system.

3. The reentry vehicle adaptive index time-varying sliding mode attitude control method according to claim 1, characterized in that: k in step 4_jIs constant, and k_α=k_β=k_μ=k。

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