A path tracking control method for a steer-by-wire vehicle based on actuator dynamics and time delay

Abstract

A kind of based on actuator dynamic and time delay's drive-by-wire steering vehicle path tracking control method, comprising: obtaining current vehicle state information and road curvature information;Establish lateral dynamics path tracking model, and construct basic state vector;Through the first-order response of steering actuator and the first-order pad approximation of communication delay, establish actuator time delay subsystem, then obtain parameter-dependent augmented state space model containing actuator time delay internal state;Build finite design envelope, and generate multiple sampling augmented controlled object;Solve static measurable output feedback gain;Calculate the curvature feedforward gain related to longitudinal vehicle speed, and then generate front wheel steering control instruction;Finally, the front wheel steering control instruction is output to drive-by-wire steering actuator.The present application can solve the problems that prior art ignores steering channel delay and actuator response lag, fixed vehicle parameters are difficult to adapt to vehicle speed and side stiffness change, and feedback control structure engineering measurability is insufficient.

Description

Technical Field

[0001] This invention relates to the field of path tracking control technology for autonomous vehicles, and more specifically to a path tracking control method for steer-by-wire vehicles based on actuator dynamics and time delay. Background Technology

[0002] Path tracking control is a crucial foundation for the safe, stable, and high-precision driving of autonomous vehicles. As a key component of autonomous driving, steer-by-wire does not generate the front wheel steering angle instantaneously from controller commands. The transmission of control commands from the central controller to the steering actuator typically involves communication delays, computation delays, scheduling delays, and filtering delays. Furthermore, the steering actuator itself exhibits mechanical response lag. If the communication delays and steering actuator dynamics are simplified to ideal inputs in the path tracking controller design, it can easily lead to a reduction in closed-loop phase margin, resulting in steering lag, increased lateral error, and even oscillating instability under high-speed single-lane change, double-lane change, or rapid curvature change conditions.

[0003] Furthermore, vehicle longitudinal speed and tire lateral stiffness vary with load, road adhesion conditions, tire operating conditions, and steering effort. Traditional controllers are typically designed based on fixed vehicle speeds or fixed lateral stiffness parameters, making it difficult to simultaneously ensure stability and tracking accuracy under different vehicle speeds and equivalent lateral stiffness conditions for the front and rear axles. While some existing methods can improve performance through complex control structures or online optimization, their feedback may depend on internal states that cannot be directly measured, or they lack a guaranteed cost-performance upper bound description of the augmented steering-by-wire channel, thus limiting engineering deployment and stability interpretation. Summary of the Invention

[0004] In view of this, the present invention provides a steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay, in order to solve the problems of existing technologies that ignore steering channel delay and actuator response lag, fixed vehicle parameters are difficult to adapt to changes in vehicle speed and lateral stiffness, and the feedback control structure has insufficient engineering measurability.

[0005] A steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay includes: Step S1: Based on the path tracking status, vehicle motion status, and road curvature of the steer-by-wire vehicle, obtain the current vehicle status information and road curvature information; wherein, the path tracking status includes at least lateral error and heading angle error, and the vehicle motion status includes at least longitudinal speed, lateral speed, yaw rate, and actual front wheel steering angle. Step S2: Based on the current vehicle state information obtained in Step S1, establish a lateral dynamic path tracking model for the steer-by-wire vehicle, and construct a basic state vector consisting of lateral error, heading angle error, lateral speed, and yaw rate. Step S3: Based on the lateral dynamic path tracking model obtained in step S2, the actuator delay subsystem is established by combining the first-order response of the steering actuator and the first-order Pad approximation of the communication delay. The actuator delay subsystem is then coupled with the lateral dynamic path tracking model to obtain a parameter-dependent augmented state space model that includes the internal state of the actuator delay. Step S4: Based on the parameter-dependent augmented state-space model obtained in step S3, a finite design envelope is constructed according to the longitudinal vehicle speed range and the variation range of the equivalent lateral stiffness of the front and rear axles, and multiple sampled augmented controlled objects are generated within the finite design envelope. Step S5: Based on the multiple sampled augmented controlled objects obtained in step S4, solve for the static measurable output feedback gain so that the feedback regulation subsystem when the curvature input is zero satisfies the asymptotic stability condition and the upper bound condition for guaranteeing cost. Step S6: Based on the static measurable output feedback gain obtained in step S5, and according to the road curvature information and steady-state path curvature balance relationship obtained in step S1, calculate the curvature feedforward gain related to the longitudinal vehicle speed, and then generate the front wheel steering control command from the static measurable output feedback gain, curvature feedforward gain and road curvature. Step S7: Output the front wheel steering control command generated in step S6 to the steer-by-wire actuator to achieve vehicle path tracking control.

[0006] The steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay provided by the present invention has the following advantages: (1) This invention embeds both communication delay and steering actuator dynamics into the path tracking augmented model simultaneously, avoiding the simplification of the steering channel as an ideal input element. This invention transforms the communication delay into a finite-dimensional state-space expression through the first-order Pad approximation, and connects it in series with the first-order response of the actuator to form a second-order strictly rational subsystem, thereby effectively compensating for steering lag and phase delay, improving the controller's adaptability under rapid curvature change conditions, and solving the problem of neglecting steering channel delay and actuator response lag in existing technologies.

[0007] (2) The feedback control law of the present invention only relies on measurable signals such as lateral error, heading angle error, lateral vehicle speed, yaw rate and actual front wheel angle. The internal state of the actuator delay is only retained in the augmented model for stability analysis and gain solution, and is not used as an online feedback quantity. The equivalent performance of state feedback can be achieved without adding additional real vehicle sensors, which effectively solves the problem of insufficient engineering measurability of feedback control structure.

[0008] (3) The present invention constructs a finite design envelope by changing the longitudinal vehicle speed and the equivalent lateral stiffness of the front and rear axles, so that the same static output feedback gain can maintain closed-loop stability and preset performance constraints under multiple vehicle speed and lateral stiffness sampling combinations. This solves the problem that fixed vehicle parameters are difficult to adapt to changes in vehicle speed and lateral stiffness, and enhances the robustness of the controller under different working conditions.

[0009] (4) By introducing a guarantee cost upper bound and a feedback command change rate penalty term to jointly design feedback gain, this invention can effectively limit high-frequency steering commands and steering oscillations while suppressing lateral tracking errors. On the one hand, it improves path tracking accuracy, and on the other hand, it reduces the mechanical load and energy consumption of the actuator and improves steering smoothness.

[0010] (5) This invention can be deployed on a steer-by-wire vehicle platform, combining position, speed, heading angle, yaw rate, and front wheel steering angle feedback to form a closed-loop control. Real vehicle verification results show that, under single and double lane change conditions, compared with the comparison algorithm that does not explicitly consider actuator response and communication delay, the method of this invention maintains a lower lateral error peak while reducing excessive steering requirements, and has better engineering feasibility and control effect. Attached Figure Description

[0011] Figure 1 A flowchart illustrating the steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay provided in an embodiment of the present invention; Figure 2 This is a comparison chart of experimental tracking results under different operating conditions. Detailed Implementation

[0012] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0013] Please see Figure 1 The present invention provides a steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay, comprising steps S1 to S7: Step S1: Based on the path tracking status, vehicle motion status, and road curvature of the steer-by-wire vehicle, obtain the current vehicle status information and road curvature information; wherein, the path tracking status includes at least lateral error and heading angle error, and the vehicle motion status includes at least longitudinal speed, lateral speed, yaw rate, and actual front wheel steering angle.

[0014] Specifically, the system acquires vehicle position, speed, yaw rate, and actual front wheel steering angle through a combination of navigation, vehicle status acquisition devices, and steering angle sensors. The desired path is then loaded into the controller, which calculates the coordinate difference, lateral error, and heading angle error based on the current position and a reference point. The coordinate difference is calculated as follows:

[0015]

[0016] in, The vehicle's current position and reference point are displayed globally. Positional deviation in direction The vehicle's current position and reference point are displayed globally. Positional deviation in direction and These are the global x and y coordinates of the vehicle's current position, respectively. and These are the global x and y coordinates of the reference point for the desired path, respectively.

[0017] The formulas for calculating lateral error and heading angle error are as follows:

[0018]

[0019] in, This refers to lateral error; This refers to the heading angle error; This refers to the vehicle's heading angle; For reference heading angle; This is the angle normalization function.

[0020] Step S2: Based on the current vehicle state information obtained in Step S1, establish a lateral dynamic path tracking model for the steer-by-wire vehicle, and construct a basic state vector consisting of lateral error, heading angle error, lateral speed, and yaw rate.

[0021] The expression for the basic state vector is:

[0022] in, Based on the basic state vector, This represents the lateral error of the vehicle relative to the desired path. This represents the heading angle error of the vehicle relative to the desired path. The lateral speed is the speed of the vehicle. The yaw rate is angular velocity. This indicates transpose.

[0023] The expression for the lateral dynamic path tracking model is:

[0024] in, Basic state vector The first derivative with respect to time, The state matrix of the basic vehicle path tracking model The input matrix is ​​the front wheel steering angle. This is the actual front wheel steering angle. The road curvature input matrix is ​​used. The curvature of the road.

[0025] In a specific symbolic expansion method, the above basic vehicle matrix can be written as:

[0026]

[0027]

[0028] in, This refers to the longitudinal speed of the vehicle. For the overall vehicle weight; This is the distance from the center of gravity to the front axle. This is the distance from the center of mass to the rear axle; The yaw moment of inertia of the vehicle; This is the equivalent lateral stiffness of the front axle; This is the equivalent lateral stiffness of the rear axle.

[0029] It should be noted that the equivalent lateral stiffness of the front axle and the equivalent lateral stiffness of the rear axle in the above matrix refer to the equivalent lateral stiffness of the front and rear axles of the whole vehicle, rather than the lateral stiffness of a single tire.

[0030] Step S3: Based on the lateral dynamic path tracking model obtained in step S2, the actuator delay subsystem is established by combining the first-order response of the steering actuator and the first-order Pad approximation of the communication delay. The actuator delay subsystem is then coupled with the lateral dynamic path tracking model to obtain a parameter-dependent augmented state-space model that includes the internal state of the actuator delay.

[0031] The transfer function of the actuator delay subsystem is obtained from the first-order response of the steering actuator and the communication delay element, and its expression is:

[0032] in, The transfer function is for the actuator delay subsystem consisting of the steering actuator and communication delay. For the Laplace operator, Actual front wheel steering angle Laplace transform, Front wheel steering control command Laplace transform, Let the first-order response time constant of the steering actuator be... This refers to the communication delay time.

[0033] The communication delay element employs the first-order Pad approximation to characterize the phase lag characteristics of the communication delay in a finite-dimensional state space, expressed as:

[0034] The first-order response of the steering actuator and the first-order Pad approximation of the communication delay are connected in series to form a second-order strictly rational actuator delay subsystem.

[0035] The actuator delay subsystem is converted into a state-space form, expressed as:

[0036]

[0037] in, This is the internal state vector of the actuator delay subsystem. for The first derivative with respect to time, The state matrix of the actuator delay subsystem is... The input matrix of the actuator delay subsystem is... The output matrix of the actuator delay subsystem. For the pass-through matrix of the actuator delay subsystem, This is a command to control the steering of the front wheels.

[0038] The internal state vector of the actuator delay subsystem includes two internal state components, and its direct transit term is zero.

[0039] Simultaneously, a parameter-dependent augmented state-space model is constructed. The basic lateral dynamics path-tracking model is coupled with the actuator delay subsystem to obtain the augmented state, measurable output, and augmented controlled object. Specifically, the augmented state vector of the parameter-dependent augmented state-space model is:

[0040] in, For parameter-dependent augmented state vectors, and For the internal state components of the actuator delay subsystem.

[0041] The parameter-dependent augmented state-space model is represented as follows:

[0042]

[0043] in, For augmented state vectors The first derivative with respect to time, For parameter-dependent augmented system matrices, For parameter-dependent control input matrix, To match longitudinal vehicle speed The relevant augmented curvature input matrix, For the scheduling parameter vector, For measurable output vectors, This is a measurable output matrix.

[0044] The augmented matrix described above can be represented in the following block matrix form:

[0045]

[0046]

[0047]

[0048] In the formula, Let be a fourth-order identity matrix, and 0 be the zero matrix of the corresponding dimension. The internal state vector of the actuator delay subsystem dimensionality 4 lines The zero matrix of columns, for A zero matrix with 4 rows and 4 columns. for A zero matrix with 1 row and 1 column.

[0049] The measurable output vector is:

[0050] The internal state of the actuator delay subsystem is preserved in the augmented state space model for delay compensation and stability assessment, but is not directly used as feedback measurement.

[0051] It should be noted that the lateral speed can be a directly measured value or an estimate obtained by the vehicle state estimator based on integrated navigation, inertial measurement, and vehicle motion information.

[0052] Step S4: Based on the parameter-dependent augmented state-space model obtained in step S3, a finite design envelope is constructed according to the longitudinal vehicle speed range and the variation range of the equivalent lateral stiffness of the front and rear axles, and multiple sampled augmented controlled objects are generated within the finite design envelope.

[0053] Among them, sampling rules are set according to the longitudinal vehicle speed range and the variation range of the equivalent lateral stiffness of the front and rear axles to generate multiple sampling augmented controlled objects. The equivalent lateral stiffness of the front and rear axles, within their respective variation ranges, is represented by normalized uncertain variables as follows:

[0054]

[0055] in, This is the equivalent lateral stiffness of the front axle. For the equivalent lateral stiffness of the rear axle, This is the nominal value of the equivalent lateral stiffness of the front axle. This is the nominal value of the equivalent lateral stiffness of the rear axle. The normalized disturbance variable for the front axle equivalent lateral stiffness is denoted as . , For the normalized disturbance variable of the equivalent lateral stiffness of the rear axle, , This represents the amplitude of the equivalent lateral stiffness change of the front axle. This represents the amplitude of the equivalent lateral stiffness change of the rear axle.

[0056] The scheduling parameter vector is represented as follows:

[0057] in, For the scheduling parameter vector, , The design envelope consists of longitudinal vehicle speed and equivalent lateral stiffness disturbances of the front and rear axles. This represents the vehicle's longitudinal speed.

[0058] The finite design envelope is formed by combining multiple longitudinal vehicle speed samples, multiple front axle equivalent lateral stiffness samples, and multiple rear axle equivalent lateral stiffness samples. The number of controlled objects whose sampling augmentation is performed is:

[0059] in, To increase the total number of controlled objects in the sampling, This represents the number of longitudinal vehicle speed samples. This represents the number of samples for the equivalent lateral stiffness of the front axle. This represents the number of samples for the equivalent lateral stiffness of the rear axle.

[0060] It should be noted that when the number of equivalent lateral stiffness sampling points of the front axle and the number of equivalent lateral stiffness sampling points of the rear axle are the same and both are the same number, the number of controlled objects for sampling augmentation can be degenerated into the product of the number of vehicle speed sampling points and the square of the number of lateral stiffness sampling points.

[0061] Step S5: Based on the multiple sampled augmented controlled objects obtained in step S4, solve for the static measurable output feedback gain so that the feedback regulation subsystem with zero curvature input satisfies the asymptotic stability condition and the upper bound condition for guaranteeing cost.

[0062] Among them, the measurable output feedback gain is used as the optimization variable. A closed-loop matrix is ​​established for each sampled augmented controlled object, and evaluation quantities such as closed-loop poles, stability margin, damping characteristics, oscillation frequency, feedback gain amplitude, and feedback command change rate are calculated.

[0063] The static measurable output feedback gain is a one-row, five-column feedback gain vector, which acts on the measurable output vector; for the first... For a sampled augmented controlled object, the closed-loop matrix when the curvature input is zero is:

[0064] in, For the first The closed-loop system matrix corresponding to each sampled augmented controlled object. For the first The system matrix of a sampled augmented controlled object For the first A sampled augmented control input matrix for the controlled object. For statically measurable output feedback gain, This is a measurable output matrix.

[0065] Define the closed-loop performance weight matrix of the feedback regulation subsystem as follows:

[0066] in, For the first The closed-loop performance weight matrix corresponding to each sampled augmented controlled object. To augment the state weight matrix, This is the weight matrix for the front wheel steering control commands.

[0067] If there exists a symmetric positive definite matrix such that Then the first The closed-loop feedback control subsystem of the sampled augmented controlled object is asymptotically stable and satisfies the upper bound condition for guaranteed cost. For the first The Lyapunov positive definite matrix corresponding to the sampled augmented controlled object.

[0068] The guaranteed cost index is a weighted quadratic integral of the closed-loop state and the front wheel steering control command. The guaranteed cost index corresponding to each sampled augmented controlled object The expression is:

[0069] in, The first derivative of the front wheel steering control command with respect to time is given. The penalty weight for the rate of change of the feedback instruction. For time.

[0070] The expression for the guarantee cost upper bound condition is:

[0071] in, To augment the initial state of the system, To ensure an upper bound on cost, the guaranteed upper bound on cost is used to limit the overall quadratic performance of the feedback regulation subsystem under a given initial state.

[0072] In this embodiment, when solving for the static measurable output feedback gain, a penalty term for the rate of change of feedback command is introduced to suppress high-frequency steering commands.

[0073] When a candidate feedback gain can make the closed-loop stability of the sampled augmented controlled object stable, the Lyapunov equation is solved and the guarantee cost term is calculated; if the closed-loop stability or engineering constraints do not meet the requirements, a penalty is imposed on the optimization objective.

[0074] For the For each sampled augmented controlled object, the closed-loop performance weight matrix after introducing a penalty term is defined as follows: :

[0075] in, Used to convert the control input weighted terms into a quadratic form with respect to the augmented state. Used to convert the feedback instruction rate of change penalty term into a quadratic form with respect to the augmented state; Furthermore, the statically measurable output feedback gain To optimize the variables and minimize the comprehensive objective function, the expression for the comprehensive objective function is:

[0076] in, For the comprehensive objective function, For the first The sampling augmented controlled object has a statically measurable output feedback gain. The following performance indicators This is a stability margin penalty term, used to impose a penalty when the real part of the maximum closed-loop pole is higher than a preset stability margin threshold; This is a damping ratio penalty term, used to apply a penalty when the closed-loop complex pole damping ratio is lower than a preset lower limit; This is an oscillation frequency penalty term, used to impose a penalty when the closed-loop complex pole oscillation frequency exceeds a preset upper limit. This is a feedback gain regularization term used to limit the magnitude of the statically measurable output feedback gain.

[0077] Specifically, the optimization process can be performed using a direct search method with multiple initial values. After each search, the comprehensive objective function value and worst-case closed-loop stability margin of the candidate feedback gain are compared across all sampled augmented controlled objects. The feedback gain that meets the stability requirements and has a smaller comprehensive objective function value is selected as the offline feedback gain.

[0078] Step S6: Based on the static measurable output feedback gain obtained in step S5, and according to the road curvature information and steady-state path curvature balance relationship obtained in step S1, calculate the curvature feedforward gain related to the longitudinal vehicle speed, and then generate the front wheel steering control command from the static measurable output feedback gain, curvature feedforward gain and road curvature.

[0079] Specifically, for a given longitudinal vehicle speed and constant road curvature, the steady-state yaw rate, steady-state lateral vehicle speed, and steady-state front wheel angle are calculated based on the steady-state path curvature balance relationship. The steady-state control command is then obtained by combining the steady-state relationship of the actuator time delay subsystem. Finally, the curvature feedforward gain is obtained by separating the steady-state control command and the feedback term.

[0080] Specifically, the curvature feedforward gain is calculated based on the steady-state path curvature balance relationship; for road curvature... The steady-state yaw rate satisfies:

[0081] in, This represents the steady-state yaw rate. Based on steady-state yaw rate Based on the steady-state relationship between the vehicle lateral dynamics path tracking model and the actuator time delay subsystem, the ratio of the steady-state front wheel steering angle control command to the road curvature and the ratio of the steady-state measurable output vector to the road curvature are obtained, thus yielding the curvature feedforward gain:

[0082] in, To be related to the longitudinal speed of the vehicle The relevant curvature feedforward gain, This is the steady-state front wheel steering angle control command. This is the steady-state measurable output vector.

[0083] In offline calculations, a curvature feedforward lookup table can be generated according to a preset vehicle speed sampling rule; during actual vehicle operation, the lookup table is interpolated based on the current longitudinal vehicle speed to obtain the curvature feedforward gain used in the current control cycle.

[0084] The final front wheel steering control command is:

[0085] in, For feedback control terms generated based on measurable output feedback, This is a feedforward control term generated based on road curvature.

[0086] The curvature feedforward gain and the static measurable output feedback gain are calculated separately. The curvature feedforward gain is used to compensate for the steady-state steering demand caused by the road curvature, and the static measurable output feedback gain is used to suppress path tracking error and vehicle lateral motion state deviation.

[0087] Step S7: Output the front wheel steering control command generated in step S6 to the steer-by-wire actuator to achieve vehicle path tracking control.

[0088] Specifically, in each sampling cycle, the controller generates a front wheel steering control command based on the measurable output, curvature feedforward scheduling relationship and road curvature, and outputs the command to the steer-by-wire actuator.

[0089] The actual front wheel steering angle is fed back in real time by the steering angle sensor and serves as a measurable output component for the next control cycle, thus forming a closed-loop path tracking control.

[0090] In the closed loop described above, the controller output is the front wheel steering control command, and the vehicle lateral dynamics model input is the actual front wheel steering angle. The two are connected through the actuator time delay subsystem and are not treated as the same physical quantity.

[0091] To verify the feasibility and control effect of this invention, a real-vehicle verification was conducted using a test vehicle equipped with steer-by-wire functionality. Key parameters of the test vehicle are shown in Table 1. The test road surface was dry asphalt, and the test conditions included single lane change and double lane change scenarios. During the verification process, the method of this invention was compared with Comparison Algorithm 1, which considers actuator response, and Comparison Algorithm 2, which does not explicitly consider actuator response and communication delay, to illustrate the path tracking effect of this invention under conditions of actuator dynamics and communication delay in the steering channel. Statistical indicators of the test results are shown in Table 2 and... Figure 2 . Figure 2 In the figure, a, b, c, and d correspond to single lane change at 25 km / h, single lane change at 40 km / h, double lane change at 25 km / h, and double lane change at 40 km / h, respectively; a(1), b(1), c(1), and d(1) are the path tracking trajectories, a(2), b(2), c(2), and d(2) are the lateral errors, and a(3), b(3), c(3), and d(3) are the front wheel steering angle responses.

[0092] Table 1 Key parameters of the test vehicle

[0093] Table 2 Statistical Indicators of Real Vehicle Test Results

[0094] Under single lane change conditions, all control methods were able to complete the lane change task at the test vehicle speed, but the tracking error and steering response differed among the methods. For example... Figure 2 As shown in Table 2, the method of the present invention exhibits a smaller root mean square value of lateral error during low-speed testing. When the test vehicle speed increases, the effect of steering channel phase lag becomes more pronounced, yet the method of the present invention still maintains a smaller peak value of lateral error. These results demonstrate that explicitly considering communication delay and actuator dynamics during the feedback gain calculation helps maintain path tracking accuracy during enhanced steering transients.

[0095] In the double lane change operation, the curvature of the reference path changes direction continuously over a short distance, requiring the steering actuator to change its response direction more frequently. This operation further highlights the impact of steering channel delay and actuator lag. Figure 2 As shown in Table 2, the comparative control method, which does not explicitly consider actuator response and communication delay, requires larger steering maneuvers and generates a larger lateral error peak. In contrast, the method of the present invention reduces excessive steering requirements while maintaining a lower lateral error peak. The above results demonstrate that the method of the present invention can balance path tracking accuracy and steering response smoothness under stronger steering transient conditions.

[0096] In summary, the steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay according to the above embodiments has the following beneficial effects: (1) This invention embeds both communication delay and steering actuator dynamics into the path tracking augmented model simultaneously, avoiding the simplification of the steering channel as an ideal input element. This invention transforms the communication delay into a finite-dimensional state-space expression through the first-order Pad approximation, and connects it in series with the first-order response of the actuator to form a second-order strictly rational subsystem, thereby effectively compensating for steering lag and phase delay, improving the controller's adaptability under rapid curvature change conditions, and solving the problem of neglecting steering channel delay and actuator response lag in existing technologies.

[0097] (2) The feedback control law of the present invention only relies on measurable signals such as lateral error, heading angle error, lateral vehicle speed, yaw rate and actual front wheel angle. The internal state of the actuator delay is only retained in the augmented model for stability analysis and gain solution, and is not used as an online feedback quantity. The equivalent performance of state feedback can be achieved without adding additional real vehicle sensors, which effectively solves the problem of insufficient engineering measurability of feedback control structure.

[0098] (3) The present invention constructs a finite design envelope by changing the longitudinal vehicle speed and the equivalent lateral stiffness of the front and rear axles, so that the same static output feedback gain can maintain closed-loop stability and preset performance constraints under multiple vehicle speed and lateral stiffness sampling combinations. This solves the problem that fixed vehicle parameters are difficult to adapt to changes in vehicle speed and lateral stiffness, and enhances the robustness of the controller under different working conditions.

[0099] (4) By introducing a guarantee cost upper bound and a feedback command change rate penalty term to jointly design feedback gain, this invention can effectively limit high-frequency steering commands and steering oscillations while suppressing lateral tracking errors. On the one hand, it improves path tracking accuracy, and on the other hand, it reduces the mechanical load and energy consumption of the actuator and improves steering smoothness.

[0100] (5) This invention can be deployed on a steer-by-wire vehicle platform, combining position, speed, heading angle, yaw rate, and front wheel steering angle feedback to form a closed-loop control. Real vehicle verification results show that, under single and double lane change conditions, compared with the comparison algorithm that does not explicitly consider actuator response and communication delay, the method of this invention maintains a lower lateral error peak while reducing excessive steering requirements, and has better engineering feasibility and control effect.

[0101] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay, characterized in that, include: Step S1: Based on the path tracking status, vehicle motion status, and road curvature of the steer-by-wire vehicle, obtain the current vehicle status information and road curvature information; wherein, the path tracking status includes at least lateral error and heading angle error, and the vehicle motion status includes at least longitudinal speed, lateral speed, yaw rate, and actual front wheel steering angle. Step S2: Based on the current vehicle state information obtained in step S1, establish a lateral dynamic path tracking model for the steer-by-wire vehicle, and construct a basic state vector consisting of lateral error, heading angle error, lateral speed, and yaw rate. Step S3: Based on the lateral dynamic path tracking model obtained in step S2, the actuator delay subsystem is established by combining the first-order response of the steering actuator and the first-order Pad approximation of the communication delay. The actuator delay subsystem is then coupled with the lateral dynamic path tracking model to obtain a parameter-dependent augmented state space model that includes the internal state of the actuator delay. Step S4: Based on the parameter-dependent augmented state-space model obtained in step S3, a finite design envelope is constructed according to the longitudinal vehicle speed range and the variation range of the equivalent lateral stiffness of the front and rear axles, and multiple sampled augmented controlled objects are generated within the finite design envelope. Step S5: Based on the multiple sampled augmented controlled objects obtained in step S4, solve for the static measurable output feedback gain so that the feedback regulation subsystem when the curvature input is zero satisfies the asymptotic stability condition and the upper bound condition for guaranteeing cost. Step S6: Based on the static measurable output feedback gain obtained in step S5, and according to the road curvature information and steady-state path curvature balance relationship obtained in step S1, calculate the curvature feedforward gain related to the longitudinal vehicle speed, and then generate the front wheel steering control command from the static measurable output feedback gain, curvature feedforward gain and road curvature. Step S7: Output the front wheel steering control command generated in step S6 to the steer-by-wire actuator to achieve vehicle path tracking control; In step S3, the transfer function of the actuator delay subsystem is obtained from the first-order response of the steering actuator and the communication delay element, and its expression is: in, The transfer function is for the actuator delay subsystem consisting of the steering actuator and communication delay. For the Laplace operator, Actual front wheel steering angle Laplace transform, Front wheel steering control command Laplace transform, Let the first-order response time constant of the steering actuator be... This refers to the communication delay time. The communication delay element adopts the first-order Pad approximation. The first-order response of the steering actuator and the first-order Pad approximation of the communication delay are connected in series to form a second-order strictly rational actuator delay subsystem. The actuator delay subsystem is converted into a state-space form, expressed as: in, This is the internal state vector of the actuator delay subsystem. for The first derivative with respect to time, The state matrix of the actuator delay subsystem is... The input matrix of the actuator delay subsystem is... The output matrix of the actuator delay subsystem. For the pass-through matrix of the actuator delay subsystem, This is a front wheel steering control command; The internal state vector of the actuator delay subsystem includes two internal state components, and its direct transit term is zero. In step S3, the augmented state vector of the parameter-dependent augmented state-space model is: in, For parameter-dependent augmented state vectors, and For the internal state components of the actuator delay subsystem, Based on the basic state vector, This represents the lateral error of the vehicle relative to the desired path. This represents the heading angle error of the vehicle relative to the desired path. The lateral speed is the speed of the vehicle. The yaw rate is angular velocity. Indicates transpose; The parameter-dependent augmented state-space model is represented as follows: in, For augmented state vectors The first derivative with respect to time, For parameter-dependent augmented system matrices, For parameter-dependent control input matrix, To match longitudinal vehicle speed The relevant augmented curvature input matrix, For the scheduling parameter vector, For measurable output vectors, For measurable output matrix, For road curvature; The measurable output vector is: in, This is the actual front wheel steering angle; The internal state of the actuator delay subsystem is retained in the augmented state space model for delay compensation and stability assessment, but is not directly used as feedback measurement. In step S4, the equivalent lateral stiffness of the front and rear axles, within their respective ranges of variation, is expressed as a normalized uncertain variable as follows: in, For the front axle equivalent lateral stiffness, For the equivalent lateral stiffness of the rear axle, This is the nominal value of the equivalent lateral stiffness of the front axle. This is the nominal value of the equivalent lateral stiffness of the rear axle. The normalized perturbation variable is the equivalent lateral stiffness of the front axle. , For the normalized disturbance variable of the equivalent lateral stiffness of the rear axle, , This represents the amplitude of the equivalent lateral stiffness change of the front axle. This represents the amplitude of the equivalent lateral stiffness change of the rear axle. The scheduling parameter vector is represented as follows: in, For the scheduling parameter vector, , The design envelope consists of longitudinal vehicle speed and equivalent lateral stiffness disturbances of the front and rear axles. The longitudinal speed of the vehicle; The finite design envelope is formed by combining multiple longitudinal vehicle speed samples, multiple front axle equivalent lateral stiffness samples, and multiple rear axle equivalent lateral stiffness samples. The number of controlled objects whose sampling augmentation is performed is: in, To increase the total number of controlled objects in the sampling, This represents the number of longitudinal vehicle speed samples. This represents the number of samples for the equivalent lateral stiffness of the front axle. This represents the number of samples for the equivalent lateral stiffness of the rear axle.

2. The steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay according to claim 1, characterized in that, In step S2, the expression for the basic state vector is: The expression for the lateral dynamic path tracking model is: in, Basic state vector The first derivative with respect to time, The state matrix of the basic vehicle path tracking model The input matrix is ​​the front wheel steering angle. The input matrix is ​​the road curvature.

3. The steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay according to claim 2, characterized in that, In step S5, the static measurable output feedback gain is a feedback gain vector with one row and five columns, and it is applied to the measurable output vector; for the first... For a sampled augmented controlled object, the closed-loop matrix when the curvature input is zero is: in, For the first The closed-loop system matrix corresponding to each sampled augmented controlled object. For the first The system matrix of a sampled augmented controlled object For the first A sampled augmented control input matrix for the controlled object. For statically measurable output feedback gain, The output matrix is ​​measurable; Define the closed-loop performance weight matrix of the feedback regulation subsystem as follows: in, For the first The closed-loop performance weight matrix corresponding to each sampled augmented controlled object. To augment the state weight matrix, This is the weight matrix for the front wheel steering control commands; If there exists a symmetric positive definite matrix such that Then the first The closed-loop feedback control subsystem of the sampled augmented controlled object is asymptotically stable and satisfies the upper bound condition for guaranteed cost. For the first The Lyapunov positive definite matrix corresponding to each sampled augmented controlled object; The expression for the guarantee cost upper bound condition is: in, For the first The guaranteed cost index corresponding to each sample augmented controlled object. To augment the initial state of the system, To ensure the upper limit of cost.

4. The steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay according to claim 3, characterized in that, In step S5, when solving for the statically measurable output feedback gain, a penalty term for the rate of change of the feedback command is introduced to suppress high-frequency steering commands; for the first... For each sampled augmented controlled object, the closed-loop performance weight matrix after introducing a penalty term is defined as follows: : in, The penalty weight for the rate of change of the feedback instruction. Used to convert the control input weighted terms into a quadratic form with respect to the augmented state. Used to convert the feedback instruction rate of change penalty term into a quadratic form with respect to the augmented state; Furthermore, the statically measurable output feedback gain To optimize the variables and minimize the comprehensive objective function, the expression for the comprehensive objective function is: in, For the comprehensive objective function, For the first The sampling augmented controlled object has a statically measurable output feedback gain. The following performance indicators This is a stability margin penalty term, used to impose a penalty when the real part of the maximum closed-loop pole is higher than a preset stability margin threshold; This is a damping ratio penalty term, used to apply a penalty when the closed-loop complex pole damping ratio is lower than a preset lower limit; This is an oscillation frequency penalty term, used to impose a penalty when the closed-loop complex pole oscillation frequency exceeds a preset upper limit. This is a feedback gain regularization term used to limit the magnitude of the statically measurable output feedback gain.

5. The steer-by-wire vehicle path tracking control method based on actuator dynamics and time delay according to claim 4, characterized in that, In step S6, the curvature feedforward gain is calculated based on the steady-state path curvature balance relationship; for road curvature... The steady-state yaw rate satisfies: in, This represents the steady-state yaw rate. Based on steady-state yaw rate Based on the steady-state relationship between the vehicle lateral dynamics path tracking model and the actuator time delay subsystem, the ratio of the steady-state front wheel steering angle control command to the road curvature and the ratio of the steady-state measurable output vector to the road curvature are obtained, thus yielding the curvature feedforward gain: in, To be related to the longitudinal speed of the vehicle The relevant curvature feedforward gain, This is the steady-state front wheel steering angle control command. The output vector is a steady-state measurable vector; The final front wheel steering control command is: in, For feedback control terms generated based on measurable output feedback, This is a feedforward control term generated based on road curvature.

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