Underactuated hypersonic aircraft rolling and yawing combined control method based on active disturbance rejection control

Abstract

The invention provides an under-actuated hypersonic aircraft rolling and yawing combined control method based on active disturbance rejection control. Aiming at the control problem of the under-actuated hypersonic aircraft with high dynamic pressure and large static instability, the method comprises the following steps: firstly, carrying out operation stability analysis on a system to obtain conditions capable of realizing stable control; then, by means of control coupling of a rolling and yaw channel, a pitching channel and a rolling channel are controlled through an active disturbance rejection method, and meanwhile the yaw channel is stabilized by means of the estimation capacity of a nonlinear expansion state observer for interference and the yaw state. In order to improve the control effect on the yaw channel, feedback of the yaw state is added in the rolling channel according to the operation stability, and therefore stabilization of the sideslip angle can be achieved. Simulation proves that the method has a better control effect.

Description

Technical Field

[0001] The present invention relates to the technical field of hypersonic aircraft attitude control, and in particular to a roll and yaw joint control method for an underactuated hypersonic aircraft based on anti-disturbance control. Background Art

[0002] The increasing complexity of the space environment and the growing desire of mankind for space exploration have led to an increasing number of joint tasks between spacecraft, which has also put forward higher requirements on the performance indicators of the spacecraft itself and its utilization efficiency in terms of mass and space. The non-axisymmetric, flat and high-slenderness aerodynamic shape of hypersonic aircraft, as well as the maneuvering characteristics of tilting and turning, make it more susceptible to the roll effect caused by the sideslip angle, and face the problem of lateral and heading motion coupling. These problems show that it is more important to maintain the lateral and heading stability of hypersonic aircraft, but in practice, the control effectiveness of the rudder for controlling yaw is often insufficient. Some hypersonic aircraft will remove the vertical tail when designing, especially waverider aircraft, because its unique flat structure will make the vertical tail more susceptible to high temperature and ablation, and at the same time it can reduce weight and manufacturing costs, such as the HTV-2 with only two flap rudders; aircraft designed with vertical tails are also prone to failure at high speed and high temperature. Therefore, it is very necessary to study the controller of underactuated hypersonic aircraft. Summary of the invention

[0003] Aiming at the control problem of current underactuated hypersonic aircraft, the present invention proposes a roll-yaw joint control method for underactuated hypersonic aircraft based on active disturbance rejection control.

[0004] The present invention is implemented by the following technical scheme. The present invention proposes a roll and yaw joint control method for an underactuated hypersonic aircraft based on active disturbance rejection control, and the method comprises the following steps:

[0005] Step 1: Establish a coordinate system, and on this basis establish the dynamics and kinematics equations of the aircraft;

[0006] Step 2: Conduct handling stability analysis to verify the feasibility of achieving stable control under under-actuated conditions;

[0007] Step 3: Design an ADRC controller for the pitch channel;

[0008] Step 4: Add yaw state feedback to the roll channel to further improve the control effect of the yaw channel;

[0009] Step 5: Conduct simulation experiment analysis of hypersonic vehicle flight mission.

[0010] Furthermore, in step 1, the ground coordinate system Axyz, the missile body coordinate system Ox1y1z1, the trajectory coordinate system Ox2y2z2 and the velocity coordinate system Ox3y3z3 are established; from the ground system to the missile system, three angles need to be rotated in sequence according to the 321 conversion order: pitch angle The yaw angle ψ and the roll angle γ; the transformation matrix is ​​expressed as

[0011]

[0012] Since the Oy3 axis and the Oy1 axis are both located in the longitudinal symmetry plane of the projectile, the velocity system to the projectile system rotates two angles in sequence according to the 32-turn sequence: the angle of attack α and the sideslip angle β, which can be expressed in a matrix as

[0013]

[0014] The transformation matrix from the ground system to the ballistic system is:

[0015]

[0016] Among them, the ballistic inclination angle θ and the ballistic deviation angle ψ v It is also transferred out in sequence according to the 32 transfer order;

[0017] From the definition of the ballistic system and the velocity system, we know that the Ox2 axis and the Ox3 axis are both along the direction of the velocity vector, and Ox2y2 is the vertical plane, and Ox3y3 is the longitudinal symmetry plane of the aircraft. Therefore, to go from the ballistic system to the velocity system, we only need to rotate a velocity inclination angle γ around the velocity vector direction. v Then, the transformation matrix is

[0018]

[0019] In each of the above rotation processes, if the axis of rotation appears to rotate counterclockwise, the angle of rotation is positive; if the axis of rotation appears to rotate clockwise, the angle of rotation is negative.

[0020] Furthermore, in step 1, the dynamic equation of the aircraft rotating around the center of mass is

[0021]

[0022] in,

[0023]

[0024] J x , J y and J z are the moments of inertia of the aircraft around the axes of the missile body coordinate system, J xy , J yz and J xz is the product of inertia; ω x ,ωy and ω z are the components of the angular velocity of the missile system relative to the ground system on each axis of the missile system; M x 、M y and M z are the components of the moment of the aerodynamic force on the center of mass on each axis of the missile system; P z is the reaction force generated by the thruster along the z-axis of the elastic system when the thruster is installed, l0 is the force arm of the thruster, M yw is the equivalent control torque produced by the flywheel when the reaction flywheel is installed;

[0025] The three-channel dynamic equation of the underactuated BTT vehicle is:

[0026]

[0027] Furthermore, in step 1, the attitude kinematics equation of the rolling channel is:

[0028]

[0029] In the above formula, the first term on the right side is much larger than the second term, so when the second term is ignored, the following simplified rolling channel attitude kinematic equation is obtained:

[0030]

[0031] Furthermore, in step 2, the handling stability analysis is specifically as follows:

[0032] Take the state variable x = [αβγω x ω y ω z ] T , control quantity u=[δ x δ z ] T ;When u=

[00] T hour,

[0033]

[0034] When u=

[10] T When B1(x)=[000-c3-d10] T ;When u=

[01] T When B2(x)=[-a50000-a3] T ; Then from Lie algebra we know

[0035]

[0036]

[0037]

[0038] Let F1=[A(x),B1(x)], F2=[A(x),B2(x)]

[0039] Similarly:

[0040]

[0041] Let F 11 =[A(x),F1],F 12 =[A(x),F2]

[0042] Because the state variable is 6-dimensional, we can first check the first six columns. If they are full rank, there is no need to calculate the subsequent columns. 11 and F 12 Zhang Cheng's function space:

[0043] F=[B1(x) B2(x) F1 F2 F 11 F 12 ] (51)

[0044] Using MATLAB to test, it is easy to determine that rank(F)=6. According to Lemmas 1, 2, and 3, the three-channel dynamic nonlinear equations of the underactuated BTT aircraft are weakly controllable, that is, using two control quantities δ x , δ z The three coupling channels can be stably controlled, that is, the aileron control amount δ x The roll channel and yaw channel can be controlled.

[0045] Furthermore, Lemmas 1, 2, and 3 are specifically:

[0046] Lemma 1: If the nonlinear system ∑ is 0 The point satisfies the controllability rank criterion condition, then ∑ at x 0 The point is locally weakly controllable;

[0047] Lemma 2: If the nonlinear system ∑ is locally weakly controllable, then the controllability rank criterion is satisfied;

[0048] Lemma 3: If a nonlinear system ∑ is analyzable, then ∑ is weakly controllable if and only if ∑ is locally weakly controllable if and only if ∑ satisfies the controllability rank criterion.

[0049] Furthermore, in step 3, the designed pitch channel controller is expressed as

[0050]

[0051] where e α =α c -α, Gd1 (s), G d2 , All refer to the values ​​in the pitch channel.

[0052] Furthermore, in step 4, in the design of the controller, in δ x Add negative feedback on the yaw angle and yaw rate based on the original value, that is, through -b7δ x This control coupling realizes the PD control of the yaw channel, using k p ,k d represents two control coefficients;

[0053] The final designed roll and yaw channel joint channel controller is expressed as

[0054]

[0055] where e γ =γ c -γ, G d2 , All refer to the values ​​in the roll channel.

[0056] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the roll and yaw joint control method of an under-actuated hypersonic aircraft based on anti-disturbance control are implemented.

[0057] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of a roll and yaw joint control method for an under-actuated hypersonic aircraft based on anti-disturbance control.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] The method described in the present invention aims at the control problem of under-actuated hypersonic aircraft with high dynamic pressure and large static instability. First, the system is analyzed for handling stability to obtain the conditions that can achieve stable control. Then, the control coupling of the roll and yaw channels is utilized, and the self-anti-disturbance method is adopted to control the pitch and roll channels. At the same time, the nonlinear extended state observer is used to estimate the interference and yaw state to stabilize the yaw channel. In order to improve the control effect of the yaw channel, the feedback of the yaw state is added to the roll channel according to the handling stability, so that the sideslip angle can be stabilized. After simulation, it is proved that this method has a better control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0061] Figure 1 It is the block diagram of the pitch channel control system;

[0062] Figure 2 It is a block diagram of the roll-yaw channel control system;

[0063] Figure 3 is a schematic diagram of tracking curves of the angle of attack, sideslip angle and roll angle of the aircraft, wherein α, β, γ are the angle of attack, sideslip angle and roll angle in the method of the present invention, α nofeedback , β nofeedback , γ nofeedback It is the angle of attack, sideslip angle and roll angle in the comparison method without the yaw state feedback;

[0064] Figure 4 This is a graph showing the change in the control rudder angle and rudder angle rate when the comparison method is used without yaw state feedback;

[0065] Figure 5 It is a graph showing the change results of the control rudder deflection angle and the rudder deflection angle rate when the method of the present invention is used for control. DETAILED DESCRIPTION

[0066] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] Combination Figure 1-Figure 5 The present invention proposes a roll and yaw joint control method for an underactuated hypersonic vehicle based on active disturbance rejection control, the method comprising the following steps:

[0068] Step 1: Establish a coordinate system, and on this basis establish the dynamics and kinematics equations of the aircraft;

[0069] In step 1, establish the ground coordinate system Axyz, the projectile coordinate system Ox1y1z1, the trajectory coordinate system Ox2y2z2 and the velocity coordinate system Ox3y3z3;

[0070] (1) Ground coordinate system Axyz (launch point inertial system)

[0071] The origin A of the ground system is located at the center of mass of the aircraft at the moment of launch, but the ground launch point of the aircraft is generally selected as the origin; the Ay axis is along the plumb direction and points upward, and it and the target position at the moment of launch form a shooting plane. The Ax axis is the intersection of the shooting plane and the horizontal plane, and points to the target; the Az axis, Ax axis and Ay axis form a right-handed coordinate system.

[0072] (2) Projectile coordinate system Ox1y1z1

[0073] The origin O of the coordinate system is taken as the center of mass of the aircraft; the Ox1 axis is along the longitudinal axis of the aircraft and points to the head as positive; the Oy1 axis is perpendicular to the Ox1 axis and is located in the longitudinal symmetry plane of the aircraft and points upward as positive; the Oz1 axis, the Ox1 axis and the Oy1 axis form a right-handed coordinate system.

[0074] Axyz and Ox1y1z1 are usually used in combination to study the attitude motion of the aircraft.

[0075] (3) Ballistic coordinate system Ox2y2z2

[0076] The origin O of the coordinate system is taken as the center of mass of the aircraft; the Ox2 axis is along the direction of the aircraft velocity vector; the Oy2 axis is located in the vertical plane containing the Ax axis (where the Ax axis is the x-axis of the inertial system of the launch point) and is perpendicular to the Ox2 axis, pointing upward; and the Oz2 axis is determined by the right-hand rule.

[0077] The ballistic system is also a moving coordinate system, which is usually used in combination with the inertial system to describe the motion of the center of mass of an aircraft.

[0078] (4) Velocity coordinate system Ox3y3z3

[0079] The coordinate system takes the center of mass of the aircraft as its origin O, and the Ox3 axis is along the direction of the velocity vector of the center of mass of the aircraft; the Oy3 axis is located in the longitudinal symmetry plane of the projectile, perpendicular to the Ox3 axis, and points upward as positive; the Oz3 axis, the Ox3 axis and the Oy3 axis form a right-handed system.

[0080] From the ground system to the missile system, the three angles need to be rotated in sequence according to the 321 rotation sequence: pitch angle The yaw angle ψ and the roll angle γ; the transformation matrix is ​​expressed as

[0081]

[0082] Since the Oy3 axis and the Oy1 axis are both located in the longitudinal symmetry plane of the projectile, the velocity system to the projectile system rotates two angles in sequence according to the 32-turn sequence: the angle of attack α and the sideslip angle β, which can be expressed in a matrix as

[0083]

[0084] The transformation matrix from the ground system to the ballistic system is:

[0085]

[0086] Among them, the ballistic inclination angle θ and the ballistic deviation angle ψ v It is also transferred out in sequence according to the 32 transfer order;

[0087] From the definition of the ballistic system and the velocity system, we know that the Ox2 axis and the Ox3 axis are both along the direction of the velocity vector, and Ox2y2 is the vertical plane, and Ox3y3 is the longitudinal symmetry plane of the aircraft. Therefore, to go from the ballistic system to the velocity system, we only need to rotate a velocity inclination angle γ around the velocity vector direction. v Then, the transformation matrix is

[0088]

[0089] In each of the above rotation processes, if the axis of rotation appears to rotate counterclockwise, the angle of rotation is positive; if the axis of rotation appears to rotate clockwise, the angle of rotation is negative.

[0090] In step 1, the dynamic equation for the vehicle's rotation around its center of mass is

[0091]

[0092] in,

[0093]

[0094] J x , J y and J z are the moments of inertia of the aircraft around the axes of the missile body coordinate system (i.e., the principal axes of inertia), J xy , J yz and J xz is the product of inertia; ω x ,ω y and ω z are the components of the angular velocity of the missile system relative to the ground system on each axis of the missile system; M x 、M y and M z are the components of the moment of the aerodynamic force on the center of mass on each axis of the missile system; P z is the reaction force generated by the thruster along the z-axis of the elastic system when the thruster is installed, l0 is the force arm of the thruster, M yw is the equivalent control torque produced by the flywheel when the reaction flywheel is installed;

[0095] According to the aircraft reference length l t and reference area S t , in the elastic system, the aerodynamic force includes the axial force Q x1 , normal force Qy1 , lateral force Q z1 ; Aerodynamic torque includes rolling torque M x1 , yaw moment M y1 , pitch moment M z1 , calculated as follows

[0096] Q x1 =-C A Q t (3)

[0097] Q y1 =C N Q t (4)

[0098] Q z1 =C z Q t (5)

[0099] M x1 =C mx Q t l t (6)

[0100] M y1 =C my Q t l t (7)

[0101] M z1 =C mz Q t l t (8)

[0102] Among them, C A , C N and C z Represent the drag coefficient, lift coefficient and lateral force coefficient respectively, C mx , C my and C mz They represent the rolling moment coefficient, yaw moment coefficient and pitch moment coefficient respectively.

[0103] When designing an aircraft control system, the dynamic equation of the aircraft center of mass motion is expressed in the missile system:

[0104]

[0105] Among them, V x 、V y and V z are the components of the velocity vector of the aircraft on each axis of the missile system; F x 、F y and F zG is the component of the aerodynamic force acting on the aircraft on each axis of the missile system; x , G y and G z It is the component of gravity acting on the aircraft on each axis of the missile system.

[0106] In order to facilitate the design and analysis of BTT aircraft autopilots, the following assumptions are usually made when establishing the mathematical model of BTT aircraft in engineering:

[0107] (1) During the design process, the aircraft is simply considered as a rigid body without considering its flexibility;

[0108] (2) Ignore the effect of gravity and only consider aerodynamic forces and reaction forces;

[0109] (3) At the ballistic characteristic points under study, the mass, moment of inertia, velocity and aerodynamic parameters of the aircraft are all considered constants.

[0110] The center of mass motion in the x-axis direction is uncontrollable, so equation (9) does not consider it. For the convenience of design and analysis, the following assumptions are made:

[0111]

[0112] BTT control requires keeping the sideslip angle β close to zero, considering that the maximum angle of attack of the aircraft generally does not exceed α max =25°, at this time α max / 57.3 and sinα max The error between V and V is less than 3.2%. x The error between them is less than 10%. Therefore, assuming that the conditions (13) and (14) are established, the accuracy is slightly lower, which can meet the engineering design requirements.

[0113] According to the assumption that the speed of the aircraft is constant at the trajectory feature point under study, the last two equations in equation (10) and equation (11) can be transformed into the following forms:

[0114]

[0115] Based on the assumptions (12)-(14), (15) and (16) can be further transformed into

[0116]

[0117] Ignoring minor factors and considering only the aerodynamic force and aerodynamic moment of the aircraft, the simplified expression after linearization near the characteristic point is

[0118]

[0119] From equations (17)-(23), the dynamic equation of the aircraft is obtained as follows:

[0120]

[0121] Ignoring the product of inertia, the aircraft attitude dynamics equation can be simplified to

[0122]

[0123] During the flight of an aircraft using BTT control technology, the roll control system quickly turns the maximum lift surface of the aircraft to the ideal maneuvering direction. At the same time, the pitch control system controls the aircraft to generate the required overload within the maximum lift surface. The yaw channel ensures that the aircraft's sideslip angle is approximately zero while the aircraft is controlled according to the guidance law. Generally, |β| < 3° is required. The tasks of each channel are as follows: the pitch channel tracks the normal overload from the guidance command; the yaw channel stabilizes the sideslip angle to make it as small as possible; the roll channel is used to track the roll angle command from the guidance command to roll the maximum lift surface of the aircraft to the required position.

[0124] According to the tasks of each channel, in addition to the above dynamic equations describing the motion of the aircraft, the attitude kinematic equation of the roll channel is also required, specifically:

[0125]

[0126] In the above formula, the first term on the right side is much larger than the second term, so when the second term is ignored, the following simplified rolling channel attitude kinematic equation is obtained:

[0127]

[0128] Most STT controlled aircraft have an axisymmetric aerodynamic shape, with the rolling channel acting as a stabilizer. x The value is small, and the influence of inter-channel motion and inertial coupling can be ignored when designing the autopilot. For BTT aircraft, since the rolling channel plays a control role, the aircraft is in the process of flight. x The value is large, so the kinematic coupling and inertial coupling effects cannot be ignored when designing the autopilot.

[0129] Lack of rudder control quantity δ in underactuated BTT aircraft control system y , introduce the aileron control value δ in the yaw channel x , that is, using the aileron control amount δ x The yaw channel and the roll channel are controlled jointly, and the sideslip angle feedback is introduced into the roll channel.

[0130] The three-channel dynamic equation of the underactuated BTT vehicle is:

[0131]

[0132] For the convenience of description, the following dynamic coefficients are defined:

[0133]

[0134]

[0135] The meanings of the physical quantities used above are as follows (Ox1y1z1 is the projectile coordinate system):

[0136] V—vehicle speed;

[0137] ω x ,ω y ,ω z —Components of the aircraft's angular velocity on the Ox1y1z1 axes;

[0138] J x ,J y ,J z —The moment of inertia of the aircraft about the Ox1y1z1 axes;

[0139] —Components of the aircraft's angular acceleration on the Ox1y1z1 axes;

[0140] m—mass of the aircraft;

[0141] δ x , δ y , δ z —Rudder deflection angle of the aircraft in each direction of Ox1y1z1;

[0142] Y α , —The lift Y of the aircraft in Ox1y1z1 affects α and δ respectively z The partial derivative of

[0143] Z β , —The lateral force Z of the aircraft in Ox1y1z1 affects β and δ respectively y The partial derivative of

[0144] —respectively the pitch moment M of the aircraft in Ox1y1z1 z , yaw moment M y and rolling moment M x Respectively for ω z ,ω y and ω x The partial derivatives of , these three quantities respectively characterize the aerodynamic damping characteristics of the aircraft in each direction;

[0145] —represent the pitch moment M of the aircraft in the missile system z , yaw moment M y and rolling moment M x The partial derivatives with respect to α and β characterize the static stability of the aircraft in longitudinal, lateral and transverse directions, respectively;

[0146] —represent the pitch moment M of the aircraft in the missile system z , yaw moment M y and rolling moment M x For δ z , δ y and δ x The partial derivatives of , these three quantities respectively characterize the rudder efficiency of the aircraft in each direction.

[0147] The units of the above physical quantities are all in the International System of Units.

[0148] Then the dynamic equations (31)-(36) describing the motion of the aircraft can be expressed as:

[0149]

[0150] Step 2: Conduct handling stability analysis to verify the feasibility of achieving stable control under under-actuated conditions;

[0151] In equations (37)-(42), only the control variable aileron δ x and elevator δ z , the yaw channel lacks the rudder control amount δ y ,To control three coupling channels using two control quantities, it is necessary to analyze whether the three coupling channels are controllable under the condition of two control quantities.

[0152] The controllability of nonlinear systems is much more complicated than that of linear systems. Let M be an m-dimensional real connected analytic manifold, V(M) be the set of all analytic vector fields on M, C ∞ (M) represents the set of all analytic functions on M, V(M) is C ∞ (M) model.

[0153] Let h1(x)∈C ∞ (M), h2(x)∈C ∞ (M), then the Lie algebra is defined as

[0154]

[0155] Given a nonlinear system:

[0156]

[0157] Among them, x∈M; y∈R n; u∈Ω, Ω is R l A subset of i ∈V(M), C is C ∞ A collection of class functions.

[0158] The nonlinear system ∑ defines a set of vector fields A, B1, B2, … B l , which determine an involution distribution, expressed as

[0159] Δ ∑ =[A,B1,B2,…B l ] (45)

[0160] Then B i ,[A,B i ]、[B i ,B j ]、 Span the function space F. If the nonlinear system ∑ is weakly controllable, then rank(F) = m.

[0161] Lemma 1. If the nonlinear system ∑ is 0 The point satisfies the controllability rank criterion condition, then ∑ at x 0 The point is locally weakly controllable.

[0162] Lemma 2. If the nonlinear system ∑ is locally weakly controllable, then the controllability rank criterion is satisfied.

[0163] Lemma 3. If a nonlinear system ∑ is analyzable, then ∑ is weakly controllable if and only if ∑ is locally weakly controllable if and only if ∑ satisfies the controllability rank criterion.

[0164] According to Lemma 1, if the system ∑ satisfies the controllability rank criterion at point x=0, then the system ∑ is locally weakly controllable at point x=0. According to Lemma 2 and Lemma 3, if the system ∑ is resolvable, then the system ∑ is weakly controllable.

[0165] The handling stability analysis is as follows:

[0166] Take the state variable x = [αβγω x ω y ω z ] T , control quantity u=[δ x δ z ] T ;When u=

[00] T hour,

[0167]

[0168] When u=

[10] T When B1(x)=[000-c3-d10]T ;When u=

[01] T When B2(x)=[-a50000-a3] T ; Then from Lie algebra (43) we know

[0169]

[0170]

[0171]

[0172] Let F1=[A(x),B1(x)], F2=[A(x),B2(x)]

[0173] Similarly:

[0174]

[0175]

[0176] Let F 11 =[A(x),F1],F 12 =[A(x),F2]

[0177] Because the state variable is 6-dimensional, we can first check the first six columns. If they are full rank, there is no need to calculate the subsequent columns. 11 and F 12 Zhang Cheng's function space:

[0178] F=[B1(x) B2(x) F1 F2 F 11 F 12 ] (51)

[0179] Using MATLAB to test, it is easy to determine that rank(F)=6. According to Lemmas 1, 2, and 3, the three-channel dynamic nonlinear equations of the underactuated BTT aircraft are weakly controllable, that is, using two control quantities δ x , δ z The three coupling channels can be stably controlled, that is, the aileron control amount δ x The roll channel and yaw channel can be controlled.

[0180] Step 3: Design an ADRC controller for the pitch channel;

[0181] Equations (37) to (42) show the mathematical model of the underactuated BTT aircraft control system, where the mathematical model of the pitch channel can be written as:

[0182]

[0183] The following design takes the pitch channel as an example.

[0184] d1=-ω x β-a4α-a5δ z

[0185] d 20 =-a1ω z -a2α-a6ω x ω y

[0186] Then we rewrite equations (52) and (53) as

[0187]

[0188] Since the air in the near space is thin, the rudder deflection angle can easily reach the saturation zone. In view of the above characteristics, the present invention considers the parameter uncertainty of the system when designing the control system, and also considers the influence of the control input saturation term, and rewrites equation (55) as follows:

[0189]

[0190] in

[0191]

[0192] is a saturation function that allows for asymmetry for given aerodynamic characteristics.

[0193] make

[0194] d 21 =d 20 +a 30 sat(δ z )-a3sat(δ z ) (58)

[0195] Then formula (56) can be written as:

[0196]

[0197] in

[0198] d2=d 21 +a3(sat(δ z )-δ z ) (60)

[0199] Considering d1 and d2 as composite disturbances, the disturbance observer can be used for online estimation and feedforward compensation can be performed in the control law design. After compensation, the system can be transformed into

[0200]

[0201] At this time, the system can be considered as a time-varying double-integral system, and the controller can be designed using the frequency domain method.

[0202] When the composite disturbances d1 and d2 can be observed, the frequency domain method can also be used to design the control law in the ADRC, and then the disturbance observer is introduced to perform feedforward compensation on the estimated results of d1 and d2. The control system design block diagram of equations (54) and (55) is as follows: Figure 1 As shown, G d is the servo transfer function, G g is the transfer function of the strapdown inertial navigation system gyroscope.

[0203] like Figure 1 As shown in the figure, the design idea of ​​the control system is: first design the observer of the composite disturbance d1 and d2, then consider the case where the composite disturbance is compensated by feedforward, and design the inner loop controller I in the system for the simple double-integral system. z and the outer loop controller C z .

[0204] In the active disturbance rejection control law, the composite disturbances d1 and d2 need to be estimated online using a disturbance observer. The nonlinear extended state observer NESO is used in the stable control system of the present invention. Taking the pitch channel as an example, the design is as follows:

[0205] a.zNESO1

[0206]

[0207] b.zNESO2

[0208]

[0209]

[0210] In the above NESO, g i (e 01 ) is the nonlinear function fal function, and its specific form is shown in formula (64).

[0211]

[0212] On the basis of the nonlinear extended state observer, in order to easily obtain a feedforward compensator with a numerator order less than or equal to the denominator order that is easy to physically implement, the dynamic links of the servo and gyroscope in the system are ignored during the design process, that is, G d =1, G g =1, but in fact, the dynamic characteristics of the servo and rate gyro are relatively fast compared to the dynamic link of the missile body, so this neglect is reasonable. Figure 1 The inner loop in is easy to find:

[0213]

[0214] Formula (65) can be simplified as

[0215]

[0216] Obviously,

[0217]

[0218] That is, the influence of d2 can be compensated. In this way, the transfer function of the inner loop can be obtained as

[0219]

[0220] Then by Figure 1 The outer loop in

[0221]

[0222] Formula (69) can be simplified to

[0223]

[0224] Finally obtained

[0225]

[0226] Obviously, the G d1 It is entirely possible that the numerator order of (s) is greater than the denominator order. When using it, a low-pass filter link can be added according to the specific situation to ensure its feasibility.

[0227] The final designed pitch channel controller is expressed as

[0228]

[0229] where e α =α c -α, G d1 (s), G d2 , All refer to the values ​​in the pitch channel.

[0230] Step 4: Add yaw state feedback to the roll channel to further improve the control effect of the yaw channel;

[0231] In step 4, for the rolling channel, since its model is

[0232]

[0233] To design an ADRC system, you only need to observe d2, d2 = -c1ωx -c2β.

[0234] However, due to the lack of control quantity in the yaw channel, although the part of d2 containing the coupling of the roll and yaw channels can be observed by the nonlinear extended state observer and offset in the feedforward, it is not enough to achieve stabilization of the yaw channel. In order to improve the control effect of the yaw channel, according to the handling stability analysis, δ x Control the yaw channel. In the design of the controller, in δ x Add negative feedback on the yaw angle and yaw rate based on the original value, that is, through -b7δ x This control coupling realizes the PD control of the yaw channel, using k p ,k d represents two control coefficients.

[0235] The final designed roll and yaw channel joint channel controller is expressed as

[0236]

[0237] where e γ =γ c -γ, G d2 , All refer to the values ​​in the roll channel.

[0238] Step 5: Conduct simulation experiment analysis of hypersonic vehicle flight mission.

[0239] Simulation part

[0240] The dynamic coefficients of the underactuated hypersonic vehicle are shown in Table 1.

[0241] Table 1. Parameters of controlled object model

[0242]

[0243] The controller designed according to the above parameters is as follows:

[0244] Pitch channel forward channel controller

[0245]

[0246] Roll channel forward channel controller

[0247]

[0248] The PD control parameter of the yaw channel in the roll channel is K p =0.3,K d =1.

[0249] According to equations (70) and (71), the feedforward controllers of the pitch channel and the roll channel are calculated to obtain the feedforward controller of the pitch channel:

[0250]

[0251] G d2_x =-0.3333 (78)

[0252] The relevant control parameters of NESO are shown in Table 2.

[0253] Table 2 NESO related control parameters

[0254]

[0255] Then the angle of attack and roll angle commands are set as

[0256]

[0257] The present invention also proposes an electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the roll and yaw joint control method of an under-actuated hypersonic aircraft based on anti-disturbance control are implemented.

[0258] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of a roll and yaw joint control method for an under-actuated hypersonic aircraft based on anti-disturbance control.

[0259] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DRRAM). It should be noted that the memory of the method described in the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0260] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a high-density digital video disc (DVD)), or a semiconductor medium (eg, a solid state disc (SSD)).

[0261] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software. The steps of the method disclosed in conjunction with the embodiment of the present application can be directly embodied as a hardware processor for execution, or a combination of hardware and software modules in a processor for execution. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it is not described in detail here.

[0262] It should be noted that the processor in the embodiment of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method embodiment can be completed by an integrated logic circuit of hardware in the processor or an instruction in the form of software. The above processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present application can be directly embodied as a hardware decoding processor to perform, or the hardware and software modules in the decoding processor can be combined and performed. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0263] The above is a detailed introduction to the roll and yaw joint control method of an under-actuated hypersonic aircraft based on anti-disturbance control proposed in the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A roll and yaw joint control method for an underactuated hypersonic vehicle based on active disturbance rejection control, characterized in that: The method comprises the following steps: Step 1: Establish a coordinate system, and on this basis establish the dynamics and kinematics equations of the aircraft; Step 2: Conduct handling stability analysis to verify the feasibility of achieving stable control under under-actuated conditions; Step 3: Design an ADRC controller for the pitch channel; Step 4: Add yaw state feedback to the roll channel to further improve the control effect of the yaw channel; Step 5: Conduct simulation experiment analysis of hypersonic vehicle flight mission.

2. The method according to claim 1, characterized in that In step 1, establish the ground coordinate system Axyz, the missile body coordinate system Ox1y1z1, the trajectory coordinate system Ox2y2z2 and the velocity coordinate system Ox3y3z3; from the ground system to the missile system, the three angles need to be rotated in sequence according to the 321 conversion order: pitch angle The yaw angle ψ and the roll angle γ; the transformation matrix is ​​expressed as Since the Oy3 axis and the Oy1 axis are both located in the longitudinal symmetry plane of the projectile, the velocity system to the projectile system rotates two angles in sequence according to the 32-turn sequence: the angle of attack α and the sideslip angle β, which can be expressed in a matrix as The transformation matrix from the ground system to the ballistic system is: Among them, the ballistic inclination angle θ and the ballistic deviation angle ψ v It is also transferred out in sequence according to the 32 transfer order; From the definition of the ballistic system and the velocity system, we know that the Ox2 axis and the Ox3 axis are both along the direction of the velocity vector, and Ox2y2 is the vertical plane, and Ox3y3 is the longitudinal symmetry plane of the aircraft. Therefore, to go from the ballistic system to the velocity system, we only need to rotate a velocity inclination angle γ around the velocity vector direction. v Then, the transformation matrix is In each of the above rotation processes, if the axis of rotation appears to rotate counterclockwise, the angle of rotation is positive; if the axis of rotation appears to rotate clockwise, the angle of rotation is negative.

3. The method according to claim 2, characterized in that In step 1, the dynamic equation for the vehicle's rotation around its center of mass is in, J x , J y and J z are the moments of inertia of the aircraft around the axes of the missile body coordinate system, J xy , J yz and J xz is the product of inertia; ω x ,ω y and ω z are the components of the angular velocity of the missile system relative to the ground system on each axis of the missile system; M x 、M y and M z are the components of the moment of the aerodynamic force on the center of mass on each axis of the missile system; P z is the reaction force generated by the thruster along the z-axis of the elastic system when the thruster is installed, l0 is the force arm of the thruster, M yw is the equivalent control torque produced by the flywheel when the reaction flywheel is installed; The three-channel dynamic equation of the underactuated BTT vehicle is:

4. The method according to claim 3, characterized in that In step 1, the attitude kinematics equation of the roll channel is In the above formula, the first term on the right side is much larger than the second term, so when the second term is ignored, the following simplified rolling channel attitude kinematic equation is obtained:

5. The method according to claim 4, characterized in that In step 2, the handling stability analysis is as follows: Take the state variable x = [αβγω x ω y ω z ] T , control quantity u=[δ x δ z ] T ;When u=[00] T hour, When u=[10] T When B1(x)=[000-c3-d10] T ;When u=[01] T When B2(x)=[-a50000-a3] T ; Then from Lie algebra we know Let F1=[A(x),B1(x)], F2=[A(x),B2(x)] Similarly: Let F 11 = [A(x), F1], F 12 = [A(x), F2] Because the state variable is 6-dimensional, we can first check the first six columns. If they are full rank, there is no need to calculate the subsequent columns. 11 and F 12 Zhang Cheng's function space: F=[B1(x) B2(x) F1 F2 F 11 F 12 ] (51) Using MATLAB to test, it is easy to determine that rank(F)=6. According to Lemmas 1, 2, and 3, the three-channel dynamic nonlinear equations of the underactuated BTT aircraft are weakly controllable, that is, using two control quantities δ x ,δ z The three coupling channels can be stably controlled, that is, the aileron control amount δ x The roll channel and yaw channel can be controlled.

6. The method according to claim 5, characterized in that Lemmas 1, 2, and 3 are as follows: Lemma 1: If the nonlinear system ∑ is 0 The point satisfies the controllability rank criterion condition, then ∑ at x 0 The point is locally weakly controllable; Lemma 2: If the nonlinear system ∑ is locally weakly controllable, then the controllability rank criterion is satisfied; Lemma 3: If a nonlinear system ∑ is analyzable, then ∑ is weakly controllable if and only if ∑ is locally weakly controllable if and only if ∑ satisfies the controllability rank criterion.

7. The method according to claim 6, characterized in that In step 3, the designed pitch channel controller is expressed as where e α =α c -α, All refer to the values ​​in the pitch channel.

8. The method according to claim 7, characterized in that In step 4, in the design of the controller, in δ x Add negative feedback on the yaw angle and yaw rate based on the original value, that is, through -b7δ x This control coupling realizes the PD control of the yaw channel, using k p ,k d represents two control coefficients; The final designed roll and yaw channel joint channel controller is expressed as where e γ =γ c -γ, All refer to the values ​​in the roll channel.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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