Steer-by-wire angle following control method based on linear quadratic regulator

Abstract

The present disclosure comprises: on the basis of establishing a dynamic model of a steer-by-wire actuator and converting an equation of the dynamic model into a state-space equation form, obtaining an angle difference and an angular velocity difference, and calculating a control quantity of an LQR controller; using the angle difference and the angular velocity difference as inputs, and constructing a system error equation on the basis of the above state-space equation; solving a Riccati equation using an iterative method to obtain a gain matrix, and, on the basis of the gain matrix, calculating an LQR torque in the design of the LQR controller; by designing an observer, implementing a feedforward compensation strategy and calculating a feedforward torque; and, on the basis of the feedforward torque and the LQR torque, obtaining a total torque input to the system. The disclosure uses the LQR solution to achieve the optimal gain, avoiding repeated parameter trial and error by engineers, while taking into account system convergence speed and system energy consumption. The feedforward is calculated in real time using the observer, enhancing the anti-interference capability of the system and improving system response speed.

Description

A steer-by-wire angle following control method based on linear quadratic regulation

[0001] This disclosure claims priority from Chinese patent application CN202410108286.9, filed January 26, 2024. This application incorporates the entire text of the aforementioned Chinese patent application. Technical Field

[0002] The present disclosure relates to the technical field of steering systems, and in particular to a wire-controlled steering angle following control method based on linear quadratic regulation. Background Art

[0003] Traditional automotive steering systems achieve wheel steering by connecting the steering wheel to a mechanical transmission mechanism. Steer-by-wire (SBW) systems eliminate the intermediate shaft connecting the steering wheel and mechanical transmission mechanism. Instead, they use control methods to control the steering actuator in response to steering wheel signals, thereby achieving wheel steering. In SBW systems, vehicle operating conditions are complex and variable, and the addition of variable transmission ratios places even higher demands on steering tracking performance. Therefore, a steering tracking control method with high steering tracking accuracy and robustness is needed to ensure that the wheels accurately and quickly respond to steering wheel command signals.

[0004] The PID algorithm (a control algorithm that combines proportional, integral, and differential control) is widely used in steering systems. However, practical applications present parameter tuning challenges. Engineers often struggle to achieve optimal gain during commissioning, as gain directly impacts system stability and response speed. Furthermore, small angle requests can lead to issues such as failure to achieve the target angle and increased response delays. Parameter gains must be re-tuned for each system, resulting in poor parameter interoperability and poor anti-interference capabilities.

[0005] Summary of the Invention

[0006] In order to overcome the shortcomings of the existing technology, the present disclosure provides a wire-controlled steering angle following control method based on linear quadratic regulation. It can not only solve the optimal gain through LQR (Linear Quadratic Regulator), avoiding engineers' repeated trial and error of parameters, but also take into account the system convergence speed and system energy consumption. The feedforward is calculated in real time through the observer, which not only enhances the system's anti-interference ability, but also helps to improve the system response speed.

[0007] To achieve the above objectives, a steer-by-wire angle following control method based on linear quadratic regulation is designed, which includes an LQR controller and an observer. The specific method is as follows:

[0008] Step 1: Establish a dynamic model of the steer-by-wire actuator;

[0009] Step 2, transforming the equation of the dynamic model in step 1 into the form of a spatial state equation;

[0010] Step 3: When designing the LQR controller, it is necessary to obtain the state information of the steering system, including the steering wheel angle and the actual angle, the angle difference is recorded as e1; the steering wheel angular velocity and the actual angular velocity, the angular velocity difference is recorded as e2;

[0011] Step 4: The control quantity of the LQR controller is: u = -Ke; where the gain matrix k1 is the gain of the angle difference, k2 is the gain of the angular velocity difference, and the error matrix

[0012] Step 5: Using the angle difference and angular velocity difference as input, construct the system error equation according to the spatial state equation in step 2;

[0013] Step 6, solve the Riccati equation by iterative method to obtain the gain matrix K;

[0014] Step 7: Based on the gain matrix K, in the design of the LQR controller, calculate the LQR torque u lqr ;

[0015] Step 8: Design an observer to implement feedforward compensation strategy and calculate the feedforward torque u f ;

[0016] Step 9: In the line control execution system, the total torque input to the system is determined by the feedforward torque u f and LQR torque u lqr The total torque of the system is: u = u lqr +u f .

[0017] The equation of the kinetic model in step 1 is Where J and B are the equivalent moment of inertia and damping coefficient; θ is the actual rotation angle; T mot , F fri and F rack are motor torque, friction force and rack force respectively, and G1 and G2 are the equivalent steering ratios of friction force and rack force.

[0018] The spatial state equation in step 2 is Among them, the matrix matrix matrix matrix State variables Interference resistance Fd =F fri +F rack , system input u=T mot , system output y. Among them,

[0019] The LQR controller is a full-state feedback controller.

[0020] In step 5, the error equation of the system is

[0021] In step 6, the specific equation is Among them, the error weight matrix The weight matrix of the control amount is R=1.

[0022] The feedforward compensation is to compensate for the steering disturbance resistance through an algorithm, which is beneficial to improving the interference resistance and response speed of the time-varying system during control.

[0023] In step 7, in the design of the LQR controller, the weight matrices Q and R are fixed. However, in practice, the inaccuracy of the modeling must be taken into account. The wire control execution system has certain simplifications and some nonlinear time-varying conditions, which will reduce the tracking accuracy of the LQR controller. Therefore, a feedforward compensation strategy is added.

[0024] In step 8, when designing the observer, the state space equation and output of the steering system are obtained, which are obtained in step 2. The state space equation is as follows: Among them, the system state quantity of the observer is Observer gain matrix Among them, l1 and l2 are the weighted deviations. Selecting appropriate gains can facilitate rapid convergence of the system.

[0025] Compared with the existing technology, the present disclosure provides a wire-controlled steering angle following control method based on linear quadratic regulation, which can not only solve the optimal gain through LQR, avoiding engineers' repeated trial and error of parameters, but also take into account the system convergence speed and system energy consumption. The feedforward is calculated in real time through the observer, which not only enhances the system's anti-interference ability, but also helps to improve the system response speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG1 is a calculation flow chart of the present disclosure.

[0027] FIG2 is a control principle diagram of the present disclosure.

[0028] FIG3 is a diagram showing the slope signal response results of a real vehicle disclosed in the present invention.

[0029] FIG4 is a diagram showing the sinusoidal signal response results of a real vehicle disclosed in the present invention. DETAILED DESCRIPTION

[0030] The present disclosure is further described below with reference to the accompanying drawings.

[0031] The present disclosure provides an angle following control method based on feedforward linear quadratic regulation. The calculation process of the angle following control method is shown in FIG1 . The specific operations are as follows:

[0032] Step 1: Establish the dynamic model of the steer-by-wire actuator: Where J and B are the equivalent moment of inertia and damping coefficient, and θ is the actual rotation angle. Figure 2 is the control principle diagram of the angle following control method, where θ in Figure 2 is d is the requested turning angle, T mot , F fri and F rack are the motor torque, friction force and rack force respectively, and G1 and G2 are the equivalent steering ratios of friction force and rack force respectively.

[0033] Step 2: Write the dynamic equation in step 1 into the form of its spatial state equation, as follows: Among them, the matrix matrix matrix matrix State variables Interference resistance F d =F fri +F rack , system input u=T mot , system output y.

[0034] Step 3: When designing the LQR controller, it is necessary to obtain the state information of the steering system, including the difference between the steering wheel angle and the actual angle, denoted as e1; and the difference between the steering wheel angular velocity and the actual angular velocity, denoted as e2.

[0035] Step 4: LQR controller design is a full-state feedback controller, and its control quantity is designed as follows: u = -Ke, where the gain matrix Error Matrix

[0036] Step 5: Using the angle difference and angular velocity difference as input, construct the error equation of the system based on the spatial equation in step 2:

[0037] Step 6: The purpose of the LQR controller is to find a set of system state variables when the control variable is small enough by introducing a cost function to meet the system stability. Then, the gain matrix K is obtained by solving the Riccati equation through an iterative method. The details are as follows: Among them, the error weight matrix The weight matrix of the control amount is R=1.

[0038] Step 7: In the design of the LQR controller, the weight matrices Q and R are fixed. However, in practice, the inaccuracy of the modeling must be taken into account. The wire-controlled execution system has certain simplifications and some nonlinear time-varying conditions, which will reduce the tracking accuracy of the LQR controller. Therefore, a feedforward compensation strategy is added.

[0039] Step 8: The idea of ​​feedforward compensation is to compensate for the steering disturbance resistance through an algorithm. This helps improve the interference resistance and response speed of the time-varying system during control. Since the actual disturbance resistance is difficult to measure with sensors, this paper introduces an observer algorithm to supplement the sensor information.

[0040] Step 9: When designing the observer, the state space equation and output of the steering system must be obtained. Both are obtained in step 2. The state space equation is as follows: Among them, the system state quantity of the observer is Observer gain matrix

[0041] Step 10: In the online control execution system, the system input consists of the feedforward part and the LQR control part. The system control quantity is as follows: u = u lqr +u f ; Among them, the LQR calculation part u lqr , feedforward calculation part u f .

[0042] As shown in Figures 3 and 4, Figure 3 shows the collected slope signal response results of an actual vehicle, where the solid line corresponds to the slope request angle and the dashed line corresponds to the actual angle; Figure 4 shows the collected sinusoidal signal response results of an actual vehicle, where the solid line corresponds to the sinusoidal request angle and the dashed line corresponds to the actual angle. It can be seen that by setting steps 1 to 10, the present disclosure not only reduces the debugging difficulty for engineers, but also improves the system's response speed and anti-interference ability. It also avoids the problem of small angles failing to achieve the target requested angle, thus demonstrating that the present disclosure is more suitable for high-precision steer-by-wire systems.

[0043] Although the specific embodiments of the present disclosure have been described above, those skilled in the art will appreciate that these are merely illustrative and that various changes or modifications may be made to these embodiments without departing from the principles and essence of the present disclosure. Therefore, the scope of protection of the present disclosure is defined by the appended claims.

Claims

1. A steer-by-wire steering angle following control method based on linear quadratic regulator, including an LQR controller and an observer, characterized in that: The specific method is as follows: Step 1: Establish the dynamic model of the steer-by-wire actuator; Step 2: Transform the equation of the dynamic model in Step 1 into the form of a state-space equation; Step 3: When designing the LQR controller, the state information of the steering system needs to be obtained, including the steering wheel angle and the actual angle, and the angle difference is denoted as e1; the angular velocity of the steering wheel and the actual angular velocity, and the angular velocity difference is denoted as e2; Step 4, the control quantity of the LQR controller is: u = -Ke; where, the gain matrix Error matrix Step 5: Using the angle difference and the angular velocity difference as inputs, construct the error equation of the system according to the state-space equation in Step 2; Step 6: Solve the Riccati equation by the iterative method to obtain the gain matrix K; Step 7, in the design of the LQR controller, calculate the LQR torque u according to the gain matrix K lqr ; Step 8, design an observer, implement a feedforward compensation strategy, and calculate the feedforward torque u f ; Step 9, in the by-wire execution system, the total torque input to the system consists of the feedforward torque u f and the LQR torque u lqr . The total torque of the system: u = u lqr + u f .

2. The angle following control method of steer-by-wire based on linear quadratic regulator according to claim 1, characterized in that: The equation of the kinetic model in Step 1 is where J and B are the equivalent moment of inertia and damping coefficient; θ is the actual rotation angle; T mot , F fri and F rack are the motor torque, frictional force, and rack force respectively, and G1 and G2 are the equivalent steering ratios of the frictional force and the rack force respectively.

3. A steer-by-wire steering angle following control method based on linear quadratic regulator according to claim 2, characterized in that: The spatial state equation in Step 2 described above is where the matrix the matrix the matrix the matrix the state variable the interference resistance F d = F fri + F rack and the system input u = T mot and the system output y.

4. A steer-by-wire steering angle following control method based on linear quadratic regulator according to claim 1, characterized in that: The LQR controller mentioned is a full-state feedback controller.

5. A steer-by-wire steering angle following control method based on linear quadratic regulator according to claim 3, characterized in that: In the said step 5, the error equation of the system is 6. A steer-by-wire steering angle following control method based on linear quadratic regulator according to claim 1, characterized in that: In the said Step 6, the specific equation is where the weight matrix of the error and the weight matrix R of the control variable is 1.

7. A steer-by-wire steering angle following control method based on linear quadratic regulator, characterized in that: The feedforward compensation mentioned compensates for the steering interference resistance through an algorithm, so that in the control, it is beneficial to improve the anti-interference ability and response speed of the time-varying system.

8. A steer-by-wire steering angle following control method based on linear quadratic regulator according to claim 1, characterized in that: In Step 7 mentioned, in the design of the LQR controller, the weight matrices Q and R are fixed, but in practice, the inaccuracy of modeling needs to be considered. There are certain simplifications and some non-linear time-varying situations in the steer-by-wire actuator system, which will reduce the tracking accuracy of the LQR controller. Therefore, a feedforward compensation strategy is added.

9. A steer-by-wire steering angle following control method based on linear quadratic regulator according to claim 1, characterized in that: In step 8 mentioned above, when designing the observer, the state space equation and output of the steering system need to be obtained, which have already been obtained in step 2. The state space equation is as follows: Among them, the system state quantity of the observer Observer gain matrix

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