Input saturation passivation control method for cooperative adaptive cruise control system

Abstract

The present invention discloses an input saturation passive control method for a collaborative adaptive cruise control system, which is used to solve the queue stability control problem in the CACC system. Specifically, it includes: 1. Establishing the kinematic equations between vehicles; 2. Converting the queue stability condition into an input saturation constraint, thereby obtaining a state space expression with saturated input; 3. Designing a passive controller for the system based on the Riccati equation, Lyapunov stability theory and matrix theory; 4. Verifying whether the designed controller can still maintain the stability of the queue in the presence of disturbances. The results verify that the device based on the passive control can not only have strong robustness to disturbances, but also has the function of input limiting, which ensures the stability of the queue and is easy to calculate.

Description

Technical Field

[0001] The present invention relates to a queue stability control problem in a cooperative adaptive cruise control system, belongs to the field of cooperative adaptive cruise control, and specifically relates to an input saturation passivation control method of a cooperative adaptive cruise control system. Background Art

[0002] With the development of my country's economy, cars have gradually become popular. By May 2021, the number of motor vehicles in my country reached 380 million. Under the current traffic conditions, the increase in vehicles has caused a series of problems, such as traffic congestion, traffic accidents, environmental pollution, and economic losses. Among the many road safety accidents, there are many accidents caused by human factors, of which 90% of traffic accidents are caused by driver fatigue, failure to change lanes according to regulations, speeding, etc. Accordingly, improving the intelligence of vehicles and developing driver assistance systems that can reduce driver participation can greatly reduce road safety accidents caused by drivers. If the cooperative adaptive cruise control system (CACC) can be widely used in the transportation process, 17% of rear-end collision accidents can be reduced. The CACC system realizes queuing cooperative cruise control through information interaction between vehicles. On the one hand, it can shorten the distance between vehicles, reduce traffic energy consumption, and improve traffic safety and traffic efficiency while ensuring safety. On the other hand, it reduces the driver's fatigue and can avoid the driver's operating errors to a certain extent. Therefore, it is of great significance to study the CACC system.

[0003] The main feature of the CACC system is to ensure that each following vehicle in a one-dimensional queue can smoothly follow the preceding vehicle and maintain the desired vehicle spacing.

[0004] In order to improve the stability of the queue, more and more control methods and the combination of multiple control methods are constantly applied to the cooperative adaptive cruise control system. At present, the common methods include passive control, PID control, optimal control, fuzzy logic control, sliding mode variable structure control and the control methods evolved based on the above. This paper uses the Riccati equation and Lyapunov stability theory to design a passive controller for the linear system. Summary of the invention

[0005] The purpose of the present invention is to provide an input saturation passivation control method for a collaborative adaptive cruise control system, which is used to solve the queue stability control problem in the CACC system. The queue can maintain queue stability during driving, ensuring that each following vehicle in the queue can smoothly follow the front vehicle and maintain the expected vehicle spacing, thereby improving traffic flow stability, throughput, driving safety and vehicle ride comfort.

[0006] To achieve the above purpose, the technical solution steps of the present invention are as follows:

[0007] a. Establish kinematic equations between vehicles;

[0008]

[0009] In the formula, ω i =a i-1 is the disturbance, u i (t) = a i,e is the control input.

[0010] b. Transform the queue stability condition into an input saturation constraint to obtain the state space expression with saturated input;

[0011]

[0012] In the formula, y i (t) is the system output, C i and D 2i is a matrix of appropriate dimension, sat(u i ) is the input saturation function.

[0013] c. Based on the Riccati equation, Lyapunov stability theory and matrix theory, design a passive controller u for the system. i ;

[0014] By choosing a suitable positive definite matrix Q i , R i , solve the Riccati equation and find P i , verify P i Whether the conditions identified in this article are met, if so, the controller can be obtained If it is not satisfied, reselect the positive definite matrix Q i , R i .

[0015] d. Verify whether the designed controller can still maintain the stability of the queue in the presence of disturbances.

[0016] Due to the adoption of the above technical solution, the technical effects achieved by the present invention are as follows:

[0017] The present application uses a saturation function to improve the passive controller, and limits the range of variation of the vehicle's acceleration and following error, respectively, so that the acceleration of the vehicles in the queue decreases one by one, and at the same time, the following error between adjacent vehicles is neither too large nor too small, effectively avoiding traffic accidents.

[0018] This application designs a passive controller with input saturation based on the saturation function processing method in the nonlinear sector method. The designed controller has strong robustness to disturbances and has the function of input limiting, which ensures the stability of the queue. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of the longitudinal movement of the queue;

[0020] Figure 2 It is a simulation diagram of a homogeneous queue under different initial conditions: the following error variation curve of the method of the present invention;

[0021] Figure 3 It is a simulation diagram of a homogeneous queue under different initial conditions: the acceleration variation curve of the method of the present invention;

[0022] Figure 4 When the leading vehicle in the heterogeneous queue accelerates or decelerates: the acceleration or deceleration change simulation of all the following vehicles, the speed change curve of the method of the present invention;

[0023] Figure 5 When the leading vehicle in the heterogeneous queue accelerates or decelerates: the acceleration change simulation of all the following vehicles, the acceleration change curve of the method of the present invention;

[0024] Figure 6 It is the simulation diagram of homogeneous queue under different initial conditions: the curve of following error variation under optimal control;

[0025] Figure 7 It is the simulation diagram of the homogeneous queue under different initial conditions: the acceleration variation curve under optimal control;

[0026] Figure 8 It is the acceleration and deceleration change simulation of all following vehicles when the leading vehicle in the heterogeneous queue accelerates and decelerates, and the speed change curve under optimal control;

[0027] Fig. 9 It is the acceleration change simulation of all following vehicles when the leading vehicle in the heterogeneous queue accelerates or decelerates, and the acceleration change curve under optimal control; DETAILED DESCRIPTION

[0028] The technical solution of the present invention is described in detail below in conjunction with specific implementation methods.

[0029] The CACC system is a V2V (Vehicle to Vehicle) and V2I (Vehicle to Infrastructure) driving assistance technology that implements platoon coordinated cruise control through information exchange between vehicles. Under the controller designed by the present invention, the CACC system not only shortens the following vehicle distance while ensuring safety, reduces traffic energy consumption, improves traffic safety and traffic efficiency, but also reduces driver fatigue.

[0030] Step 1: When establishing the longitudinal dynamics model of the platoon, the system is modeled as a linear system with disturbances based on the relationship between variable vehicle spacing, constant headway, communication mode between vehicles, and communication delay. The model is constructed as follows:

[0031] The parameters of the vehicles when building a platoon are shown in Table 1:

[0032] Table 1 Vehicle parameters

[0033]

[0034] Note: The vehicle parameters of the homogeneous queue are the first row of the table.

[0035] Step 1.1: Select the desired vehicle spacing suitable for calculation in this paper: d i,e =τ h,i v i (t)+d 0

[0036] Where: τ h,i is the headway time, which is a positive constant; v i (t) is the speed of the i-th vehicle; t is the time, d 0 It is the minimum safe distance between the i-th vehicle and the i-1-th vehicle in front after they stop, usually 2m to 4m.

[0037] Step 1.2: According to Figure 1 The longitudinal motion diagram of the queue shows the longitudinal kinematic relationship between the front and rear vehicles:

[0038]

[0039] In the formula, Δd i is the inter-vehicle distance error; d i ,d i,e are the actual and expected distances between the i-th and i-1-th vehicles, respectively; Δv i is the relative speed between the i-th car and the i-1-th car.

[0040] Step 1.3: Relationship between the actual acceleration and expected acceleration of the vehicle: Where: a i , ai,e are the actual acceleration and the expected acceleration, τ i is the time constant, k L,i is the system gain.

[0041] Based on the above three points, the kinematic state equation of the workshop can be established:

[0042]

[0043] Step 2: The stability condition of the queue is regarded as the saturation constraint of the queue vehicle input;

[0044] In order to ensure the stability of the queue, the acceleration of the following vehicles in the queue needs to be reduced vehicle by vehicle. That is, when the acceleration of vehicle No. 0 changes during the driving process of the queue, the following error between all vehicles can converge to zero asymptotically. In other words, the acceleration of all following vehicles should be reduced vehicle by vehicle, that is: This is to regard the stability condition of the queue as the saturation constraint of the queue vehicle input, which can be expressed by the input saturation function as follows: (u max is u i The upper bound of -u min is u i The lower bound of ), so the state space expression of the system is:

[0045]

[0046] Step 3, determine whether the state space expression of the system is strictly passive;

[0047] If there exists a semi-positive definite function V i (x i (t)) and the positive definite function W i (x i (t)), such that:

[0048]

[0049] If , then the system is strictly passive.

[0050] Then choose a suitable positive definite matrix Q i , R i , according to the Riccati equation:

[0051] A i T P i +P i A i -P i B i R i -1 B i T Pi +Q i =0

[0052] Find the only positive solution P i .

[0053] According to Obtain the controller, and then verify whether the controller is a passive controller.

[0054] Requested controller:

[0055] Homogeneous queue: u i =-[1.4 6.1 1.0]x i

[0056] Heterogeneous queue: u 1 =-[1.4 6.1 1.0]x 1 ,u 2 =-[1.4 7.4 1.4]x 2 ,u 3 =-[1.4 6.6 1.1]x 3 ,u 4 =-[1.4 8.1 1.3]x 4

[0057] Verification conditions:

[0058] 1) A i ,B i Can control,

[0059] 2)

[0060] Among them, λ min (·) represents the minimum eigenvalue of the matrix. By constructing the storage function: V i (x i )=x i T P i x i , and then derive it to get:

[0061]

[0062] Let W i (x i )=δx i T x i ,δ>0, we have:

[0063]

[0064] according to have:

[0065]

[0066] From the above formula and the Riccati equation, we can get:

[0067]

[0068] From verification condition 2, we can know that:

[0069]

[0070] Right now:

[0071]

[0072] therefore, It is the passive controller of the system.

[0073] Step 4: Verify whether the designed controller can still maintain the stability of the queue in the presence of disturbances. The verification process is as follows: Build homogeneous and heterogeneous queue models respectively.

[0074] Under the homogeneous queue model:

[0075] Under the action of the proposed controller, the following error and acceleration between vehicles are reduced quickly and smoothly. After about 18 seconds, the following error and acceleration are close to zero, achieving asymptotic stability of the platoon. The maximum following error is -8m, and the peak acceleration is 1.08m·s -2 Under optimal control, after about 20 seconds, the following error and acceleration are close to zero. Although the platoon can also achieve stability, the maximum following error is -13m, which is 5m smaller than the following error under the controller of this paper. The distance between the two vehicles is too small. In case of emergency, the vehicle will be in danger if it fails to respond in time. The peak acceleration is 1.89m·s -2 , there is a risk of vehicle collision due to failure to satisfy queue stability.

[0076] Under the heterogeneous queue model:

[0077] Depend on Figure 4 It can be seen that in the first 50 seconds, the queue is in a uniform speed state. At 50 seconds, vehicle 0 is moving at a speed of 0.5 m·s -2 The 4 following cars also changed their speeds, with the longest response time being 0.8s. All the following cars 1 to 4 reached 25m·s -1 The maximum time is 8s. -1 When driving at a constant speed, the maximum overshoot of the speed of the four following vehicles is 0.8%. Figure 5It can be seen that the maximum overshoot of the acceleration of the four following vehicles is 12%, and the longest adjustment time is 12s. From the above data, it can be seen that during the acceleration process, the speed and acceleration of the following vehicles 1 to 4 can be synchronized with the leading vehicle in turn to achieve smooth following. During the deceleration process, similar conclusions can be drawn from the analysis of the figure.

[0078] Depend on Figure 8 It can be seen that under the optimal control, although the following vehicles 1 to 4 can also smoothly follow their leading vehicles, the maximum response time among the four vehicles is 1.2s, which is 0.4s longer than the response time under the control of this paper. The speed of vehicles 1 to 4 reaches 25m·s -1 The maximum time is 10s, which is 2s longer than the response time of the controller in this paper. -1 When driving at a constant speed, the maximum overshoot of the speed of the four following vehicles is 1.2%, which is 0.4% larger than the maximum overshoot under the control of this paper. Fig. 9 It can be seen that the maximum overshoot of the acceleration of the four following vehicles is 16%, and the longest adjustment time is 14s. This is 4% larger than the maximum overshoot of the acceleration under the control of this paper, and the longest adjustment time is 2s longer. From the comparison of the above transient indicators, it can be seen that for the CACC system of heterogeneous queues, the control scheme of this paper is obviously better than the optimal control.

[0079] In both models, the transient indicators such as speed, acceleration, and the time for the following error to approach zero are compared with those under the optimal controller, and it is finally verified that the controller designed in this paper is better than the optimal controller under disturbance conditions.

Claims

1. A method for input saturation passivation control of a cooperative adaptive cruise control system, characterized in that The steps include: a. Establish a linear system model of vehicle platoon with disturbance; In step a, the system is modeled as a linear system with disturbance according to the relationship between the variable vehicle distance, the constant headway, the communication mode between vehicles and the communication delay; b. To ensure the stability of the platoon, the acceleration of all following vehicles is reduced one by one, and the platoon stability condition is converted into an input saturation constraint; c. Use the passivation method to design a controller with input saturation to ensure the stability of the queue; In step c, a passive controller u is designed based on the Riccati equation, Lyapunov stability theory and matrix theory. i ; d. Finally, verify the effectiveness of the designed input saturation passivation control method.

2. The input saturation passivation control method of a cooperative adaptive cruise control system according to claim 1, characterized in that: The specific operations of step a are: Step 1.1: Select the desired vehicle spacing suitable for calculation in this paper: d i,e =τ h,i v i (t)+d0 Where: τ h,i is the headway time, which is a positive constant; v i (t) is the speed of the i-th vehicle; t is the time, d0 is the minimum safe distance between the i-th vehicle and the i-1-th vehicle in front after they stop, usually 2m to 4m; Step 1.2: According to the longitudinal motion diagram of the queue, the longitudinal kinematic relationship between the front and rear vehicles can be obtained: In the formula, Δd i is the inter-vehicle distance error; d i ,d i,e are the actual and expected distances between the i-th and i-1-th vehicles, respectively; Δv i is the relative speed between the i-th car and the i-1-th car; Step 1.3: Relationship between the actual acceleration and expected acceleration of the vehicle: Where: a i , a i,e are the actual acceleration and the expected acceleration, τ i is the time constant, k L,i is the system gain; Based on the above three points, the kinematic state equation of the workshop can be established: In the formula, ω i =a i-1 is the disturbance, u i (t) = a i,e is the control input.

3. The input saturation passivation control method of a cooperative adaptive cruise control system according to claim 2, characterized in that: When studying the cooperative adaptive cruise control system in step b, the stability of the queue must be ensured first. At this time, the stability of the queue is defined as: The stability condition of the queue is regarded as the saturation constraint of the queue vehicle input, which can be expressed by the input saturation function as follows: u max is u i The upper bound of -u m i n is u i The lower bound of is obtained, and then a model with input saturation and disturbance is established, so the state space expression of the system is: In the formula, y i (t) is the system output, C i and D 2i is a matrix of appropriate dimension.

4. The input saturation passivation control method of a cooperative adaptive cruise control system according to claim 3, characterized in that: The specific method of step c is: If there exists a semi-positive definite function V i (x i (t)) and the positive definite function W i (x i (t)), such that: If it holds, the system is strictly passive; Then choose a suitable positive definite matrix Q i , R i , according to the Riccati equation: A i T P i +P i A i -P i B i R i -1 B i T P i +Q i =0, Find the only positive solution P i ; According to Obtain the controller, and then verify whether the controller is a passive controller; Verification conditions: 1) A i ,B i Controllable; 2)、 Among them, λ min (·) represents the minimum eigenvalue of the matrix, and the storage function is constructed: V i (x i )=x i T P i x i , and then take its derivative and substitute it into the equation, we can verify that P i Satisfy the conditions.

5. The input saturation passivation control method of a cooperative adaptive cruise control system according to claim 1, characterized in that: The specific method of step d is: verify whether the designed controller can still maintain the stability of the queue in the presence of disturbances. The verification process is as follows: build homogeneous and heterogeneous queue models respectively, and compare the transient indicators under the optimal controller in the two models.

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