Steer-by-wire system corner tracking and fault-tolerant control method with preset performance

Abstract

The application discloses a kind of corner tracking and fault-tolerant control methods of steer-by-wire system with preset performance, the method includes the following steps: one, the establishment of the dynamics model of the steering actuator of steer-by-wire system;Two, the design of rack force estimator;Three, the design of corner tracking controller of finite time convergence;Four, the design of fault-tolerant strategy of rack displacement sensor.The corner tracking control method of preset performance control based on finite time convergence of the application can guarantee the transient performance and steady-state performance of corner tracking simultaneously, and converges to preset residual set within preset time, even under the condition of rack displacement sensor failure, still can realize good corner tracking performance.The fault-tolerant strategy based on rotary transformer of the application can realize the fault-tolerant capability of steer-by-wire system under rack displacement sensor failure without increasing the cost and space of installing additional sensors, and improve the reliability of corner tracking control method.

Description

Technical Field

[0001] This invention belongs to the field of automotive steer-by-wire technology, and relates to a method for angle tracking and fault-tolerant control of a steer-by-wire system, specifically a method for angle tracking based on preset performance and fault-tolerant control under rack displacement sensor failure. Background Technology

[0002] With the rapid development of vehicle electrification and intelligence, steer-by-wire systems are urgently needed due to their advantages in personalized driving experience, active safety, and driving comfort. Compared to traditional mechanical steering systems, steer-by-wire systems eliminate the mechanical connection between the steering wheel and the steering actuator, instead transmitting steering commands via electrical signals. The road information required by the driver and the wheel rotation required for steering are controlled by the road sensor motor and steering motor, respectively. This not only avoids the disadvantages of mechanical steering systems, such as adverse road vibrations, fixed transmission ratios, and potential safety hazards, but also meets the requirement of individually controllable wheel angles in intelligent vehicles. Angle tracking control, as one of the key technologies of steer-by-wire systems, is crucial to the realization of normal vehicle steering function and has a vital impact on safe driving. Therefore, high transient and high-precision angle tracking control methods can effectively achieve the desired steering of the vehicle and also lay the foundation for the stability control of active safety.

[0003] Currently, steering angle tracking control methods for steer-by-wire systems mainly include sliding mode control, model predictive control, and adaptive control. However, high-frequency switching near the sliding surface in sliding mode control can cause chattering, which negatively impacts the system. To mitigate chattering, adaptive sliding mode control and saturation switching functions have been proposed, but these increase the complexity of system design and implementation difficulty, and chattering cannot be completely eliminated. In addition, controller gain based on self-tuning PID using particle swarm optimization and backstepping has achieved good steering angle tracking results, but the introduced intelligent optimization algorithm introduces a large computational load, making it difficult to embed into applications. Furthermore, existing research focuses more on the steady-state performance of steering angle tracking, paying less attention to its transient performance. However, steer-by-wire systems require a high transient response to driver commands to quickly complete the steering function; therefore, focusing solely on the steady-state performance of steering angle tracking cannot meet the requirements of steer-by-wire systems for steering angle tracking control. Furthermore, the studies mentioned above all assume that the steering angle sensor always works properly. However, in actual engineering applications, the steering angle sensor may malfunction due to factors such as the working environment, leading to the overall failure of the control algorithm. This can cause the vehicle to be unable to complete normal steering, posing a significant safety hazard. Therefore, it is meaningful to study steering angle tracking control under steering angle sensor failure. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a steer-by-wire system angle tracking and fault-tolerant control method with preset performance. This method estimates external disturbances in the steer-by-wire system using an extended state observer and implements feedforward compensation in the angle tracking controller design. Then, a finite-time convergent performance function is designed, and the angle tracking controller is designed using backstepping technology, ensuring that the angle tracking error converges to a preset residual set within a finite time, while simultaneously guaranteeing the transient and steady-state performance of the steer-by-wire system's angle tracking control. To address the problem of potential rack displacement sensor failure leading to angle tracking algorithm failure, a fault-tolerant strategy based on motor-resolver redundancy is designed.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for angle tracking and fault-tolerant control of a steer-by-wire system with preset performance includes the following steps:

[0007] Step 1: Establishing the dynamic model of the steering actuator in the steer-by-wire system:

[0008] Step 11: The dynamic model of the steering actuator consists of a steering motor and a steering mechanism connecting the steering wheels. The dynamic differential equation of the steering motor is:

[0009]

[0010] In the above formula, J m B m and K m θ represents the moment of inertia, damping coefficient, and torsional stiffness of the steering motor, respectively. m , and These are the rotation angle, angular velocity, and angular acceleration of the steering motor, respectively, G. m The reduction ratio from the motor crankshaft to the rack, r p T is the pitch circle radius of the pinion in a gear and rack mechanism. m This refers to the output torque of the crankshaft of the steering motor;

[0011] Steps 1 and 2: The steering wheel is rigidly connected to the rack and pinion mechanism. The dynamic model of the steering wheel is represented by the dynamic differential equation of the rack:

[0012]

[0013] In the above formula, m r and B r These represent the mass and damping coefficient of the rack, respectively. r , and F represents the displacement, velocity, and acceleration of the rack, respectively.f The frictional force F generated during the movement of the rack is the frictional force. r It is the rack force acting on the outside of the wheel;

[0014] Step 13: Based on the mechanical connection between the motor output crankshaft and the rack mechanism, the second-order differential equation of the steering actuator is obtained as follows:

[0015]

[0016] In the above formula, and These are the equivalent mass and the equivalent damping coefficient, respectively.

[0017] F e =F f +F r For generalized rack force;

[0018] Step 2: Design of the rack force estimator:

[0019] Step 2.1. Estimate the generalized rack force given in Step 1. Based on the second-order differential equation of the steering actuator, establish the following differential equation for the rack force estimator:

[0020]

[0021] In the above formula, x1 = X r and The state variable of the estimator is x3 = F. e For the defined extended state, y = x1 is the output variable of the estimator. and These are the estimated values ​​of the corresponding state variables, and z1, z2, and z3 are the feedback gain values ​​of the estimator to be designed, defined as follows:

[0022]

[0023] In the above formula, α1, α2, α3 and ε are the parameters to be designed;

[0024] Step 22: The estimation error of the estimator is defined as follows:

[0025]

[0026] The differential equation for the estimation error is then expressed as:

[0027]

[0028] In the above formula, It is the differential of the generalized rack force.

[0029] According to the Routh-Hulwitz stability criterion, when the first derivative of the external disturbance is zero, the necessary and sufficient condition for the stability of the differential equation for the estimation error given in the above equation is:

[0030]

[0031] Step 3: Design of the corner tracking controller:

[0032] Step 31: The performance function for finite-time convergence is defined as follows:

[0033]

[0034] in,

[0035]

[0036] In the above formula, t and t f These are the algorithm execution time and the user-preset error convergence time, respectively, ω. tf ω0 is the maximum allowable steady-state error after convergence, h is the initial error of the system, and h is the user-defined minimum allowable convergence rate.

[0037] Step 3.2, the error transformation function is defined as:

[0038]

[0039] The new error variable after the transformation is:

[0040]

[0041] In the above formula, e1(t) = x1 - x 1d x represents the rack displacement tracking error. 1d ξ1(t) represents the desired rack force displacement after conversion from the steering wheel angle command, and ξ1(t) represents the new error variable after error conversion.

[0042] Step 3: Design the control law for the angle tracking controller in two steps based on the backstepping method:

[0043] Step 1: For ease of writing, define ρ(t) = e1(t) / ω(t). Taking the derivative of the error variable after the transformation in step 3.2, we get:

[0044]

[0045] In the above formula, k ρ = (πsec) 2 (πρ / 2)) / (2ω(t)) is a positive number;

[0046] Then, the error in the rack speed is defined as e2(t) = x2 - x 2d Then the virtual control law x2d Represented as:

[0047]

[0048] In the above formula, k1 is the positive gain value to be designed;

[0049] The second step involves differentiating the rack speed tracking error from the first step and combining it with the formulas from steps one and two to obtain the desired control law. for:

[0050]

[0051] In the above formula, d = F e Here, k is the feedforward compensation value for the rack force estimator, and k2 is the positive gain value to be designed. This is the derivative of the virtual control law in the first step;

[0052] Step 4: Fault Tolerance Strategy Design for Displacement Sensor Failures:

[0053] This paper utilizes the rotary transformer of a permanent magnet synchronous motor to measure the motor angle and detect whether the rack displacement sensor is faulty. When a fault occurs, the displacement value converted from the measurement value by the motor rotary transformer is used as the displacement correction value after the fault, replacing the rack displacement signal involved in steps two and three. This implements a fault-tolerant strategy based on the displacement sensor fault. To prevent false detection and improve the accuracy of fault detection, the designed fault-tolerant strategy for the displacement sensor fault is to ensure at least continuous t thr The measurement error of the periodic rotary transformer and displacement sensor exceeds the fault threshold θ thr The fault tolerance strategy for displacement sensor failure is expressed as follows:

[0054]

[0055] In the above formula, θ r θ is the angle measured by the displacement sensor. s The angle θ is the motor angle measured by the rotary transformer and converted by the reduction ratio. thr t is the set threshold for the deviation of the sensor measurement value. thr For the set fault detection time threshold, t err This refers to the time when the fault occurred.

[0056] Compared with the prior art, the present invention has the following advantages:

[0057] I. The corner tracking control method based on finite-time convergence preset performance control of the present invention can simultaneously guarantee the transient and steady-state performance of corner tracking, and converge to the preset residual set within a preset time. Even under the condition of rack displacement sensor failure, it can still achieve good corner tracking performance, which is of great significance to the development of autonomous driving and chassis drive-by-wire in intelligent vehicles.

[0058] Second, the feedforward compensation method based on rack force estimator of the present invention can reduce the adverse effects of external disturbances on corner tracking control and at the same time improve the response speed of corner tracking.

[0059] Third, the fault-tolerant strategy based on the rotary transformer of the present invention can realize the fault tolerance capability of the steer-by-wire system under the condition of rack displacement sensor failure without increasing the cost and space of installing additional sensors, thereby improving the reliability of the steering angle tracking control method.

[0060] Fourth, the steer-by-wire system angle tracking and fault-tolerant control method of the present invention with preset performance has high computational efficiency, good real-time performance, can be easily implemented in embedded applications, and improves the reliability of the steer-by-wire system. Attached Figure Description

[0061] Figure 1 A flowchart of a steering-by-wire system with preset performance, showing the angle tracking and fault-tolerant control method.

[0062] Figure 2 The results show the rotation tracking under the angular step condition;

[0063] Figure 3 The results show the rotation angle tracking under serpentine pile driving conditions with sensor failure. Detailed Implementation

[0064] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0065] This invention provides a dynamic model based on the gear and rack structure of a steer-by-wire system. The method designs a rack force estimator to compensate for external disturbances, then proposes a preset performance function with finite-time convergence, designs a steering angle tracking controller, and proposes a fault-tolerant strategy based on a motor rotary transformer to address rack displacement sensor failures. Figure 1 As shown, the specific steps include the following:

[0066] Step 1: Establishing the dynamic model of the steering actuator in the steer-by-wire system:

[0067] Step 11: The dynamic model of the steering actuator consists of a steering motor and a steering mechanism connecting the steering wheels. The dynamic differential equation of the steering motor is:

[0068]

[0069] In the above formula, J m B m and K m θ represents the moment of inertia, damping coefficient, and torsional stiffness of the steering motor, respectively. m , and These are the rotation angle, angular velocity, and angular acceleration of the steering motor, respectively, G. m The reduction ratio from the motor crankshaft to the rack, r p T is the pitch circle radius of the pinion in a gear and rack mechanism. m This is the output torque of the crankshaft of the steering motor.

[0070] Steps 1 and 2: The steering wheel is rigidly connected to the rack and pinion mechanism. The dynamic model of the steering wheel can be expressed as the dynamic differential equation of the rack:

[0071]

[0072] In the above formula, m r and B r These represent the mass and damping coefficient of the rack, respectively. r , and F represents the displacement, velocity, and acceleration of the rack, respectively. f The frictional force F generated during the movement of the rack is the frictional force. r It is the rack force exerted on the outside of the wheel.

[0073] Step 13: Based on the mechanical connection between the motor output crankshaft and the rack mechanism, the second-order differential equation of the steering actuator is obtained as follows:

[0074]

[0075] In the above formula, and These are the equivalent mass and the equivalent damping coefficient, respectively.

[0076] F e =F f +F r For generalized rack force.

[0077] Step 2: Design of the rack force estimator:

[0078] Step 2.1. Estimate the generalized rack force given in Step 1. Based on Equation (3), establish the differential equation of the rack force estimator as follows:

[0079]

[0080] In the above formula, x1 = X r and The state variable of the estimator is x3 = F. e For the defined extended state, y = x1 is the output variable of the estimator. and These are the estimated values ​​of the corresponding state variables, and z1, z2, and z3 are the feedback gain values ​​of the estimator to be designed, defined as follows:

[0081]

[0082] In the above formula, α1, α2, α3 and ε are the parameters to be designed.

[0083] Step 22: The estimation error of the estimator is defined as follows:

[0084]

[0085] Differentiating the above equation and combining it with equations (3) and (6), the differential equation for the estimation error is expressed as:

[0086]

[0087] In the above formula, It is the differential of the generalized rack force.

[0088] According to the Routh-Herwitz stability criterion, when the first derivative of the external disturbance is zero, the necessary and sufficient condition for the stability of the estimation error differential equation expressed by equation (7) is:

[0089]

[0090] Step 3: Design of the corner tracking controller:

[0091] Step 31: The performance function for finite-time convergence is defined as follows:

[0092]

[0093] in,

[0094]

[0095] In the above formula, t and t f These are the algorithm execution time and the user-preset error convergence time, respectively, ω. tf ω0 is the maximum allowable steady-state error after convergence, h is the initial error of the system, and h is the user-defined minimum allowable convergence rate.

[0096] Step 3.2, the error transformation function is defined as:

[0097]

[0098] The new error variable after the transformation is:

[0099]

[0100] In the above formula, e1(t) = x1 - x 1d x represents the rack displacement tracking error. 1d ξ1(t) represents the desired rack force displacement after conversion from the steering wheel angle command, and ξ1(t) represents the new error variable after error conversion.

[0101] Step 3: Design the control law for the angle tracking controller in two steps based on the backstepping method:

[0102] First, for ease of writing, define ρ(t) = e1(t) / ω(t). Taking the derivative of the error variable in equation (11), we get:

[0103]

[0104] In the above formula, k ρ = (πsec) 2 (πρ / 2)) / (2ω(t)) is a positive number;

[0105] Then, the error in the rack speed is defined as e2(t) = x2 - x 2d Then the virtual control law x 2d It can be represented as:

[0106]

[0107] In the above formula, k1 is the positive gain value to be designed.

[0108] The second step is to define the error of the rack speed as e2(t) = x2 - x 2d Differentiating the error in the rack speed and combining it with equation (11), the desired control law of the angle tracking controller is obtained as follows:

[0109]

[0110] In the above formula, d = F e Here, k is the feedforward compensation value for the rack force estimator, and k2 is the positive gain value to be designed. This is the differential of the virtual control law in the first step.

[0111] Step 4: Fault Tolerance Strategy Design for Displacement Sensor Failures:

[0112] Before executing the algorithms in steps two and three, the motor angle measured by the rotary transformer of the permanent magnet synchronous motor is used to detect whether the rack displacement sensor has malfunctioned. When a fault occurs, the displacement value converted from the measurement value by the motor rotary transformer is used as the displacement correction value after the fault, replacing the rack displacement signal involved in steps two and three. This realizes the fault-tolerant strategy design based on displacement sensor faults. To achieve fault-tolerant control of the sensor and prevent false detections to improve fault detection accuracy, the designed fault-tolerant strategy for displacement sensor faults is to ensure at least continuous t... thr The measurement error of the periodic rotary transformer and displacement sensor exceeds the fault threshold θ thr The fault tolerance strategy for displacement sensor failure is expressed as follows:

[0113]

[0114] In the above formula, θ r θ is the angle measured by the displacement sensor. s The angle θ is the motor angle measured by the rotary transformer and converted by the reduction ratio. thr t is the set threshold for the deviation of the sensor measurement value. thr For the set fault detection time threshold, t err This refers to the time when the fault occurred.

[0115] Example:

[0116] This embodiment takes a rack and pinion steer-by-wire mechanism as an example, derives the dynamic model of the actuator of the steer-by-wire system, designs a rack force estimator to observe unmeasurable external disturbances in the system and compensates for the disturbances in the angle tracking controller design using a feedforward method, proposes a preset performance function with finite-time convergence and designs an angle tracking controller based on the backstepping method, and finally designs a fault-tolerant strategy for rack displacement sensor failure based on a motor rotary transformer.

[0117] This embodiment uses a steer-by-wire test bench for hardware-in-the-loop (HIL) experimental verification. Two domain controllers control the steering motor to track the desired steering angle and control the reaction force simulation motor to track the desired resistance torque, respectively. The controllers communicate with each other via the vehicle's CAN local area network, and experimental data is collected in the computer. The algorithm execution cycle is 1ms. The desired steering angle and desired resistance torque of the vehicle are provided by high-precision vehicle dynamics software. The experimental test conditions are selected as angular step steering and slalom steering, respectively. A sensor failure occurs at 5.5s.

[0118] Figure 2 The results of the angle tracking control method given in the embodiment show that the results of rack force estimation and angle tracking are good, and the steady-state performance and transient performance requirements of angle tracking are met, which significantly improves the angle tracking performance of the steer-by-wire system.

[0119] Figure 3 The results show the angle tracking under the condition of rack displacement sensor failure. It can be seen that the fault-tolerant strategy proposed in this embodiment can maintain normal angle tracking function under the condition of sensor failure, thus improving the reliability of the steer-by-wire system.

Claims

1. A method for angle tracking and fault-tolerant control of a steer-by-wire system with preset performance, characterized in that... The method includes the following steps: Step 1: Establishing the dynamic model of the steering actuator in the steer-by-wire system: Step 11: The dynamic model of the steering actuator consists of a steering motor and a steering mechanism connecting the steering wheels. The dynamic differential equation of the steering motor is: ； In the above formula, , and These represent the moment of inertia, damping coefficient, and torsional stiffness of the steering motor, respectively. , and These are the rotation angle, angular velocity, and angular acceleration of the steering motor, respectively. This is the reduction ratio from the motor crankshaft to the rack. Let be the pitch circle radius of the pinion in the gear and rack mechanism. This refers to the output torque of the crankshaft of the steering motor; Steps 1 and 2: The steering wheel is rigidly connected to the rack and pinion mechanism. The dynamic model of the steering wheel is represented by the dynamic differential equation of the rack: ； In the above formula, and These are the mass and damping coefficient of the rack, respectively. , and These represent the displacement, velocity, and acceleration of the rack, respectively. It is the frictional force generated during the movement of the rack and pinion. It is the rack force acting on the outside of the wheel; Step 13: Based on the mechanical connection between the motor output crankshaft and the rack mechanism, the second-order differential equation of the steering actuator is obtained as follows: ； In the above formula, and These are the equivalent mass and the equivalent damping coefficient, respectively. For generalized rack force; Step 2: Design of the rack force estimator: Step 2.

1. Estimate the generalized rack force given in Step 1. Based on the second-order differential equation of the steering actuator, establish the following differential equation for the rack force estimator: ； In the above formula, and These are the state variables of the estimator. For the defined expansion state, For the output variable of the estimator, , and These are the estimated values ​​of the corresponding state variables. , and The feedback gain value is provided for the estimator to be designed; Step 22: The estimation error of the estimator is defined as follows: ； The differential equation for the estimation error is then expressed as: ； In the above formula, It is the differential of the generalized rack force. , ; In the above formula, , , and These are the parameters to be designed; Step 3: Design of the corner tracking controller: Step 31: The performance function for finite-time convergence is defined as follows: ； in, ， ； In the above formula, and These are the algorithm execution time and the user-preset error convergence time, respectively. This represents the maximum allowable steady-state error after convergence. This is the initial error of the system. Minimum allowed convergence rate as defined by the user; Step 3.2, the error transformation function is defined as: ； The new error variable after the transformation is: ； In the above formula, For rack displacement tracking error, The desired rack force displacement is the result of the steering wheel angle command. The new error variable after error transformation; Step 3: Design the control law for the angle tracking controller in two steps based on the backstepping method: Step 1, Definition Taking the derivative of the transformed error variable in step 3.2, we get: ； In the above formula, It is a positive number; Then, the error of the rack speed is defined as... Then virtual control law Represented as: ； In the above formula, The positive gain value to be designed; The second step involves differentiating the rack speed tracking error from the first step and combining it with the formulas from steps one and two to obtain the desired control law. for: ； In the above formula, This is the feedforward compensation value for the rack force estimator. The positive gain value to be designed. This is the derivative of the virtual control law in the first step; Step 4: Fault Tolerance Strategy Design for Displacement Sensor Failures: The motor angle is measured by the rotary transformer of the permanent magnet synchronous motor to detect whether the rack displacement sensor has failed. When a failure occurs, the displacement value converted from the measurement value of the motor rotary transformer is used as the displacement correction value after the failure to replace the rack displacement signal involved in steps two and three, thus realizing the fault-tolerant strategy design based on displacement sensor failure.

2. The method for angle tracking and fault-tolerant control of a steer-by-wire system with preset performance as described in claim 1, characterized in that... In step two, , and Defined as: ， ， 。 3. The method for angle tracking and fault-tolerant control of a steer-by-wire system with preset performance as described in claim 1, characterized in that... In step two, according to the Routh-Herwitz stability criterion, when the first derivative of the external disturbance is zero, the necessary and sufficient condition for the stability of the differential equation for the estimation error is: ， ， 。 4. The method for angle tracking and fault-tolerant control of a steer-by-wire system with preset performance as described in claim 1, characterized in that... In step four, to prevent false detections and improve the accuracy of fault detection, the designed fault-tolerant strategy for displacement sensor faults is at least continuous The measurement error of the periodic rotary transformer and displacement sensor exceeds the fault threshold. The fault tolerance strategy for displacement sensor failure is expressed as follows: ； In the above formula, The angle measured by the displacement sensor. The angle of the motor measured by the rotary transformer is the angle after conversion by the reduction ratio. The set threshold for the deviation of the sensor measurement values. The set fault detection time threshold, This refers to the time when the fault occurred.

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