Preset time tracking control method based on vehicle model

Abstract

The invention provides a preset time tracking control method based on a vehicle model, and aims to improve the response rate under the condition of vehicle following, reduce the problem of'ghost vehicle 'under the condition of vehicle following, and improve the traffic efficiency. On the basis that air resistance, ramp resistance and rolling resistance borne by the following vehicle in the vehicle following process are considered, the preset time control theory and vehicle tracking control are combined, and the controller is designed to achieve tracking control over the vehicle within the safe vehicle distance. The controller needs to meet two requirements of tracking stability and position tracking error convergence, that is, in the vehicle tracking control process, it needs to be guaranteed that a stable relation exists between the motion state of a following vehicle and the motion state of a front vehicle; namely, the following vehicle should keep the speed consistent with that of the front vehicle within the preset time so as to ensure safe vehicle distance driving, meanwhile, the position tracking error of the rear vehicle is converged to a field near zero within the preset time, and it is ensured that the rear vehicle accurately follows the front vehicle.

Description

Technical Field

[0001] The invention belongs to the technical field of vehicle tracking and safe driving, and in particular relates to a preset time tracking control method based on a vehicle model. Technical Background

[0002] In recent years, with the rapid development of intelligent transportation systems, traffic congestion is facing severe challenges. In the long-term driving cycle of vehicles, maintaining a small and safe distance between vehicles in the same lane and following the vehicle in front can effectively improve traffic efficiency and alleviate traffic congestion. The stability of a vehicle includes internal stability and chord stability. Internal stability requires that any single vehicle maintains the required distance from the vehicle in front, and chord stability prevents the distance error from increasing along the convoy.

[0003] In the study of vehicle stability, in addition to vehicle tracking stability, the error convergence speed is usually another important indicator to measure performance. Regarding the problem of error convergence speed, current research results are indeed difficult to obtain fast convergence performance, and usually can only obtain asymptotic stability, that is, a stable state when time tends to infinity. In actual industry, error convergence needs to be achieved in a short time. Therefore, it is particularly important to design a reasonable inter-vehicle distance to maintain the stability of the vehicle in a short time. Summary of the invention

[0004] The purpose of the present invention is to provide a preset time tracking control method based on a vehicle model. On the basis of considering the air resistance, slope resistance and rolling resistance suffered by the following vehicle during the following process, the overall stability between the motion state of the following vehicle and the motion state of the leading vehicle is achieved to the maximum extent within a specified time. That is, the following vehicle should maintain a speed consistent with the leading vehicle within a preset time to ensure safe vehicle distance driving. At the same time, the position tracking error of the rear vehicle is converged to a range near zero within a preset time to ensure that the rear vehicle accurately follows the leading vehicle.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a preset time tracking control method based on a vehicle model, comprising the following steps:

[0006] Step S1: Establishing a longitudinal dynamic model of the following vehicle and providing an ideal following distance;

[0007] Step S2: Analyze the main factors affecting the safety of following the vehicle and reasonably design the ideal following model of the following vehicle;

[0008] Step S3: Design an observer to observe the road conditions and design a compensation controller to dynamically adjust the following vehicle in response to dynamic traffic conditions, so that it can adapt to different road conditions and external interference;

[0009] Step S4: Based on the nonlinear vehicle dynamics model, with the backstepping method as the framework, combined with the preset time control theory, Young's inequality and other inequality techniques, a preset time controller based on the ideal vehicle distance is designed to track the position and speed of the leading vehicle.

[0010] Step S5: According to the vehicle hardware parameters, the appropriate following condition is selected, appropriate controller parameters are designed, and the effectiveness, robustness and fast following performance of the invented control are verified through Matlab simulation.

[0011] Preferably, step S1 of establishing a longitudinal dynamics model of the following vehicle and providing an ideal following distance comprises:

[0012] (1) Establish the longitudinal dynamics model of the following vehicle:

[0013]

[0014] Among them, x f 、m f 、v f Respectively represent the position, mass and speed of the following vehicle; F t Indicates the traction of the vehicle, F a Indicates the air resistance of the vehicle during driving, F r is the rolling resistance of the vehicle, F g is the slope resistance of the vehicle; at the same time, the air resistance is related to the vehicle's speed v f , air density ρ, air resistance coefficient C d It is closely related to the frontal area A. The air resistance, slope resistance and rolling resistance of the following vehicle during the following process are expressed as:

[0015]

[0016] In the formula, f r represents the rolling resistance coefficient, g represents the acceleration due to gravity, and θ represents the slope of the road.

[0017] Therefore, the longitudinal dynamics model of the vehicle can finally be written as:

[0018]

[0019] Where ε = f r cosθ+sinθ, b=g. The road surface condition and the road slope are represented by ε, and are set as disturbance terms of the vehicle tracking system.

[0020] (2) Ideal following distance:

[0021] Assume that the ideal following distance is

[0022] d = xp -x f -l f (4)

[0023] Where d is the ideal following distance (the minimum distance between vehicles that does not collide with the vehicle in front under braking at the current speed), l f is the length of the following vehicle.

[0024] Preferably, in step S3, according to the actual traffic conditions, an observer is designed to observe the road conditions and a compensation controller is designed to dynamically adjust the following vehicle, and the method is as follows:

[0025] (1) Constructing the observer: Since the road traffic conditions are unpredictable, a related observer is designed to observe and estimate the unpredictable states in the longitudinal dynamics model of the following vehicle so that it can adapt to different road conditions and external interference. express.

[0026] (2) Construct a compensation controller to obtain the compensated target system: The function of the compensation controller is mainly to dynamically adjust the following vehicle to overcome the influence of road resistance on the vehicle's driving speed and traction, thereby improving the safety and stability of the vehicle.

[0027] Define auxiliary variables with observers:

[0028]

[0029] Where a0>0 is the observer gain, Represents the estimated value of the disturbance term ε of the tracking system.

[0030] Due to the traction force F t With preset time controller output F u and compensation control to overcome road resistance So it can be expressed as

[0031] Construct compensation controller F ε , and gives the estimated error of the observer Combined traction F t , compensation controller F ε and observer estimation error The target system after the unmeasured variables are observed and compensated by the compensation controller is obtained, that is:

[0032]

[0033] Preferably, in step S3, based on the nonlinear vehicle dynamics model, with the backstepping method as the framework, combined with the preset time control theory, Young's inequality and other inequality technology designs, a preset time controller based on the ideal vehicle distance is used to track the position and speed of the leading vehicle, and the method is as follows:

[0034] (1) In the first step of the backstepping method, the first subsystem of the target system after observation and compensation is Given the coordinate transformation z1=x f -d; define Lyapunov function And combine the coordinate transformation to derive it; introduce the virtual controller α, define the virtual error variable z2 = v f -α, the expression of the virtual controller α is obtained according to the first-order derivative function of the Lyapunov function.

[0035] (2) In the second step of the backstepping method, the second subsystem of the target system after observation and compensation is Constructing Lyapunov functions Combined with the virtual error variable z2=v f -α Derivative the Lyapunov function V2 and construct the corresponding actual preset time controller.

[0036] (3) Substitute the controller constructed in each step of the backstepping method into the Lyapunov function Verify whether it meets the preset time stability theory If it is proved that the designed controller satisfies the preset time stability theorem, the following vehicle can maintain the same speed as the leading vehicle at a safe distance within the preset time, and the position tracking error of the following vehicle can converge within the preset time.

[0037] According to the above steps, the rear vehicle on the road can safely track the front vehicle within the specified time, and the tracking error converges to a small neighborhood near the origin.

[0038] The beneficial effects of adopting this technical solution are:

[0039] 1. Based on the vehicle longitudinal dynamics model and combined with the preset time control theory, the present invention proposes a preset time tracking control algorithm to ensure tracking stability and position tracking error convergence, that is, the following vehicle maintains a speed consistent with the leading vehicle within the preset time, and the position tracking error converges to a neighborhood near zero within the preset time, thereby ensuring the stability and accuracy of tracking control.

[0040] 2. Aiming at actual traffic conditions, the present invention designs an observer to observe road conditions (such as unmeasurable environmental factors such as air resistance, slope resistance, rolling resistance, etc. encountered by the following vehicle during the following process) and designs a compensation controller to dynamically adjust the following vehicle so that it can adapt to different road conditions and external interference, thereby improving the safety and stability of vehicle driving.

[0041] 3. The present invention combines the preset time stability theory to design a controller under the framework of the backstepping method to achieve vehicle stability and accurate tracking within a given time. Compared with fixed time control, preset time control has a more compact convergence interval and can achieve stability within any specified time range, avoiding the problem that the upper bound of the stability time is too far away from the actual stability time due to the conservatism and complexity of theoretical analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 This is a structural diagram of a preset time tracking control scheme based on a vehicle model of the present invention;

[0044] Figure 2 Figure 1 is an adaptive vehicle tracking system diagram;

[0045] Figure 3 Tracking diagram for the speed you want to achieve;

[0046] Figure 4 This is the displacement tracking diagram that we want to achieve. DETAILED DESCRIPTION

[0047] The present invention is a preset time tracking control method based on a vehicle model, and the specific implementation steps are as follows:

[0048] See also Figures 1 to 4

[0049] Step S1: Establish a longitudinal dynamic model of the following vehicle and provide an ideal following distance.

[0050] (1) The present invention takes the following of two vehicles as an example, with the leading vehicle being the target vehicle. The controller designed by the invention acts on the power system of the following vehicle. In actual use, the present invention can be used on dynamic roads with multiple vehicles on a single lane, and is not limited to vehicle following in a two-vehicle situation.

[0051] (2) Based on the kinematic and dynamic model of the four-wheel vehicle and the dynamic uncertain variables in the following process, the model is appropriately simplified and the following longitudinal dynamic model of the following vehicle can be established:

[0052]

[0053] Among them, x f 、m f 、v f Respectively represent the position, mass and speed of the following vehicle; F t Indicates the traction of the vehicle, F a Indicates the air resistance of the vehicle during driving, F r is the rolling resistance of the vehicle, F g is the slope resistance of the vehicle; at the same time, the air resistance is related to the vehicle's speed v f , air density ρ, air resistance coefficient C d Closely related to the frontal area A.

[0054] (3) When following a vehicle, the front windshield is subject to changing air resistance. At the same time, there is gravity resistance on a sloped road surface. The rolling friction resistance under different environments and different tires also changes all the time. Therefore, the present invention uses dynamic functions to represent the balancing forces in the following process, namely, F a Indicates the air resistance of the vehicle during driving, F r is the rolling resistance of the vehicle, F g is the slope resistance of the vehicle, which is expressed as follows:

[0055]

[0056] In the formula, f r represents the rolling resistance coefficient, g represents the acceleration due to gravity, and θ represents the slope of the road.

[0057] (4) Considering the mechanical effects and motion process of the vehicle, the longitudinal dynamics model of the following vehicle can be described by a second-order nonlinear state space equation, which is written as:

[0058]

[0059] Where ε = f r cosθ+sinθ, b=g. The road surface condition and the road slope are represented by ε, and are set as disturbance terms of the vehicle tracking system. The present invention considers the vehicle following condition under slope conditions, and its application scope is not limited to flat roads. For the convenience of research, it is assumed that the road condition remains unchanged and the influence of the road slope change is ignored.

[0060] Step S2: Design an ideal following distance model for the following vehicle in dynamic conditions

[0061] (1) Establish the influencing factors of the following distance model. In the process of following a vehicle, it is necessary to maintain a safe distance, which is related to the vehicle's own speed, and avoid the vehicle falling behind due to excessive distance. The present invention tests the following factors for the safe following distance of the vehicle: the vehicle's own length, the position of the leading vehicle, the position of the following vehicle, the speed of the following vehicle, the acceleration of the following vehicle, etc.

[0062] (2) The ideal following distance of the following vehicle selected by the present invention:

[0063] d = x p -x f -l f (10)

[0064] Where d is the ideal following distance (the minimum distance between vehicles that does not collide with the vehicle in front under braking at the current speed), x p is the position of the following vehicle, x f is the position of the front vehicle, l f is the length of the following vehicle.

[0065] (3) The present invention adopts a fixed-interval following strategy, and the designed preset time controller is also applicable to different following strategies, including but not limited to the following strategies: fixed time interval, variable time interval, fixed spacing, maximum / minimum safety spacing, secondary safety spacing, etc.

[0066] Step S3: In view of the different drag coefficients of the following vehicle under different road conditions and different types of tires, an observer is designed to observe and identify the road conditions. A compensation controller is designed based on the estimation of the road resistance function, and the following vehicle is dynamically adjusted to adapt to different road conditions and external interference.

[0067] (1) Constructing the observer: Since the road traffic conditions are unpredictable, a related observer is designed to observe and estimate the unpredictable states in the longitudinal dynamics model of the following vehicle so that it can adapt to different road conditions and external interference. express.

[0068] (2) Construct a compensation controller to obtain the compensated target system: The compensation controller is mainly used to dynamically adjust the following vehicle to overcome the influence of road resistance on the vehicle's driving speed and traction, thereby improving the safety and stability of the vehicle.

[0069] (3) In order to overcome the disturbance in the observation process and improve the robustness of the observation system, an auxiliary variable with an observer is defined:

[0070]

[0071] Where a0>0 is the observer gain, Represents the estimated value of the disturbance term ε of the tracking system.

[0072] (4) Due to the traction force F t With preset time controller output F u and compensation control to overcome road resistance Related, it can be expressed as Construct compensation controller F ε , and gives the estimated error of the observer Combined traction F t , compensation controller F ε and observer estimation error The target system after the unmeasured variables are observed and compensated by the compensation controller is obtained, that is:

[0073]

[0074] Step S4: Based on the nonlinear vehicle dynamics model, a dynamic function with a preset time is introduced into the feedback loop of the closed-loop system to form a hybrid feedback loop with system state and preset function, so as to achieve the following vehicle tracking the expected safe distance within the preset time set manually.

[0075] (1) The present invention adopts a second-order vehicle longitudinal dynamics model. The applicability of the controller designed by the present invention is not limited to a single-vehicle second-order vehicle model. It adopts a backstepping design structure and is still applicable to multi-vehicle platoons and higher dimensions.

[0076] (2) The present invention is a preset time stable controller with certain conservatism and robustness. It combines the preset time control method and multiple inequality technologies to design a preset time controller based on the ideal vehicle distance to achieve tracking of the position and speed of the vehicle in front.

[0077] (3) In the first step of the backstepping method, the present invention targets the first subsystem of the target system after observation and compensation. Given the coordinate transformation z1=x f -d; define Lyapunov function And combine the coordinate transformation to derive it; introduce the virtual controller α, define the virtual error variable z2 = v f -α, the expression of the virtual controller α is obtained according to the first-order derivative function of the Lyapunov function.

[0078] (4) In the second step of the backstepping method, the second subsystem of the target system after observation and compensation is Constructing Lyapunov functions Combined with the virtual error variable z2=v f-α Derivative the Lyapunov function V2 and construct the corresponding actual preset time controller.

[0079] (5) Substitute the controller constructed in each step of the backstepping method into the Lyapunov function Combining Young's inequality, Cauchy-Schwarz inequality and other inequality techniques to verify whether it satisfies the preset time stability theory If it is proved that the designed controller satisfies the preset time stability theorem, it can be said that the following vehicle can maintain the same speed as the leading vehicle at a safe distance within the preset time, and at the same time, the position tracking error of the following vehicle converges to a range near zero within the preset time.

[0080] Step S5: The preset time stable controller obtained in the above steps is used to prove the effectiveness and practicability of the invention through a Matlab simulation program.

[0081] (1) Select appropriate following vehicle parameters and road traffic parameters, select the vehicle mass as 1332 kg, the body length as 3.5 meters, and the air density as 1.29 kg / m 3 , the rolling resistance coefficient is 0.32m / s, and the air resistance coefficient is 0.32.

[0082] (2) According to the established second-order dynamic model of the following vehicle, set the initial state of the following vehicle. Assume that the initial position, acceleration and speed of the leading vehicle are 25m and 2.5m / s respectively. 2 and 5m / s, the initial position, velocity and acceleration of the following vehicle are set to 0m, 0m / s and 0m / s respectively 2 .

[0083] (3) Select the preset time as 10s and set reasonable controller parameters. Through Matlab simulation, we can get Figure 3 Vehicle speed profile and Figure 4 The vehicle displacement curve shows that the speed of the following vehicle can follow the speed of the leading vehicle within 10 seconds, and there is no collision between the front and rear vehicles.

[0084] (4) According to the above steps, the rear vehicle on the road can safely track the front vehicle within a specified time, and the position tracking error can be converged to a very small range.

Claims

1. A preset time tracking control method based on a vehicle model, mainly comprising the following steps: First, establish the longitudinal dynamics model of the following vehicle and give the ideal following distance; second, design an observer to observe the road conditions according to the actual traffic conditions and design a compensation controller to dynamically adjust the following vehicle so that it can adapt to different road conditions and external interference; finally, based on the nonlinear vehicle dynamics model, use the backstepping method as the framework, combine the preset time control theory, Young's inequality and other inequality technologies to design a preset time controller based on the ideal vehicle distance to achieve the tracking of the position and speed of the leading vehicle. Specifically, it includes the following steps: Step S1: Establishing a longitudinal dynamic model of the following vehicle and providing an ideal following distance; Step S2: Analyze the main factors affecting the safety of following the vehicle and reasonably design the ideal following model of the following vehicle; Step S3: Design an observer to observe the road conditions and design a compensation controller to dynamically adjust the following vehicle in response to dynamic traffic conditions, so that it can adapt to different road conditions and external interference; Step S4: Based on the nonlinear vehicle dynamics model, with the backstepping method as the framework, combined with the preset time control theory, Young's inequality and other inequality techniques, a preset time controller based on the ideal vehicle distance is designed to track the position and speed of the leading vehicle. Step S5: According to the vehicle hardware parameters, the appropriate following condition is selected, appropriate controller parameters are designed, and the effectiveness, robustness and fast following performance of the invented control are verified through Matlab simulation.

2. The preset time tracking control method based on vehicle model according to claim 1 is characterized in that: Step S1 of establishing a longitudinal dynamic model of the following vehicle and providing an ideal following distance includes: (1) Establish the longitudinal dynamics model of the following vehicle: Among them, x f 、m f 、v f Respectively represent the position, mass and speed of the following vehicle; F t Indicates the traction of the vehicle, F a Indicates the air resistance of the vehicle during driving, F r is the rolling resistance of the vehicle, F g is the slope resistance of the vehicle; at the same time, the air resistance is related to the vehicle's speed v f , air density ρ, air resistance coefficient C d It is closely related to the frontal area A. The air resistance, slope resistance and rolling resistance of the following vehicle during the following process are expressed as: In the formula, f r represents the rolling resistance coefficient, g represents the acceleration due to gravity, and θ represents the slope of the road. Therefore, the longitudinal dynamics model of the vehicle can finally be written as: Where ε = f r cosθ+sinθ, b=g. The road surface condition and the road slope are represented by ε, and are set as the disturbance term of the vehicle tracking system. For the convenience of research, it is assumed that the road condition remains unchanged and the influence of the road slope change is ignored. According to the requirements of the rights letter, the steps involved in S2 are: analyzing the main factors affecting the safety of following vehicles and rationally designing an ideal following model for the following vehicle; Assume that the ideal following distance is d=x p -x f -l f (4) Where d is the ideal following distance (the minimum distance between vehicles that does not collide with the vehicle in front under braking at the current speed), l f is the length of the following vehicle.

3. The preset time tracking control method based on vehicle model according to claim 1, characterized in that: In step S3, according to the actual traffic conditions, an observer is designed to observe the road conditions and a compensation controller is designed to dynamically adjust the following vehicle. The method is as follows: (1) Constructing the observer: Since the road traffic conditions are unpredictable, a related observer is designed to observe and estimate the unpredictable states in the longitudinal dynamics model of the following vehicle so that it can adapt to different road conditions and external interference. express. (2) Construct a compensation controller to obtain the compensated target system: The function of the compensation controller is mainly to dynamically adjust the following vehicle to overcome the influence of road resistance on the vehicle's driving speed and traction, thereby improving the safety and stability of the vehicle. Define auxiliary variables with observers: Where a0>0 is the observer gain, Represents the estimated value of the disturbance term ε of the tracking system. Due to the traction force F t With preset time controller output F u and compensation control to overcome road resistance So it can be expressed as Construct compensation controller F ε , and gives the estimated error of the observer Combined traction F t , compensation controller F ε and observer estimation error The target system after the unmeasured variables are observed and compensated by the compensation controller is obtained, that is:

4. The preset time tracking control method based on vehicle model according to claim 1 is characterized in that: In step S4, based on the nonlinear vehicle dynamics model, with the backstepping method as the framework, combined with the preset time control theory, Young's inequality and other inequality technologies, a preset time controller based on the ideal vehicle distance is designed to track the position and speed of the leading vehicle. The method is as follows: (1) In the first step of the backstepping method, the first subsystem of the target system after observation and compensation is Given the coordinate transformation z1=x f -d; define Lyapunov function And combine it with coordinate transformation to derive it; introduce Virtual controller α, define virtual error variable z2 = v f -α, the expression of the virtual controller α is obtained according to the first-order derivative function of the Lyapunov function. (2) In the second step of the backstepping method, the second subsystem of the target system after observation and compensation is Constructing Lyapunov functions Combined with the virtual error variable z2=v f -α Derivative the Lyapunov function V2 and construct the corresponding actual preset time controller. (3) Substitute the controller constructed in each step of the backstepping method into the Lyapunov function Combining Young's inequality, Cauchy-Schwarz inequality and other inequality techniques to verify whether it satisfies the preset time stability theory If it is proved that the designed controller satisfies the preset time stability theorem, it can be said that the following vehicle can maintain the same speed as the leading vehicle at a safe distance within the preset time, and at the same time, the position tracking error of the following vehicle converges to a range near zero within the preset time.

5. The preset time tracking control method based on vehicle model according to claim 1, characterized in that: In step S5, the following vehicle parameters and traffic condition parameters are appropriately selected, the vehicle following time is selected, and the validity of the obtained results is confirmed through Matlab software programming and simulation. According to the above steps, the rear vehicle on the road can safely track the front vehicle within the specified time, and the tracking error converges to a small neighborhood near the origin.

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