A self-adaptive control method for a steer-by-wire system considering nonlinear characteristics

Abstract

The application is a kind of steering-by-wire system corner adaptive control method considering nonlinear characteristics. It includes: 1. Building a steering-by-wire system model for controller design, including steering execution motor model, rack and pinion steering gear model; 2. Designing position loop controller based on sliding mode variable structure theory, and applying radial basis neural network to adaptively compensate for the external disturbance of tire return torque and system parameter uncertainty faced by steering-by-wire system; 3. Applying linear active disturbance rejection control theory to design current loop controller, realizing decoupling control of steering execution motor excitation shaft current and torque shaft current. The double-loop corner control method combining position loop controller and current loop controller effectively helps steering-by-wire system to overcome nonlinear problems such as external disturbance of tire return torque, system parameter uncertainty and steering execution motor electromagnetic characteristic coupling, and realizes high-precision and fast-response corner tracking control.

Description

Technical Field

[0001] This invention belongs to the field of intelligent vehicle technology, specifically a method for adaptive control of steering angle in a steer-by-wire system that considers nonlinear characteristics. Background Technology

[0002] The rapid development of automotive intelligence and electrification has placed new functional demands on automotive chassis steering systems, such as active steering. Traditional hydraulic and electric power steering systems, due to the complex mechanical connection between the steering wheel and steering gear, suffer from delayed and inaccurate steering feedback, thus affecting driver control and safety, and limiting the realization of active steering. Therefore, steer-by-wire technology has gradually attracted the attention of numerous research institutions both domestically and internationally to overcome the limitations of traditional mechanical connections and adapt to the challenges brought about by automotive intelligence and electrification.

[0003] Unlike hydraulic and electric power steering systems, steer-by-wire systems eliminate the limitations of complex mechanical connections, using a high-performance permanent magnet synchronous motor as the steering power source. Steering information transmission and control are entirely achieved through electrical signals, providing greater freedom and flexibility for active steering and enabling higher levels of autonomous driving. However, during active steering, steer-by-wire systems face challenges such as external disturbances to tire return torque, uncertainties in system parameters, and electromagnetic coupling of the steering actuator motor, posing challenges to high-quality angle control. Summary of the Invention

[0004] To address the aforementioned issues, this invention provides an adaptive angle control method for steer-by-wire systems that considers nonlinear characteristics. This method combines a position loop controller and a current loop controller in a dual-loop angle control approach, effectively helping steer-by-wire systems overcome nonlinear problems such as external disturbances to tire return torque, system parameter uncertainties, and electromagnetic coupling of the steering actuator motor. It achieves high-precision, fast-response angle tracking control, laying the foundation for the active steering function of mechatronic steer-by-wire systems and meeting the demands of automotive intelligence and electrification.

[0005] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0006] An adaptive control method for steering angle in a steer-by-wire system considering nonlinear characteristics includes the following steps:

[0007] Step 1: Build a steer-by-wire system model for controller design, including a steering actuator motor model and a rack and pinion steering gear model;

[0008] Step 2: Design a position loop controller based on sliding mode variable structure theory, and apply radial basis neural network to adaptively compensate for external disturbances of tire return torque and uncertainties in system parameters faced by the steer-by-wire system;

[0009] Step 3: Apply linear active disturbance rejection control theory to design a current loop controller to achieve decoupled control of the excitation shaft current and torque shaft current of the steering actuator motor.

[0010] Furthermore, the specific method for step one is as follows:

[0011] The steering actuator used is a surface-mounted permanent magnet synchronous motor, and its electromagnetic torque is expressed as:

[0012]

[0013] In the formula, T e P represents the electromagnetic torque of the motor. n ψ is the number of pole pairs of the motor; f For the permanent magnet flux linkage of the motor rotor; i q This is the torque shaft current of the motor;

[0014] The torque balance equation at the output shaft of the steering actuator motor is expressed as:

[0015]

[0016] In the formula, θ m J is the mechanical rotation angle of the motor; m B is the moment of inertia of the motor; m T is the damping coefficient of the motor; e T represents the electromagnetic torque of the motor. p T represents the torque exerted by the rack and pinion steering mechanism on the motor shaft. mf This represents the frictional torque of the motor.

[0017] The output torque of the steering actuator motor is transmitted to the rack and pinion steering gear through the reduction mechanism. From the mechanical connection between the steering actuator motor and the rack and pinion steering gear, we can deduce:

[0018]

[0019] In the formula, θ m θ is the mechanical rotation angle of the motor. p T is the steering pinion angle; s The torque equivalent to the pinion gear of the steering actuator motor; T p is the torque exerted by the rack and pinion steering gear on the motor shaft; k is the reduction ratio of the reduction mechanism;

[0020] The rack and pinion steering gear starts working under the output torque of the motor, and is simultaneously subjected to external disturbances such as the positive torque of the steering wheel return. This can be represented as follows:

[0021]

[0022] In the formula, M r B is the equivalent mass of the rack; r X is the equivalent damping coefficient of the rack and pinion mechanism; r r is the rack displacement; p Where F is the radius of the pinion; rf T is the Coulomb friction force at the rack end; r External disturbance for the positive torque of the steering wheel; T s The torque of the steering actuator motor is equivalent to that on the pinion gear;

[0023] According to formulas (2)-(4), the equivalent dynamic equations of the steer-by-wire system are obtained as follows:

[0024]

[0025] J eq =M r r p 2 +k 2 J m (6)

[0026] B eq =B r r p 2 +k 2 B m (7)

[0027]

[0028] In the formula, θ p J is the steering pinion angle; eq B is the system's equivalent rotational inertia. eq T is the equivalent damping coefficient; f This is the equivalent frictional torque; T r The external disturbance is the positive torque of the steering wheel; k is the reduction ratio of the reduction mechanism; T e M represents the electromagnetic torque of the motor. r r is the equivalent mass of the rack; p J is the radius of the pinion; m B is the moment of inertia of the motor; r B is the equivalent damping coefficient of the rack and pinion mechanism; m F is the damping coefficient of the motor; rf T is the Coulomb friction force at the rack end; mf T represents the frictional torque of the motor. eq It is the equivalent friction coefficient; This refers to the rotational speed of the pinion gear.

[0029] Let the external disturbances of the tire return torque be denoted as Δf(θ) and d(θ), respectively, and let the pinion rotation angle be θ.p and pinion speed For system state variables, i.e. The target motor's electromagnetic torque is the system control input u = T e Therefore, the equivalent dynamic equation can be written as:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035] In the formula, θ is the system state variable; u is the system control input; The derivative of the first state variable of the system; θ is the differential of the second state variable of the system; f(θ) and g are known system parameter functions; Δf(θ) is the uncertainty of the system parameters; d(θ) is the external disturbance of the tire self-centering torque; θ p J is the steering pinion angle; eq B is the system's equivalent rotational inertia. eq T is the equivalent damping coefficient; eq T is the equivalent friction coefficient; r This represents the external disturbance of the positive torque of the steering wheel before turning; k is the reduction ratio of the reduction mechanism; ΔJ eq ΔB eq ΔT eq These are the uncertainties related to the moment of inertia, damping coefficient, and friction coefficient, respectively.

[0036] Furthermore, the specific method for step two is as follows:

[0037] A sliding mode variable structure design is used for the position loop controller; firstly, the position loop rotation angle error is defined as:

[0038] e1=θ p * -θ p (14)

[0039] In the formula, e1 is the position ring rotation angle error; θ p * θ is the rotation angle of the target pinion. p The rotation angle of the steering pinion; to eliminate steady-state error, the sliding surface with an integral term is designed as follows:

[0040]

[0041] In the formula, s is the sliding surface; e1 is the position ring rotation angle error; c1 and c2 are the derivatives of the system rotation angle error; c1 and c2 are the sliding surface control parameters, both of which are positive.

[0042] Design an improved exponential reaching law for the saturation function:

[0043]

[0044]

[0045] In the formula, s is the sliding surface; is the differential of the sliding surface; sat(s) is the saturation function of the sliding surface; Δ is the dynamic boundary layer; m and η are the approach law control parameters and are both greater than 0;

[0046] The control law of the position loop controller is:

[0047]

[0048] In the formula, θ is the system state variable; u is the system control input; denoted as the differential of the second state variable of the system; f(θ) and g are known system parameter functions; Δf(θ) represents the uncertainty of the system parameters; d(θ) represents the external disturbance of the tire self-aligning torque; e1 represents the position ring rotation angle error. denoted as the derivative of the rotation angle error; c1 and c2 are the sliding surface control parameters, respectively; m and η are the approach law control parameters; sat(s) is the sliding surface saturation function.

[0049] The ideal value approximated using a radial basis function neural network is expressed as:

[0050]

[0051] In the formula, Δf(θ) represents the uncertainty value of the system parameters; d(θ) represents the external disturbance value of the tire self-aligning torque; W * and V * The ideal weights for a radial basis function neural network; ε Δf and ε d For the neural network approximation error; |ε Δf |≤ε Mf ,|ε d |≤ε Md , ε Mf and ε Md All are bounded positive values; h Δf (θ) and h d (θ) is the neural network training function; For neural network input; θ p The steering pinion angle; This refers to the rotational speed of the pinion gear.

[0052] The system parameter uncertainties and the estimated values ​​of the tire self-aligning torque external disturbance are approximated using a radial basis function neural network, i.e.:

[0053]

[0054] In the formula, and These are estimates of the uncertainties in the system parameters and the external disturbances to the tire self-centering torque; and The estimated weights for a radial basis function neural network; h Δf (x) and h d (x) is the neural network training function;

[0055] Substituting the obtained estimate into formula (18), the new position loop control law is obtained as follows:

[0056]

[0057] In the formula, u p Here, θ represents the new position loop control law; θ is the system state variable. Let f(θ) be the differential of the second state variable of the system; f(θ) and g are known system parameter functions. and e1 represents the estimated values ​​of system parameter uncertainties and external disturbances of tire self-aligning torque; e1 represents the position ring angle error. denoted as the derivative of the rotation angle error; c1 and c2 are the sliding surface control parameters, respectively; m and η are the approach law control parameters; sat(s) is the sliding surface saturation function.

[0058] Substituting the simplified system control input (21) into the differential of the sliding surface, we get:

[0059]

[0060] In the formula, For the differential of the sliding surface; h Δf (θ) and h d (θ) is the neural network training function; m and η are the reaching law control parameters; sat(s) is the sliding surface saturation function; ε Δf and ε d This represents the approximation error of the neural network. and The difference between the ideal weights and the estimated weights of the radial basis function neural network is denoted as . W * and V * For ideal weights in a radial basis function neural network, and These are the estimated weights for a radial basis function neural network;

[0061] Define Lyapunov functions γ1 and γ2 are adaptive law parameters, and γ1>0, γ2>0. Combining with equation (22), the differential of the Lyapunov function is:

[0062]

[0063] In the formula, s is the sliding surface; The sliding surface differential; γ1 and γ2 are adaptive law parameters; h Δf (θ) and h d (θ) is the neural network training function; m and η are the reaching law control parameters; sat(s) is the sliding surface saturation function; ε Δf and ε d This represents the approximation error of the neural network. and This represents the difference between the ideal weights and the estimated weights of the radial basis function neural network. and The derivative of the ideal weights and the estimated weight error; and This is the derivative of the estimated weights of the radial basis function neural network;

[0064] The adaptive law for estimating weights in a radial basis function neural network is as follows:

[0065]

[0066] In the formula, and Here, γ1 and γ2 are the adaptive laws for estimating the weights of a radial basis function neural network; s is the sliding surface; h is the adaptive law parameters. Δf (θ) and h d (θ) is the neural network training function;

[0067] Substituting the adaptive law (24) of the estimated weights of the designed radial basis neural network into the differential of the Lyapunov function (23), we get:

[0068]

[0069] In the formula, ε is the differential of the Lyapunov function; s is the sliding surface; ε Δf and ε d denoted as the neural network approximation error; m and η are the approach law control parameters; sat(s) is the sliding surface saturation function.

[0070] Due to ε Mf and ε Md All are very small positive numbers, |ε Δf|≤ε Mf ,|ε d |≤ε Md As long as the parameters are chosen to ensure that |ηsat(s)|≥|ε Mf +ε Md |, then This allows the system to gradually stabilize;

[0071] According to the electromagnetic torque formula (1) for a permanent magnet synchronous motor, the target torque shaft current of the motor is obtained:

[0072]

[0073] In the formula, i q * The target torque shaft current; u * P represents the target electromagnetic torque of the motor. n ψ is the number of pole pairs of the motor; f It is the permanent magnet flux linkage of the motor rotor.

[0074] Furthermore, the specific method for step three is as follows:

[0075] use The current control of the permanent magnet synchronous motor; from the excitation shaft voltage equation (27) and the torque shaft voltage equation (28), it is known that the excitation shaft voltage is affected by the current disturbance term L of the torque shaft. q i q The torque shaft voltage is affected by the current disturbance term L of the excitation shaft. d i d The effect, and it changes with the motor speed ω e The increase is intensifying.

[0076]

[0077]

[0078] In the formula, u d and u q These are the excitation shaft voltage and the torque shaft voltage, respectively; R s For stator resistance; i d and i q These are the excitation shaft current and the torque shaft current, respectively; L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively; ω e ψ is the motor speed; f For rotor permanent magnet flux linkage.

[0079] Torque shaft current coupling term L q i qConsidering the non-ideal and unmeasurable external disturbances to the excitation shaft, and taking into account the inductance and resistance that change with the motor's operating state, a total excitation shaft disturbance f is established. d ; the excitation shaft current coupling term L d i d Considering the non-ideal, unmeasurable external disturbances along the torque axis, and taking into account the effects of inductance and resistance, we establish the total torque axis disturbance f. q The total disturbance of the excitation shaft and the total disturbance of the torque shaft are expressed as follows:

[0080]

[0081]

[0082] In the formula, f d Total disturbance of the excitation shaft; f q Total disturbance of the torque shaft; R s For stator resistance; i d and i q These are the excitation shaft current and the torque shaft current, respectively; L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively; ω e ψ is the motor speed; f For rotor permanent magnet flux linkage;

[0083] Let the excitation shaft current loop control input be the excitation shaft voltage, and the torque shaft current loop control input be the torque shaft voltage. Then the state-space equations for the excitation shaft and torque shaft are expressed as follows:

[0084]

[0085]

[0086] In the formula, f d Total disturbance of the excitation shaft; f q Total disturbance of the torque axis; i d and i q These are the excitation shaft current and the torque shaft current, respectively; b d b q These are the current loop state parameters. L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively; u d * and u q * These are the current loop control inputs for the excitation shaft and torque shaft, respectively;

[0087] Design an extended state observer to estimate the total disturbance of the excitation shaft and the total disturbance of the torque shaft. The torque shaft extended state observer is expressed as follows:

[0088]

[0089]

[0090] In the formula, z 1q z 2q For output i respectively q The estimated value and the total disturbance f on the torque axis q The estimated value; These are the derivatives of the estimated values; β1 and β2 are the state observer gain coefficients, respectively; u q Torque shaft current loop control input, b q These are the current loop state parameters;

[0091] Linear error feedback is used to compensate for the estimated disturbances, resulting in the following control laws for the excitation shaft current and torque shaft current:

[0092]

[0093]

[0094] In the formula, u d u q The output voltages for the excitation shaft and torque shaft are respectively; u d0 u q0 The voltages of the excitation shaft and torque shaft are obtained respectively through linear error feedback; i d * i q * These are the target currents for the excitation shaft and torque shaft, respectively; z 1d z 2d The outputs of the excitation shaft current loop expansion state observer are the estimates of the current and the total disturbance; z 1q z 2q The outputs of the excitation shaft current loop expansion state observer are the estimates of the current and the total disturbance; k pd k pq The current loop control gains for the excitation shaft and torque shaft are respectively; b d b q Current loop state parameters L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively.

[0095] The beneficial effects of this invention are as follows:

[0096] 1) The dynamic model of the steer-by-wire system built in this invention takes into account nonlinear problems such as external disturbances of tire return torque and system parameter uncertainties encountered during active steering angle control;

[0097] 2) This invention is based on the sliding mode variable structure theory and the radial basis function neural network control method to design a highly robust and high-precision position loop controller. The adaptive radial basis neural network effectively compensates for external disturbances in tire return torque and uncertainties in system parameters.

[0098] 3) The current loop controller designed based on the linear active disturbance rejection theory of this invention effectively overcomes the electromagnetic characteristic coupling problem between the excitation shaft current and the torque shaft current of the steering actuator motor;

[0099] 4) The dual-loop angle control method of the present invention, which combines a position loop controller and a current loop controller, effectively ensures the accuracy and robustness of angle tracking under nonlinear disturbances and improves the dynamic response performance of the steer-by-wire system. Attached Figure Description

[0100] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0101] Figure 1 This is a schematic diagram of the structure of the present invention;

[0102] Figure 2 This is a schematic diagram of the steer-by-wire system.

[0103] Figure 3 This is a schematic diagram of the current loop active disturbance rejection controller.

[0104] Figure 4 This is a schematic diagram of the steering angle tracking performance curve of the steer-by-wire system under mixed operating conditions. Detailed Implementation

[0105] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0106] See Figure 1 This invention provides a method for adaptive steering angle control of a steer-by-wire system considering nonlinear characteristics, comprising the following steps:

[0107] Step 1: Build a steer-by-wire system model for controller design, including the steering actuator motor model and the rack and pinion steering gear model. The specific method is as follows:

[0108] Figure 2 The diagram shows a simplified structure of a steer-by-wire system. After receiving the target steering angle signal, the steer-by-wire system controls the steering motor to operate. The motor's output torque, through a reduction mechanism, helps the rack and pinion steering gear overcome rack resistance, pushing the steering tie rod to control the steering wheels and achieve active steering.

[0109] The steering actuator used in this invention is a surface-mounted permanent magnet synchronous motor, and its electromagnetic torque is expressed as:

[0110]

[0111] In the formula, T e P represents the electromagnetic torque of the motor. n ψ is the number of pole pairs of the motor; f For the permanent magnet flux linkage of the motor rotor; i q This is the torque shaft current of the motor;

[0112] The torque balance equation at the output shaft of the steering actuator motor is expressed as:

[0113]

[0114] In the formula, θ m J is the mechanical rotation angle of the motor; m B is the moment of inertia of the motor; m T is the damping coefficient of the motor; e T represents the electromagnetic torque of the motor. p T represents the torque exerted by the rack and pinion steering mechanism on the motor shaft. mf This represents the frictional torque of the motor.

[0115] The output torque of the steering actuator motor is transmitted to the rack and pinion steering gear through the reduction mechanism. From the mechanical connection between the steering actuator motor and the rack and pinion steering gear, we can deduce:

[0116]

[0117] In the formula, θ m θ is the mechanical rotation angle of the motor. p T is the steering pinion angle; s The torque equivalent to the pinion gear of the steering actuator motor; T p is the torque exerted by the rack and pinion steering gear on the motor shaft; k is the reduction ratio of the reduction mechanism;

[0118] The rack and pinion steering gear starts working under the output torque of the motor, and is simultaneously subjected to external disturbances such as the positive torque of the steering wheel return. This can be represented as follows:

[0119]

[0120] In the formula, Mr B is the equivalent mass of the rack; r X is the equivalent damping coefficient of the rack and pinion mechanism; r r is the rack displacement; p Where F is the radius of the pinion; rf T is the Coulomb friction force at the rack end; r External disturbance for the positive torque of the steering wheel; T s The torque of the steering actuator motor is equivalent to that on the pinion gear;

[0121] According to formulas (2)-(4), the equivalent dynamic equations of the steer-by-wire system are obtained as follows:

[0122]

[0123] J eq =M r r p 2 +k 2 J m (6)

[0124] B eq =B r r p 2 +k 2 B m (7)

[0125]

[0126] In the formula, θ p J is the steering pinion angle; eq B is the system's equivalent rotational inertia. eq T is the equivalent damping coefficient; f This is the equivalent frictional torque; T r The external disturbance is the positive torque of the steering wheel; k is the reduction ratio of the reduction mechanism; T e M represents the electromagnetic torque of the motor. r r is the equivalent mass of the rack; p J is the radius of the pinion; m B is the moment of inertia of the motor; r B is the equivalent damping coefficient of the rack and pinion mechanism; m F is the damping coefficient of the motor; rf T is the Coulomb friction force at the rack end; mf T represents the frictional torque of the motor. eq It is the equivalent friction coefficient; This refers to the rotational speed of the pinion gear.

[0127] Due to gaps and elastic deformation between components in a steer-by-wire system, system parameters such as moment of inertia, damping coefficient, and friction coefficient exhibit certain uncertainties under different steering states. To better handle these nonlinear factors and improve tracking accuracy, this invention denotes the external disturbances of tire return torque as Δf(θ) and d(θ), respectively, and lets the pinion angle θ... p and pinion speed For system state variables, i.e. The target motor's electromagnetic torque is the system control input u = T e Therefore, the equivalent dynamic equation can be written as:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] In the formula, θ is the system state variable; u is the system control input; The derivative of the first state variable of the system; θ is the differential of the second state variable of the system; f(θ) and g are known system parameter functions; Δf(θ) is the uncertainty of the system parameters; d(θ) is the external disturbance of the tire self-centering torque; θ p J is the steering pinion angle; eq B is the system's equivalent rotational inertia. eq T is the equivalent damping coefficient; eq T is the equivalent friction coefficient; r The external disturbance is the positive torque of the steering wheel before turning; k is the reduction ratio of the reduction mechanism; ΔJ eq ΔB eq ΔT eq These are the uncertainties related to the moment of inertia, damping coefficient, and friction coefficient, respectively.

[0134] The equivalent dynamic equilibrium equation takes into account the nonlinear problems faced by the steer-by-wire system, such as the uncertainty of system parameters and the external disturbance of tire return torque, and provides a basis for the subsequent controller design.

[0135] Step 2: Design a position loop controller based on sliding mode variable structure theory, and apply radial basis function neural network to adaptively compensate for external disturbances in tire return torque and uncertainties in system parameters faced by the steer-by-wire system, as detailed below:

[0136] A sliding mode variable structure design is used for the position loop controller; firstly, the position loop rotation angle error is defined as...

[0137] e1=θ p * -θ p (14)

[0138] In the formula, e1 is the position ring rotation angle error; θ p * θ is the rotation angle of the target pinion. p The rotation angle of the steering pinion; to eliminate steady-state error, the sliding surface with an integral term is designed as follows:

[0139]

[0140] In the formula, s is the sliding surface; e1 is the position ring rotation angle error; c1 and c2 are the derivatives of the system rotation angle error; c1 and c2 are the sliding surface control parameters, both of which are positive.

[0141] To quickly and smoothly approach the sliding surface, an improved exponential reaching law for the saturation function is designed:

[0142]

[0143]

[0144] In the formula, s is the sliding surface; is the differential of the sliding surface; sat(s) is the saturation function of the sliding surface; Δ is the dynamic boundary layer; m and η are the approach law control parameters and are both greater than 0;

[0145] The control law of the position loop controller is:

[0146]

[0147] In the formula, θ is the system state variable; u is the system control input; denoted as the differential of the second state variable of the system; f(θ) and g are known system parameter functions; Δf(θ) represents the uncertainty of the system parameters; d(θ) represents the external disturbance of the tire self-aligning torque; e1 represents the position ring rotation angle error. Let c1 and c2 be the differential of the rotation angle error, respectively; m and η be the approach law control parameters; and sat(s) be the saturation function of the sliding surface.

[0148] Considering the uncertainty of system parameters and the difficulty in accurately obtaining external disturbances of tire self-alignment torque, this invention uses a radial basis function neural network with simple structure and strong generalization ability to adaptively approximate Δf(θ) and d(θ).

[0149] The ideal value approximated using a radial basis function neural network is expressed as:

[0150]

[0151] In the formula, Δf(θ) represents the uncertainty value of the system parameters; d(θ) represents the external disturbance value of the tire self-aligning torque; W * and V * The ideal weights for a radial basis function neural network; ε Δf and ε d For the neural network approximation error; |ε Δf |≤ε Mf ,|ε d |≤ε Md , ε Mf and ε Md All are bounded positive values; h Δf (θ) and h d (θ) is the neural network training function; For neural network input; θ p The steering pinion angle; This refers to the rotational speed of the pinion gear.

[0152] The system parameter uncertainties and the estimated values ​​of the tire self-aligning torque external disturbance are approximated using a radial basis function neural network, i.e.:

[0153]

[0154] In the formula, and These are estimates of the uncertainties in the system parameters and the external disturbances to the tire self-centering torque; and The estimated weights for a radial basis function neural network; h Δf (x) and h d (x) is the neural network training function;

[0155] Substituting the obtained estimate into formula (18), the new position loop control law is obtained as follows:

[0156]

[0157] In the formula, u p Here, θ represents the new position loop control law; θ is the system state variable. Let f(θ) be the differential of the second state variable of the system; f(θ) and g are known system parameter functions. and e1 represents the estimated values ​​of system parameter uncertainties and external disturbances of tire self-aligning torque; e1 represents the position ring angle error. denoted as the derivative of the rotation angle error; c1 and c2 are the sliding surface control parameters, respectively; m and η are the approach law control parameters; sat(s) is the sliding surface saturation function.

[0158] Substituting the simplified system control input (21) into the differential of the sliding surface, we get:

[0159]

[0160] In the formula, For the differential of the sliding surface; h Δf (θ) and h d (θ) is the neural network training function; m and η are the reaching law control parameters; sat(s) is the sliding surface saturation function; ε Δf and ε d This represents the approximation error of the neural network. and The difference between the ideal weights and the estimated weights of the radial basis function neural network is denoted as . W * and V * For ideal weights in a radial basis function neural network, and These are the estimated weights for a radial basis function neural network;

[0161] Define Lyapunov functions γ1 and γ2 are adaptive law parameters, and γ1>0, γ2>0. Combining with equation (22), the differential of the Lyapunov function can be obtained as follows:

[0162]

[0163] In the formula, s is the sliding surface; The sliding surface differential; γ1 and γ2 are adaptive law parameters; h Δf (θ) and h d (θ) is the neural network training function; m and η are the reaching law control parameters; sat(s) is the sliding surface saturation function; ε Δf and ε d This represents the approximation error of the neural network. and This represents the difference between the ideal weights and the estimated weights of the radial basis function neural network. and The derivative of the ideal weights and the estimated weight error; and This is the derivative of the estimated weights of the radial basis function neural network;

[0164] The adaptive law for estimating weights in a radial basis function neural network is as follows:

[0165]

[0166] In the formula, and Here, γ1 and γ2 are the adaptive laws for estimating the weights of a radial basis function neural network; s is the sliding surface; h is the adaptive law parameters. Δf (θ) and h d (θ) is the neural network training function;

[0167] Substituting the adaptive law (24) of the estimated weights of the designed radial basis neural network into the differential of the Lyapunov function (23), we get:

[0168]

[0169] In the formula, ε is the differential of the Lyapunov function; s is the sliding surface; ε Δf and ε d denoted as the neural network approximation error; m and η are the approach law control parameters; sat(s) is the sliding surface saturation function.

[0170] Due to ε Mf and ε Md All are very small positive numbers, |ε Δf |≤ε Mf ,|ε d |≤ε Md As long as the parameters are chosen to ensure that |ηsat(s)|≥|ε Mf +ε Md |, then This allows the system to gradually stabilize;

[0171] According to the electromagnetic torque formula (1) for a permanent magnet synchronous motor, the target torque shaft current of the motor is obtained:

[0172]

[0173] In the formula, i q * The target torque shaft current; u * P represents the target electromagnetic torque of the motor. n ψ is the number of pole pairs of the motor; f It is the permanent magnet flux linkage of the motor rotor.

[0174] Step 3: Apply linear active disturbance rejection control theory to design a current loop controller to achieve decoupled control of the excitation shaft current and torque shaft current of the steering actuator motor, as detailed below:

[0175] This invention adopts The current control of the permanent magnet synchronous motor; from the excitation shaft voltage equation (27) and the torque shaft voltage equation (28), it is known that the excitation shaft voltage is affected by the current disturbance term L of the torque shaft. q iq The torque shaft voltage is affected by the current disturbance term L of the excitation shaft. d i d The effect, and it changes with the motor speed ω e The increase is intensifying.

[0176]

[0177]

[0178] In the formula, u d and u q These are the excitation shaft voltage and the torque shaft voltage, respectively; R s For stator resistance; i d and i q These are the excitation shaft current and the torque shaft current, respectively; L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively; ω e ψ is the motor speed; f For rotor permanent magnet flux linkage.

[0179] To resolve electromagnetic coupling and improve the dynamic response of the motor, a current loop controller is designed using linear active disturbance rejection theory. The control principle is as follows: Figure 3 As shown.

[0180] Torque shaft current coupling term L q i q Considering the non-ideal and unmeasurable external disturbances to the excitation shaft, and taking into account the inductance and resistance that change with the motor's operating state, a total excitation shaft disturbance f is established. d ; the excitation shaft current coupling term L d i d Considering the non-ideal, unmeasurable external disturbances along the torque axis, and taking into account the effects of inductance and resistance, we establish the total torque axis disturbance f. q The total disturbance of the excitation shaft and the total disturbance of the torque shaft are expressed as follows:

[0181]

[0182]

[0183] In the formula, f d Total disturbance of the excitation shaft; f q Total disturbance of the torque shaft; R s For stator resistance; i d and i q These are the excitation shaft current and the torque shaft current, respectively; L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively; ω e ψ is the motor speed; fFor rotor permanent magnet flux linkage;

[0184] Let the excitation shaft current loop control input be the excitation shaft voltage, and the torque shaft current loop control input be the torque shaft voltage. Then the state-space equations for the excitation shaft and torque shaft can be expressed as:

[0185]

[0186]

[0187] In the formula, f d Total disturbance of the excitation shaft; f q Total disturbance of the torque axis; i d and i q These are the excitation shaft current and the torque shaft current, respectively; b d b q These are the current loop state parameters. L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively; u d * and u q * These are the current loop control inputs for the excitation shaft and torque shaft, respectively;

[0188] To reduce the impact of excitation shaft-torque shaft coupling on motor performance, an extended state observer is designed to estimate the total excitation shaft disturbance and the total torque shaft disturbance. The torque shaft extended state observer is expressed as follows:

[0189]

[0190]

[0191] In the formula, z 1q z 2q For output i respectively q The estimated value and the total disturbance f on the torque axis q The estimated value; These are the derivatives of the estimated values; β1 and β2 are the state observer gain coefficients, respectively; u q Torque shaft current loop control input, b q These are the current loop state parameters;

[0192] Linear error feedback is used to compensate for the estimated disturbances, resulting in the following control laws for the excitation shaft current and torque shaft current:

[0193]

[0194]

[0195] In the formula, ud u q The output voltages for the excitation shaft and torque shaft are respectively; u d0 u q0 The voltages of the excitation shaft and torque shaft are obtained respectively through linear error feedback; i d * i q * These are the target currents for the excitation shaft and torque shaft, respectively; z 1d z 2d The outputs of the excitation shaft current loop expansion state observer are the estimates of the current and the total disturbance; z 1q z 2q The outputs of the excitation shaft current loop expansion state observer are the estimates of the current and the total disturbance; k pd k pq The current loop control gains for the excitation shaft and torque shaft are respectively; b d b q Current loop state parameters L d and L q These are the excitation shaft inductance and the torque shaft inductance, respectively.

[0196] Example

[0197] In this embodiment, the adaptive steering angle control method for the steer-by-wire system considering nonlinear characteristics designed in this patent was tested in a simulation platform built using MATLAB / Simulink and Carsim software.

[0198] Figure 4 The image shows the steering angle control performance curve of the steer-by-wire system under mixed operating conditions with a target amplitude of 60°. The experimental performance test results clearly show that the actual steering angle curve almost coincides with the target steering angle curve, the steady-state tracking error is basically controlled within 1°, and there is no obvious hysteresis throughout the process. The curves showing the changes in excitation shaft current and torque shaft current clearly demonstrate that the current of the steering actuator motor closely follows the target value and changes smoothly, indicating good current control performance.

[0199] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for adaptive steering angle control of a steer-by-wire system considering nonlinear characteristics, characterized in that, Includes the following steps: Step 1: Construct a steer-by-wire system model for controller design, including a steering actuator motor model and a rack and pinion steering gear model. The steering actuator used is a surface-mounted permanent magnet synchronous motor, and its electromagnetic torque is expressed as: （1） In the formula, This refers to the electromagnetic torque of the motor. This represents the number of pole pairs of the motor. The permanent magnet flux linkage of the motor rotor; This is the torque shaft current of the motor; The torque balance equation at the output shaft of the steering actuator motor is expressed as: （2） In the formula, This refers to the mechanical rotation angle of the motor; This is the moment of inertia of the motor. This is the damping coefficient of the motor; This refers to the electromagnetic torque of the motor. This refers to the torque exerted on the motor shaft by the rack and pinion steering gear. This represents the frictional torque of the motor. The output torque of the steering actuator motor is transmitted to the rack and pinion steering gear through the reduction mechanism. From the mechanical connection between the steering actuator motor and the rack and pinion steering gear, we can deduce: （3） In the formula, This refers to the mechanical rotation angle of the motor; The steering pinion angle; The torque of the steering actuator motor is equivalent to that on the pinion gear; is the torque exerted by the rack and pinion steering gear on the motor shaft; k is the reduction ratio of the reduction mechanism; The rack and pinion steering gear starts working under the output torque of the motor, and is simultaneously subjected to external disturbances such as the positive torque of the steering wheel return. This can be represented as follows: （4） In the formula, The equivalent mass of the rack; This is the equivalent damping coefficient of the rack and pinion mechanism; This represents the rack displacement; The radius of the pinion; The Coulomb friction force at the rack end; External disturbances to the positive torque of the steering wheel before turning; The torque of the steering actuator motor is equivalent to that on the pinion gear; According to formulas (2)-(4), the equivalent dynamic equations of the steer-by-wire system are obtained as follows: （5） （6） （7） （8） In the formula, The steering pinion angle; This is the system's equivalent moment of inertia. This is the equivalent damping coefficient; This is the equivalent frictional torque; The external disturbance is the positive torque of the steering wheel before turning; k is the reduction ratio of the reduction mechanism; This refers to the electromagnetic torque of the motor. The equivalent mass of the rack; The radius of the pinion; This is the moment of inertia of the motor. This is the equivalent damping coefficient of the rack and pinion mechanism; This is the damping coefficient of the motor; The Coulomb friction force at the rack end; This represents the frictional torque of the motor. It is the equivalent friction coefficient; This refers to the rotational speed of the pinion gear. Step 2: Design a position loop controller based on sliding mode variable structure theory, and apply radial basis neural network to adaptively compensate for external disturbances of tire return torque and uncertainties in system parameters faced by the steer-by-wire system; Step 3: Apply linear active disturbance rejection control theory to design a current loop controller to achieve decoupled control of the excitation shaft current and torque shaft current of the steering actuator motor.

2. The adaptive steering angle control method for a steer-by-wire system considering nonlinear characteristics according to claim 1, characterized in that, The specific method for step one is as follows: The external disturbance to the tire return torque is denoted as follows: and Make the small gear rotate. and pinion speed For system state variables, i.e. =[ The target motor's electromagnetic torque is the system control input. Therefore, the equivalent dynamic equation can be written as: （9） （10） （11） （12） （13） In the formula, Here, u represents the system state variable; u represents the system control input. The derivative of the first state variable of the system; The derivative of the second state variable of the system; And g is a known system parameter function; Due to system parameter uncertainties; External disturbances to the tire return torque; The steering pinion angle; This is the system's equivalent moment of inertia. This is the equivalent damping coefficient; It is the equivalent friction coefficient; This indicates the external disturbance of the positive torque of the steering wheel before turning; k is the reduction ratio of the reduction mechanism; , , These are the uncertainties related to the moment of inertia, damping coefficient, and friction coefficient, respectively.

3. The adaptive steering angle control method for a steer-by-wire system considering nonlinear characteristics according to claim 1, characterized in that, The specific method for step two is as follows: A sliding mode variable structure design is used for the position loop controller; firstly, the position loop rotation angle error is defined as: （14） In the formula, This refers to the position ring rotation angle error; The target pinion rotation angle; The steering pinion angle; To eliminate steady-state error, the sliding surface with an integral term is designed as follows: （15） In the formula, s is the sliding surface; This refers to the position ring rotation angle error; This is the derivative of the system's rotation angle error; These are the control parameters for the sliding surface, and all are positive values. Design an improved exponential reaching law for the saturation function: （16） （17） In the formula, s is the sliding surface; Differential of the sliding surface; For the saturation function of the sliding surface; For dynamic boundary layers; , These are the control parameters for the approach law, and all are greater than 0; The control law of the position loop controller is: （18） In the formula, For system state variables; For system control input; The derivative of the second state variable of the system; and The system parameters are known functional expressions; Due to system parameter uncertainties; External disturbances to the tire return torque; This refers to the position ring rotation angle error; This is the derivative of the rotation angle error; These are the control parameters for the sliding surface; , These are the parameters for the approach law control. For the saturation function of the sliding surface; The ideal value approximated using a radial basis function neural network is expressed as: （19） In the formula, This represents the uncertainty value of the system parameters; This represents the external disturbance value of the tire return torque; and These are the ideal weights for a radial basis function neural network. and This represents the approximation error of the neural network. , , and All are bounded positive values; and This is the training function for the neural network. Input to the neural network; The steering pinion angle; This refers to the rotational speed of the pinion gear. The system parameter uncertainties and the estimated values ​​of the tire self-aligning torque external disturbance are approximated using a radial basis function neural network, i.e.: （20） In the formula, and These are estimates of the uncertainties in the system parameters and the external disturbances to the tire self-centering torque; and These are the estimated weights for a radial basis function neural network; and This is the training function for the neural network. Substituting the obtained estimate into formula (18), the new position loop control law is obtained as follows: （21） In the formula, For the new position loop control law; For system state variables; The derivative of the second state variable of the system; and The system parameters are known functional expressions; and These are estimates of the uncertainties in the system parameters and the external disturbances to the tire self-centering torque; This refers to the position ring rotation angle error; This is the derivative of the rotation angle error; These are the control parameters for the sliding surface; , These are the parameters for the approach law control. For the saturation function of the sliding surface; Substituting the simplified system control input (21) into the differential of the sliding surface, we get: （22） In the formula, Differential of the sliding surface; and This is the training function for the neural network. , These are the parameters for the approach law control. For the saturation function of the sliding surface; and This represents the approximation error of the neural network. and The difference between the ideal weights and the estimated weights of the radial basis function neural network is denoted as . , , and For ideal weights in a radial basis function neural network, and These are the estimated weights for a radial basis function neural network; Define Lyapunov functions Let be the adaptive law parameters, and Combining equation (22), the differential of the Lyapunov function is: In the formula, s is the sliding surface; Differential of the sliding surface; These are the parameters of the adaptive law; and This is the training function for the neural network. , These are the parameters for the approach law control. For the saturation function of the sliding surface; and This represents the approximation error of the neural network. and This represents the difference between the ideal weights and the estimated weights of the radial basis function neural network. and The derivative of the ideal weights and the estimated weight error; and This is the derivative of the estimated weights of the radial basis function neural network; The adaptive law for estimating weights in a radial basis function neural network is as follows: （24） In the formula, and This is the adaptive law for estimating the weights of a radial basis function neural network; Here are the adaptive law parameters; s is the sliding surface; and This is the training function for the neural network. Substituting the adaptive law (24) of the estimated weights of the designed radial basis neural network into the differential of the Lyapunov function (23), we get: （25） In the formula, is the differential of the Lyapunov function; s is the sliding surface; and This represents the approximation error of the neural network. , These are the parameters for the approach law control. For the saturation function of the sliding surface; because and They are all very small positive numbers. , As long as the parameters are selected to ensure ,but This allows the system to gradually stabilize; According to the electromagnetic torque formula (1) of the permanent magnet synchronous motor, the target torque shaft current of the motor is obtained: （26） In the formula, The target torque shaft current; The target electromagnetic torque of the motor; This represents the number of pole pairs of the motor. It is the permanent magnet flux linkage of the motor rotor.

4. The adaptive steering angle control method for a steer-by-wire system considering nonlinear characteristics according to claim 1, characterized in that, The specific method for step three is as follows: use The current control of the permanent magnet synchronous motor; from the excitation shaft voltage equation (27) and the torque shaft voltage equation (28), it is known that the excitation shaft voltage is affected by the current disturbance term of the torque shaft. The torque shaft voltage is affected by the current disturbance term of the excitation shaft. The impact, and with the motor speed The increase is intensifying. （27） （28） In the formula, and These are the excitation shaft voltage and the torque shaft voltage, respectively. Stator resistance; and These are the excitation shaft current and the torque shaft current, respectively. and These are the excitation shaft inductance and the torque shaft inductance, respectively. This refers to the motor speed; For rotor permanent magnet flux linkage; Torque axis current coupling term Considering the non-ideal and unmeasurable external disturbances to the excitation shaft, and taking into account the inductance and resistance that change with the motor's operating state, a total excitation shaft disturbance is established. ; Coupling the excitation shaft current term Considering the non-ideal, unmeasurable external disturbances along the torque axis, and taking into account the effects of inductance and resistance, we establish the total disturbance along the torque axis. The total disturbance of the excitation shaft and the total disturbance of the torque shaft are expressed as follows: （29） （30） In the formula, Total interference on the excitation shaft; Total disturbance on the torque axis; Stator resistance; and These are the excitation shaft current and the torque shaft current, respectively. and These are the excitation shaft inductance and the torque shaft inductance, respectively. This refers to the motor speed; For rotor permanent magnet flux linkage; Let the excitation shaft current loop control input be the excitation shaft voltage, and the torque shaft current loop control input be the torque shaft voltage. Then the state-space equations for the excitation shaft and torque shaft are expressed as follows: In the formula, Total interference on the excitation shaft; Total disturbance on the torque axis; and These are the excitation shaft current and the torque shaft current, respectively. These are the current loop state parameters. , , and These are the excitation shaft inductance and the torque shaft inductance, respectively. and These are the current loop control inputs for the excitation shaft and torque shaft, respectively; Design an extended state observer to estimate the total disturbance of the excitation shaft and the total disturbance of the torque shaft. The torque shaft extended state observer is expressed as follows: （33） （34） In the formula, , For the output The estimated value and the total disturbance to the torque axis The estimated value; These are the derivatives of the estimated values; , These are the state observer gain coefficients; Torque shaft current loop control input These are the current loop state parameters; Linear error feedback is used to compensate for the estimated disturbances, resulting in the following control laws for the excitation shaft current and torque shaft current: （35） （36） In the formula, These are the output voltages for the excitation shaft and torque shaft, respectively. The voltages of the excitation shaft and torque shaft are obtained through linear error feedback, respectively. These are the target currents for the excitation shaft and torque shaft, respectively. , The output of the excitation shaft current loop expansion state observer is the estimated value of the current and the estimated value of the total disturbance. , The output of the excitation shaft current loop expansion state observer is the estimated value of the current and the estimated value of the total disturbance. The current loop control gains for the excitation shaft and torque shaft are respectively. Current loop state parameters , , and These are the excitation shaft inductance and the torque shaft inductance, respectively.

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