Super-helix terminal sliding mode active disturbance rejection tracking control method for multi-axle steering vehicle

Abstract

The application relates to a super-helix terminal sliding mode self-anti-interference tracking control method for a multi-axle steering vehicle, which comprises the following steps: considering system strong dynamic nonlinearity, road unevenness interference and unknown internal and external disturbances, establishing a multi-axle steering vehicle system dynamics equation and a tracking control model; based on an inverse hyperbolic sine function, designing a novel disturbance observer to estimate the multi-axle steering vehicle system lumped disturbance; combining the designed novel disturbance observer, constructing a super-helix terminal sliding mode controller composed of a non-singular terminal sliding mode nominal control law and a super-helix sliding mode switching control law to suppress the system lumped disturbance and weaken system control chattering; considering vehicle steering efficiency and tire load rate, optimizing the multi-axle steering vehicle wheel angle of each axle based on a quadratic programming algorithm; the application can realize estimation and compensation of internal and external disturbances such as vehicle parameter variation, system strong dynamic nonlinearity and road unevenness interference, and can optimize the wheel angle of each axle to improve the trajectory tracking performance of the multi-axle steering vehicle.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle tracking control, in particular to a super-helix terminal sliding mode self-disturbance rejection tracking control method for a multi-axle steering vehicle. BACKGROUND

[0002] Multi-axle steering vehicles can effectively transport 100-meter wind turbine blades and long-distance transport of super-heavy bridge structures / chemical equipment due to their powerful dynamic performance and high load-carrying capacity. They are the core engineering equipment for ensuring the complete transportation of "non-disintegrable" large pieces and meeting various special operation requirements. They are developing towards electrification and intelligentization. Improving the precision of trajectory tracking and the anti-interference performance of the whole vehicle is a key link to improve the intelligence of the vehicle. However, as the number of axles of multi-axle steering vehicles increases further, the driving environment becomes more demanding, and the vehicle frame becomes longer, the traditional tracking control method cannot resist the influence of high dynamic nonlinearity of the system itself, changes in vehicle parameters, external environmental excitations such as uneven road input, strong crosswind interference, and internal and external unknown disturbances, and achieve the expected tracking performance, thereby causing the tracking control performance of the system to decline. Therefore, an innovative tracking control method is needed that can resist the influence of internal parameter changes and external unknown disturbances and achieve high-precision trajectory tracking and stable driving of multi-axle steering vehicles. Existing precise tracking and anti-interference problems in vehicle motion control, such as the reference patent CN117519130 A, proposes a trajectory tracking control method for multi-axle unmanned transport vehicles. It obtains the position and driving information of the controlled vehicle, constructs a model predictive controller, and solves the controlled vehicle's steering control command with constraints to achieve trajectory tracking control of the multi-axle unmanned transport vehicle. The reference patent CN 105467996 B proposes a four-wheel steering vehicle trajectory tracking control method based on differential flatness and self-disturbance rejection. According to the differential flatness theory, the underactuated four-wheel steering vehicle single-track control model is transformed into an input-output coupled model without a zero dynamic subsystem with disturbances. A linear active disturbance rejection controller is designed to obtain the actual steering control amount, achieving trajectory tracking of the four-wheel steering vehicle. These control methods have good anti-interference performance and good tracking performance, but still have some deficiencies and limitations, mainly manifested in:

[0003] (1) The tracking performance of the traditional tracking control method decreases under the action of multi-axle steering vehicle parameter changes and internal and external unknown disturbances. It usually relies on appropriate control parameters or accurate mathematical models, but in actual driving, especially on complex roads, the mathematical model has a lot of nonlinearity and uncertainty. At the same time, external environmental excitations such as low adhesion road, strong crosswind interference, and unknown disturbances can destroy the stability of the controller, causing the control performance of the controller to decline, and thus causing the driving trajectory of the multi-axle steering vehicle to deviate.

[0004] (2) The advantage of active disturbance rejection control is that it does not depend on the accurate mathematical model of the object and has strong robustness to external uncertainties, but the traditional active disturbance rejection control method has a large number of nonlinear functions, and the control parameters lack clear physical meaning, so that selecting larger control parameters can produce better steady-state performance, but also can lead to worse transient performance, so that the multi-axle steering vehicle is more susceptible to noise, resulting in reduced trajectory tracking accuracy, so that the configuration parameters have certain difficulty and challenge. SUMMARY

[0005] The purpose of the present application is to provide a super-spiral terminal sliding mode active disturbance rejection tracking control method for a multi-axle steering vehicle, which can estimate and compensate for internal and external disturbances such as vehicle parameter variation, system strong dynamic nonlinearity, road unevenness disturbance, and optimize the distribution of each axle wheel angle to improve the trajectory tracking performance of the multi-axle steering vehicle.

[0006] To achieve the above purpose, the present application provides the following technical solution: a super-spiral terminal sliding mode active disturbance rejection tracking control method for a multi-axle steering vehicle, comprising the following steps:

[0007] Step S1: considering the strong dynamic nonlinearity of the system, the road unevenness disturbance and the unknown internal and external disturbances, establishing the system dynamics equation and the tracking control model of the multi-axle steering vehicle;

[0008] Step S2: based on the established system dynamics equation and control model, a new type of disturbance observer is designed based on the inverse hyperbolic sine function to estimate the lumped disturbance of the multi-axle steering vehicle system;

[0009] Step S3: in combination with the designed new type of disturbance observer, a super-spiral terminal sliding mode controller composed of a non-singular terminal sliding mode nominal control law and a super-spiral sliding mode switching control law is constructed to suppress the lumped disturbance of the system and weaken the system control chattering;

[0010] Step S4: considering the vehicle steering efficiency and the tire load rate, the wheel angles of each axle of the multi-axle steering vehicle are optimized based on the quadratic programming algorithm to improve the trajectory tracking accuracy;

[0011] Step S5: the parameters of the observer and the controller are optimized to enhance the tracking control performance of the multi-axle steering vehicle and ensure the stability and convergence of the entire closed-loop system.

[0012] Further, the implementation of step S1 is as follows:

[0013] Considering the strong nonlinearity of the multi-axle steering vehicle in complex dynamic environment and the unknown internal and external disturbance, the multi-axle steering vehicle dynamics equation including system internal parameter uncertainty, external unknown disturbance, lateral motion and yaw motion is established, and its expression is as follows:

[0014]

[0015] where β is the yaw angle of the center of mass; is the yaw rate of the center of mass; ω z is the yaw angle of the center of mass; is the yaw angle of the center of mass; n represents the number of axes of the multi-axle steering vehicle; δ ij represents the wheel angle of the ith axis, i∈1~n, j∈{left, right}, when j=left, it represents the wheel angle of the left side of the ith axis; when j=right, it represents the wheel angle of the right side of the ith axis; m is the mass of the vehicle; V x is the longitudinal speed of the vehicle; L i represents the distance from the center of mass of the vehicle to the ith axis, which is positive before the center of mass and negative after the center of mass; C i is the cornering stiffness of the tire of the ith axis, assuming that the cornering stiffness of the left and right tires of the ith axis is the same, both are C i ; I z is the moment of inertia of the vehicle around the Z axis; and are unknown disturbances, which are respectively the internal parameter uncertainty disturbance of the vehicle and the external unknown disturbance.

[0016] The tracking control problem of the multi-axle steering vehicle is converted into the state tracking control problem of the multi-axle steering vehicle, and the dynamic tracking is realized by independently controlling the wheel angles of each axis of the multi-axle steering vehicle. The Laplace transform and inverse transform are performed on the above nominal system equation of the multi-axle steering vehicle to obtain a system tracking control model:

[0017]

[0018] where, is the yaw acceleration of the center of mass; is the yaw acceleration of the center of mass; is the differential of the wheel angle of the left and right wheels of the ith axis; a, b, c, d i , g i , f i , and e i are self-defined functions, which can be obtained by the following formula:

[0019]

[0020] d i =-mV x 2 C i L i ;

[0021] g i =-C i I z V x ;

[0022] Let state variable x1 = [β, ω z ] T , The system tracking control model can be reconstructed as:

[0023]

[0024] wherein,

[0025]

[0026] U = [U1, U2] T = b0u;

[0027]

[0028] In the formula, y is the output of the system; b = [b1, b2] T is the control gain vector of the system; U is the virtual control quantity of the system defined by the user; b0= [b 01 , b 02 ] T is the vector defined by the user; u is the control input of the system, u = [δ 1j , δ 2j , …, δ nj ] T ; d(t) represents unknown disturbance, including road disturbance, system unmodeled dynamics, etc. is the lumped disturbance of the system; is the lumped disturbance component.

[0029] Further, the ideal center of mass side slip angle β d = 0 required for the multi-axle steering vehicle to track the preset trajectory, and the ideal yaw rate ω zd is obtained through the pre-look reference trajectory, and the specific method is as follows:

[0030]

[0031] In the formula, ω pre is the ideal yaw rate of the vehicle obtained by pre-look; y GC is the vertical distance between the center of mass of the vehicle and the pre-look point; t p is the pre-look time, t p = 2; x GC is the pre-look distance; θ is the central angle of the current trajectory of the vehicle; u max is the maximum adhesion coefficient that the ground can provide; g is the acceleration of gravity, g = 9.8.

[0032] Further, in the step S2, the super-helix terminal sliding mode disturbance-observer-based tracking controller can estimate the internal and external lumped disturbance of the system in real time through the new disturbance observer, and compensate the disturbance through the super-helix terminal sliding mode controller, so as to ensure that the multi-axle steering vehicle accurately tracks the preset path, and the new disturbance observer is designed as follows:

[0033] The lumped disturbance f is selected as the extended vector x3 of the system, it is assumed that f is differentiable, and the differential of the lumped disturbance f is defined as:

[0034]

[0035] The extended multi-axle steering vehicle system tracking control model can be reconstructed as:

[0036]

[0037] In the formula, h is bounded, the new disturbance observer is constructed by introducing the inverse hyperbolic sine function to replace the nonlinear function of the extended state observer, so as to improve the observability of the observer, and the mathematical expression of the new disturbance observer is as follows:

[0038]

[0039] In the formula, represents the estimation error of the observer; z1, z2 and z3 are outputs of the observer, which respectively represent the estimated values of the system state x1, x2 and the lumped disturbance f; β1, β2 and β3 are gain matrices of the observer; asinh(x) is the inverse hyperbolic sine function.

[0040] Further, the implementation mode of the step S3 is:

[0041] In order to ensure that the system state tracking error converges in a finite time and avoid the non-singular problem, the non-singular terminal sliding mode surface S is constructed by selecting the multi-axle steering vehicle state tracking error, and the expression is as follows:

[0042]

[0043] In the formula, Θ is a system state tracking error matrix; θ1, e β is the tracking error of the center of mass side slip angle; θ2, is the tracking error of the yaw rate; ε1, ε2 and ψ are self-defined positive numbers; ψ, p and q are self-defined controller parameters and satisfy ψ=p / q, 1<ψ=p / q<2.

[0044] Combined with the estimation of the system state x2 and the lumped disturbance f by the new observer, the differential expression of the non-singular terminal sliding mode surface S is as follows:

[0045]

[0046] wherein x d = [β d , ω zd ] T is the system ideal state vector; let The non-singular terminal sliding mode nominal control law U eq = [U eq1 , U eq2 ] T is expressed as follows:

[0047]

[0048] When the multi-axle steering vehicle system state is located outside the non-singular terminal sliding mode surface, in order to make the system state quickly converge to the sliding mode surface in a finite time and reduce system chattering, a super-helical sliding mode switching approach law U stc = [U stc1 , U stc2 ] T is constructed as follows:

[0049]

[0050] wherein υ is a self-defined function vector; υ1 and υ2 are self-defined functions; κ i1 and κ i2 are self-defined positive numbers. Further, the super-helical sliding mode switching control law U stc = [U stc1 , U stc2 ] T is as follows:

[0051]

[0052] The super-helical terminal sliding mode comprehensive control law U is composed of the non-singular terminal sliding mode nominal control law U eq and the super-helical sliding mode switching approach law U stc , and is expressed as follows:

[0053] U = [U1, U2] T = U eq + U stc

[0054] Further, the implementation method of step S4 is as follows:

[0055] The super-helical terminal sliding mode active-disturbance-rejection tracking control method takes steering efficiency and tire load rate as performance optimization objectives, and optimizes the wheel steering angles of each axle of the multi-axle steering vehicle through a quadratic programming algorithm, so as to further improve the vehicle trajectory tracking accuracy. The objective function J1 for optimizing the steering efficiency is expressed as follows:

[0056]

[0057] where W is a self-defined matrix; I n×n is an n-order unit matrix; u T is the transpose matrix of the control input u of the system.

[0058] By assuming that the tire works in a linear region, the objective function J2 for optimizing the tire load rate can be expressed as:

[0059] min J2 = 1 / 2u T W v u + f v T u

[0060]

[0061] where W v , f v are self-defined matrices, f v T is the transpose matrix of f v ; μ is the ground adhesion coefficient; F z1 , F z2 , F zn are the vertical loads of the first axis, the second axis, and the n-th axis, respectively; V y is the lateral speed of the vehicle; and T is the track between the left and right wheels of the same axis of the vehicle.

[0062] Then, the comprehensive objective function J can be written as:

[0063]

[0064] wherein, is a weight coefficient, Q, f are self-defined matrices, f T is the transpose matrix of f. The constraint conditions satisfied when solving the quadratic programming problem are as follows:

[0065] A eq u = B eq

[0066] B eq = U

[0067] wherein, A eq , B eq represent self-defined matrices.

[0068] Further, the implementation method of step S5 is:

[0069] 1) To ensure that the observation error of the new observer converges, the observer gain β 1i , β2i , beta 3i (i = 1, 2) should satisfy the following conditions:

[0070] beta 1i beta 2i -beta 3i > 0

[0071] 2) According to Lyapunov stability theorem, in order to make the system state quickly converge to the sliding mode surface S, and at the same time, ensure that the tracking errors theta 1, theta 2 converge to zero in finite time and are in a globally stable state, the control parameters of the super-helix terminal sliding mode controller should satisfy the following conditions:

[0072]

[0073] The beneficial effects of the present application are:

[0074] 1) The present application is aimed at the problem that the tracking control performance is degraded and the driving trajectory is deviated due to the influence of strong dynamic nonlinear disturbance, road unevenness, strong lateral wind and unknown disturbance of the system in the actual driving process of the multi-axle steering vehicle. The super-helix terminal sliding mode control is combined with active disturbance rejection control, and the steering efficiency and load rate are taken as the performance optimization targets to optimize the distribution of the wheel steering angle of each axle, effectively estimate and compensate the lumped disturbance of the multi-axle steering vehicle system, reduce the influence of the internal and external disturbances of the system on the tracking accuracy, and improve the control performance and trajectory tracking accuracy.

[0075] 2) The present application is aimed at the problem that the tracking accuracy is difficult to further improve due to the difficulty in parameter tuning and the lack of clear physical meaning of a large number of control parameters when the traditional active disturbance rejection control vehicle tracks the preset trajectory. A new disturbance observer is designed based on the inverse hyperbolic sine function, and a super-helix terminal sliding mode controller is constructed to compensate the disturbance, improve the control performance and verifiability of the active disturbance rejection control, and provide a new solution for improving the tracking control accuracy of the multi-axle steering vehicle. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 is the method implementation flowchart of the embodiment of the present application;

[0077] Figure 2 is the overall architecture diagram of the super-helix terminal sliding mode active disturbance rejection control method in the embodiment of the present application;

[0078] Figure 3 is the planar dynamics model of the multi-axle steering vehicle in the embodiment of the present application;

[0079] Figure 4 is the pre-look reference trajectory schematic diagram in the embodiment of the present application;

[0080] Figure 5is a trajectory tracking effect diagram of the multi-axle steering vehicle in different vehicle speeds in the embodiment of the application. DETAILED DESCRIPTION

[0081] The application will be further described below with reference to the drawings.

[0082] Please refer to Figures 1 to 5 The application provides an embodiment: a super-spiral terminal sliding mode active disturbance tracking control method for a multi-axle steering vehicle, comprising the following steps:

[0083] Step S1: considering the strong dynamic nonlinearity of the system, the uneven road disturbance and unknown internal and external disturbances, a multi-axle steering vehicle system dynamics equation and a tracking control model are established;

[0084] Step S2: according to the established system dynamics equation and control model, a new type of disturbance observer is designed based on the inverse hyperbolic sine function, and the multi-axle steering vehicle system lumped disturbance is estimated;

[0085] Step S3: in combination with the designed new type of disturbance observer, a super-spiral terminal sliding mode controller composed of a non-singular terminal sliding mode nominal control law and a super-spiral sliding mode switching control law is constructed, so as to suppress the system lumped disturbance and weaken the system control chattering;

[0086] Step S4: considering the steering efficiency and tire load rate of the vehicle, the multi-axle steering vehicle wheel angle of each axle is optimized based on the quadratic programming algorithm, so as to improve the trajectory tracking accuracy;

[0087] Step S5: the observer and controller parameters are optimized and selected, the tracking control performance of the multi-axle steering vehicle is enhanced, and the stability and convergence of the entire closed-loop system are ensured.

[0088] As Figure 2 shown, the overall control architecture of the super-spiral terminal sliding mode active disturbance tracking control method is as follows: first, the ideal yaw rate ω zd of the vehicle is obtained through the preview preset trajectory, and the ideal mass center side slip angle β d = 0, then the multi-axle steering system state x1, x2 and the lumped disturbance f are estimated through the new type of disturbance observer, and the super-spiral terminal sliding mode comprehensive control law U is designed to realize the compensation of the lumped disturbance, finally, the steering efficiency and tire load rate comprehensive objective function J is optimized under the equality constraint based on the quadratic programming algorithm, and the wheel angle δ ij of each axle is obtained, so as to realize the high-precision trajectory tracking control of the multi-axle steering vehicle.

[0089] Figure 3 is a schematic diagram of a multi-axle steering vehicle planar dynamics model in the embodiment, a lateral dynamics model including lateral motion and yaw motion of the multi-axle steering vehicle system is established.

[0090] Figure 4 This is a schematic diagram of the pre-aiming reference trajectory in this embodiment. The longitudinal distance from the current position of the multi-axle steering vehicle after the pre-aiming is x. GC The horizontal distance is y GC The point is calculated at the set pre-aiming time t. p The central angle θ of the trajectory taken by the vehicle to reach the pre-aiming point is used to obtain the vehicle's ideal yaw rate ω. pre .

[0091] In this embodiment, a three-axis steering test vehicle built in the laboratory is used as an example, and its overall vehicle parameters are as follows:

[0092]

[0093] The following section will elaborate on the relevant aspects of this method.

[0094] Please continue reading. Figures 1 to 5 As shown, in one embodiment of the present invention, step S1 is implemented as follows:

[0095] Considering the strong nonlinearity and unknown internal and external disturbances of a multi-axle steering vehicle driving in a complex dynamic environment, a 2-DOF lateral dynamic model is established, incorporating uncertainties in internal system parameters, unknown external disturbances, lateral motion, and yaw motion, to reduce modeling complexity. The expressions describing its lateral and yaw motion are as follows:

[0096]

[0097] F yil =C i α il

[0098] F yir =C i α ir

[0099]

[0100]

[0101] In the formula, F Y M is the resultant force of the vehicle along the Y-axis; z I is the yaw moment of the vehicle about the Z-axis. z Let F be the moment of inertia of the vehicle about the Z-axis; n represents the number of axles in a multi-axle steering vehicle; F yil F is the lateral force on the left wheel of the i-th axis; yir δ represents the lateral force on the right wheel of the i-th axis; il δ ir These are the left and right wheel angles of the i-th axis, respectively; L idenotes the distance from the vehicle center of mass to the ith axle, positive before the center of mass and negative after the center of mass; V y is the vehicle lateral velocity; is the vehicle lateral acceleration; V x is the vehicle longitudinal velocity; ω z is the yaw rate; is the yaw angular acceleration; m is the total vehicle mass; C i is the tire cornering stiffness of the ith axle, assuming the left and right tires of the ith axle have the same cornering stiffness, both of which are C i ; α il , α ir are the left and right wheel cornering angles of the ith axle, respectively; and are unknown disturbances, which are the internal parameter uncertainty disturbance and the external unknown disturbance of the vehicle, respectively.

[0102] Further, by assuming that the tire cornering angle changes little and works in the linear region, the lateral dynamics equation can be reconstructed as:

[0103]

[0104] In the formula, δ ij is the wheel cornering angle of the ith axle, i∈1~n, j∈{left, right}, when j=left, it represents the left wheel cornering angle of the ith axle; when j=right, it represents the right wheel cornering angle of the ith axle; β is the center of mass cornering angle; is the center of mass cornering angle rate.

[0105] The tracking control problem of the multi-axle steering vehicle is converted into the state tracking control problem of the multi-axle steering vehicle, and the dynamic tracking is realized by independently controlling the wheel cornering angles of the multi-axle steering vehicle. The system tracking control model is obtained by Laplace transform and inverse transform on the above nominal system equation of the multi-axle steering vehicle:

[0106]

[0107] In the formula, is the center of mass cornering angle acceleration; is the yaw angular acceleration; is the differential of the left and right wheel cornering angles of the ith axle; a, b, c, d i , g i , f i , and e i are self-defined functions, which can be obtained from the following formula:

[0108]

[0109] d i =-mV x2 C i L i ;

[0110] g i =-C i I z V x ;

[0111] Let state variable x1 = [β, ω z ] T , The system tracking control model can be reconstructed as:

[0112]

[0113] wherein,

[0114]

[0115] U = [U1, U2] T = b0u;

[0116]

[0117] In the formula, y is the output of the system; b = [b1, b2] T is the control gain vector of the system; U is the self-defined virtual control quantity of the system; b0 = [b 01 , b 02 ] T is the self-defined vector; u is the control input of the system, u = [δ 1j , δ 2j , …, δ nj ] T ; d(t) represents unknown disturbance, including road disturbance, system unmodeled dynamics, etc.; is the lumped disturbance of the system; is the lumped disturbance component.

[0118] Further, the ideal center of mass side slip angle β d = 0 required for the multi-axle steering vehicle to track the preset trajectory, and the ideal yaw rate ω zd is obtained through the preview reference trajectory, and the specific method is:

[0119]

[0120] In the formula, ω pre is the ideal yaw rate of the vehicle obtained by preview; y GC is the vertical distance between the center of mass of the vehicle and the preview point; t p is the preview time, tp = 2; x GC is the preview distance; θ is the central angle of the current trajectory of the vehicle; u max is the maximum adhesion coefficient provided by the ground; g is the acceleration of gravity, g = 9.8.

[0121] Please continue to refer to Figure 5 As shown in the figure, in an embodiment of the application, in the step S2, the super-helical terminal sliding mode disturbance rejection tracking controller replaces the extended state observer in the traditional active disturbance rejection controller by introducing the inverse hyperbolic sine function to construct a new disturbance observer to estimate the internal and external lumped disturbances in the system in real time, and compensates the disturbances through the super-helical terminal sliding mode controller to ensure that the multi-axle steering vehicle accurately tracks the preset path. The new disturbance observer is designed as follows:

[0122] The lumped disturbance f is selected as the extended vector x3 of the system, it is assumed that f is differentiable, and the differential of the lumped disturbance f is defined as:

[0123]

[0124] The extended multi-axle steering vehicle system tracking control model can be reconstructed as:

[0125]

[0126] In the formula, h is bounded, the nonlinear function of the extended state observer is replaced by introducing the inverse hyperbolic sine function to construct a new disturbance observer to improve the observable verifiability of the observer. The mathematical expression of the new disturbance observer is as follows:

[0127]

[0128] In the formula, represents the estimation error of the observer; z1, z2 and z3 are the outputs of the observer, which respectively represent the estimated values of the system states x1, x2 and the lumped disturbance f; β1, β2 and β3 are the gain matrices of the observer; asinh(x) is the inverse hyperbolic sine function.

[0129] Please continue to refer to Figures 1 to 5 As shown in the figure, in an embodiment of the application, the implementation mode of the step S3 is as follows:

[0130] In order to ensure that the system state tracking error converges in a finite time and avoid the non-singular problem, the multi-axle steering vehicle state tracking error is selected to construct a non-singular terminal sliding mode surface S, and the expression is as follows:

[0131]

[0132] In the formula, Θ is the system state tracking error matrix; θ1, e β is the tracking error of the center of mass side slip angle; θ2, is the yaw angle velocity tracking error; ε1, ε2, ψ are positive numbers defined by self; ψ, p, q are controller parameters defined by self and satisfy ψ = p / q, 1 < ψ = p / q < 2.

[0133] Combined with the estimation of system state x2 and lumped disturbance f by the new observer, the differential expression of the non-singular terminal sliding mode surface S is as follows:

[0134]

[0135] In the formula, x d = [β d , ω zd ] T is the ideal state vector of the system; let The expression of the non-singular terminal sliding mode nominal control law U eq = [U eq1 , U eq2 ] T is as follows:

[0136]

[0137] When the multi-axle steering vehicle system state is located outside the non-singular terminal sliding mode surface, in order to ensure that the system state converges to the sliding mode surface quickly in a limited time and reduce system chattering, the super-helical sliding mode switching approach law U stc = [U stc1 , U stc2 ] T is constructed as follows:

[0138]

[0139] In the formula, υ is a function vector defined by self; υ1, υ2 are functions defined by self; κ i1 , κ i2 are positive numbers defined by self. Further, the super-helical sliding mode switching control law U stc = [U stc1 , U stc2 ] T is as follows:

[0140]

[0141] The super-helical terminal sliding mode comprehensive control law U is composed of the non-singular terminal sliding mode nominal control law U eq and the super-helical sliding mode switching approach law U stc , and is expressed as follows:

[0142] U = [U1, U2] T = U eq + U stc

[0143] Please continue to see Figures 1 to 5 As shown in the embodiment of the application, the implementation method of step S4 is:

[0144] The super-spiral terminal sliding mode active disturbance rejection tracking control method takes steering efficiency and tire load rate as performance optimization targets, and allocates optimized wheel steering angles of each axle of the multi-axle steering vehicle through a quadratic programming algorithm, so as to further improve vehicle trajectory tracking accuracy. The objective function J1 for optimizing steering efficiency is represented as:

[0145]

[0146] In the formula, W is a self-defined matrix; I n×n is an n-order unit matrix; u T is a transpose matrix of the control input u of the system.

[0147] By assuming that the tire works in a linear region, the objective function J2 for optimizing the tire load rate can be represented as:

[0148] minJ2=1 / 2u T W v u+f v T u

[0149]

[0150] In the formula, W v , f v are self-defined matrices, f v T is a transpose matrix of f v ; μ is a ground adhesion coefficient; F z1 , F z2 , F zn are vertical loads of the first axle, the second axle and the n-th axle respectively; V y is a vehicle lateral speed; is a wheel track between left and right wheels of the same axle of the vehicle.

[0151] Then, the comprehensive objective function J can be written as:

[0152]

[0153] In the formula, is a weight coefficient, Q, f are self-defined matrices, f T is a transpose matrix of f. The constraint conditions satisfied when solving the quadratic programming problem are as follows:

[0154] A eq u=B eq

[0155]

[0156] In the formula, A eq , B eq Indicate the custom matrix.

[0157] Please continue to refer to Figures 1 to 5 In an embodiment of the present application, the implementation method of step S5 is as shown in the figure:

[0158] To enhance the tracking control performance of the multi-axle steering vehicle, ensure the stability and convergence of the entire closed-loop system, and optimize the selection of the parameters of the new disturbance observer and the super-helix terminal sliding mode controller, the selection criteria are as follows:

[0159] 1) Let the observation errors of the observer be e1=z1-x1, e2=z2-x2, and e3=z3-f, and assume that is a constant value, then the error equation of the designed new disturbance observer can be written as:

[0160]

[0161] In the formula, σ0 is the initial value of σ, and to ensure the stability of the observer, only the appropriate parameters are selected to make the error equation of the observer asymptotically stable at the equilibrium point, and the error equation can be rewritten as:

[0162]

[0163] In the formula, γ is a self-defined function, γ=asinh(e1)e1; β2γ>0, and β3γ>0.

[0164] A matrix R with all positive diagonal elements is constructed, and the conditions for its establishment are as follows:

[0165] β 1i β 2i -β 3i >0(i=1, 2)

[0166] The matrix R can be written as:

[0167]

[0168] In the formula, ν is a self-defined function, ν=1(β 1i β 2i γ-β 3i γ); ρ, ρ1, and ρ2 are infinitesimal positive numbers. It can be obtained that RQ(e) is a symmetric positive definite matrix. Further, the stability of the observer is proved by constructing a Lyapunov function V, and the expression of V is as follows:

[0169]

[0170] where t is the simulation time; z is a sufficiently large positive number. By substituting R, Q(e), and the expression of e, the Lyapunov function V can be rewritten as:

[0171]

[0172] The differential expression of the Lyapunov function V is as follows:

[0173]

[0174] It can be seen that the observation error of the new disturbance observer converges gradually, and therefore the parameter selection principle of the observer is:

[0175] β 1i β 2i -β 3i >0

[0176] 2) The quadratic positive definite Lyapunov function V1 is selected to prove the stability of the super-helix terminal sliding mode controller, and the expression of V1 is as follows:

[0177]

[0178] V1 is rewritten as follows:

[0179]

[0180]

[0181] where Ξ i＝1,2 is a self-defined matrix, and ζ i＝1,2 is a self-defined vector. The differential expression of the Lyapunov function V1 is as follows:

[0182]

[0183] where is a self-defined matrix. It can be seen that, to ensure that the designed super-helix terminal sliding mode controller is stable, it is only required to ensure that that is, the controller parameters are selected to satisfy the following conditions:

[0184]

[0185] In summary, to ensure the stability and convergence of the entire closed-loop system, the parameter selection criteria of the super-helix terminal sliding mode active-disturbance-rejection tracking control method are as follows:

[0186]

[0187] In summary, the application provides a super-helix terminal sliding mode active disturbance rejection tracking control method for a multi-axle steering vehicle, which can estimate and compensate internal and external disturbances such as vehicle parameter variation, strong dynamic nonlinearity of the system, road unevenness disturbance, optimally distribute wheel steering angles of each axle, and improve trajectory tracking performance of the multi-axle steering vehicle, effectively solving the problems of tracking control performance decline, driving trajectory deviation, and difficult parameter adjustment of the traditional active disturbance rejection control, and difficult further improvement of tracking accuracy caused by unknown internal and external disturbances in the actual driving process of the multi-axle steering vehicle.

[0188] Figure 5 Fig. 4 is a trajectory tracking effect diagram of the multi-axle steering vehicle in different vehicle speeds in the embodiment.

[0189] According to the super-helix terminal sliding mode active disturbance rejection tracking control method, the three-axle steering experimental vehicle can accurately track the preset trajectory under different vehicle speed conditions, as shown in Fig. 4. Figure 5

[0190] The above description is only the preferred embodiment of the application, and should not be understood as a limitation on the application. Any equivalent changes and modifications made within the scope of the application should be included in the scope of the application.​

Claims

1. A superspiral terminal sliding mode active disturbance rejection tracking control method for multi-axle steering vehicles, characterized in that, Includes the following steps: Step S1: Considering the strong dynamic nonlinearity of the system, the disturbance of uneven road surface and unknown internal and external disturbances, establish the dynamic equations and tracking control model of the multi-axle steering vehicle system; Step S2: Based on the established system dynamics equations and control model, design a novel disturbance observer based on the inverse hyperbolic sine function to estimate the lumped disturbance of the multi-axle steering vehicle system; Step S3: Combining the designed novel disturbance observer, construct a superspiral terminal sliding mode controller consisting of a non-singular terminal sliding mode nominal control law and a superspiral sliding mode switching control law to suppress system lumped disturbances and reduce system control chattering; Step S4: Considering vehicle steering efficiency and tire load rate, optimize the allocation of wheel angles for each axle of the multi-axle steering vehicle based on the quadratic programming algorithm to improve trajectory tracking accuracy; Step S5: Optimize the selection of observer and controller parameters to enhance the tracking control performance of multi-axle steering vehicles and ensure the stability and convergence of the entire closed-loop system; The implementation method of step S1 is as follows: Considering the strong nonlinearity and unknown internal and external disturbances of a multi-axle steering vehicle driving in a complex dynamic environment, the dynamic equations of the multi-axle steering vehicle are established, including uncertainties in internal system parameters, unknown external disturbances, lateral motion, and yaw motion. The expression is as follows: ； In the formula, It is the centroid sideslip angle; The velocity of the centroid's sideslip. This refers to the yaw rate; This is the yaw acceleration; Indicates the number of axles in a multi-axle steering vehicle; Indicates the first Axle wheel rotation angle, , ,when At that time, it represents the first The left wheel of the axle turns; when At that time, it represents the first Right wheel angle on the axle; m For the overall vehicle weight; The longitudinal speed of the vehicle; Indicates the vehicle's center of gravity to the 1st The distance between axes is set to positive when it is before the center of mass and negative when it is after the center of mass; For the first Lateral stiffness of the axle tire, assuming the first The lateral stiffness of the tires on both sides of the axle is the same. ; For vehicles to bypass Moment of inertia of the shaft; and These are unknown disturbances, namely, uncertainties in the vehicle's internal parameters and unknown external disturbances; The tracking control problem of a multi-axle steering vehicle is transformed into a state tracking control problem. Dynamic tracking is achieved by independently controlling the wheel angles of each axle of the multi-axle steering vehicle. The nominal system equations of the multi-axle steering vehicle are subjected to Laplace transform and inverse transform to obtain the system tracking control model. ； In the formula, This is the sideslip acceleration of the center of mass; The yaw rate is the acceleration rate. No. The differentials of the rotation angles of the left and right wheels on the axle; and For user-defined functions, the following formula can be used: ； Let the state variable The system tracking control model can be reconstructed as follows: ； in, ； ； ； In the formula, It is the system output; It is the system's control gain vector; It is a custom system virtual control variable; For custom vectors; For the system's control input, ; This represents unknown disturbances, including road interference and unmodeled system dynamics; For the lumped disturbance of the system; For lumped disturbance components; To further explain, the ideal centroid sideslip angle required for a multi-axle steering vehicle to track a preset trajectory Ideal yaw rate It is obtained through pre-aiming reference trajectory, and the specific method is as follows: ； In the formula, To obtain the ideal yaw rate of the vehicle for pre-aiming; It is the vertical distance between the vehicle's center of gravity and the aiming point; For the aiming time, ; Pre-aiming distance; Let be the central angle of the vehicle's current trajectory; The maximum coefficient of adhesion that the ground can provide; It is the acceleration due to gravity. .

2. The superspiral terminal sliding mode active disturbance rejection tracking control method for multi-axle steering vehicles according to claim 1, characterized in that, In step S2, the superspiral terminal sliding mode active disturbance rejection tracking controller can estimate the lumped disturbances inside and outside the system in real time through a novel disturbance observer, and compensate for the disturbances through the superspiral terminal sliding mode controller to ensure that the multi-axis steering vehicle accurately tracks the preset path. The novel disturbance observer is designed as follows: Selecting lumped disturbance System extension vector Assuming Differentiability, defined as lumped perturbation The differential is: ； The expanded multi-axle steering vehicle system tracking control model can then be reconstructed as follows: ； In the formula, Since it is bounded, a novel perturbation observer is constructed by introducing an inverse hyperbolic sine function to replace the nonlinear function of the extended state observer, thereby improving the observability verifiability of the observer. The mathematical expression of the novel perturbation observer is as follows: ； ； In the formula, This represents the estimation error matrix of the observer; and The outputs of the observer represent the system states, respectively. and aggregate disturbance The estimate; and The gain matrix of the observer; It is an inverse hyperbolic sine function.

3. The superspiral terminal sliding mode active disturbance rejection tracking control method for multi-axle steering vehicles according to claim 1, characterized in that, Step S3 is implemented as follows: To ensure that the system state tracking error converges within a finite time and to avoid nonsingular problems, a nonsingular terminal sliding surface is constructed using the state tracking error of a multi-axis steering vehicle. Its expression is as follows: ； ； ； ； In the formula, This is the system state tracking error matrix; This refers to the tracking error of the centroid sideslip angle. This refers to the yaw rate tracking error. A user-defined positive number; Custom controller parameters and satisfying , ; Combining novel observers to assess system state and aggregated disturbance The estimate of the non-singular terminal sliding surface The differential expression is as follows: ； In the formula, Let be the ideal state vector of the system; let Non-singular terminal sliding mode nominal control law The expression is as follows: ； When the system state of a multi-axle steering vehicle is outside the non-singular terminal sliding surface, in order to ensure that the system state converges to the sliding surface quickly within a finite time and reduce system chattering, a super-spiral sliding mode switching reaching law is constructed. as follows: ； ； In the formula, It is a user-defined function vector; This is a user-defined function; , It is a user-defined positive number; further, the super-spiral sliding mode switching control law can be obtained. as follows: ； The superspiral terminal sliding mode integrated control law nominal control law of non-singular terminal sliding mode And the approach law of superspiral sliding mode switching Composition, represented as follows: 。 4. The superspiral terminal sliding mode active disturbance rejection tracking control method for multi-axle steering vehicles according to claim 1, characterized in that, The implementation method for step S4 is as follows: The superspiral terminal sliding mode active disturbance rejection tracking control method optimizes steering efficiency and tire load rate as performance targets. It uses a quadratic programming algorithm to allocate and optimize the wheel angles of each axle in a multi-axle steering vehicle, further improving vehicle trajectory tracking accuracy. The objective function for optimizing steering efficiency is... Represented as: ； In the formula, It is a custom matrix; yes n An identity matrix of order 1; It is the system's control input The transpose of the matrix; By assuming the tire operates in a linear region, the objective function for optimizing the tire load rate is determined. It can be represented as: ； In the formula, , For a custom matrix, for The transpose of the matrix; The ground adhesion coefficient; They are respectively the first axis, the second axis, and the third axis. n Vertical load on the shaft; The vehicle's lateral speed; The wheelbase between the left and right wheels on the same axle of a vehicle; Then the comprehensive objective function It can be written as: ； In the formula, , These are the weighting coefficients. ; , For a custom matrix, for The transpose of the given matrix; the constraints to be satisfied when solving the quadratic programming problem are as follows: ； ； In the formula, , This represents a custom matrix.

5. The superspiral terminal sliding mode active disturbance rejection tracking control method for multi-axle steering vehicles according to claim 1, characterized in that, The implementation method for step S5 is as follows: 1) To ensure the convergence of observation errors of the new observer, the observer gain... , , ,in The following conditions must be met: ； 2) According to Lyapunov's stability theorem, in order to make the system state converge quickly to the sliding surface... At the same time, ensure tracking error , For a superspiral terminal sliding mode controller to converge to zero and reach a globally stable state within a finite time, the control parameters should be selected to meet the following conditions: 。

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