CN106842912B - Hypersonic speed maneuvering flight control surface saturation robust control method - Google Patents

Hypersonic speed maneuvering flight control surface saturation robust control method Download PDF

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CN106842912B
CN106842912B CN201611085785.2A CN201611085785A CN106842912B CN 106842912 B CN106842912 B CN 106842912B CN 201611085785 A CN201611085785 A CN 201611085785A CN 106842912 B CN106842912 B CN 106842912B
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张鹏
都延丽
孙萍
项凯
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a hypersonic maneuvering flight control surface saturation robust control method, and belongs to flight control methods in the technical field of aerospace. The invention aims to solve the problem that the performance of a hypersonic flight vehicle (HSV) control system is poor due to amplitude saturation and compound interference of a control surface in a hypersonic maneuvering flight process, and provides a design of an anti-saturation robust control method. The method provides a novel anti-saturation auxiliary design system, the order of the system is the same as that of an attitude control system, and the system is not only suitable for a SISO system but also suitable for a MIMO system. The auxiliary system variable is introduced into a backstepping error variable, and an HSV maneuvering flight control law is designed by applying the backstepping idea, so that the closed loop stability of the system is ensured. In addition, the invention provides a hybrid tracking differentiator-based interference observer (HTDDO) for tracking and approximating the composite interference and designing a compensation control law.

Description

Hypersonic speed maneuvering flight control surface saturation robust control method
The technical field is as follows:
the invention relates to a flight control method in the technical field of aerospace, in particular to a hypersonic maneuvering flight control surface saturation robust control method, which is particularly suitable for a flight control method under the conditions of control surface saturation and compound interference during hypersonic maneuvering flight.
Background art:
high ultrasonic Vehicles (HSV) refer to aircraft with flight speeds above mach 5, which are mainly active in airspace from 20km to 100km from the ground. HSV has the characteristics of large flight envelope, complex flight environment, high maneuverability, multitask mode and the like, so that uncertainty caused by an internal structure and aerodynamic parameters and interference caused by an external environment are inevitable, and when flying in a near space region, all state variables are highly coupled, and a controlled object presents strong nonlinear dynamic characteristics. These factors increase the difficulty of the design of the attitude control algorithm, such as the adoption of the classical linear control method can cause the reduction of the control precision and even the instability of the system. Therefore, the strong robust nonlinear control method is designed and researched to become a research hotspot of HSV flight control.
The maneuver of the HSV is a process of changing a flight state (height, speed and flight direction) of the HSV within a certain time, and at present, longitudinal conventional maneuvers such as acceleration, deceleration, jump and dive and transverse conventional maneuvers such as turning and circling are mainly researched. In order to complete the maneuvering actions, the mandatory constraint requirements are applied to the flight states, particularly state quantities such as an attack angle, a sideslip angle, a roll angular velocity and the like; in addition, the HSV flight airspace atmosphere is thin, and the deflection of the control surface is easy to saturate. When the actuator is saturated, the output signal of the controller is further increased, and the input of the actuator to the controlled object cannot be increased, so that the output of the controller is inconsistent with the actual control input of the system, which inevitably causes the performance reduction and even instability of the control system, and causes serious consequences. Therefore, in order to ensure the stability of the HSV maneuvering flight, the anti-control surface saturation is the problem to be solved in the design of the maneuvering flight control method.
Due to the unique HSV flight airspace, the maneuvering flight of the HSV flight control system has uncertain model parameters and external large moment disturbance, and the maneuvering flight control system has strong robust stabilizing capability. Although a laboratory obtains the aerodynamic parameters of simulated flight of a prototype under the hypersonic flight condition through a wind tunnel experiment, in fact, the near space flight environment is complex, and various unknown factors existing in the real flight environment are not mastered, so that uncertainty in structure and parameters exists between an aircraft model and an actual aircraft. Therefore, in the HSV maneuvering flight process, anti-interference is also an important problem to be solved by the maneuvering flight control method.
If the uncertain disturbance items of the system can be accurately estimated, the controller can be designed to compensate the disturbance, so as to improve the robustness of the system, so that scholars at home and abroad have made a lot of researches on disturbance observers, and the disturbance observer based on a tracking differentiator has better approaching tracking capability to the uncertain disturbance items, namely Bu X W, Wu X Y, Chen Y X, et al. Considering that the hybrid tracking differentiator is a differentiator designed based on the singular perturbation principle, the whole course convergence is fast, and the buffeting phenomenon can be avoided, the invention provides the interference observer designed based on the hybrid differentiator, and the approaching tracking capability of the interference observer is good. The JungZhou professor of Norwegian science and technology university (Zhou, J., Wen, C.: Robust adaptive control of unknown nonlinear systems in the presence of input evaluation. in: Proceedings of 14th IFACSymphosis on System Identification, Newcastle, Australia (2006)) proposes an anti-saturation auxiliary System for a single-input single-output System model, which has a good anti-saturation effect but can only be applied to SISO systems, and the form of a control object model is different from that of HSV. The invention is inspired by the anti-saturation auxiliary system, and designs an anti-control surface saturation auxiliary control system suitable for HSV maneuvering flight.
The invention content is as follows:
the invention aims at solving the practical control problems that when HSV is in maneuvering flight in a near space, the control surface is easy to saturate and the external interference is large. In order to solve the problem of saturation of a control surface, a novel anti-saturation auxiliary control system is provided and introduced into an HSV maneuvering flight control method. The method can ensure the global gradual stability of the closed loop system, and the tracking error is clear and controllable. Aiming at the composite interference borne by the aircraft, a nonlinear interference observer (HTDDO) based on a hybrid tracking differentiator is provided for tracking and approximating the interference, and a compensation control law is designed for inhibiting the interference influence. The HTDDO tracking approximation effect is good.
The invention adopts the following technical scheme: a hypersonic speed maneuvering flight control surface saturation robust control method comprises the following steps:
(1) converting the HSV (hue, saturation and value) motion equation under the spherical geodetic assumption condition into an affine nonlinear equation which is used for designing a maneuvering flight control law and contains control surface amplitude limitation, wherein the affine nonlinear equation comprises a track loop affine nonlinear equation, an attitude slow loop affine nonlinear equation and an attitude fast loop affine nonlinear equation;
(2) designing a hypersonic flight trajectory loop control law by utilizing a backstepping method according to a maneuvering flight instruction signal aiming at the affine nonlinear equation of the HSV trajectory loop constructed in the step (1);
(3) aiming at the composite interference terms of the HSV attitude slow loop and fast loop affine nonlinear equations constructed in the step (1), respectively designing an interference observer (HTDDO) based on a hybrid tracking differentiator to approach the composite interference terms;
(4) aiming at two groups of affine nonlinear equations of the HSV attitude fast loop and the HSV attitude slow loop constructed in the step (1), designing an anti-saturation auxiliary control system with the same order as the system;
(5) and (3) introducing the auxiliary control system variables designed in the step (2) into error variables in a backstepping method, and deducing an attitude control law considering the amplitude saturation of the control surface by applying the design idea of the backstepping method.
Further, the three affine nonlinear equations for the HSV maneuver flight in the step (1) are formed as follows:
A. trajectory loop affine nonlinear equation
Figure GDA0002424884220000031
Wherein, P ═ χ, γ]TTaking a track control vector as X and gamma, and respectively taking a track azimuth angle and a track inclination angle; f. ofv＝[fχ,fγ]TAs a non-linear function of the state quantity of the trajectory control loop, gvFor the trajectory loop control gain matrix, the specific expression is as follows:
Figure GDA0002424884220000032
Figure GDA0002424884220000033
where u isv＝[CLαsinσ CLαcosσ]TIs a control vector of the trajectory loop;
Figure GDA0002424884220000034
is dynamic pressure, S is effective reference area of wing, m is mass of aircraft, V is airspeed, gamma is track inclination, R is distance from aircraft to geocentric, chi is track azimuth, latitude, omegaEIs the angular velocity of rotation of the earth;
B. attitude slow loop affine nonlinear equation
Figure GDA0002424884220000035
Wherein, Ω is [ α, σ ═ g]TThe attitude slow loop airflow attitude angle vector, α, sigma, is attack angle, sideslip angle and track roll angle, omegac＝[pc,qc,rc]TThe method comprises the steps that angular rate tracking signals of an attitude fast loop are obtained, and p, q and r are pitching angular rates, rolling angular rates and yaw angular rates respectively; ds∈R3Is the composite interference error of the attitude slow loop; f. ofs＝[fα,fβ,fσ]TIs a nonlinear function of the attitude slow loop state vector, gsFor the attitude slow loop control gain matrix, the specific expression is as follows:
Figure GDA0002424884220000041
Figure GDA0002424884220000042
Figure GDA0002424884220000043
Figure GDA0002424884220000044
Figure GDA0002424884220000045
Figure GDA0002424884220000046
Figure GDA0002424884220000047
here, CL,aIs a basic coefficient of lift, CC,βIs the basic lateral force coefficient;
C. attitude fast loop affine nonlinear equation
Figure GDA0002424884220000048
Wherein ω is [ p, q, r ═ p]TAn angular velocity vector of the attitude fast loop is obtained;c＝[e,a,r]Tis the deflection angle of the pneumatic control surface,e,a,rdeflection angles of the left and right aileron elevators and the rudder respectively; sat (c) The actual deflection of the control surface after the amplitude of the control surface is saturated is the final control quantity of the attitude control system; df∈R3The composite interference error of the attitude fast loop is obtained; f. off＝[fp,fq,fr]TIs a nonlinear function of the attitude fast loop state vector, gfFor the attitude fast loop control gain matrix, the specific expression is as follows:
Figure GDA0002424884220000051
Figure GDA0002424884220000052
Figure GDA0002424884220000053
Figure GDA0002424884220000054
Figure GDA0002424884220000055
Figure GDA0002424884220000056
Figure GDA0002424884220000057
Figure GDA0002424884220000058
Figure GDA0002424884220000059
Figure GDA00024248842200000510
Figure GDA00024248842200000511
Figure GDA00024248842200000512
Figure GDA00024248842200000513
Figure GDA00024248842200000514
here, Ix,Iy,IzRotational inertia around the x, y, z axes, respectively; b is a wingspan; c is the average aerodynamic chord length; xcgIs the distance between the centroid and the focal point,
Figure GDA00024248842200000515
is an aircraft aerodynamic parameter.
Further, in the step (3), for the composite interference terms of the attitude slow loop and the attitude fast loop, the designed HTDDO form is:
attitude slow loop HTDDO:
Figure GDA00024248842200000516
attitude fast loop HTDDO:
Figure GDA00024248842200000517
wherein f (x)1,x2) The function is in the specific form:
Figure GDA0002424884220000061
sig(x)a＝sgn(x)|x|a
sgn(x)＝diag(sgn(x1),sgn(x2),...,sgn(xn))
wherein a is0,a1,a2,b0,b1∈ are design parameters, which are all positive values.
Further, the anti-saturation aided design system constructed in the step (2) is as follows:
Figure GDA0002424884220000062
wherein Δ ═ sat (c)-cIs an input signal of the auxiliary system; lambda [ alpha ]1∈R3And λ2∈R3Is the auxiliary system state quantity, c1∈R3×3And c2∈R3×3Are design parameter matrices which are diagonal matrices whose diagonal elements are normal numbers, and c1Should also satisfy lambdamin(c1)-0.5＞0。
Further, the HSV maneuvering flight control law deduced by applying the lyapunov stability theory in the step (3) is as follows:
Figure GDA0002424884220000063
Figure GDA0002424884220000064
Figure GDA0002424884220000065
wherein z isv、z1And z2Is a defined variable of the error that is,
zv＝P-Pc,z1＝Ω-Ωc-λ1,z2＝ω-ωc-λ2，kv∈R2×2,k1∈R3×3,k2∈R3×3,c1∈R3×3,c2∈R3×3
are design parameter matrices which are diagonal matrices whose diagonal elements are normal numbers, and c1Should also satisfy lambdamin(c1)-0.5＞0，λmin(. cndot.) represents the minimum eigenvalue of the matrix.
The invention has the following beneficial effects:
(1) the anti-saturation auxiliary control system provided by the invention has the advantages of simple structure and better performance, gives an inequality of instantaneous error tracking performance of the system, and provides a basis for adjusting design parameters of the auxiliary system in engineering realization, thereby better improving the system performance.
(2) The invention provides a nonlinear disturbance observer (HTDDO) based on a hybrid tracking differentiator, which has faster approaching tracking capability to the complex disturbance borne by a system, and has a relatively simple structure and less design parameters. The hypersonic maneuvering flight control method combined with the HTDDO has strong adaptability to the dynamic uncertainty of a hypersonic aircraft system and the external disturbance in maneuvering flight, so that the robust performance of the flight control system can be effectively improved.
Description of the drawings:
fig. 1 is a block diagram of a control system configuration.
Fig. 2(a) and 2(b) show the operation results of the track azimuth angle and the track inclination angle of the system without the anti-saturation auxiliary system.
FIGS. 3(a), 3(b), and 3(c) are the results of the operation of the angle of attack, sideslip angle, and roll angle without the addition of an anti-saturation assist system.
Fig. 4(a), 4(b) and 4(c) are operational results of pitch, roll and yaw rates without the anti-saturation assist system.
Fig. 5(a), 5(b) and 5(c) are the results of the operation of the left, right and left aileron rudders and rudders without the anti-saturation assist system.
FIGS. 6(a), 6(b) are the results of the operation with the addition of the anti-saturation aiding system for both track azimuth and track inclination.
Fig. 7(a), 7(b) and 7(c) are the results of the operation of the angle of attack, sideslip angle, roll angle with the addition of the anti-saturation assist system.
Fig. 8(a), 8(b) and 8(c) are operational results of pitch, roll and yaw rates with the addition of an anti-saturation assist system.
Fig. 9(a), 9(b) and 9(c) are the results of the operation of the left, right and rudder with the anti-saturation assist system added.
10(a), 10(b) and 10(c) are the results of the operation of the slow loop complex interference approximation tracking with the anti-saturation auxiliary system added.
11(a), 11(b) and 11(c) are the results of the fast loop complex interference approximation tracking with the anti-saturation auxiliary system added.
The specific implementation mode is as follows:
the hypersonic maneuvering flight control surface saturation robust control method provided by the invention is explained in detail below by combining the embodiment and the attached drawings. Example a model of Winged Cone (wined-Cone) configuration proposed by NASA lanley research center was used as the subject.
The twelve state equation for HSV is established (Mooij E.motion of a vehicle in a planetarytospherer [ J ]. NASA STI/Recon Technical Report N,1994,96: 11743). The concrete form is as follows:
Figure GDA0002424884220000081
Figure GDA0002424884220000082
Figure GDA0002424884220000083
Figure GDA0002424884220000084
Figure GDA0002424884220000085
Figure GDA0002424884220000086
Figure GDA0002424884220000087
Figure GDA0002424884220000088
Figure GDA0002424884220000089
Figure GDA00024248842200000810
Figure GDA00024248842200000811
Figure GDA00024248842200000812
aerodynamic models for aircraft are mainly available from Keshmiri S, Colgren R, Mirmiani M.Six Dofnonlinear proportions of Motion for a general Hypersonic Vehicle [ C ]. AIAAAtmospheric Flight Mechanics Conference and inhibition, United States: AIAA,2007,1-28.
The invention only considers the control problem of HSV reentry maneuver flight and does not consider the maneuvering trajectory planning and guidance problem, so the trajectory loop state quantity does not consider the control of the speed V. And rewriting the state equation of the track azimuth angle χ and the track inclination angle gamma into an affine nonlinear equation form.
Figure GDA0002424884220000091
Wherein, P ═ χ, γ]TA track control vector is obtained; u. ofv＝[CLαsinσ CLαcosσ]TIs a control vector of the trajectory loop; f. ofv＝[fχ,fγ]TAs a non-linear function of the state quantity of the trajectory control loop, gvThe gain matrix is controlled for the trajectory loop as follows.
Figure GDA0002424884220000092
Figure GDA0002424884220000093
Setting a maneuvering flight command signal P according to a trajectory loop affine nonlinear equationc＝[χc,γc]TThe design control law according to the NGPC method is as follows:
Figure GDA0002424884220000094
wherein z isv＝[P-Pc]T，kvIs a control parameter. u. ofv＝[CLasinσ,CLacosσ]T，CLaIs a nonlinear function related to the attack angle α, and the attitude control signal required by the tracking maneuver command signal can be obtained by a Newton iteration methodαc,σcReferring to the banked BTT control, a sideslip-free turn is implemented to reduce the control surface and protection system design pressure the sideslip angle control signal β is setc0, thereby obtaining a complete tracking command signal omega of the attitude control systemc＝[αc,βc,σc]T。
According to the state equation for establishing the attitude variable, the attitude variable is converted into an attitude loop affine nonlinear equation form for HSV maneuvering flight, according to the response time of the attitude variable, the attitude variable can be divided into a slow variable (alpha, beta, sigma) and a fast variable (p, q, r), and the attitude slow loop affine nonlinear equation and the attitude fast loop affine nonlinear equation are respectively established. The concrete form is as follows:
A. attitude slow loop affine nonlinear equation:
Figure GDA0002424884220000101
wherein f iss＝[fα,fβ,fσ]TAs a non-linear function of the state vector, gsTo control the gain matrix, specific expressions are as follows.
Figure GDA0002424884220000102
Figure GDA0002424884220000103
Figure GDA0002424884220000104
Figure GDA0002424884220000105
Figure GDA0002424884220000106
Figure GDA0002424884220000107
Figure GDA0002424884220000108
Figure GDA0002424884220000109
Figure GDA00024248842200001010
Figure GDA00024248842200001011
Wherein Ω is [ α, σ ═ g]TThe attitude slow loop airflow attitude angle vector α, sigma is attack angle, sideslip angle and roll angle, omegac＝[pc,qc,rc]TIs an angular rate tracking signal of a fast attitude loop, and p, q and r are pitch, roll and yaw angular rates respectively.
B. Attitude fast loop affine nonlinear equation:
Figure GDA00024248842200001012
where ω is [ p, q, r ═ p]TAn angular velocity vector of the attitude fast loop is obtained;c＝[e,a,r]Tis the deflection angle of the pneumatic control surface,e,a,rdeflection angles of the left and right aileron elevators and the rudder respectively; sat (c) The actual deflection of the control surface after the amplitude of the control surface is saturated is the final control quantity of the attitude control system; f. off＝[fp,fq,fr]TIs a nonlinear function of the attitude fast loop state vector, gfFor the attitude fast loop control gain matrix, the specific expression is as follows.
Figure GDA0002424884220000111
Figure GDA0002424884220000112
Figure GDA0002424884220000113
Figure GDA0002424884220000114
Figure GDA0002424884220000115
Figure GDA0002424884220000116
Figure GDA0002424884220000117
Figure GDA0002424884220000118
Figure GDA0002424884220000119
Figure GDA00024248842200001110
Figure GDA00024248842200001111
And designing HTDDO for the complex interference in the attitude slow loop and the attitude fast loop to carry out approximate tracking on the interference.
The attitude slow loop HTDDO is designed as follows:
Figure GDA00024248842200001112
the attitude fast loop HTDDO is designed as follows:
Figure GDA00024248842200001113
wherein f (x)1,x2) The function is in the specific form:
Figure GDA00024248842200001114
sig(x)a＝sgn(x)|x|a
sgn(x)＝diag(sgn(x1),sgn(x2),...,sgn(xn))
where a is0,a1,a2,b0,b1∈ are design parameters, which are both normal numbers.
In order to effectively compensate the influence caused by the saturation of the control surface, an anti-saturation auxiliary control system is constructed, and the specific form is as follows:
Figure GDA0002424884220000121
wherein λ1∈R3And λ2∈R3Is the auxiliary system state quantity, c1∈R3×3And c2∈R3×3Are design parameter matrices which are diagonal matrices whose diagonal elements are normal numbers, and c1Should also satisfy lambdamin(c1)-0.5＞0，λmin(. cndot.) represents the minimum eigenvalue of the matrix. Δ sat (a:)c)-cIs the input signal of the auxiliary system.
Defining an error variable z1＝Ω-Ωc-λ1And z2＝ω-ωc-λ2. If the control surface is not saturated, i.e. Δ is 0, the auxiliary system state variable λ1And λ2Zero, the auxiliary system does not affect the error vector.
(1) To z1And (5) obtaining a derivative:
Figure GDA0002424884220000122
(2) considering the Lyapunov function
Figure GDA0002424884220000123
And (5) obtaining a derivative:
Figure GDA0002424884220000124
(3) designing a slow loop control law:
Figure GDA0002424884220000125
is substituted into
Figure GDA0002424884220000126
And (4) obtaining:
Figure GDA0002424884220000127
where the first term is negative and the second term can be eliminated in the next step.
(4) To z2And (5) obtaining a derivative:
Figure GDA0002424884220000128
(5) considering the amplified Lyapunov function V ═ V1+0.5z2 Tz2And (5) obtaining a derivative:
Figure GDA0002424884220000129
designing a slow loop control law:
Figure GDA0002424884220000131
is substituted into
Figure GDA0002424884220000132
And (4) obtaining:
Figure GDA0002424884220000133
the control laws of the fast loop and the slow loop are finally obtained as follows:
Figure GDA0002424884220000134
Figure GDA0002424884220000135
according to the derivation method of the control law, the state tracking error can meet the following conditions:
Figure GDA0002424884220000136
the transient tracking error performance of the airflow attitude angle can be obtained by simultaneous attitude loop affine nonlinear equation and auxiliary design system equation:
Figure GDA0002424884220000137
wherein | · | purple2L representing a quantity of state2Norm, specifically defined as:
Figure GDA0002424884220000138
the controller parameters may be adjusted according to the above inequality to improve controller performance.
The method is subjected to simulation verification in an MATLAB2014a environment, and the initial flight state is that the height H is 35km, the flight speed V is 3000m/s, the mass of an aircraft is 136820kg, the amplitude limit of a control surface is +/-28 degrees, and the initial attitude angle and the angular speed are α0＝3.0°，β0＝0°，σ0＝2.5°，p0＝q0＝r 00 rad/s. Machine for workingDynamic flight command signal Pc＝[χc,γc]TAs shown in fig. 5(a) and 5 (b). The simulated design parameters are shown in the following table. Attitude slow loop composite disturbance ds＝[ds1,ds2,ds3]TWherein d iss1＝0.001sin(t+1)cos(2t)，ds2＝0.003·cos(t+1)sin(2t+2)，ds30.005sin (t +1) sin (2t), and a fast-attitude-loop complex interference term df＝[df1,df2,df3]TWherein d isf1＝0.05sin(t+1)，df2＝0.04cos(2t+2)，df3＝0.03sin(t+1)。
In order to highlight the effect of the auxiliary system in the HSV maneuvering flight, the invention provides two sets of simulation results, wherein the maneuvering flight results without the anti-saturation auxiliary control system are shown in FIGS. 2(a) to 5(c), and the operation results with the anti-saturation auxiliary control system are shown in FIGS. 6(a) to 11 (c).
Figure GDA0002424884220000139
Figure GDA0002424884220000141
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (4)

1. A hypersonic speed maneuvering flight control surface saturation robust control method is characterized by comprising the following steps: comprises the following steps
(1) Converting the HSV (hue, saturation and value) motion equation under the spherical geodetic assumption condition into an affine nonlinear equation which is used for designing a maneuvering flight control law and contains control surface amplitude limitation, wherein the affine nonlinear equation comprises a track loop affine nonlinear equation, an attitude slow loop affine nonlinear equation and an attitude fast loop affine nonlinear equation;
(2) designing a hypersonic flight trajectory loop control law by utilizing a backstepping method according to a maneuvering flight instruction signal aiming at the affine nonlinear equation of the HSV trajectory loop constructed in the step (1);
(3) aiming at the composite interference terms of the HSV attitude slow loop affine nonlinear equations and the HSV attitude fast loop affine nonlinear equations constructed in the step (1), respectively designing an interference observer based on a hybrid tracking differentiator to approximate the composite interference terms;
(4) aiming at two groups of affine nonlinear equations of the HSV attitude fast loop and the HSV attitude slow loop constructed in the step (1), designing an anti-saturation auxiliary control system with the same order as the system;
(5) introducing the auxiliary control system variable designed in the step (4) into an error variable in a backstepping method, and designing an attitude control law considering the amplitude saturation of the control surface by applying a backstepping method design idea;
the HSV maneuver flight three groups of affine nonlinear equations in the step (1) have the following forms:
A. trajectory loop affine nonlinear equation
Figure FDA0002424884210000011
Wherein, P ═ χ, γ]TTaking a track control vector as X and gamma, and respectively taking a track azimuth angle and a track inclination angle; f. ofv＝[fχ,fγ]TAs a non-linear function of the state quantity of the trajectory control loop, gvFor the trajectory loop control gain matrix, the specific expression is as follows:
Figure FDA0002424884210000012
Figure FDA0002424884210000013
wherein u isv＝[CLαsinσ CLαcosσ]TIs a control vector of the trajectory loop, CLaIs a non-linear function with respect to angle of attack α;
Figure FDA0002424884210000021
is dynamic pressure, S is effective reference area of wing, m is mass of aircraft, V is airspeed, gamma is track inclination, R is distance from aircraft to geocentric, chi is track azimuth, latitude, omegaEIs the angular velocity of rotation of the earth;
B. attitude slow loop affine nonlinear equation
Figure FDA0002424884210000022
Wherein, Ω is [ α, σ ═ g]TThe attitude slow loop airflow attitude angle vector is α, sigma is attack angle, sideslip angle and track rolling angle respectively, omegac＝[pc,qc,rc]TIs an angular rate tracking signal of a fast attitude loop, p, q and r are respectively a rolling angular rate, a pitching angular rate and a yaw angular rate, pc,qc,rcTracking signals of roll, pitch and yaw angular rates of the attitude fast loop respectively; ds∈R3Is the composite interference error of the attitude slow loop; f. ofs＝[fα,fβ,fσ]TIs a nonlinear function of the attitude slow loop state vector, gsFor the attitude slow loop control gain matrix, the specific expression is as follows:
Figure FDA0002424884210000023
Figure FDA0002424884210000024
Figure FDA0002424884210000025
Figure FDA0002424884210000026
Figure FDA0002424884210000027
Figure FDA0002424884210000028
Figure FDA0002424884210000029
Figure FDA00024248842100000210
wherein, CL,aIs a basic coefficient of lift, CC,βIs the basic lateral force coefficient;
C. attitude fast loop affine nonlinear equation
Figure FDA00024248842100000211
Wherein ω is [ p, q, r ═ p]TAn angular velocity vector of the attitude fast loop is obtained;c＝[e,a,r]Tis the deflection angle of the pneumatic control surface,e,a,rdeflection angles of the left and right aileron elevators and the rudder respectively; sat (c) The actual deflection of the control surface after the amplitude of the control surface is saturated is the final control quantity of the attitude control system; df∈R3The composite interference error of the attitude fast loop is obtained; f. off＝[fp,fq,fr]TIs a nonlinear function of the attitude fast loop state vector, gfFor the attitude fast loop control gain matrix, the specific expression is as follows:
Figure FDA0002424884210000031
Figure FDA0002424884210000032
Figure FDA0002424884210000033
Figure FDA0002424884210000034
Figure FDA0002424884210000035
Figure FDA0002424884210000036
Figure FDA0002424884210000037
Figure FDA0002424884210000038
Figure FDA0002424884210000039
Figure FDA00024248842100000310
Figure FDA00024248842100000311
Figure FDA00024248842100000312
Figure FDA00024248842100000313
Figure FDA00024248842100000314
wherein, Ix,Iy,IzRespectively the rotational inertia around the x, y and z axes of the machine body; b is a wingspan; c is the average aerodynamic chord length; xcgIs the distance between the centroid and the focal point,
Figure FDA00024248842100000315
Figure FDA00024248842100000316
is an aircraft aerodynamic parameter;
Figure FDA00024248842100000317
the yaw moment aerodynamic parameters caused by the left aileron elevator; cl,β,Cm,α,Cn,βRepresenting an aerodynamic moment parameter caused by an airflow attitude angle of an attitude slow loop; cD,αRepresenting an aerodynamic resistance parameter caused by an attack angle of the attitude slow loop; cl,p,Cl,r,Cm,q,Cn,p,Cn,rRepresenting an aerodynamic moment parameter caused by the angular velocity of the attitude fast loop.
2. The hypersonic maneuvering flight control surface saturation robust control method according to claim 1, characterized by comprising the following steps: in the step (3), for the composite interference items of the attitude slow loop and the attitude fast loop, the designed HTDDO form is as follows:
attitude slow loop HTDDO:
Figure FDA0002424884210000041
wherein,
Figure FDA0002424884210000042
is the composite interference error of the attitude slow loop HTDDO;
attitude fast loop HTDDO:
Figure FDA0002424884210000043
wherein f (x)1,x2) The function is in the specific form:
Figure FDA0002424884210000044
sig(x)a＝sgn(x)|x|a
sgn(x)＝diag(sgn(x1),sgn(x2),...,sgn(xn))
wherein a is0,a1,a2,b0,b1∈ are design parameters, which are all positive values.
3. The hypersonic maneuvering flight control surface saturation robust control method according to claim 1, characterized by comprising the following steps: the anti-saturation aided design system constructed in the step (2) is as follows:
Figure FDA0002424884210000045
wherein Δ ═ sat (c)-cIs an input signal of the auxiliary system; lambda [ alpha ]1∈R3And λ2∈R3Is an auxiliary quantity of state, c1∈R3×3And c2∈R3×3Is a diagonal matrix designed with diagonal elements being normal, and c1Should also satisfy lambdamin(c1)-0.5＞0，λmin(. cndot.) represents the minimum eigenvalue of the matrix.
4. The hypersonic maneuvering flight control surface saturation robust control method according to claim 3, characterized by comprising the following steps: the HSV maneuvering flight control law deduced by applying the Lyapunov stability theory in the step (3) is as follows:
Figure FDA0002424884210000046
Figure FDA0002424884210000047
Figure FDA0002424884210000048
wherein z isv、z1And z2Is a defined error variable, zv＝P-Pc,z1＝Ω-Ωc-λ1,z2＝ω-ωc-λ2；kv∈R2×2,k1∈R3×3,k2∈R3×3,c1∈R3×3，c2∈R3×3Are design parameter matrices which are diagonal matrices whose diagonal elements are normal numbers, and c1Should satisfy lambdamin(c1)-0.5＞0，λmin(. cndot.) represents the minimum eigenvalue of the matrix.
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