Steer-by-wire vehicle stability control method under actuator fault and input hysteresis, terminal and medium

Abstract

The invention relates to the technical field of vehicle stability control and fault-tolerant control, and discloses a steer-by-wire vehicle stability control method under actuator faults and input hysteresis, a terminal and a medium. The method comprises the following steps: establishing a kinetic model of a steer-by-wire vehicle, and constructing a front wheel subsystem kinetic model in a steer-by-wire system by comprehensively considering an actuator fault, input hysteresis and a state constraint condition; according to the steering angle instruction of the driver and the ideal vehicle model, the expected yaw velocity and the expected sideslip angle of the vehicle are obtained through calculation; designing an upper-layer stability controller of the front wheel subsystem; generating a desired front wheel steering angle for the front wheel subsystem; and a lower-layer steering angle tracking controller of the front wheel steering system is designed, the front wheel steering angle tracking performance of the steer-by-wire system under the working conditions of actuator faults and input hysteresis is ensured, and the actual front wheel steering angle of the vehicle approaches the expected front wheel steering angle. According to the invention, the steer-by-wire system can still maintain the stability of the vehicle under the conditions of actuator fault and input hysteresis.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle stability control and fault-tolerant control, and particularly to a stability control method for a steer-by-wire vehicle under actuator faults and input hysteresis, as well as a computer terminal and a computer-readable storage medium applying this method. Background Art

[0002] As a promising automotive technology, steer-by-wire technology has received extensive attention from the academic and industrial communities in recent years. As an important branch of automotive by-wire technology, the steer-by-wire system cancels the mechanical connection between the traditional steering column and the steering gear, and instead uses a feedback motor and a steering motor to achieve steering control, providing precise road feel feedback for the driver and ensuring that the front wheel angle can closely follow the reference angle. This by-wire structure not only improves the vehicle's handling stability and driving comfort, but also provides greater flexibility for vehicle design. However, the complex electronic structure of the steer-by-wire system also makes it more sensitive to electronic component faults such as actuator faults and input hysteresis.

[0003] For a vehicle equipped with a steer-by-wire system, vehicle stability is related to driving comfort and safety. If actuator faults and input hysteresis are not considered in vehicle stability control, it may ultimately cause irreparable losses to the system. However, in the prior art, there is no research on the vehicle stability control method for the steer-by-wire system under actuator faults and input hysteresis, making it difficult to ensure the stability and driving safety of the vehicle under complex working conditions. Summary of the Invention

[0004] To solve the technical problems existing in the prior art, the present invention provides a stability control method, a terminal and a medium for a steer-by-wire vehicle under actuator faults and input hysteresis, enabling the steer-by-wire system to maintain vehicle stability under actuator faults and input hysteresis.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention discloses a stability control method for a steer-by-wire vehicle under actuator faults and input hysteresis, including the following steps, namely S1 to S5.

[0007] S1. Establish a dynamic model of the steer-by-wire vehicle, and comprehensively consider actuator faults, input hysteresis and state constraint conditions to construct a dynamic model of the front wheel subsystem in the steer-by-wire system;

[0008] S2. Calculate the desired yaw rate and the desired sideslip angle of the vehicle according to the driver's steering angle command and the ideal vehicle model;

[0009] S3. Define an error signal based on the desired yaw rate and the desired sideslip angle, and thus design a fixed-time hierarchical integral sliding mode controller based on fixed-time stability theory and integral sliding mode theory as the upper-layer stability controller of the front-wheel subsystem to ensure the lateral stability of the vehicle under lateral wind speed and vehicle parameter perturbations;

[0010] S4. Combine the driver's steering angle command and the front-wheel steering angle correction value output by the upper-layer stability controller to generate the desired front-wheel steering angle of the front-wheel subsystem;

[0011] S5. Design an adaptive fuzzy fixed-time controller based on fixed-time stability theory and barrier Lyapunov theory as the lower-layer angle tracking controller of the front-wheel steering system to ensure the front-wheel angle tracking performance of the steer-by-wire system under actuator failure and input hysteresis conditions, and make the actual front-wheel steering angle of the vehicle approach the desired front-wheel steering angle.

[0012] As a further improvement of the above solution, in step S1, the dynamic model of the steer-by-wire vehicle is expressed as follows:

[0013]

[0014] In the formula, β represents the vehicle sideslip angle, γ represents the vehicle yaw rate, and are the first-order derivatives of β and γ respectively; C f represents the front tire steering stiffness; C r represents the rear tire steering stiffness; m represents the mass of the vehicle; V x represents the vehicle longitudinal speed; l r represents the distance from the rear wheel axis to the center of gravity; l f represents the distance from the front wheel axis to the center of gravity; θ fd represents the front-wheel steering angle to be designed; I z represents the moment of inertia about the center of gravity; F2 and w represent the lumped perturbations;

[0015] The construction method of the front-wheel subsystem dynamic model includes the following specific steps:

[0016] S121. Initial front-wheel subsystem dynamic model, expressed as follows:

[0017]

[0018] In the formula, J e represents the equivalent moment of inertia, θ f represents the actual front-wheel steering angle, and are the first-order derivative and second-order derivative of θ f respectively, B e represents the equivalent damping coefficient, τe Denotes the tire self-aligning torque, τ f Denotes the front wheel friction, k s Denotes the transmission ratio constant, τ m (t) denotes the output torque of the steering motor; t is the time variable;

[0019] S122. Model the input hysteresis as follows:

[0020]

[0021] Where, τ c Denotes the input control torque to be designed, is the first derivative of τ c ; Denotes the output torque of the steering motor in a healthy state; k h and B r are unknown positive real numbers; B l is an unknown negative real number, ξ(τ c ) is a bounded unknown function;

[0022] S123. Model the actuator fault as follows:

[0023]

[0024] Where, ρ f Denotes the actuator effectiveness factor, Denotes the actuator bias fault;

[0025] S124. According to the modeling results of steps S121, S122 and S123, obtain the dynamic model of the front wheel subsystem considering actuator faults and input hysteresis as follows:

[0026]

[0027] Where, x1 = θ f and Denote the system states; f e (x1,x2) = τ e +τ f is the non - linear term containing the self - aligning torque and the front wheel friction; Is the system output; the state constraint conditions are: |x1| < k c1 , |x2| < k c2 , where, k c1 and k c2 are constants strictly greater than zero, representing the constraint boundaries of the state variables x1 and x2 respectively.

[0028] As a further improvement of the above solution, in step S2, the calculation formula for the desired yaw rate of the vehicle is:

[0029]

[0030] In the formula, γ d represents the desired yaw rate of the vehicle; μ represents the road-tire friction coefficient; g is the acceleration due to gravity; γ t is the middle term, sign(·) is the sign function;

[0031] The calculation formula for the desired sideslip angle of the vehicle is:

[0032]

[0033] In the formula, β d is the desired sideslip angle of the vehicle; β max = arctan(0.02μg); arctan(·) is the arctangent function; β t is the middle term, K is a parameter representing insufficient vehicle steering coefficient, K = m(l r C r - l f C r )(2C f C r (l r + l r ) 2 ); θ cmd is the driver's steering angle command.

[0034] As a further improvement of the above solution, in step S3, step S3 includes the following specific steps:

[0035] S31. Convert the dynamic model of the steer-by-wire vehicle in step S1 into the following form:

[0036]

[0037] In the formula, δ cmd is the driver's output steering angle; Δδ f is the correction steering angle;

[0038] M is the vehicle mass; F2 is the parameter uncertainty disturbance; w is the external disturbance;

[0039] S32. Define the sideslip angle error signal e1 and the yaw rate error signal e2, which are expressed as follows:

[0040] e1 = β - β d

[0041] e2 = γ - γ d

[0042] Establish the following error dynamics equations:

[0043]

[0044] where and are the first-order derivatives of e1 and e2 respectively;

[0045] S33. Define two first-order sliding surfaces s1 and s2, expressed as follows:

[0046]

[0047] where κ s1 , l 11 , p1, q1, l 11 , l 12 , κ s2 , p2, q2, l 21 and l 22 are all constants greater than zero;

[0048] S34. Design a second-order sliding surface S, expressed as follows:

[0049]

[0050] where and are all design parameters greater than zero;

[0051] S35. Design a fixed-time integral hierarchical sliding mode control law u:

[0052]

[0053] where u eq1 , u eq2 , u sw are the equivalent control term 1, equivalent control term 2, and sliding mode switching term respectively; κ1, κ2, κ3, κ4, p3, and q3 are all design parameters greater than zero;

[0054] S36. Stability proof:

[0055] Select the Lyapunov function: V s1 = S 2 , and take the derivative of V s1 to obtain the following result:

[0056]

[0057] In the formula, V s1 , the first-order derivative of S, s1, s2; d l is the intermediate term, is d l The upper bound of And meet ; When selecting parameters When , the sliding mode variable S is stable at the origin for a fixed time;

[0058] It is proved that under the fixed-time hierarchical integral sliding mode control law u, the first-level sliding surface s 11 and s2 are stable at the origin for a fixed time. The proof process is as follows: First, design two sliding surfaces S m1 and S m2 , the expression is as follows:

[0059] S m1 =m1s1+bs2

[0060] S m2 =m2s1+bs2

[0061] Where m1, m2 and b are arbitrary constants, and satisfy m1>m2>0, b>0;

[0062] If S m1 and S m2 Respectively in T 11 and T 12 It converges to the origin in time, and we get:

[0063] |S m1 -S m2 |=|(m1-m2)s1|

[0064] Then s1 will be at a fixed time T1 = max{T 11 ,T 12} converges to the origin within a fixed time. Similarly, s2 stabilizes within a fixed time, so that the sideslip angle error signal e1 and the yaw angular velocity error signal e2 will converge to zero within a fixed time, that is, the lateral stability control of the vehicle is ensured.

[0065] As a further improvement of the above solution, in step S4, the expression formula of the expected front wheel steering angle of the front wheel subsystem is:

[0066] θ fd =θ cmd +Δθ f

[0067] In the formula, θ fd is the desired front wheel steering angle of the front wheel subsystem; θ cmdis the driver's steering angle command; Δθ f is the front wheel steering angle correction value output by the upper layer stability controller, and Δθ f is designed as the sliding mode control law in step S35, denoted as Δθ f = u.

[0068] As a further improvement of the above solution, step S5 includes the following specific steps:

[0069] S51. For the front wheel subsystem dynamics model constructed in step S124, define the error signal as follows:

[0070]

[0071] where z1 and z2 are the front wheel steering angle tracking error and the virtual second-order error respectively; y d = θ fd is the desired front wheel steering angle; α1 is the virtual control law;

[0072] S52. Define the barrier Lyapunov function V1, which is expressed as follows:

[0073]

[0074] where k b1 is a constant greater than zero;

[0075] Take the derivative of V1 to get:

[0076]

[0077] where are the first-order derivatives of V1, z1, and y d respectively;

[0078] Design the virtual control law α1 as:

[0079]

[0080] where λ 11 and λ 12 are designed constants greater than zero;

[0081] Substitute the designed virtual control law α1 into to get:

[0082]

[0083] S53. Define the barrier Lyapunov function V2, which is expressed as follows:

[0084]

[0085] where k b2And r is a constant greater than zero; denotes the estimation error, denotes the estimated value of θ, where θ is the two-norm of the fuzzy basis vector; r is a constant greater than zero;

[0086] Taking the derivative of V2 gives:

[0087]

[0088] where, is the first derivative of; is the first derivative of α1;

[0089] encapsulates an unknown function is expressed as follows:

[0090]

[0091] where,

[0092] Using the fuzzy logic system to approximate with any precision ε is expressed as follows:

[0093]

[0094] where, ε ＇ (Z) is the approximation error; ε is a bounded constant greater than zero; ε ＇ (Z) is the approximation error; W is the fuzzy weight; the superscript T is the transpose symbol; is the Gaussian function basis vector, and each basis vector component is expressed as:

[0095]

[0096] where, v i =[v i1 (Z),…,v iq (Z)] represents the center of the Gaussian function; η i represents the width of the Gaussian function; exp[·] is the natural exponential function;

[0097] S54. Design the input control torque τ according to the adaptive fuzzy fixed-time controller c as:

[0098]

[0099] where, is the intermediate term; ∈, λ 21 and λ 22 are all constants greater than zero; is the parameter The lower bound, i.e.,

[0100] In the adaptive fuzzy fixed-time control law, The adaptive law Is designed as:

[0101]

[0102] Wherein, r, And Are all constants strictly greater than zero;

[0103] S55. Stability proof: According to the complete square theorem and Young's inequality, the following inequalities are obtained:

[0104]

[0105] Wherein, θ = ‖W‖ 2 ;

[0106] Substitute the above three inequalities into To get:

[0107]

[0108] Wherein, η2 is a constant greater than zero; b is a constant greater than zero;

[0109] Since To get:

[0110]

[0111] Then the system is stable in a fixed time, that is, the front wheel steering angle tracking error z1 will converge to a neighborhood of zero within a fixed time, so that the actual front wheel steering angle of the vehicle approaches the desired front wheel steering angle.

[0112] The present invention also discloses a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the stability control method for a steer-by-wire vehicle under actuator faults and input hysteresis as described above are implemented.

[0113] The present invention also discloses a computer-readable storage medium, on which a computer program is stored. The program is characterized in that when it is executed by a processor, the steps of the stability control method for a steer-by-wire vehicle under actuator faults and input hysteresis as described above are implemented.

[0114] Compared with the prior art, the beneficial effects of the present invention are:

[0115] 1. The present invention provides a vehicle stability control method for a steer-by-wire system with actuator faults and input hysteresis, which solves the vehicle stability problem of the steer-by-wire system under actuator faults and input hysteresis. By introducing the fixed-time theory and the hierarchical sliding mode theory to improve the integral sliding mode control method, a fixed-time integral hierarchical sliding mode controller is designed, which can effectively control the upper-layer stability of the vehicle. The vehicle dynamics model is modeled as an underactuated system, and the proposed controller can ensure the stability of the system. The application of the fixed-time theory makes the controller have better robustness.

[0116] 2. The present invention designs an adaptive fuzzy fixed-time controller by combining the fixed-time theory and the barrier Lyapunov method, which ensures the accurate front-wheel angle tracking of the steer-by-wire system under actuator faults and input hysteresis. The fuzzy logic system is used to approximate the unknown continuous function, and the adaptive law can adjust the weight two-norm online. By introducing the adaptive method and the fuzzy logic system, the controller does not require the system parameters to be known. At the same time, the barrier Lyapunov method ensures that the state of the steer-by-wire system will not exceed the constraint conditions.

[0117] 3. The present invention realizes the stability control of the steer-by-wire vehicle under complex working conditions by introducing the vehicle hierarchical control architecture. The upper-layer stability controller is used to generate the front-wheel angle correction value, and the lower-layer angle tracking controller is used to ensure the accurate front-wheel angle tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 It is a flowchart of the vehicle stability control method for the steer-by-wire vehicle with actuator faults and input hysteresis in Embodiment 1 of the present invention.

[0119] Figure 2 It is a schematic diagram of the hierarchical control method in Embodiment 1 of the present invention.

[0120] Figure 3 It is the driver's angle command signal curve in Embodiment 1 of the present invention.

[0121] Figure 4 It is the vehicle stability control tracking curve in Embodiment 1 of the present invention. Among them, Figure 4 The left side is the yaw rate tracking curve, Figure 4 The right side is the sideslip angle tracking curve.

[0122] Figure 5 It is the front-wheel angle tracking curve of the steer-by-wire system in Embodiment 1 of the present invention.

[0123] Figure 6 It is the front-wheel angle tracking error curve of the steer-by-wire system in Embodiment 1 of the present invention.

[0124] Figure 7 This is a schematic structural diagram of the computer terminal in Embodiment 2 of the present invention. Detailed implementation manners

[0125] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0126] Embodiment 1

[0127] Please refer to Figure 1 and Figure 2 , this embodiment provides a stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis, including the following steps, namely S1 to S5.

[0128] S1. Establish a dynamic model of the steer-by-wire vehicle, and comprehensively consider actuator failure, input hysteresis, and state constraint conditions to construct a dynamic model of the front wheel subsystem in the steer-by-wire system.

[0129] In step S1, the dynamic model of the steer-by-wire vehicle is expressed as follows:

[0130]

[0131] In the formula, β represents the vehicle sideslip angle, γ represents the vehicle yaw rate, and are the first-order derivatives of β and γ respectively; C f represents the front tire steering stiffness; C r represents the rear tire steering stiffness; m represents the vehicle mass; V x represents the vehicle longitudinal speed; l r represents the distance from the rear wheel axis to the center of gravity; l f represents the distance from the front wheel axis to the center of gravity; θ fd represents the front wheel steering angle to be designed; I z represents the moment of inertia about the center of gravity; F2 and w represent lumped disturbances.

[0132] In this embodiment, the construction method of the front wheel subsystem dynamic model includes the following specific steps, namely S121 to S124.

[0133] S121. The initial front wheel subsystem dynamic model is expressed as follows:

[0134]

[0135] Wherein, J e represents the equivalent moment of inertia, θ f represents the actual front wheel steering angle, and are the first derivative and the second derivative of θ f respectively, B e represents the equivalent damping coefficient, τ e represents the tire self-aligning moment, τ f represents the front wheel friction, k s represents the transmission ratio constant, τ m (t) represents the output torque of the steering motor; t is the time variable.

[0136] S122. Model the input hysteresis, which is expressed as follows:

[0137]

[0138] Wherein, τ c represents the input control torque to be designed, is the first derivative of τ c ; represents the output torque of the steering motor in a healthy state; k h and B r are unknown positive real numbers; B l is an unknown negative real number, ξ(τ c ) is a bounded unknown function.

[0139] S123. Model the actuator fault, which is expressed as follows:

[0140]

[0141] Wherein, ρ f represents the actuator effective factor, represents the actuator bias fault.

[0142] S124. According to the modeling results of steps S121, S122 and S123, obtain the dynamic model of the front wheel subsystem considering actuator faults and input hysteresis, which is expressed as follows:

[0143]

[0144] Wherein, x1 = θ f and represent the system state; f e (x1,x2) = τ e +τ f is a non-linear term including the self-aligning moment and the front wheel friction; For the system output; the state constraint condition is: |x1| < k c1 , |x2| < k c2 , where k c1 and k c2 are constants strictly greater than zero, representing the constraint boundaries of the state variables x1 and x2 respectively.

[0145] S2. Calculate the desired yaw rate and desired sideslip angle of the vehicle according to the driver's steering angle command and the ideal vehicle model.

[0146] In step S2, the calculation formula for the desired yaw rate of the vehicle is:

[0147]

[0148] In the formula, γ d represents the desired yaw rate of the vehicle; μ represents the road-tire friction coefficient; g is the acceleration due to gravity; γ t is an intermediate term, sign(·) is the sign function.

[0149] The calculation formula for the desired sideslip angle of the vehicle is:

[0150]

[0151] In the formula, β d is the desired sideslip angle of the vehicle; β max = arctan(0.02μg); arctan(·) is the arctangent function; β t is an intermediate term, K is a parameter representing the understeer coefficient of the vehicle, K = m(l r C r - l f C r )(2C f C r (l r + l r ) 2 ); θ cmd is the driver's steering angle command.

[0152] S3. Define an error signal according to the desired yaw rate and desired sideslip angle, and thus design a fixed-time hierarchical integral sliding mode controller as the upper-layer stability controller of the front-wheel subsystem based on the fixed-time stability theory and the integral sliding mode theory to ensure the lateral stability of the vehicle under lateral wind speed and vehicle parameter perturbations.

[0153] In this embodiment, step S3 includes the following specific steps, namely S31 to S36.

[0154] S31. Convert the dynamic model of the steer-by-wire vehicle in step S1 into the following form:

[0155]

[0156] In the formula, δ cmd is the driver's output steering angle; Δδ f is the correction steering angle;

[0157] M is the vehicle mass; F2 is the parameter uncertainty disturbance; w is the external disturbance.

[0158] S32. Define the sideslip angle error signal e1 and the yaw rate error signal e2, which are expressed as follows:

[0159] e1 = β - β d

[0160] e2 = γ - γ d

[0161] Establish the following error dynamic equation:

[0162]

[0163] In the formula, and are the first-order derivatives of e1 and e2 respectively.

[0164] S33. Define two first-order sliding mode surfaces s1 and s2, which are expressed as follows:

[0165]

[0166]

[0167] In the formula, κ s1 、l 11 、p1、q1、l 11 、l 12 、κ s2 、p2、p2、l 21 and l 22 are all constants greater than zero.

[0168] S34. Design the second-order sliding mode surface S, which is expressed as follows:

[0169]

[0170] In the formula, and are all design parameters greater than zero.

[0171] S35. Design the fixed-time integral hierarchical sliding mode control law u:

[0172]

[0173] Wherein, u eq1 , u eq2 , u sw are the equivalent control term 1, the equivalent control term 2, and the sliding mode switching term respectively; κ1, k2, κ3, k4, p3, and q3 are all design parameters greater than zero.

[0174] S36. Stability proof:

[0175] Select the Lyapunov function: V s1 = S 2 , and take the derivative of V s1 to obtain the following results:

[0176]

[0177] Wherein, are the first-order derivatives of V s1 , S, s1, and s2 respectively; d l is the intermediate term, is the upper bound of d l , and satisfies ; when the parameters are selected, the sliding mode variable S is fixed-time stable at the origin.

[0178] Prove that under the action of the fixed-time hierarchical integral sliding mode control law u, the first-level sliding mode surfaces s1 and s2 are fixed-time stable at the origin. The proof process is as follows: First, design two sliding mode surfaces S m1 and S m2 , and the expressions are as follows:

[0179] S m1 = m1s1 + bs2

[0180] S m2 = m2s1 + bs2

[0181] Wherein, m1, m2, and b are arbitrary constants, and satisfy m1 > m2 > 0, b > 0.

[0182] If S m1 and S m2 converge to the origin within the time of T 11 and T 12 respectively, we get:

[0183] |S m1 - S m2 | = |(m1 - m2)s1|

[0184] Then s1 will converge to the origin within a fixed time T1 = max{T 11 , T 12}, and similarly, s2 is stable within a fixed time. As a result, both the sideslip angle error signal e1 and the yaw rate error signal e2 will converge to zero within a fixed time, which ensures the lateral stability control of the vehicle.

[0185] S4. Combine the driver's steering angle command and the front wheel steering angle correction value output by the upper-layer stability controller to generate the desired front wheel steering angle of the front wheel subsystem.

[0186] In step S4, the expression formula for the desired front wheel steering angle of the front wheel subsystem is:

[0187] θ fd = θ cmd + Δθ f

[0188] In the formula, θ fd is the desired front wheel steering angle of the front wheel subsystem; θ cmd is the driver's steering angle command; Δθ f is the front wheel steering angle correction value output by the upper-layer stability controller. Δθ f is designed as the sliding mode control law in step S35, denoted as Δθ f = u.

[0189] S5. According to the fixed-time stability theory and the barrier Lyapunov theory, design an adaptive fuzzy fixed-time controller as the lower-layer steering angle tracking controller of the front wheel steering system to ensure the front wheel steering angle tracking performance of the steer-by-wire system under actuator failure and input hysteresis conditions, and make the actual front wheel steering angle of the vehicle approach the desired front wheel steering angle.

[0190] In this embodiment, step S5 includes the following specific steps, namely S51 to S55.

[0191] S51. For the front wheel subsystem dynamic model constructed in step S124, define the error signals as follows:

[0192]

[0193] In the formula, z1 and z2 are the front wheel steering angle tracking error and the virtual second-order error respectively; y d = θ fd is the desired front wheel steering angle; α1 is the virtual control law.

[0194] S52. Define the barrier Lyapunov function V1, which is expressed as follows:

[0195]

[0196] In the formula, kb1 is a constant greater than zero;

[0197] Taking the derivative of V1 gives:

[0198]

[0199] wherein, are the first-order derivatives of V1, z1, and y respectively d respectively.

[0200] Design the virtual control law α1 as:

[0201]

[0202] wherein, λ 11 and λ 12 are designed constants greater than zero.

[0203] Substitute the designed virtual control law α1 into to obtain:

[0204]

[0205] S53. Define the barrier Lyapunov function V2, which is expressed as follows:

[0206]

[0207] wherein, k b2 and r are constants greater than zero; represents the estimation error, represents the estimated value of θ, θ is the two-norm of the fuzzy basis vector; r is a constant greater than zero.

[0208] Taking the derivative of V2 gives:

[0209]

[0210] wherein, is the first-order derivative; is the first-order derivative of α1.

[0211] Enclose some functions and variables in as an unknown function, which is expressed as follows:

[0212]

[0213] wherein,

[0214] Use the fuzzy logic system to approximate with arbitrary precision ε, which is expressed as follows:

[0215]

[0216] where ε ′ (Z) is the approximation error; ε is a bounded constant greater than zero; ε ′ (Z) is the approximation error; W is the fuzzy weight; the superscript T is the transpose symbol; is the Gaussian function basis vector, and each basis vector component is expressed as:

[0217]

[0218] where v i =[v i1 (Z),…,v iq (Z)] represents the center of the Gaussian function; η i represents the width of the Gaussian function; exp[·] is the natural exponential function.

[0219] S54. Design the input control torque τ according to the adaptive fuzzy fixed-time controller c as:

[0220]

[0221] where is the middle term; ∈, λ 21 and λ 22 are all constants greater than zero; is the lower bound of the parameter , that is

[0222] In the adaptive fuzzy fixed-time control law, the adaptive law of is designed as:

[0223]

[0224] where r, and are all constants strictly greater than zero.

[0225] S55. Stability proof: According to the complete square theorem and Young's inequality, the following inequalities are obtained:

[0226]

[0227] where θ = ‖W‖ 2 ;

[0228] Substitute the above three inequalities into to get:

[0229]

[0230] In the formula, η2 is a constant greater than zero; b is a constant greater than zero;

[0231] Since we get:

[0232]

[0233] Therefore, the system is actually fixed-time stable, that is, the front wheel steering angle tracking error z1 will converge to the neighborhood of zero within a fixed time, and the application of the obstacle Lyapunov function can ensure that the system state does not exceed the constraint conditions.

[0234] In this embodiment, in order to verify the effectiveness of the proposed vehicle stability control method for the steer-by-wire system with actuator faults and input hysteresis, experimental verification is carried out, and the experimental results are as follows:

[0235] Please refer to Figures 4 to 6 , the experiment injects actuator faults by changing ρ f and Input hysteresis is an inherent nonlinear characteristic of the system. ρ f and are set to: ρ f = 0.8, Figure 4 is the driver's steering angle command in this embodiment. Figure 4 is the vehicle stability control result of the steer-by-wire system with actuator faults and input hysteresis, where Figure 4 the left side is the yaw rate control result, Figure 4 the right side is the sideslip angle control result; Figure 5 is the front wheel steering angle tracking result; Figure 6 is the front wheel steering angle tracking error result. It can be seen from Figure 4 that the proposed hierarchical control architecture can effectively ensure the vehicle stability of the steer-by-wire system with actuator faults and input hysteresis. It can be seen from Figure 5 and Figure 6 that the proposed adaptive fuzzy fixed-time controller can achieve accurate front wheel steering angle tracking and will not exceed the constraint conditions. In this embodiment, the relevant parameters of the fixed-time hierarchical integral sliding mode controller are: κ s1 = 0.1, κ s2 = 0.1, l 11 = 0.1, l 12 = 0.1, l 21 = 0.1, l 22= 0.1, p1 = 1, q1 = 1, p2 = 1, q2 = 1, p3 = 0.5, q3 = 2, κ1 = 5, κ2 = 0.1, κ3 = 0.2, κ4 = 0.1; The relevant parameters of the adaptive fuzzy fixed-time controller are: k b1 = 0.5, k b1 = 0.8, λ 11 = 0.08, λ 12 = 0.5, λ 21 = 0.4, λ 22 = 3, r = 3, η ζ1 = 0.1, η ζ2 = 0.1.

[0236] In this embodiment, the parameter values of the vehicle dynamics model of the steer-by-wire system are shown in Table 1 below:

[0237] Table 1: Parameter values of the vehicle dynamics model

[0238] Parameter Parameter value Parameter Parameter value <![CDATA[C f > 9500 N / rad <![CDATA[C r > 9500 N / rad <![CDATA[l f > 1.463m <![CDATA[l r > 1.585m <![CDATA[t m > 0.016m <![CDATA[t p > 0.023m m 1818.2 kg <![CDATA[V x > 10 km / h <![CDATA[I z > <![CDATA[3885 kg·m2]]>

[0239] Embodiment 2

[0240] This embodiment provides a computer terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the steer-by-wire vehicle stability control method under actuator failure and input hysteresis as described in Embodiment 1 are implemented.

[0241] As Figure 7 shown, the computer terminal provided in this embodiment includes: at least one processor 101, and a memory 102 connected to at least one processor 101. In this embodiment, the specific connection medium between the processor 101 and the memory 102 is not limited. Figure 7 Here, it is taken as an example that the processor 101 and the memory 102 are connected through a bus 100. The bus 100 is represented by a thick line in Figure 7 . The connection manners between other components are only for illustrative purposes and are not to be taken as limitations. The bus 100 can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, Figure 7 it is only represented by a thick line in, but it does not mean that there is only one bus or one type of bus. Alternatively, the processor 101 can also be called a controller, and there is no limitation on the name.

[0242] In this embodiment, the memory 102 stores instructions executable by at least one processor 101. By executing the instructions stored in the memory 102, at least one processor 101 can execute the foregoing method.

[0243] Among them, the processor 101 is the control center of the device. It can connect various parts of the entire control device through various interfaces and lines. By running or executing the instructions stored in the memory 102 and calling the data stored in the memory 102, various functions of the device and data processing are performed, thereby monitoring the device as a whole.

[0244] In a possible design, the processor 101 may include one or more processing units. The processor 101 may integrate an application processor and a modem processor. Among them, the application processor mainly processes the operating system, user interface, application programs, etc., and the modem processor mainly processes wireless communication. It can be understood that the above-mentioned modem processor may not be integrated into the processor 101 either. In some embodiments, the processor 101 and the memory 102 may be implemented on the same chip, and in some embodiments, they may also be separately implemented on independent chips.

[0245] The processor 101 can be a general-purpose processor, such as a central processing unit (CPU), a digital signal processor, an application-specific integrated circuit, a field programmable gate array, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, which can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments. The general-purpose processor can be a microprocessor or any conventional processor, etc. The steps of the steer-by-wire vehicle stability control method under actuator failure and input hysteresis disclosed in conjunction with Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules in the processor 101.

[0246] The memory 102, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. The memory 102 may include at least one type of storage medium, for example, it may include flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic memory, magnetic disk, optical disc, and so on. The memory 102 is any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory 102 in this embodiment may also be a circuit or any other device capable of implementing a storage function for storing program instructions and / or data.

[0247] By designing and programming the processor 101, the code corresponding to the security verification method introduced in the foregoing embodiment can be solidified into the chip, so that the chip can execute Figure 1 the steps of the steer-by-wire vehicle stability control method under actuator failure and input hysteresis shown. How to design and program the processor 101 is a well-known technology to those skilled in the art and will not be elaborated here.

[0248] Embodiment 3

[0249] This embodiment provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps of the steer-by-wire vehicle stability control method under actuator failure and input hysteresis as described in Embodiment 1.

[0250] The computer-readable storage medium may include flash memory, a hard disk, a multimedia card, a card-type memory (e.g., SD or DX memory, etc.), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the storage medium may be an internal storage unit of the computer device, such as the hard disk or memory of the computer device. In other embodiments, the storage medium may also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. Of course, the storage medium may also include both the internal storage unit and the external storage device of the computer device. In this embodiment, the memory is generally used to store the operating system installed in the computer device and various application software. In addition, the memory may also be used to temporarily store various data that have been output or are to be output.

[0251] As described above, only the preferred specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution of the present invention and its inventive concept, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. A stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis, characterized in that, It includes the following steps: S1. Establish a dynamic model of a steer-by-wire vehicle, and comprehensively consider actuator faults, input hysteresis, and state constraint conditions to construct a dynamic model of the front-wheel subsystem in the steer-by-wire system; S2. Calculate the desired yaw rate and desired sideslip angle of the vehicle according to the driver's steering angle command and the ideal vehicle model; S3. Define an error signal based on the desired yaw rate and desired sideslip angle, and thus, based on the fixed-time stability theory and integral sliding mode theory, design a fixed-time hierarchical integral sliding mode controller as the upper-layer stability controller of the front-wheel subsystem to ensure the lateral stability of the vehicle under lateral wind speed and vehicle parameter perturbations; S4. Combine the driver's steering angle command and the corrected value of the front-wheel steering angle output by the upper-layer stability controller to generate the desired front-wheel steering angle of the front-wheel subsystem; S5. According to the fixed-time stability theory and the barrier Lyapunov theory, design an adaptive fuzzy fixed-time controller as the lower-layer angle tracking controller of the front-wheel steering system to ensure the front-wheel angle tracking performance of the steer-by-wire system under actuator faults and input hysteresis conditions, so that the actual front-wheel steering angle of the vehicle approaches the desired front-wheel steering angle.

2. The stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis according to claim 1, characterized in that, In step S1, the dynamic model of the steer-by-wire vehicle is expressed as follows: where β represents the vehicle sideslip angle, and γ represents the vehicle yaw rate, and are the first-order derivatives of β and γ respectively; C f represents the front tire steering stiffness; C r represents the rear tire steering stiffness; m represents the vehicle mass; V x represents the vehicle longitudinal speed; l r represents the distance from the rear wheel axis to the center of gravity; l f represents the distance from the front wheel axis to the center of gravity; θ fd represents the front wheel steering angle to be designed; I z represents the moment of inertia about the center of gravity; F2 and w represent the lumped disturbances; The construction method of the dynamic model of the front-wheel subsystem includes the following specific steps: S121. The initial dynamic model of the front-wheel subsystem is expressed as follows: where, J e represents the equivalent moment of inertia, θ f represents the actual front wheel steering angle, and are the first derivative and the second derivative of θ f respectively, B e represents the equivalent damping coefficient, τ e represents the tire self-aligning torque, τ f represents the front wheel friction, k s represents the transmission ratio constant, τ m (t) represents the output torque of the steering motor; t is the time variable; S122. Model the input hysteresis, which is expressed as follows: In the formula, τ c represents the input control torque to be designed, is the first derivative of τ c ; represents the output torque of the steering motor in a healthy state; k h and B r are unknown positive real numbers; B l is an unknown negative real number, and ξ(τ c ) is a bounded unknown function; S123. Model the actuator fault, which is expressed as follows: where ρ f represents the actuator effectiveness factor, represents the actuator bias fault; S124. According to the modeling results of steps S121, S122, and S123, obtain the dynamic model of the front-wheel subsystem that comprehensively considers actuator faults and input hysteresis, which is expressed as follows: where \(x1 = \theta\) f and represent the system state; f e (x1, x2) = τ e + τ f is a non - linear term containing the self - righting moment and the front - wheel friction; is the system output; the state constraint conditions are: |x1| < k c1 , |x2| < k c2 , where k c1 and k c2 are constants strictly greater than zero, representing the constraint boundaries of the state variables x1 and x2 respectively.

3. The stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis according to claim 2, wherein In step S2, the calculation formula for the desired yaw rate of the vehicle is: where γ d represents the desired yaw rate of the vehicle; μ represents the road surface-tire friction coefficient; g is the acceleration due to gravity; γ t is the intermediate term, sign(·) is the sign function; The calculation formula for the desired sideslip angle of the vehicle is: Where β d is the desired sideslip angle of the vehicle; β max = arctan(0.02μg); arctan(·) is the arctangent function; β t is the intermediate term, K is a parameter representing the understeer coefficient of the vehicle, K = m(l r C r - l f C r )(2C f C r (l r + l r ) 2 ); θ cmd is the driver's steering angle command.

4. The stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis according to claim 3, characterized in that, In step S3, step S3 includes the following specific steps: S31. Convert the dynamic model of the steer-by-wire vehicle in step S1 into the following form: where δ cmd is the driver's output steering angle; Δδ f is the correction steering angle; M is the vehicle mass; F2 is the parameter uncertainty disturbance; w is the external disturbance; S32. Define the sideslip angle error signal e1 and the yaw rate error signal e2, which are expressed as follows: e1 = β - βd e2 = γ - γd Establish the following error dynamic equation: In the formula, and are the first-order derivatives of e1 and e2 respectively; S33. Define two first-order sliding surfaces s1 and s2, which are expressed as follows: where κ s1 , p1, q1, κ s2 , p2, q2, and are all constants greater than zero; S34. Design the second-order sliding surface S, which is expressed as follows: In the formula, and are both design parameters greater than zero; S35. Design the fixed-time integral hierarchical sliding mode control law u: where u eq1 , u eq2 , u sw are the equivalent control term 1, equivalent control term 2, and sliding mode switching term, respectively; κ1, κ2, κ3, κ4, p3, and q3 are all design parameters greater than zero; S36. Stability proof: Select the Lyapunov function: V s1 = S 2 , and take the derivative of V s1 to obtain the following result: In the formula, are the first-order derivatives of V s1 , S, s1, and s2 respectively; d l is the intermediate term, is the upper bound of d l , and satisfies When the parameter is selected, the sliding mode variable S is stabilized at the origin in a fixed time; Prove that under the action of the fixed-time hierarchical integral sliding mode control law \(u\), the first-order sliding surfaces \(s_1\) and \(s_2\) are fixed-time stable at the origin. The proof process is as follows: First, design two sliding surfaces \(S\) m1 and \(S\) m2 , and the expressions are as follows: S m1 = m1s1 + bs2 S m2 = m2s1 + bs2 Where m1, m2, and b are arbitrary constants, and satisfy m1 > m2 > 0, b > 0; If S m1 and S m2 converge to the origin within times T 11 and T 12 respectively, we obtain: |S m1 -S m2 | = |(m1 - m2)s1| Then s1 will converge to the origin within a fixed time T1 = max{T 11 , T 12}, and similarly, s2 is stable within a fixed time. Thus, both the sideslip angle error signal e1 and the yaw rate error signal e2 will converge to zero within a fixed time, which ensures the lateral stability control of the vehicle.

5. The stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis according to claim 4, wherein In step S4, the expression formula for the desired front-wheel steering angle of the front-wheel subsystem is: θ fd = θ cmd + Δθ f where θ fd is the desired front wheel steering angle of the front wheel subsystem; θ cmd is the driver's steering angle command; Δθ f is the front wheel steering angle correction value output by the upper layer stability controller. Δθ f is designed as the sliding mode control law in step S35, denoted as Δθ f = u.

6. The stability control method for a steer-by-wire vehicle under actuator failure and input hysteresis according to claim 4, characterized in that Step S5 includes the following specific steps: S51. For the dynamic model of the front-wheel subsystem constructed in step S124, define the error signal as follows: where z1 and z2 are the front wheel angle tracking error and the virtual second-order error, respectively; y d = θ fd is the desired front wheel angle; α1 is the virtual control law; S52. Define the barrier Lyapunov function V1, which is expressed as follows: where k b1 is a constant greater than zero; Take the derivative of V1 to get: In the formula, are the first-order derivatives of V1, z1, and y respectively; d ​ Design the virtual control law α1 as: where λ 11 and λ 12 are constants designed to be greater than zero; Substitute the designed virtual control law α1 into to obtain: S53. Define the barrier Lyapunov function V2, which is expressed as follows: where k b2 and r are constants greater than zero; represents the estimation error, represents the estimated value of θ, where θ is the two-norm of the fuzzy basis vector; r is a constant greater than zero; Take the derivative of V2 to get: In the formula, is the first derivative of; is the first derivative of α1;; Encapsulate an unknown function It is expressed as follows: In the formula, Approximating with arbitrary precision ε using a fuzzy logic system is expressed as follows: where ε ′ (Z) is the approximation error; ε is a bounded constant greater than zero; ε ′ (Z) is the approximation error; W is the fuzzy weight; the superscript T is the transpose symbol; is the Gaussian function basis vector, and each basis vector component is expressed as: where, v i = [v i1 (Z), …, v iq (Z)] represents the center of the Gaussian function; η i represents the width of the Gaussian function; exp[·] is the natural exponential function; Design the input control torque τ according to the adaptive fuzzy fixed-time controller c as follows: Wherein, is the middle term; ∈, λ 21 and λ 22 are both constants greater than zero; is the lower bound of the parameter , that is In the adaptive fuzzy fixed-time control law, the adaptive law is designed as: where r, and are all constants strictly greater than zero; S55. Stability proof: According to the complete square theorem and the Young's inequality, obtain the following inequality: where θ = ‖W‖ 2 ; Substitute the above three inequalities into to obtain: In the formula, η2 is a constant greater than zero; b is a constant greater than zero; Due to Obtain: Then the system is stable at a fixed time, that is, the front wheel steering angle tracking error z1 will converge to a neighborhood of zero within a fixed time, so that the actual front wheel steering angle of the vehicle approaches the desired front wheel steering angle.

7. A computer terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the steer-by-wire vehicle stability control method under actuator failure and input hysteresis as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the steer-by-wire vehicle stability control method under actuator failure and input hysteresis as described in any one of claims 1 to 6.

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