Vehicle longitudinal following sliding mode control construction method

Abstract

The invention relates to a vehicle longitudinal following sliding mode control construction method. The method comprises the steps that a vehicle third-order dynamic model based on bounded variable parameters is established; establishing a tracking error model based on a fixed spacing strategy; designing a sliding mode surface and a sliding mode control law based on the vehicle three-order dynamic model; on the basis of a Lyapunov method and a sliding mode control law, motion reachability analysis is carried out on the sliding mode surface, and whether the current system state is asymptotically reachable along the sliding mode surface is verified, so that the exponential stability of the system is improved; on the basis of a Lyapunov method and a tracking error model, carrying out subtraction processing on sliding mode surfaces of adjacent vehicles to obtain a sliding mode motion equation of a vehicle distance error and a speed error, and determining whether an index of the sliding mode motion equation of a current system state is stable or not so as to improve the index chord stability of the system; according to the method, the system is accurately converged to an expected state under complex working conditions, and the index stability of the system is improved.

Description

Technical Field

[0001] The present application relates to the field of vehicle longitudinal following control, and in particular to a method for constructing a vehicle longitudinal following sliding mode control. Background Art

[0002] Vehicle longitudinal following control technology is one of the key technologies in modern intelligent transportation systems, which aims to coordinate and optimize the relative position and speed between vehicles. Existing vehicle longitudinal following control systems are difficult to ensure the exponential stability of the system under complex working conditions. In other words, the distance and speed between vehicles are difficult to accurately converge to the desired state, which has an adverse impact on the reliability of the vehicle longitudinal following control system. Summary of the invention

[0003] Based on the above technical problems, the present application provides a method for constructing a vehicle longitudinal following sliding mode control, which enables the system to accurately converge to a desired state under complex working conditions and improves the exponential stability of the system.

[0004] The present application provides a method for constructing a vehicle longitudinal following sliding mode control, the method comprising:

[0005] Establish a third-order vehicle dynamics model based on bounded variable parameters;

[0006] Establish a tracking error model based on a fixed spacing strategy;

[0007] Design sliding surface and sliding mode control law based on the third-order dynamics model of the vehicle;

[0008] Based on the Lyapunov method and sliding mode control law, the kinematic reachability analysis of the sliding surface is performed to verify whether the current system state is asymptotically reachable along the sliding surface, so as to improve the exponential stability of the system.

[0009] Based on the Lyapunov method and tracking error model, the sliding mode surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equation of the vehicle spacing error and speed error. It is determined whether the exponent of the sliding mode motion equation of the current system state is stable, so as to improve the exponential chord stability of the system.

[0010] The vehicle longitudinal following sliding mode control construction method of the present application models the third-order dynamic model of the vehicle, designs the sliding surface and the sliding mode control law to make the system state slide along the sliding surface and converge to the desired state, thereby enhancing the robustness of the system; at the same time, the Lyapunov method is used to analyze the stability of the system, and it is verified that the system has exponential stability under the action of the sliding mode control law and the exponential chord stability of the sliding mode motion equation, which can improve the exponential stability of the system and ensure that the distance and speed between vehicles in the system accurately converge to the desired state under complex working conditions.

[0011] Specifically, based on the third-order dynamics model of the vehicle, the sliding surface and sliding mode control law are designed, including:

[0012] Design a sliding surface based on the weighted sum of state errors. The sliding surface formula is:

[0013]

[0014] Where i = 1, ..., N, Δ is the communication time lag, assuming that the lag of the i-th vehicle relative to the (i-1)-th vehicle and the leading vehicle is equal, p0 is the longitudinal displacement of the leading vehicle, p i , p i-1 are the longitudinal displacements of the i-th vehicle and the (i-1)-th vehicle, v0 is the longitudinal speed of the leading vehicle, v i , v i-1 are the longitudinal speeds of the i-th vehicle and the (i-1)-th vehicle, a0 is the longitudinal acceleration of the leading vehicle, a i , a i-1 are the longitudinal accelerations of the i-th vehicle and the (i-1)-th vehicle, L i is the length of the i-th vehicle, and q1, q2, q3, q4, q5, and q6 are control parameters.

[0015] Specifically, after designing the sliding surface based on the weighted sum of state errors, it includes:

[0016] Based on the third-order dynamics model of the vehicle, the sliding surface is differentiated to obtain the derivative of the sliding surface;

[0017] Based on the derivative of the sliding surface, the equivalent control law and the switching control law are determined;

[0018] The sliding mode control law is obtained by adding the equivalent control law and the switching control law.

[0019] Specifically, based on the Lyapunov method and sliding mode control law, the motion reachability analysis of the sliding surface is performed to verify whether the current system state is asymptotically reachable along the sliding surface, including:

[0020] According to the Lyapunov method, the time derivative of the sliding surface is processed to obtain the time derivative of the sliding surface; the formula of the Lyapunov method is: S i is the sliding surface;

[0021] Verify whether the time derivative of the sliding surface approaches zero to determine whether the current system state is asymptotically reachable along the sliding surface.

[0022] Specifically, based on the Lyapunov method and the tracking error model, the sliding surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equations of the inter-vehicle distance error and the speed error, and determine whether the exponent of the sliding mode motion equation of the current system state is stable, including:

[0023] Based on the tracking error model, the sliding mode surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equations of the inter-vehicle distance error and speed error.

[0024] Verify whether the sliding mode motion equation complies with the preset stability theorem rules to determine whether the exponent of the sliding mode motion equation of the current system state is stable; the preset stability theorem rules are designed based on the Lyapunov method.

[0025] Specifically, the sliding mode motion equation is:

[0026]

[0027] Where i = 1,...,N, Δ is the communication time lag, e 1,i is the position error between the i-th vehicle and the (i-1)-th vehicle, e 2,i is the speed error between the i-th vehicle and the (i-1)-th vehicle, l1, l2, l3 and l4 are the evaluation ratios of the control parameters of the currently selected sliding surface.

[0028] Specifically, the formula of the vehicle third-order dynamics model based on bounded variable parameters is:

[0029]

[0030] Where i = 1, 2, ... N, Δ1 is the fixed system time delay, and satisfies [p i (s),v i (s),a i (s)] T =φ i (s), Δ1<s≤0, p i is the longitudinal displacement of the vehicle, v i is the longitudinal speed of the vehicle, a i is the longitudinal acceleration of the vehicle, τ i is the time constant of the vehicle, u i is the vehicle's throttle / brake input, b i is the ratio of the air resistance value to the mass value of vehicle i, g i is the ratio of vehicle resistance value to mass value of vehicle i, d i is the inverse of the mass value of vehicle i.

[0031] Specifically, the formula of the tracking error model based on the fixed spacing strategy is:

[0032]

[0033] Among them, e 1,i is the position error between the i-th vehicle and the (i-1)-th vehicle, e2,i is the speed error between the i-th vehicle and the (i-1)-th vehicle, e 3,i is the acceleration error between the i-th vehicle and the (i-1)-th vehicle, p i is the longitudinal displacement of the i-th vehicle, p i-1 is the longitudinal displacement of the (i-1)th vehicle, v i is the longitudinal speed of the ith vehicle, v i-1 is the longitudinal speed of the (i-1)th vehicle, a i is the longitudinal acceleration of the i-th vehicle, a i-1 is the longitudinal acceleration of the (i-1)th vehicle, d i-1,i is the actual distance between the i-th vehicle and the (i-1)-th vehicle, d des,i is the ideal distance between the i-th car and the (i-1)-th car, L i is the length of the i-th vehicle, r i For the ideal spacing, a fixed spacing strategy is adopted, r i is a constant. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A schematic flow chart of a method for constructing a vehicle longitudinal following sliding mode control according to an embodiment of the present application;

[0035] Figure 2 A simulation diagram of the movement trajectory of the leading vehicle in an embodiment of the present application;

[0036] Figure 3 This is a simulation diagram of the position-time characteristic of a vehicle with bounded variable parameters according to an embodiment of the present application;

[0037] Figure 4 This is a simulation diagram of the time characteristic of the bounded variable parameter vehicle position error of an embodiment of the present application;

[0038] Figure 5 This is a simulation diagram of the time characteristic of the bounded variable parameter vehicle speed of an embodiment of the present application;

[0039] Figure 6 This is a simulation diagram of the time characteristic of the bounded variable parameter vehicle speed error of an embodiment of the present application;

[0040] Figure 7 This is a simulation diagram of the acceleration time characteristic of a bounded variable parameter type vehicle according to an embodiment of the present application;

[0041] Figure 8 This is a simulation diagram of the time characteristic of the acceleration error of a bounded variable parameter type vehicle according to an embodiment of the present application;

[0042] Fig. 9 This is a simulation diagram of the time characteristic of the inter-vehicle spacing of vehicles with bounded variable parameters according to an embodiment of the present application;

[0043] Fig.10 It is a simulation diagram of the time characteristic of the sliding mode switching function of a bounded variable parameter vehicle according to an embodiment of the present application;

[0044] Fig.11 This is a simulation result diagram of position error comparison under different sliding mode boundary layers of an embodiment of the present application;

[0045] Fig.12 This is a simulation result diagram of velocity error comparison under different sliding mode boundary layers of an embodiment of the present application;

[0046] Fig.13 This is a simulation result diagram of acceleration error comparison under different sliding mode boundary layers of an embodiment of the present application;

[0047] Fig.14 This is a simulation result diagram comparing sliding mode switching functions under different sliding mode boundary layers in an embodiment of the present application. DETAILED DESCRIPTION

[0048] The present invention is described in detail below in conjunction with specific embodiments.

[0049] like Figure 1 As shown, the embodiment of the present application proposes a method for constructing a vehicle longitudinal following sliding mode control. The embodiment of the present application achieves the robustness and exponential stability of the vehicle longitudinal following control system under complex working conditions by designing a sliding mode control algorithm that adapts to unknown parameters and time lag effects.

[0050] The specific technical solutions of the embodiments of this application are as follows:

[0051] Step 1: Establish a third-order vehicle dynamics model based on bounded variable parameters.

[0052] First, a third-order vehicle dynamics model with system time delay is established, as shown in formula (1):

[0053]

[0054] Where i = 1, 2, ... N, p i is the longitudinal displacement of the vehicle, v i is the longitudinal speed of the vehicle, a i is the vehicle longitudinal acceleration, They are p i , v i , a i The derivative of i is the time constant of the vehicle, u i is the vehicle's throttle / brake input, Δ1 is the fixed system delay, and satisfies [p i (s),v i (s),a i (s)]T =φ i (s), Δ1<s≤0, m i , c i , f i are the mass of vehicle i, the air resistance system, and the vehicle resistance, and they satisfy the following formula (2):

[0055] m i,min ≤m i ≤m i,max , c i,min ≤c i ≤c i,max , f i,min ≤f i ≤f i,max (2)

[0056] Among them, m i,min , m i,max is m i The minimum and maximum values ​​that can be taken, c i,min , c i,max c i The maximum and minimum values ​​that can be taken, f i,min , f i,max f i The maximum and minimum possible values.

[0057] In the above formula (2), the values ​​are as follows:

[0058]

[0059] In the above formula (3), let:

[0060]

[0061] c i '=c i -c i,0 , b i '=b i -b i,0 , d i '=d i -d i,0 , g i '=g i -g i,0 (5)

[0062]

[0063] in,

[0064] Therefore, based on formulas (1)-(6), a vehicle third-order dynamics model with bounded variable parameters and system time lag is established. The vehicle third-order dynamics model is as follows:

[0065]

[0066] Where i = 1, 2, ... N, Δ1 is the fixed system time delay, and satisfies [p i (s),v i (s),a i (s)] T =φ i (s), Δ1<s≤0, p i is the longitudinal displacement of the vehicle, v i is the longitudinal speed of the vehicle, a i is the longitudinal acceleration of the vehicle, τ i is the time constant of the vehicle, u i is the vehicle's throttle / brake input, b i is the ratio of the air resistance value to the mass value of vehicle i, g i is the ratio of vehicle resistance value to mass value of vehicle i, d i is the inverse of the mass value of vehicle i.

[0067] Step 2: Establish a tracking error model based on the fixed spacing strategy.

[0068] The tracking error model using a fixed spacing strategy is established as follows:

[0069]

[0070] Among them, e 1,i is the position error between the i-th vehicle and the (i-1)-th vehicle, e 2,i is the speed error between the i-th vehicle and the (i-1)-th vehicle, e 3,i is the acceleration error between the i-th vehicle and the (i-1)-th vehicle. i , p i-1 are the longitudinal displacements of the i-th vehicle and the (i-1)-th vehicle, respectively, v i , v i-1 are the longitudinal speeds of the i-th vehicle and the (i-1)-th vehicle, respectively, and a i , a i-1 are the longitudinal accelerations of the i-th vehicle and the (i-1)-th vehicle, d i-1,i is the actual distance between the i-th vehicle and the (i-1)-th vehicle, d des,i is the ideal distance between the i-th car and the (i-1)-th car, L i is the length of the i-th vehicle, r iFor the ideal spacing, a fixed spacing strategy is adopted, which is a constant here.

[0071] Step 3: Based on the third-order dynamics model of the vehicle, design the sliding surface and sliding mode control law.

[0072] In order to achieve exponential stability of the system, the embodiment of the present application designs a sliding surface and a sliding mode control law so that the system state can slide along the sliding surface and eventually converge to the desired state.

[0073] Sliding surface S i It can be designed as the weighted sum of state errors, and the sliding surface S i The following formula (9):

[0074]

[0075] Where Δ is the communication time lag, where it is assumed that the lag of the i-th vehicle relative to the (i-1)-th vehicle and the leading vehicle is equal, p0 is the longitudinal displacement of the leading vehicle, and p i , p i-1 are the longitudinal displacements of the i-th vehicle and the (i-1)-th vehicle, v0 is the longitudinal speed of the leading vehicle, v i , v i-1 are the longitudinal speeds of the i-th vehicle and the (i-1)-th vehicle, a0 is the longitudinal acceleration of the leading vehicle, a i , a i-1 are the longitudinal accelerations of the i-th vehicle and the (i-1)-th vehicle, L i is the length of the i-th vehicle, q1, q2, q3, q4, q5, q6 are unknown control parameters.

[0076] Combining formulas (1)-(9), the sliding surface S i Perform the derivative processing to obtain the derivative S of the sliding surface i , as follows formula (10):

[0077]

[0078] The meanings of the parameters in the formulas are shown in formulas (1)-(9).

[0079] Design the sliding mode control law, first obtain the equivalent control law and switching control law of the sliding mode control, and then use the equivalent control law and switching control law to ensure the sliding mode reachability of the system.

[0080] In the above formula (10), let the equivalent control law be the following formula (11):

[0081] u i,equ =u i,0 / d i,0 (11)

[0082] in,

[0083]

[0084] The meanings of the parameters in the formulas are shown in formulas (1)-(9).

[0085] At the same time, in order to ensure the accessibility of the sliding mode, the switching control law is taken as follows:

[0086]

[0087] Among them, λ>0 is the control parameter, and other parameters are shown in formulas (1)-(6), and in the formula,

[0088]

[0089] Therefore, the equivalent control law and the switching control law are added to obtain the sliding mode control law, as shown in formula (14):

[0090] u i =u i,equ +u i,N (14)

[0091] The sliding surface and sliding mode control law obtained in the above steps, the embodiment of the present application further verifies whether the sliding mode of the power system (such as Formula 7 above) is asymptotically reachable under the sliding mode control law (such as Formula 14 above), and the sliding mode motion equation obtained through the sliding surface (such as Formula 29 below), verifies whether the sliding mode motion equation conforms to the preset stability theorem rules, and proves whether the obtained sliding mode motion equation is exponentially stable. If the sliding mode motion equation conforms to the preset stability theorem rules, it is proved that the contained spacing error and speed error are also exponentially stable.

[0092] It should be noted that the preset stability theorem rule of the embodiment of the present application is to first establish an error state equation of a relatively general time-delay vehicle system, and then establish a stability theorem and a proof process for the state equation. In this way, the subsequent sliding mode motion equation can directly determine its stability according to the stability theorem.

[0093] The following is an explanation of the design of preset stability theorem rules.

[0094] The error state equation of the longitudinal following control system of the fixed time-delay vehicle is established and expressed by the following differential equation (15):

[0095]

[0096] Among them, x i ∈R n represents the longitudinal following error vector of the i-th vehicle, A,B,C∈R n×n , xT and A T Respectively represent the transpose of vector x and matrix A. Δ∈[0,Δ d ] represents the time delay of vehicle-to-vehicle communication, assuming that the initial condition of the system (Formula 15) is x i (s) = φ i (s), Δ d ≤s≤0,φ i In the interval [-Δ d ,0] is bounded and continuous. At the same time, it is assumed that the system (15) satisfies the existence and uniqueness conditions of the equilibrium point. We use the following notation: λ(A) denotes the characteristic root of the matrix A, λ max (A) represents the largest eigenvalue of matrix A, ||x|| and ||A|| are the 2-norms of vector x and matrix A, respectively. ||A||=({λ:λ is A T The largest characteristic root of A}) 1 / 2 . Time function v i About x i The partial derivative of where x k,i is x i The kth item of .

[0097] Therefore, the isolated subsystem of the system is:

[0098]

[0099] Introduce Definition 1, Definition 2 and Lemma 1 as follows:

[0100] Definition 1: The equilibrium point of a system (Equation 15) is chord-stable if for any given ε>0, there exists δ>0 such that

[0101] Definition 2: The equilibrium point of a system (Formula 15) is exponentially chord-stable if the origin is chord-stable and there exist constants λ>0 and M>0 for all t≥0, satisfying sup i ||x i (t)||≤M||Φ i (s)||e -λt ,in

[0102] Lemma 1: Assume And satisfy the differential inequality (17):

[0103] In the above formula, τ1,...,τ i is the time lag, for v i (t)≥0, with gi (·)>0,γ i0 >0,γ ij ≥0.

[0104] If there exists v=(v 1,s ,v 2,s ,...,v i,s ) makes:

[0105]

[0106] and inf i {v 10}=α>0,sup i {v 10}=β>0, then for any given ε>0, there exists δ>0 such that

[0107] Using Definition 1, Definition 2 and Lemma 1, we prove the following:

[0108] Get the collection:

[0109] γ={z(l):z i =lv i,s ,l>0,i=1,2,...,N},Ω(z)={u:0≤u≤z,z∈γ},For any given ε>0,there exists l0>0 satisfying ε=sup i {l0v i,s}, take δ=inf i {l0v i,s}. At the same time, define O = {u:u i =l0v i,s ,u j ≤l0v j,s ,j≠i,i,j=1,2,...,N}, it is easy to get, If sup i |v i (s)| ∞ <δ, we get v i (s)∈Ω(z(l0)), and

[0110] The following proof by contradiction proves that when t>0, sup i |v i (t)| ∞ <ε. Assume that there is a time t0>0 such that sup i |v i (t)| ∞ =ε, then there exists a time t1∈[0,t0] and an i such that v i (t1)∈O, that is, v i(t1) = l0v i,0 , v j (t1)≤l0v j,0 , t∈[0,t1], j=1,2,...,N, j≠i. This means that at t=t1, However, according to equation (17), equation (18) and g(·)>0, γ i0 >0,γ ij ≥0; inferred:

[0111]

[0112] This is similar to Contradiction, so the assumption is not true, that is, there is no time t0>0 such that sup i |v i (t0)| ∞ =ε. Therefore, sup i |v i (t)| ∞ <ε. Then for any ε>0, there exists δ>0 such that when sup i |v i (s)| ∞ <δ, there is sup i |v i (t)| ∞ <ε.

[0113] According to Theorem 1: If the system (15) satisfies the following conditions (i), (ii) and (iii), then its zero solution is exponentially chord-stable.

[0114] (i) 0<||C||<1;

[0115] (ii) For the isolated subsystem (Equation 16), there exists a Lyapunov function v i and constant β l >0, β h >0, β p >0, β q >0, so that: β l ||x i || 2 ≤v i ≤β h ||x i || 2 ,

[0116] Therefore, it is proved that: From formula (15), we can get:

[0117]

[0118] Where Δ is the communication time lag.

[0119] Command: w i (t) = e ξt v i (t) (20)

[0120] Where ξ is an arbitrarily small positive number, and the above formula (20) is an auxiliary function for proving exponential stability.

[0121] Taking the derivative of equation (20) along the system (Equation 15), we have:

[0122]

[0123] According to condition (ii) of Theorem 1 above, the formula can be written as:

[0124]

[0125] According to formula (20), we have:

[0126]

[0127] According to the conditions We know that there exists ξ>0 and e ξ(i-j-1)τ) / 2 w j (t-(ij-1)τ)>0(j=1,...,i-1) such that

[0128]

[0129] Therefore, formula (15) is as follows:

[0130]

[0131] According to Lemma 1 and the above formula (25), for any ε o >0, there exists δ0>0 such that Then the system (15) is string-stable.

[0132] By sup i ||w i (s)|| ∞ <ε0 and α l >0

[0133]

[0134] Therefore, according to Definition 2, we can obtain that system (15) is exponentially chord stable.

[0135] Step 4: Based on the Lyapunov method and sliding mode control law, perform motion reachability analysis on the sliding surface to verify whether the current system state is asymptotically reachable along the sliding surface to improve the exponential stability of the system.

[0136] Using the above preset stability theorem rules, it is proved that under the sliding mode control law (Formula 14), the sliding mode of the dynamic system (Formula 7) is asymptotically reachable.

[0137] According to the Lyapunov method, the time derivative of the sliding surface is processed to obtain the time derivative of the sliding surface; the formula of the Lyapunov method is: S i is the sliding surface; specifically, take the Lyapunov function Derivative along the sliding surface Taking the derivative of (Formula 10) with respect to time, we get the following formula (27):

[0138]

[0139] In the formula, the meanings of the parameters are as given in (1)-(7) and (9).

[0140] When selecting sliding mode control, it is necessary to ensure that the selected sliding surface is reachable. In short, it is necessary to prove that the selected sliding surface is available, that is, the sliding surface can reach 0. From the above formula (27), it can be seen that as long as q3+q6>0, and S i ≠0, That is, when t→∞, S i →0, then the sliding mode of the system is asymptotically reachable. In other words, verify the time derivative of the sliding surface Whether it approaches zero can determine whether the current system state is asymptotically reachable along the sliding surface.

[0141] Step 5: Based on the Lyapunov method and tracking error model, the sliding surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equation of the vehicle spacing error and speed error, and determine whether the exponent of the sliding mode motion equation of the current system state is stable to improve the exponential chord stability of the system.

[0142] Next, we analyze the stability of the inter-vehicle distance error and speed error on the sliding mode plane. Determine the control parameters q1~q6 set in formula (9). When t→∞, e 1,i →0,e 2,i →0,e 3,i → 0. By S i =0, i=1,...,N, there are:

[0143]

[0144] make Definition 1,i =0,e 2,i = 0, the sliding mode motion equations of the inter-vehicle distance error and speed error are obtained as follows:

[0145]

[0146] in,

[0147]

[0148] And, i = 1, ..., N, Δ is the communication time lag, e 1,i is the position error between the i-th vehicle and the (i-1)-th vehicle, e 2,i is the speed error between the i-th vehicle and the (i-1)-th vehicle. In simple terms, l1, l2, l3 and l4 are the evaluation ratios of the control parameters of the currently selected sliding surface.

[0149] Combined with the error state equation (Formula 15) of the above-mentioned fixed time-delay vehicle longitudinal following system, it can be known that the sliding mode motion equation (Formula 29) is a special case thereof, that is, the time-delay vehicle longitudinal following system applied in the embodiment of the present application is a special case of the fixed time-delay vehicle longitudinal following system, and the exponential chord stability of the system can be determined according to the above-mentioned preset stability theorem rule. The sliding mode motion equation (Formula 29) obtained by the sliding surface includes the vehicle spacing error and the speed error, and then according to theorem 1 proposed by the above-mentioned preset stability theorem rule, if the conditions (i), (ii), and (iii) are met, the obtained sliding mode motion equation (Formula 29) is exponentially stable, and the included spacing error and speed error are also exponentially stable.

[0150] Combined with the above steps 1-5, the vehicle longitudinal following sliding mode control construction method of the embodiment of the present application can effectively cope with the changes of bounded unknown parameters through system modeling and sliding surface design in terms of enhanced robustness, ensuring that the system can still maintain stable control performance under the condition of parameter uncertainty, and the design of the sliding mode control law further enhances the system's adaptability to parameter changes by adjusting the control gain and equivalent control terms. In terms of optimizing the processing of time lag effects, the embodiment of the present application adopts the vector Lyapunov method for stability analysis to ensure that the system can achieve exponential stability in the presence of time lag. This not only solves the control lag and oscillation problems caused by time lag, but also improves the response speed and accuracy of the system. In terms of ensuring exponential stability, the embodiment of the present application can ensure the exponential stability of the system under complex working conditions through sliding mode control law and stability analysis, which is crucial to the safety and reliability of the vehicle control system, verifies the exponential stability and exponential chord stability, and ensures that the distance and speed between vehicles can quickly and accurately reach the desired state.

[0151] Based on the above-established dynamic model, tracking error model and designed sliding mode control system, a simulation test of the vehicle longitudinal following control system is carried out. By designing the controller parameters through stability analysis, the time response diagram of the position, speed, acceleration and the distance between each vehicle and the preceding vehicle can be obtained under different parameters.

[0152] Specifically, a simulation experiment is conducted on the constructed sliding mode control system (i.e., Formula 29). The vehicle longitudinal following control system used in the simulation consists of 5 vehicles, 1 leading vehicle (vehicle 0) and 4 following vehicles (vehicles 1-4). The vehicle model parameter boundaries are shown in Table 1 below, the vehicle model control parameters are shown in Table 2 below, the vehicle control parameters are shown in Table 3 below, and the vehicle initial conditions are shown in Table 4 below. The leading vehicle action trajectory is shown in Figure 1 As shown in the figure, a) is the acceleration diagram and b) is the velocity diagram. The simulation time is 30s and the simulation step is 0.01s.

[0153] Table 1 Boundaries of vehicle model parameters

[0154]

[0155] Table 2 Vehicle model control parameters

[0156]

[0157]

[0158] Table 3 Vehicle control parameters

[0159]

[0160] Table 4 Vehicle initial conditions

[0161]

[0162] According to Table 3, the sliding mode control system (i.e., Formula 29) can be written as follows:

[0163]

[0164] So there is λ max (A) = -3, ||C||=1 / 3, at this time, condition (i) in Theorem 1 is satisfied, and the Lyapunov function is taken Let α l =α h =1,α p =-λ max (A) = 3, α q =2, which satisfies condition (ii) of Theorem 1, ||B+CA||=3Δ, then like Then there is If condition (iii) in Theorem 1 is satisfied, then the system (31) is exponentially chord stable.

[0165] The simulation results are as follows Figures 3 to 10 As shown in FIG. 1 , the dashed line represents the leading vehicle, and the solid line represents the following vehicle. Figure 3 is the time characteristic diagram of vehicle position with bounded variable parameters, Figure 4 is the time characteristic diagram of the vehicle position error with bounded variable parameters, Figure 5 is the time characteristic diagram of vehicle speed with bounded variable parameters, Figure 6 is the time characteristic diagram of the vehicle speed error with bounded variable parameters, Figure 7 is the time characteristic diagram of the vehicle acceleration with bounded variable parameters, Figure 8 is the time characteristic diagram of the acceleration error of a bounded variable parameter vehicle, Fig. 9 is the time characteristic diagram of the vehicle inter-vehicle spacing with bounded variable parameters, Fig.10 is the time characteristic diagram of the sliding mode switching function of the bounded variable parameter vehicle (also known as the sliding mode diagram). Figure 5 and Figure 7 It can be seen that the speed and acceleration of the following vehicle can quickly approach the speed of the leading vehicle. Figure 4 , Figure 6 and Figure 8 It can be seen that the position error, velocity error and acceleration error of the vehicle in the vehicle have a faster convergence speed. Fig. 9 It can be seen that the workshop spacing can quickly reach the ideal workshop spacing. Fig.10 It can be seen that the sliding mode can quickly approach 0. At the same time, according to Figure 3 to Figure 8 It can be seen that this method can stabilize the vehicle when the initial error is not zero.

[0166] Due to the on-demand design characteristics of the sliding mode, the sliding mode motion of the system is independent of the parameter changes of the control object and the external disturbance of the system. The robustness of the sliding mode variable structure control system is stronger than that of the general conventional continuous system. However, in essence, the discontinuous switching characteristics will cause the system to vibrate. In practice, the vibration is inevitable and cannot be eliminated. Therefore, the vibration can only be weakened to a certain extent. In order to achieve the purpose of correcting the control term to weaken the vibration, the concepts of "quasi-sliding mode" and "boundary layer" are used. The quasi-sliding surface refers to the mode in which the motion trajectory of the system is restricted to a certain boundary layer neighborhood of the ideal sliding mode. From the perspective of phase trajectory, the control with the ideal sliding mode is to make all the state points within a certain range be attracted to the switching surface, while the quasi-sliding mode control is to make all the state points within a certain range be attracted to a certain boundary layer neighborhood of the switching surface. In the boundary layer, the sliding mode does not require the existence conditions of the sliding mode to be satisfied, so the quasi-sliding mode does not require the switching of the control structure on the switching surface. It can be a control system that performs structural transformation on the boundary layer, or it can be a continuous state feedback control system that does not perform structural transformation at all. This difference in the implementation of quasi-sliding mode control fundamentally avoids or weakens chattering, and thus has been widely used in practice. There are two common quasi-sliding mode controls: using a saturation function to replace the sign function in the ideal sliding mode, and using relay characteristics for continuity, replacing the sign function with a continuous function. The saturation function (sat(S i )) replaces the sign function (sgn(S i )),Right now:

[0167]

[0168] Where Δ is the boundary layer.

[0169] The simulation results are as follows Figure 11 to Figure 14 As shown, Fig.11 a), Fig.12 a) and Fig.13 a) are the simulation results of position, velocity and acceleration errors when the boundary layer thickness is 0.2, Fig.11 b) Fig.12 b) and Fig.13 b) are the simulation results of position, velocity and acceleration errors when the boundary layer thickness is 0.4. Figure 3 to Figure 8 and Figure 11 to Figure 14 It can be seen that when the quasi-sliding mode control is adopted, the vibration can be effectively weakened. The larger the value of the boundary layer thickness is, the smaller the vibration is, the control gain is reduced, and the control effect is poor; the smaller the value of the boundary layer thickness is, the larger the vibration is, the control gain is larger, and the control effect is good.

[0170] Therefore, the sliding mode control algorithm designed in the vehicle longitudinal following sliding mode control construction method of the embodiment of the present application has good effects in adapting to unknown parameters and optimizing time lag effects.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A method for constructing a vehicle longitudinal following sliding mode control, characterized in that: The method execution comprises: Establish a third-order vehicle dynamics model based on bounded variable parameters; Establish a tracking error model based on a fixed spacing strategy; Design sliding surface and sliding mode control law based on the third-order dynamics model of the vehicle; Based on the Lyapunov method and sliding mode control law, the kinematic reachability analysis of the sliding surface is performed to verify whether the current system state is asymptotically reachable along the sliding surface, so as to improve the exponential stability of the system. Based on the Lyapunov method and tracking error model, the sliding mode surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equation of the vehicle spacing error and speed error. It is determined whether the exponent of the sliding mode motion equation of the current system state is stable, so as to improve the exponential chord stability of the system.

2. The method according to claim 1, characterized in that Based on the third-order dynamics model of the vehicle, the sliding surface and sliding mode control law are designed, including: Design a sliding surface based on the weighted sum of state errors. The sliding surface formula is: Where i = 1, ..., N, Δ is the communication time lag, assuming that the lag of the i-th vehicle relative to the (i-1)-th vehicle and the leading vehicle is equal, p0 is the longitudinal displacement of the leading vehicle, p i , p i-1 are the longitudinal displacements of the i-th vehicle and the (i-1)-th vehicle, v0 is the longitudinal speed of the leading vehicle, v i , v i-1 are the longitudinal speeds of the i-th vehicle and the (i-1)-th vehicle, a0 is the longitudinal acceleration of the leading vehicle, a i , a i-1 are the longitudinal accelerations of the i-th vehicle and the (i-1)-th vehicle, L i is the length of the i-th vehicle, and q1, q2, q3, q4, q5, and q6 are control parameters.

3. The method according to claim 2, characterized in that After designing the sliding surface based on the weighted sum of state errors, it includes: Based on the third-order dynamics model of the vehicle, the sliding surface is differentiated to obtain the derivative of the sliding surface; Based on the derivative of the sliding surface, the equivalent control law and the switching control law are determined; The sliding mode control law is obtained by adding the equivalent control law and the switching control law.

4. The method according to claim 1, characterized in that: Based on the Lyapunov method and sliding mode control law, the motion reachability analysis of the sliding surface is performed to verify whether the current system state is asymptotically reachable along the sliding surface, including: According to the Lyapunov method, the time derivative of the sliding surface is processed to obtain the time derivative of the sliding surface; the formula of the Lyapunov method is: S i is the sliding surface; Verify whether the time derivative of the sliding surface approaches zero to determine whether the current system state is asymptotically reachable along the sliding surface.

5. The method according to claim 1, characterized in that: Based on the Lyapunov method and tracking error model, the sliding surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equations of the inter-vehicle distance error and speed error, and determine whether the exponent of the sliding mode motion equation of the current system state is stable, including: Based on the tracking error model, the sliding mode surfaces of adjacent vehicles are subtracted to obtain the sliding mode motion equations of the inter-vehicle distance error and speed error. Verify whether the sliding mode motion equation complies with the preset stability theorem rules to determine whether the exponent of the sliding mode motion equation of the current system state is stable; the preset stability theorem rules are designed based on the Lyapunov method.

6. The method according to claim 1, characterized in that The equation of motion for sliding mode is: Where i = 1,...,N, Δ is the communication time lag, e 1,i is the position error between the i-th vehicle and the (i-1)-th vehicle, e 2,i is the speed error between the i-th vehicle and the (i-1)-th vehicle, l1, l2, l3 and l4 are the evaluation ratios of the control parameters of the currently selected sliding surface.

7. The method according to claim 1, characterized in that The formula of the vehicle third-order dynamics model based on bounded variable parameters is: Where i = 1, 2, ... N, Δ1 is the fixed system time delay, and satisfies [p i (s),v i (s),a i (s)] T =φ i (s), Δ1<s≤0, p i is the longitudinal displacement of the vehicle, v i is the longitudinal speed of the vehicle, a i is the longitudinal acceleration of the vehicle, τ i is the time constant of the vehicle, u i is the vehicle's throttle / brake input, b i is the ratio of the air resistance value to the mass value of vehicle i, g i is the ratio of vehicle resistance value to mass value of vehicle i, d i is the inverse of the mass value of vehicle i.

8. The method according to claim 1, characterized in that The formula for the tracking error model based on the fixed spacing strategy is: Among them, e 1,i is the position error between the i-th vehicle and the (i-1)-th vehicle, e 2,i is the speed error between the i-th vehicle and the (i-1)-th vehicle, e 3,i is the acceleration error between the i-th vehicle and the (i-1)-th vehicle, p i is the longitudinal displacement of the i-th vehicle, p i-1 is the longitudinal displacement of the (i-1)th vehicle, v i is the longitudinal speed of the ith vehicle, v i-1 is the longitudinal speed of the (i-1)th vehicle, a i is the longitudinal acceleration of the i-th vehicle, a i-1 is the longitudinal acceleration of the (i-1)th vehicle, d i-1,i is the actual distance between the i-th vehicle and the (i-1)-th vehicle, d des,i is the ideal distance between the i-th car and the (i-1)-th car, L i is the length of the i-th vehicle, r i For the ideal spacing, a fixed spacing strategy is adopted, r i is a constant.

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