An aircraft backstepping super-spiral sliding mode guidance and control integrated method

Abstract

This invention discloses an integrated method for backstepping superhelical sliding mode guidance and control of an aircraft, belonging to the field of guidance and control technology. The integrated method includes the following steps: S1, establishing a three-dimensional relative motion model between the projectile and the target in terminal guidance, as well as the kinematic and dynamic models of the aircraft, and constructing an integrated guidance and control model; S2, designing a backstepping superhelical sliding mode controller for the three subsystems of guidance loop, attitude loop, and control loop, and using a high-order sliding mode differentiator to observe the time derivative of the virtual control quantity, enabling the aircraft to hit the target. This invention, employing the above-mentioned integrated method for backstepping superhelical sliding mode guidance and control of an aircraft, can solve the problem of instability in aircraft guidance and control.

Description

Technical Field

[0001] This invention relates to the field of guidance and control technology, and in particular to an integrated method for backstepping superhelical sliding mode guidance and control of aircraft. Background Technology

[0002] With the modernization of weaponry, guided aircraft are playing an increasingly important role and have become a symbol of modern national defense security. The guidance and control technology of guided aircraft is of paramount importance in achieving precise strikes against maneuvering targets in flight.

[0003] Traditional guidance and control systems employ proportional-integral-derivative (PID) controllers. However, for aircraft operating in complex aerodynamic environments, external disturbances and model uncertainties can cause these controllers to fail, compromising guidance accuracy. To address this, many researchers have applied modern nonlinear control methods, such as sliding mode control, robust control, and adaptive control, to aircraft control systems. Sliding mode control, in particular, is favored due to its insensitivity to parameter uncertainties and external disturbances. However, classical sliding mode control laws can only handle bounded disturbances. Furthermore, the introduction of discontinuous switching terms is detrimental to engineering practice, and the resulting chattering can degrade control performance and, in severe cases, compromise system stability. In contrast, the superspiral sliding mode controller, in principle, can handle disturbances with bounded time derivatives, not just bounded disturbances, and its continuous control law avoids chattering, leading to its widespread application in other fields.

[0004] On the other hand, traditional guidance and control systems typically adopt a guidance and control separate-loop design approach, which treats the control system as an ideal system when designing the guidance law and ignores its dynamic process. This may lead to a mismatch between the guidance and control systems, resulting in reduced maneuverability of the entire system, worse guidance performance, and even instability of the closed-loop system. Summary of the Invention

[0005] The purpose of this invention is to provide an integrated method for the backstepping superhelical sliding mode guidance and control of aircraft, thereby solving the problem of unstable guidance and control of aircraft.

[0006] To achieve the above objectives, the present invention provides an integrated method for backstepping superhelical sliding mode guidance and control of an aircraft, comprising the following steps:

[0007] S1. Establish a three-dimensional relative motion model between the missile and the target in terminal guidance, as well as a kinematic and dynamic model of the aircraft, and construct an integrated guidance and control model;

[0008] S2. For the three subsystems of guidance loop, attitude loop and control loop, a backstepping superhelical sliding mode controller is designed, and a high-order sliding mode differentiator is used to observe the time derivative of the virtual control quantity so that the aircraft hits the target.

[0009] Preferably, in S1, the terminal-guided three-dimensional projectile-target relative motion model is as follows:

[0010]

[0011]

[0012] In the formula: r is the relative distance between the projectile and the target, q ε q represents the elevation angle of the line of sight. β Let V be the azimuth angle of the line of sight, V be the velocity of the aircraft, and σ = cosθcosq. ε cosη+sinθsinq ε θ is the lead angle, θ is the track inclination angle, and ψ is the lead angle. V Let η be the deflection angle of the flight path. V -q β V t θ t ψ Vt These are the target's speed, target's trajectory inclination angle, and target's trajectory deflection angle, respectively, σ. t η is the target leading angle. t =ψ Vt -q β a ts =[a tsx a tsv a tsz ] T Let a be the representation of the acceleration of an unknown target in the line-of-sight coordinate system. ms =[a msx a msy a msz ] T This is the representation of the aircraft's acceleration in the line-of-sight coordinate system.

[0013] Preferably, in S1, the kinematic and dynamic model of the aircraft is as follows:

[0014]

[0015]

[0016] In the formula: γ is the roll angle, θ is the pitch angle, and γ V It is the roll angle of the track; J x J y J z ω is the moment of inertia. x ω y ω z M is the angular velocity of rotation in the body coordinate system. x M y M zα represents the pitch, roll, and yaw moments; α is the angle of attack; and β is the sideslip angle.

[0017]

[0018] In the formula: Q is dynamic pressure, L is reference length, and S is reference area; δ is the partial derivative of the aerodynamic torque with respect to the airflow angle, the angular velocity of rotation in the body coordinate system, and the rudder deflection angle; x δ y δ z This refers to the rudder deflection angle for the pitch, roll, and yaw channels.

[0019] Preferably, in S1, the integrated guidance and control model is as follows:

[0020]

[0021] In the formula: u=[δ x δ y δ z ] T For control laws, x2 = [α, β, γ] T x3=[ω x ω y ω z ] T This refers to the states of the three subsystems: guidance loop, attitude loop, and control loop. d1, d2, and d3 are the total disturbance terms consisting of external disturbances and unmodeled dynamics;

[0022]

[0023]

[0024]

[0025] g1 = AB

[0026]

[0027]

[0028]

[0029]

[0030] Where m is the mass of the aircraft and g is the acceleration due to gravity.

[0031] Preferably, in step S2, the process of designing a backstepping superhelical sliding mode controller for the guidance loop subsystem is as follows:

[0032] Define a sliding manifold s1 = x1, and design a backstepping superspiral sliding mode virtual control variable.

[0033]

[0034] Where: control gain K a1 K a2 It is a diagonal matrix, v1 is a higher-order virtual control variable; ζ a Defined as

[0035]

[0036] In the formula: the superscript (i, *) indicates the i-th row of the matrix, and P is a positive definite symmetric matrix. ai ∈R 2×2 .

[0037] Preferably, in step S2, the process of designing a backstepping superhelical sliding mode controller for the attitude loop subsystem is as follows:

[0038] remember Define a sliding manifold Design the following virtual control variable

[0039] Where: control gain K b1 K b2 It is a diagonal matrix, and v2 is a higher-order virtual control variable; defined ζ b as follows:

[0040]

[0041]

[0042]

[0043] In the formula: That is, the tracking error of x3; μ1∈R 2 , P bi ∈R 2×2 It is a positive definite symmetric matrix, and the superscript (*, i) denotes the i-th column of the matrix.

[0044] Preferably, in step S2, the process of designing a backstepping superhelical sliding mode controller for the control loop subsystem is as follows:

[0045] Design control inputs:

[0046]

[0047] Where: control gain K c1 Kc2 It is a diagonal matrix, and v3 is a higher-order virtual control variable, defined as follows: as follows:

[0048]

[0049]

[0050] In the formula: μ2∈R 2 , P ci ∈R 2×2 It is a positive definite symmetric matrix.

[0051] The advantages and positive effects of the integrated method for backstepping superhelical sliding mode guidance and control of aircraft described in this invention are as follows:

[0052] 1. To address the external disturbances and modeling uncertainties in the guidance and control system of aircraft, achieve stable control under the condition that the time derivative of the disturbance is bounded.

[0053] 2. The control law does not directly introduce switching terms, and the control quantity is continuous, avoiding the degradation of control performance caused by chattering.

[0054] 3. The integrated guidance and control technology is adopted to avoid guidance accuracy problems caused by the separate design of guidance and control loops, effectively improving guidance quality and the ability to complete strike missions.

[0055] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0056] Figure 1 This is a structural diagram of an embodiment of the integrated method for anti-stepping superhelical sliding mode guidance and control of an aircraft according to the present invention;

[0057] Figure 2 This is a three-dimensional missile-target relationship diagram of an embodiment of the integrated method for anti-stepping superhelical sliding mode guidance and control of an aircraft according to the present invention;

[0058] Figure 3 The target flight trajectory is an embodiment of the integrated method for anti-stepping superhelical sliding mode guidance and control of an aircraft according to the present invention.

[0059] Figure 4 This is a curve showing the relative distance between the missile and the target in an embodiment of the integrated anti-stepping super-helical sliding mode guidance and control method for aircraft according to the present invention.

[0060] Figure 5 This is a curve showing the change in the deflection angle of the control surface in an embodiment of the integrated method for anti-stepping superhelical sliding mode guidance and control of an aircraft according to the present invention. Detailed Implementation

[0061] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0062] An integrated method for backstepping superhelical sliding mode guidance and control of an aircraft includes the following steps:

[0063] S1. Establish a three-dimensional relative motion model between the missile and the target, as well as a kinematic and dynamic model of the aircraft, and construct an integrated guidance and control model.

[0064] 1. According to Figure 1 The diagram shows the three-dimensional projectile-target relationship. A three-dimensional relative motion model of the terminal-guided projectile and target is then established.

[0065]

[0066]

[0067] In the formula: r is the relative distance between the projectile and the target; q ε The elevation angle of the line of sight; q β Let θ be the azimuth angle of the line of sight; V be the velocity of the aircraft, which is ignored as a function of time. σ = cosθcosq ε cosη+sinθsinq ε θ is the lead angle, θ is the track inclination angle, and ψ is the lead angle. V Let η be the deflection angle of the flight path. V -q β V t θ t ψ Vt The target's speed, target's trajectory inclination angle, and target's trajectory deflection angle are all unknown. σ t η is the target leading angle. t =ψ Vt -q β a ts =[a tsx a tsy a tsz ] T Let a be the representation of the acceleration of an unknown target in the line-of-sight coordinate system. ms =[a msx a msy a msz ] T This is the representation of the aircraft's acceleration in the line-of-sight coordinate system.

[0068] Acceleration a, expressed in the track coordinate system m =[a mx a my a mz ] T Described as

[0069]

[0070] In the formula: Δ a This represents model uncertainty.

[0071] Taking the derivative of cosσ with respect to time, we have The superscript (i) denotes the i-th element of the vector.

[0072]

[0073] The tangential acceleration a of the aircraft my a mz Generated by aerodynamic forces Y and Z and gravity mg:

[0074]

[0075]

[0076] In the formula: Q is dynamic pressure, S is the reference area, m is the mass of the aircraft, and g is the gravitational acceleration; Let be the partial derivative of the lift coefficient with respect to the angle of attack α. This is the partial derivative of the lateral force coefficient with respect to the sideslip angle β.

[0077] 2. Establish the kinematics and dynamics model of the aircraft:

[0078]

[0079]

[0080] In the formula: γ is the roll angle, θ is the pitch angle, and γ V It is the roll angle of the track; J x J y J z ω is the moment of inertia. x ω y ω z M is the angular velocity of rotation in the body coordinate system. x M y M z α represents the pitch, roll, and yaw moments; α is the angle of attack; and β is the sideslip angle.

[0081]

[0082] In the formula: Q is dynamic pressure, L is reference length, and S is reference area; δ is the partial derivative of the aerodynamic torque with respect to the airflow angle, the angular velocity of rotation in the body coordinate system, and the rudder deflection angle; x δ y δ z This refers to the rudder deflection angle for the pitch, roll, and yaw channels.

[0083] 3. Establish an integrated guidance and control model:

[0084]

[0085] In the formula: u=[δ x δ y δ z ] T For control laws, x2 = [α, β, γ] T x3=[ω x ω y ω z ] T This refers to the states of the three subsystems: guidance loop, attitude loop, and control loop. d1, d2, and d3 represent the total disturbance term consisting of external disturbances and unmodeled dynamics, such as the maneuvering of an unknown target.

[0086]

[0087]

[0088]

[0089] g1 = AB

[0090]

[0091]

[0092]

[0093]

[0094] S2. For the three subsystems of guidance loop, attitude loop and control loop, a backstepping superhelical sliding mode controller is designed, and a high-order sliding mode differentiator is used to observe the time derivative of the virtual control quantity so that the aircraft hits the target.

[0095] 1. Design of a backstepping superhelical sliding mode controller for the guidance loop subsystem

[0096] Before proceeding with the controller design, we will first present one assumption and two lemmas.

[0097] Assumption 1. In the aircraft guidance and control system, the total disturbance terms d1, d2, and d3 are Lipschitz bounded and satisfy the following conditions: Where L i For positive constants, i = 1, 2, 3, j = 1, 2, (3);

[0098] Lemma 1. For the system Where v is the control input, and ρ is the Lipschitz bounded total disturbance term, i.e., there exists L > 0 such that Select appropriate values ​​for k1 > 0 and k2 > 0 to form the control input:

[0099]

[0100] In the formula:

[0101]

[0102] For a closed-loop system, define auxiliary state variables.

[0103]

[0104] Then there exist positive definite symmetric matrices P and Q such that V = z T Pz is the Lyapunov function of the closed-loop system, whose time derivative satisfies almost everywhere... Remember symA=(A+A T If ) / 2, then we have

[0105]

[0106] Lemma 2. For a nonnegative continuous function V(x(t)) = x T Px, where P∈R n×n Let x be a positive definite symmetric matrix, x∈R n If the system has V as its Lyapunov function and there exists a positive definite symmetric matrix Q∈R n×n , making If this holds true, then there exists σ > 0 such that Thus, the trajectory starting from the initial state x(0) converges to the origin in a finite amount of time.

[0107] Define the sliding manifold s1 = x1, and the guidance loop subsystem can be transformed into:

[0108] Design a virtual control quantity for a backstepping superhelical sliding mode.

[0109]

[0110] Where: control gain K a1 K a2 For a diagonal matrix, the elements on the diagonal... i = 1, 2 are designed according to Lemma 1, and have the corresponding positive definite symmetric matrix P. ai ∈R 2×2 Q ai ∈R 2×2 ;ζa Defined as

[0111]

[0112] In the formula: the superscript (i, *) represents the i-th row of the matrix, and the superscript (*, i) appearing in the following text represents the i-th column of the matrix.

[0113] 2. Design of a backstepping superhelical sliding mode controller for the attitude loop subsystem

[0114] remember Define a sliding manifold That is, the tracking error of x2, the attitude loop subsystem can be transformed into:

[0115] Design the following virtual control variable

[0116]

[0117] Where: control gain K b1 K b2 For a diagonal matrix, the elements on the diagonal... For i = 1 and 2, the design is also based on Lemma 1, and there is a corresponding positive definite symmetric matrix P. bi ∈R 2×2 Q bi ∈R 2×2 ; That is, expectation The roll angle γ is stable.

[0118] definition ζ b as follows:

[0119]

[0120]

[0121]

[0122] In the formula: That is, the tracking error of x3; μ1∈R 2 ,

[0123] 3. Design a backstepping superspiral sliding mode controller for the control loop subsystem.

[0124] The control loop subsystem can be transformed into:

[0125]

[0126] Design control inputs:

[0127]

[0128] Where: control gain K c1 K c2 For a diagonal matrix, the elements on the diagonal... The numbers i = 1, 2, 3 are designed according to Lemma 1, and have corresponding positive definite symmetric matrices P. ci ∈R 2×2 Q c1 ∈R 2×2 .

[0129] definition as follows:

[0130]

[0131]

[0132] In the formula: μ2∈R 2 ,

[0133] The controller designed above enables the closed-loop system state tracking error to converge to zero within a finite time.

[0134] The proof is as follows:

[0135] Let w1 = v1 + d1 i = 1, 2; w2 = v2 + d2, i = 1, 2; w3 = v3 + d3 i = 1, 2, 3. Define the Lyapunov candidate function as: For V1, V 2i and V 3i Find the time derivatives respectively:

[0136]

[0137] In the formula: W 1i W 2i With W 3i for:

[0138]

[0139] According to Lemma 1, we have:

[0140]

[0141] Substituting, we get:

[0142]

[0143] Therefore, the time derivative of V0 is:

[0144]

[0145] From the definition, we can obtain:

[0146]

[0147] Then the time derivative of V0 satisfies:

[0148]

[0149] From Lemma 2, we know that σ min =min{σ 1i , σ 2i , σ 3i , i = 1, 2, (3)}:

[0150]

[0151] Therefore, the designed backstepping superhelical sliding mode control law can make the state tracking error of the closed-loop system converge to zero in a finite time.

[0152] Q.E.D.

[0153] 4. Use a high-order sliding mode differentiator to observe the time derivative of the virtual control quantity.

[0154] The time derivative of the virtual control quantity that appears in the backstepping design process, i.e. For computationally complex problems, a high-order sliding mode differentiator is used to obtain their numerical values ​​online. If the k-th time derivative of variable x has an upper bound L... d Then, the general form of its k-1 order higher-order sliding mode differentiator is as follows:

[0155]

[0156] In the formula: z i It is an observation of the i-th time derivative of x, i = 0, ..., k, λ i >0 is a control parameter.

[0157] The structural diagram of the integrated controller for backstepping superhelical sliding mode guidance and control of the aircraft described in this invention is as follows: Figure 2 As shown.

[0158] Example

[0159] In S1, consider the initial spatial position of the target as [0, 0, 0]. T m, line of sight elevation angle is 0°, line of sight azimuth angle is 0°, velocity is 180m / s, acceleration occurs from 0 to 5s [0, 50, 0]. T The speed is m / s, and the flight is uniform in a straight line from 5 to 10 seconds. After 10 seconds, there is acceleration [0, -50, 0].T m / s. Set the aircraft's flight speed to V = 400 m / s, the initial relative distance between the projectile and the target to r(0) = 3000 m, and the line-of-sight elevation angle to q. ε (0) = -10°, and the azimuth angle of the line of sight is q. β (0) = 30°, pitch angle θ(0) = 10°, yaw angle ψ(0) = -5°, roll angle γ(0) = -20°, and rotational angular velocity ω(0) = [0, 5.73, -11.46]. T rad / s. To demonstrate the effectiveness of this invention, the flight conditions of the aircraft under five different initial flight directions are shown, along with the corresponding initial track inclination and track deflection angles [θ, ψ]. V ] T They are: [0°, 45°] T [-10°, 150°] T [-20°, 100°] T [-15°, -60°] T [60°, 0°] T .

[0160] For S2, the control parameters selected in the embodiment are: Select the parameters of the fifth-order differentiator as L d =5, [λ0, λ1, λ2, λ3, λ4] = [1.5, 2, 3, 5, 8, 10].

[0161] Figure 3 The flight trajectories of the aircraft and targets show that the five groups of aircraft had different initial velocities and directions, but all ultimately hit the maneuvering targets; Figure 4 The curves showing the relative distance between the projectile and the target also demonstrate that all five groups of aircraft successfully completed their strike missions. This indicates that the method can achieve target hits even under conditions where unmodeled dynamics such as target maneuvering exist.

[0162] Depend on Figure 5 The first set of aircraft control surface deflection angle variation curves shows that the integrated guidance and control law based on backstepping superhelical sliding mode control provides continuous control signals, avoids the chattering problem commonly found in sliding mode controllers, and optimizes control performance.

[0163] The results show that the aircraft system using the integrated method of antistep superhelical sliding mode guidance and control can achieve flight missions that hit maneuvering targets under conditions of comprehensive disturbances and uncertainties such as target maneuvers, and its control signal is continuous, avoiding the chattering phenomenon of sliding mode controllers.

[0164] Therefore, the present invention employs the above-mentioned integrated method for anti-stepping superhelical sliding mode guidance and control of aircraft, which can solve the problem of unstable guidance and control of aircraft.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An integrated backstepping super-twisting sliding mode guidance and control method for a flight vehicle, characterized in that, Includes the following steps: S1. Establish a three-dimensional relative motion model between the missile and the target in terminal guidance, as well as a kinematic and dynamic model of the aircraft, and construct an integrated guidance and control model; S2. For the three subsystems of guidance loop, attitude loop and control loop, design a backstepping superhelical sliding mode controller, and use a high-order sliding mode differentiator to observe the time derivative of the virtual control quantity so that the aircraft hits the target; In S1, the three-dimensional relative motion model between the projectile and the target in terminal guidance is as follows: In the formula: The relative distance between the projectile and the target. For the elevation angle of the line of sight, The azimuth angle of the line of sight. For the speed of the aircraft, Forward angle, For the inclination angle of the flight path, For the track deflection angle, ; , , These are the target's speed, the target's trajectory inclination angle, and the target's trajectory deflection angle, respectively. For the target's forward angle, , This represents the acceleration of an unknown target in the line-of-sight coordinate system. This represents the aircraft's acceleration in the line-of-sight coordinate system. In S1, the kinematic and dynamic model of the aircraft is as follows: In the formula: It's a roll angle. It is the pitch angle. It is the roll angle of the track; , , It is the moment of inertia; , , The rotational angular velocity of the body coordinate system; , , For pitch, roll and yaw moments; For the angle of attack, Sideslip angle; In the formula: It is dynamic pressure. For reference length, For reference area; , , , , , , , It is the partial derivative of the aerodynamic torque with respect to the airflow angle, the angular velocity of the body coordinate system rotation, and the rudder deflection angle; , , The rudder deflection angle for the pitch, roll, and yaw channels; In S1, the integrated guidance and control model is as follows: In the formula: For control laws, , , This refers to the states of the three subsystems: guidance loop, attitude loop, and control loop. , , , This is the total disturbance term consisting of external disturbances and unmodeled dynamics; in, m For the mass of the aircraft, g It is the acceleration due to gravity; In S2, the process of designing a backstepping superhelical sliding mode controller for the guidance loop subsystem is as follows: Define a sliding manifold Design of virtual control quantity for backstepping superhelical sliding mode : Where: control gain , It is a diagonal matrix. It is a high-order virtual control variable; Defined as In the formula: superscript Represents the matrix of the first Line, positive definite symmetric matrix ; In S2, the process of designing a backstepping superhelical sliding mode controller for the attitude loop subsystem is as follows: remember Define the sliding manifold Design the following virtual control quantity : Where: control gain , It is a diagonal matrix. For higher-order virtual control variables; defined , , as follows: In the formula: ,Right now Tracking error; , , It is a positive definite symmetric matrix, with superscript... Represents the matrix of the first List; In S2, the process of designing a backstepping superhelical sliding mode controller for the control loop subsystem is as follows: Design control inputs: Where: control gain , It is a diagonal matrix. Defined as a high-order virtual control variable , as follows: In the formula: , , , It is a positive definite symmetric matrix.

Images