A Cascaded Nonlinear Robust Trajectory Tracking Control Method with Dynamic Constraints

Abstract

The present invention provides a cascaded nonlinear robust trajectory tracking control method with dynamic constraints, including: establishing the motion equation of an aircraft; calculating the control efficiency matrix of angular velocity, and designing a nonlinear incremental fault-tolerant control law of angular velocity; taking angular velocity as a control quantity, calculating the control efficiency matrix of airflow angle, and designing a nonlinear incremental fault-tolerant control law of airflow angle; taking airflow angle as a control quantity, designing a nonlinear control law of track angle and speed; setting the boundary of track tracking error, and selecting a performance function for error transformation, and designing a track virtual control quantity; taking track angle as a control quantity, designing a track fault-tolerant control law with preset performance, and according to the track instruction, realizing the track tracking control of the aircraft in the presence of interference through the cascaded fault-tolerant trajectory control law. The control law of cascaded nonlinear trajectory tracking with dynamic constraints designed by the present invention can not only effectively improve the robustness of the flight trajectory control system, but also ensure the dynamic tracking performance of the flight trajectory.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft trajectory tracking control, and in particular to a cascaded nonlinear robust trajectory tracking control method with dynamic constraints. Background Art

[0002] Since the birth of the aircraft, ensuring safe flight has become the focus of the aviation industry and a goal that is constantly pursued. From a control perspective, enhancing the robustness of the flight control system to interference is a reliable way to improve flight safety. In addition to ensuring the expected flight quality of the aircraft under normal conditions, the advanced flight control system must also reduce the impact of faults and disturbances on the aircraft, thereby ensuring its steady-state and transient performance, and making it possible for damaged / disturbed aircraft to still track the command signal quickly and accurately.

[0003] Existing nonlinear trajectory tracking control laws usually rely on accurate nonlinear models and have insufficient robustness in complex flight environments, which in turn reduces the dynamic performance of the aircraft. Therefore, a new trajectory tracking control law is urgently needed to improve the robustness of the trajectory controller, thereby eliminating the impact of interference on the aircraft, and at the same time, making the transient and steady-state performance of the aircraft after the disturbance meet the expected requirements. Summary of the invention

[0004] To solve the above problems, the present invention provides the following technical solutions.

[0005] A cascaded nonlinear robust trajectory tracking control method with dynamic constraints comprises the following steps:

[0006] Establish the aircraft's angular velocity, airflow angle, track angle, speed, and trajectory motion equations;

[0007] Taking the control surface as the control quantity, the control efficiency matrix of angular velocity is calculated, and the nonlinear incremental fault-tolerant control law of angular velocity is designed;

[0008] Taking the angular velocity as the control variable, the control efficiency matrix of the airflow angle is calculated, and the nonlinear incremental fault-tolerant control law of the airflow angle is designed;

[0009] Taking the airflow angle as the control variable, the nonlinear control law of track angle and speed is designed;

[0010] Set the boundary of the track tracking error and select the appropriate performance function for error transformation to design the virtual control amount of the track;

[0011] Taking the track angle as the control variable, a trajectory fault-tolerant control law with preset performance is designed according to the trajectory virtual control variable;

[0012] According to the angular velocity nonlinear incremental fault-tolerant control law, the airflow angle nonlinear incremental fault-tolerant control law, the track angle and velocity nonlinear control law, and the trajectory fault-tolerant control law with preset performance, a cascade nonlinear robust trajectory control law with dynamic constraints is formed in series;

[0013] According to the trajectory command, the trajectory tracking control of the aircraft is realized through the cascade fault-tolerant trajectory control law.

[0014] Preferably, the establishment of the aircraft angular velocity, airflow angle, track angle, speed and trajectory motion equations comprises the following steps:

[0015] Draw a 3D aircraft model using CATIA software to obtain normal aircraft mass m, wing area S, span b, and average aerodynamic chord length And the moment of inertia I xx , I yy , I zz , I xz ;

[0016] Establish the differential equations for the aircraft angular velocity p, q, r:

[0017]

[0018] In the formula, They represent the rolling, pitching and yaw moments respectively; the inertia coefficients c1 to c9 are composed of the rotational inertia and are defined as follows:

[0019]

[0020] Establish the differential equations for the angle of attack α, sideslip angle β and track inclination angle μ:

[0021]

[0022] In the formula, m represents the mass of the aircraft, g represents the acceleration due to gravity, G Y and G Z Respectively represent the components of gravity in the y and z directions of the track system; V a represents true airspeed; L, D, Y and T represent lift, drag, side force and thrust respectively;

[0023] Establish speed V a , the differential equations of the track inclination angle γ and the track azimuth angle χ are:

[0024]

[0025] Develop differential equations for the forward direction x, lateral position y, and height h:

[0026]

[0027] In the equations of motion, the forces and moments resulting from aerodynamic properties are expressed as:

[0028]

[0029]

[0030] In the formula, b and denote the span and the average aerodynamic chord length respectively; δ=[δ e ,δ a ,δ r ] T represents the control input vector, which is composed of the elevator δ e 、Aileron δ a and rudder δ r Composition; Q represents dynamic pressure, S represents wing area; C ** Represents the aerodynamic coefficients related to the state and the control coefficients related to the control surfaces.

[0031] Preferably, the method of taking the control surface as the control quantity, calculating the control efficiency matrix of the angular velocity, and designing the nonlinear incremental fault-tolerant control law of the angular velocity comprises the following steps:

[0032] According to the aerodynamic parameters obtained offline, taking the control surface δ as the control quantity, the control efficiency matrix G of the angular velocity loop of the aircraft at the previous moment is calculated. ω (x0), specifically:

[0033]

[0034] The “proportional” strategy is used to design the virtual control law, that is, ν ω =K ω (ω c -ω), where ω=[p,q,r] T represents the angular velocity, and ω c is the angular velocity command signal; K ω It is a third-order diagonal matrix with diagonal elements greater than zero, representing the bandwidth of the angular velocity loop;

[0035] Obtain the angular acceleration at the previous moment by the difference method Then, a nonlinear incremental angular velocity fault-tolerant control law is designed, and the results are as follows:

[0036]

[0037] Preferably, the method of taking the angular velocity as the control input, calculating the control efficiency matrix of the airflow angle loop, and designing the nonlinear incremental fault-tolerant control law of the airflow angle comprises the following steps:

[0038] In the airflow angle loop, the angular velocity is selected as the control input, and the approximate control efficiency matrix of the airflow angle loop under the previous state is calculated. Specifically:

[0039]

[0040] The “proportional” strategy is used to design the virtual control law of the airflow angle, that is, in represents the airflow angle loop state vector, Indicates the command signal for the track angle loop solution; It is a third-order diagonal matrix with diagonal elements greater than zero, representing the bandwidth of the airflow angular loop;

[0041] The angular velocity of the airflow at the previous moment is obtained by the difference method Then, a nonlinear incremental airflow angle fault-tolerant control law is designed, which is as follows:

[0042]

[0043] Preferably, the design of the nonlinear control law of track angle and speed by taking the airflow angle as the control variable comprises the following steps:

[0044] At the track angle η=[χ,γ] T In the loop, the airflow angle is selected as the control input; considering the requirements of flight quality, the sideslip angle is usually kept at zero during actual flight, so β c =0;

[0045] The track angle motion equation is simplified, and the control efficiency matrix G of the track loop is obtained by analytical method. η (x0):

[0046]

[0047] in

[0048] The “proportional” strategy is used to design the virtual control law of the track angle, that is, ν η =K η (η c -η); where η c is the track angle command, K η is a second-order diagonal matrix with diagonal elements greater than zero; the nonlinear incremental fault-tolerant control law of the track angle is designed as:

[0049]

[0050] Design of speed virtual control law using the strategy of "proportional + integral" Specifically:

[0051]

[0052] Where V a,c Indicates speed command, k V and k i Represent the proportional and integral coefficients respectively, then the automatic throttle feedback inverse control law is designed as:

[0053]

[0054] Preferably, the step of setting the boundary of the track tracking error and selecting a suitable performance function for error transformation, thereby designing the track virtual control amount, comprises the following steps:

[0055] According to the expected trajectory dynamics of the aircraft, the performance boundary function τ(t) is set, and the boundary function τ(t) is required to be greater than 0 and monotonically decreasing;

[0056] In order to ensure the transient performance of the aircraft in the process of tracking trajectory instructions, that is, to avoid excessive dynamics of tracking errors, the aircraft altitude and lateral errors are restricted to meet the following conditions:

[0057] -Lτ i (t)<e i (t)<Rτ i (t),i=h,y (16)

[0058] In the formula, L and R represent constants greater than zero, e h (t) and e y (t) represents the height and lateral error, which can be expressed as follows:

[0059] e h (t) = h c (t)-h(t),e y (t) = y c (t)-y(t) (17)

[0060] In the formula, h c (t) and y c (t) indicates height and lateral command

[0061] Since it is impossible to directly constrain the tracking error through the formula, a new tracking error z(t) is introduced, which is called the conversion error, and the conversion function is expressed as Γ(z(t)). The relationship between the errors is as follows:

[0062] e i (t) = τ i (t)Γ(z i (t))i=h,y (18)

[0063] The conversion error Design the virtual control quantity ν of height and lateral displacement under the requirement of Lyapunov stability h and ν y , the results are as follows:

[0064]

[0065] In the formula, k h and k y Indicates the proportionality coefficient, usually greater than 0; h c (t) and y c (t) represents the command signal of height and lateral displacement.

[0066] Preferably, the method of designing a trajectory fault-tolerant control law with preset performance by taking the track angle as the control variable comprises the following steps:

[0067] In the trajectory loop, the track angle is selected as the control variable, and the height and lateral displacement control laws are designed using the analytical method. The specific design is as follows:

[0068]

[0069] In the formula, represents the derivative of the forward displacement.

[0070] Beneficial effects of the present invention:

[0071] The present invention takes improving the robustness of the flight trajectory tracking system as the starting point, and designs a cascade nonlinear trajectory tracking control law with dynamic constraints. The flight trajectory control law has strong robustness, and can constrain the dynamic performance of the aircraft, so that the aircraft can weaken the influence of faults and interferences, and avoid the aircraft from causing transient performance deterioration due to excessive dynamic response. Furthermore, the trajectory control law improves the transient performance of the aircraft while ensuring steady-state performance. From the perspective of the control law configuration, the structure of the designed cascade nonlinear trajectory tracking control law with dynamic constraints is clear and simple, does not rely on an accurate model during the design process, and does not require a complex parameter adjustment process, thereby effectively reducing development time and labor costs. From the perspective of control effect, the designed trajectory control law has strong robustness, which can not only overcome the influence of interference and faults on the aircraft, but also ensure the desired transient performance during the aircraft trajectory tracking process, that is, avoid excessive dynamic response. In addition, due to good flexibility, the architecture and method extracted from the design of the robust cascade nonlinear trajectory control law are easy to expand to other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is the overall structural framework of the cascaded nonlinear robust trajectory tracking control law with dynamic constraints of the present invention.

[0073] Figure 2A comparison diagram of three-dimensional trajectories verified by simulation of an embodiment of the present invention;

[0074] Figure 3 This is a height response comparison diagram of the simulation verification of the embodiment of the present invention;

[0075] Figure 4 This is a comparison diagram of the side deviation response verified by simulation of an embodiment of the present invention;

[0076] Figure 5 A height error comparison diagram for simulation verification of an embodiment of the present invention;

[0077] Figure 6 A comparison diagram of the side slip error verified by simulation in an embodiment of the present invention;

[0078] Figure 7 This is a comparison diagram of the rudder surface deflection verified by simulation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0080] Example 1

[0081] The present invention provides a cascaded nonlinear robust trajectory tracking control method with dynamic constraints. Figure 1 As shown:

[0082] S1: Establish the complete angular velocity, airflow angle, track angle and trajectory motion equations of the aircraft;

[0083] Draw a 3D aircraft model using CATIA software to obtain normal aircraft mass m, wing area S, span b, and average aerodynamic chord length And the moment of inertia I xx ,I yy ,I zz ,I xz Then, the differential equations of angular velocity p, q, and r are established, and the results are as follows:

[0084]

[0085] in, They represent the rolling, pitching and yaw moments respectively. The inertia coefficients c1 to c9 are composed of rotational inertia and are defined as follows:

[0086]

[0087] Establish the differential equations of airflow angles α, β, μ, and the results are as follows:

[0088]

[0089] In the formula, m represents the mass of the aircraft, g represents the acceleration due to gravity, G Y and G Z Respectively represent the components of gravity in the y and z directions of the track system; V a represents true airspeed; L, D, Y and T represent lift, drag, side force and thrust respectively;

[0090] Establish speed V a , the differential equations of the track inclination angle γ and the track azimuth angle χ are:

[0091]

[0092] Develop differential equations for the forward direction x, lateral position y, and height h:

[0093]

[0094] In the equations of motion, the forces and moments resulting from aerodynamic properties are expressed as:

[0095]

[0096]

[0097] In the formula Control input δ = [δ e ,δ a ,δ r ] T It is the combination of rudder surfaces. ** represents the state-related aerodynamic coefficient and the control coefficient related to the control surface, where represents the aerodynamic derivative related to the state, Represents the control derivative related to the control surface. The above aerodynamic derivatives are calculated by Xflow software or actual wind tunnel experiments.

[0098] S2: Based on S1, design a nonlinear incremental fault-tolerant control law for angular velocity.

[0099] According to the aerodynamic parameters obtained offline, the angular velocity control efficiency matrix G of the aircraft at the previous moment is calculated with the control surface deflection δ as the control quantity. ω (x0):

[0100]

[0101] The “proportional” strategy is used to design the virtual control law, that is, ν ω =K ω (ω c -ω). Among them, ωc is the command signal for solving the airflow angle loop. The angular acceleration at the previous moment is obtained by the difference method. Then, a nonlinear incremental angular velocity fault-tolerant control law is designed, and the results are as follows:

[0102]

[0103] S3: According to S1 and on the basis of S2, a nonlinear incremental fault-tolerant control law of the airflow angle loop is designed.

[0104] With angular velocity ω c As the input quantity, calculate the approximate control efficiency matrix of the airflow angle loop under the previous state

[0105]

[0106] The “proportional” strategy is used to design the virtual control law of the airflow angle, that is, in represents the airflow angle loop state vector, is the command signal for solving the track angle loop, is a third-order diagonal matrix with diagonal elements greater than zero. The angular velocity of the airflow at the previous moment is obtained by the difference method Then, a nonlinear incremental airflow angle fault-tolerant control law is designed, and the results are as follows:

[0107]

[0108] S4: According to S1, design a nonlinear fault-tolerant control law for track angle based on S3.

[0109] At the track angle η=[χ,γ] T In the circuit, the airflow angle Considering the requirements of flight quality, the sideslip angle should be kept at zero during actual flight, so β c = 0. Simplify the motion equation of the track angle loop in step 1, and obtain the control efficiency matrix G of the track loop by analytical method η (x0):

[0110]

[0111] in The proportional strategy is used to design the virtual control law of the track angle, that is, ν η =K η (η c -η), K η is a second-order diagonal matrix with diagonal elements greater than zero. Then the nonlinear incremental control law of the track angle is designed as follows:

[0112]

[0113] There is an obvious correspondence between the differential of aircraft speed and thrust, so the "proportional + integral" strategy is directly used to design the virtual control law:

[0114]

[0115] The automatic throttle feedback inverse control law is designed as follows:

[0116]

[0117] S5: Based on S4, performance functions and error transformation functions are designed to constrain trajectory tracking dynamics.

[0118] -Lτ i (t)<e i (t)<Rτ i (t),i=h,y (16) In the formula, L and R represent constants greater than zero, e h (t) and e y (t) represents the height and lateral error, which can be expressed as follows:

[0119] e h (t) = h c (t)-h(t),e y (t) = y c (t)-y(t) (17)

[0120] In the formula, h c (t) and y c (t) indicates height and lateral command

[0121] Since it is impossible to directly constrain the tracking error through the formula, a new tracking error z(t) is introduced, which is called the conversion error, and the conversion function is expressed as Γ(z(t)). The relationship between the errors is as follows:

[0122] e i (t) = τ i (t)Γ(z i (t))i=h,y (18)

[0123] The conversion error Design the virtual control quantity ν of height and lateral displacement under the requirement of Lyapunov stability h and ν y , the results are as follows:

[0124]

[0125] In the formula, k h and ky Indicates the proportionality coefficient, usually greater than 0; h c (t) and y c (t) represents the command signal of height and lateral displacement.

[0126] S6: Based on S1, take the track angle as the control variable and design a trajectory fault-tolerant control law with preset performance.

[0127] In the trajectory loop, the track angle is selected as the control variable, and the height and lateral displacement control laws are designed using the analytical method. The specific design is as follows:

[0128]

[0129] In the formula, represents the derivative of the forward displacement.

[0130] In this embodiment, the designed cascade fault-tolerant trajectory control law is simulated and verified under a damage fault.

[0131] The results of parameter selection of the designed cascade fault-tolerant control law are as follows:

[0132]

[0133] The performance boundary of this patent is selected as τ(t)=(τ0-τ ∞ ) -at +τ ∞ .in, And a>0. The specific choices are:

[0134] τ y (t) = (15-1)e -0.3t +1, τ h (t) = (5-1)e -0.6t +1 (22)

[0135] and L h =2,R h =3. The conversion function is selected as in

[0136] In this embodiment,

[0137] Assume that the aircraft is flying at an altitude of 4000m and a speed of 60m / s. The initial state of the aircraft is θ0=α0=4.13°, and the elevator is The designed robust cascade trajectory tracking control law is simulated under normal conditions and wing damage faults. The simulation results are shown in Figure 2-7 shown.

[0138] The comparison results show that the cascaded nonlinear fault-tolerant trajectory tracking control law designed in this patent has good robustness and control performance, so it can overcome the impact of damage faults on the aircraft and ensure that the aircraft trajectory response can quickly track the command signal. In addition, from the perspective of transient performance, the dynamic performance of the damaged aircraft is not reduced due to the occurrence of damage, and throughout the process, the height and lateral errors are within the boundaries of the preset performance, meeting the expected requirements. It shows that the designed cascaded nonlinear trajectory control law not only ensures the steady-state performance of the aircraft, but also takes into account the transient performance, and finally achieves the unity of the steady-state and transient performance of the damaged aircraft.

[0139] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A cascaded nonlinear robust trajectory tracking control method with dynamic constraints, characterized in that: The following steps are involved: Establish the equations of motion for the aircraft's angular velocity, airflow angle, track angle, speed, and trajectory; Taking the rudder as the control variable, the control efficiency matrix of angular velocity is calculated, and the nonlinear incremental fault-tolerant control law of angular velocity is designed. Taking the angular velocity as the control variable, the control efficiency matrix of the airflow angle is calculated, and the nonlinear incremental fault-tolerant control law of the airflow angle is designed; Taking the airflow angle as the control variable, the nonlinear control law of track angle and speed is designed; Set the boundary of the track tracking error, select the performance function for error transformation, and design the virtual control amount of the track; Taking the track angle as the control variable, a trajectory fault-tolerant control law with preset performance is designed according to the trajectory virtual control variable; According to the angular velocity nonlinear incremental fault-tolerant control law, the airflow angle nonlinear incremental fault-tolerant control law, the track angle and velocity nonlinear control law, and the trajectory fault-tolerant control law with preset performance, a cascade nonlinear robust trajectory control law with dynamic constraints is formed in series; According to the trajectory command, the aircraft trajectory tracking control is realized through the cascade fault-tolerant trajectory control law; The method of establishing the aircraft angular velocity, airflow angle, track angle, speed and trajectory motion equations comprises the following steps: Draw a 3D aircraft model using CATIA software to obtain normal aircraft mass m, wing area S, span b, and average aerodynamic chord length And the moment of inertia I xx , I yy , I zz , I xz ; Establish the differential equations for the aircraft angular velocity p, q, r: In the formula, They represent the rolling, pitching and yaw moments respectively; the inertia coefficients c1 to c9 are composed of the rotational inertia and are defined as follows: Establish the differential equations for the angle of attack α, sideslip angle β and track inclination angle μ: In the formula, m represents the mass of the aircraft, g represents the acceleration due to gravity, G Y and G Z Respectively represent the components of gravity in the y and z directions of the track system; V a represents true airspeed; L, D, Y and T represent lift, drag, side force and thrust respectively; Establish speed V a , the differential equations of the track inclination angle γ and the track azimuth angle χ are: Develop differential equations for the forward direction x, lateral position y, and height h: In the equations of motion (1)-(4), the forces and moments generated by aerodynamic characteristics are expressed as: In the formula, b and denote the span and the average aerodynamic chord length respectively; δ=[δ e ,δ a ,δ r ] T represents the control input vector, which is composed of the elevator δ e 、Aileron δ a and rudder δ r Composition; Q represents dynamic pressure, S represents wing area; C ** Indicates the aerodynamic coefficients related to the state and the control coefficients related to the control surfaces; The method of taking the rudder surface as the control quantity, calculating the control efficiency matrix of the angular velocity, and designing the nonlinear incremental fault-tolerant control law of the angular velocity comprises the following steps: According to the aerodynamic parameters obtained offline, taking the control surface δ as the control quantity, the control efficiency matrix G of the angular velocity loop of the aircraft at the previous moment is calculated. ω (x0), specifically: The "proportional" strategy is used to design the virtual control law, that is, ν ω =K ω (ω c -ω), where ω=[p,q,r] T represents the angular velocity, and ω c is the angular velocity command signal; K ω It is a third-order diagonal matrix with diagonal elements greater than zero, representing the bandwidth of the angular velocity loop; Obtain the angular acceleration at the previous moment by the difference method Then, a nonlinear incremental angular velocity fault-tolerant control law is designed, and the results are as follows: The method of taking the angular velocity as the control input, calculating the control efficiency matrix of the airflow angle loop, and designing the airflow angle nonlinear incremental fault-tolerant control law comprises the following steps: In the airflow angle loop, the angular velocity is selected as the control input, and the approximate control efficiency matrix of the airflow angle loop under the previous state is calculated. Specifically: The "proportional" strategy is used to design the virtual control law of the airflow angle, that is, in represents the airflow angle loop state vector, Indicates the command signal for the track angle loop solution; It is a third-order diagonal matrix with diagonal elements greater than zero, representing the bandwidth of the airflow angular loop; The angular velocity of the airflow at the previous moment is obtained by the difference method Then, a nonlinear incremental airflow angle fault-tolerant control law is designed, which is as follows: The method of designing a nonlinear control law of track angle and speed by taking the airflow angle as the control variable comprises the following steps: At the track angle η=[χ,γ] T In the loop, the airflow angle is selected as the control input; considering the requirements of flight quality, the sideslip angle is usually kept at zero during actual flight, so β c =0; The track angle motion equation is simplified, and the control efficiency matrix G of the track loop is obtained by analytical method. η (x0): in The "proportional" strategy is used to design the virtual control law of the track angle, that is, ν η =K η (η c -η); where η c is the track angle command, K η is a second-order diagonal matrix with diagonal elements greater than zero; the nonlinear incremental fault-tolerant control law of the track angle is designed as: The speed virtual control law ν is designed by using the "proportional + integral" strategy Va , specifically: Where V a,c Indicates speed command, k V and k i Represent the proportional and integral coefficients respectively, then the automatic throttle feedback inverse control law is designed as: The step of setting the boundary of the track tracking error and selecting a performance function for error transformation, thereby designing a track virtual control amount, includes the following steps: According to the expected trajectory dynamics of the aircraft, the performance boundary function τ(t) is set, and the boundary function τ(t) is required to be greater than 0 and monotonically decreasing; In order to ensure the transient performance of the aircraft in the process of tracking trajectory instructions, that is, to avoid excessive dynamics of tracking errors, the aircraft altitude and lateral errors are restricted to meet the following conditions: -Lτ i (t)<e i (t)<Rτ i (t),i=h,y (16) In the formula, L and R represent constants greater than zero, e h (t) and e y (t) represents the height and lateral error, which can be expressed as follows: e h (t)=h c (t)-h(t),e y (t)=y c (t)-y(t) (17) In the formula, h c (t) and y c (t) indicates height and lateral command Since it is impossible to directly constrain the tracking error through equation (17), a new tracking error z(t) is introduced, which is called the conversion error, and the conversion function is expressed as Γ(z(t)). The relationship between the errors is as follows: e i (t)=τ i (t)Γ(z i (t))i=h,y (18) The conversion error Design the virtual control quantity ν of height and lateral displacement under the requirement of Lyapunov stability h and ν y , the results are as follows: In the formula, k h and k y Indicates the proportionality coefficient, usually greater than 0; h c (t) and y c (t) Command signals indicating height and lateral displacement; The method of designing a trajectory fault-tolerant control law with preset performance by taking the track angle as the control variable comprises the following steps: In the trajectory loop, the track angle is selected as the control variable, and the height and lateral displacement control laws are designed using the analytical method. The specific design is as follows: In the formula, represents the derivative of the forward displacement.

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