CN116859952A - Vehicle team longitudinal composite control method and system based on second-order continuous sliding mode - Google Patents
Vehicle team longitudinal composite control method and system based on second-order continuous sliding mode Download PDFInfo
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Abstract
The invention discloses a vehicle team longitudinal compound control method and system based on a second-order continuous sliding mode, and relates to the technical field of automobile control. The method comprises the following steps: constructing a vehicle longitudinal dynamics model of a target motorcade containing actuator dynamics; based on the vehicle longitudinal dynamics model, a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface are utilized to dynamically control the head space deviation of the target motorcade under the non-zero initial deviation condition, so that the head space of the target motorcade is an expected value, and the chord stability of a motorcade system is ensured. The invention can ensure the limited time stability of the estimation error, and adopts the continuous control signal to avoid the buffeting problem caused by discontinuous control signal in the prior art scheme, thereby improving the performance of the longitudinal control system of the motorcade.
Description
Technical Field
The invention relates to the technical field of vehicle control, in particular to a vehicle team longitudinal compound control method and system based on a second-order continuous sliding mode.
Background
With the progress of modern automobile manufacturing industry, people travel and transport of goods become more convenient, and serious traffic jam and other problems are brought to people while convenience is brought to people. The causes of traffic congestion can be commonly categorized into macroscopic and microscopic: from macroscopic analysis, because the supply and demand relationship is unbalanced, the infrastructure construction speed is difficult to keep up with the speed of traffic demand growth, so that the highway traffic in the key area is in a state of supply and demand for a long time; from a microscopic perspective, traffic events result in reduced traffic capacity, inappropriate traffic flow control measures, and traffic concussions caused by artificially uncontrolled driving behavior. In order to further improve the macroscopic and microscopic cooperative relationship, domestic and foreign scholars propose a networking vehicle. From macroscopic view, the network-connected vehicle can finish dynamic traffic flow dispatching, and can better meet the relationship of traffic supply and demand balance; from microcosmic, the network-connected vehicle can better cooperate with the vehicle and the vehicle, timely react to traffic events, reduce the possibility of occurrence and transmission of traffic concussion, and reduce or even eliminate traffic jams.
Related fleet longitudinal following control algorithms are based on sliding mode variable structure control (SMC) algorithms, which are effective methods to address parameter uncertainty and external disturbances in the system. Based on the SMC algorithm, many important results have been achieved in the longitudinal control of the internet protocol vehicles. However, one inherent disadvantage of SMC is buffeting. In order to reduce the influence of buffeting on the performance of a motorcade system, a related technical scheme provides an adaptive SMC control algorithm. More recently, aiming at a motorcade system influenced by the dynamics uncertainty of an actuator, when a vehicle-to-vehicle communication fault occurs in the motorcade and the acceleration of a front vehicle is not available, the acceleration of the front vehicle and the uncertainty in the system are taken as lumped interference together, an interference observer is adopted for estimation, and then a composite control algorithm based on interference compensation and SMC is designed. However, the disturbance observer employed in the above-described solution is asymptotically stable, rather than stable over a finite time. In addition, the control signal employed is a discontinuous control signal, which may lead to potential system performance degradation.
Disclosure of Invention
The invention aims to provide a vehicle team longitudinal composite control method and system based on a second-order continuous sliding mode, which can ensure limited time stability of estimation errors, avoid buffeting caused by discontinuous control signals and improve longitudinal control performance of a vehicle team system by designing continuous control signals.
In order to achieve the above object, the present invention provides the following solutions:
a motorcade longitudinal compound control method based on a second-order continuous sliding mode comprises the following steps:
constructing a vehicle longitudinal dynamics model of a target motorcade containing actuator dynamics; the expected head space of the motorcade is described by using a fixed time interval strategy;
based on the vehicle longitudinal dynamics model, a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface are utilized to dynamically control the head space deviation of the target motorcade under the non-zero initial deviation condition, so that the head space of the target motorcade is an expected value, and the chord stability of the whole motorcade system is ensured.
Optionally, the desired head space of the target fleet is expressed as:
wherein ,indicating the desire of vehicle i at time tThe distance between the heads of the vehicles; v i (t) represents a speed; />Representing a predefined fixed time interval; delta i Representing the head space when the vehicle i is stationary.
Optionally, the head space deviation of the target fleet is expressed as:
wherein ,τi Indicating a lag time of the actuator to achieve the desired acceleration; kappa (kappa) i A ratio indicating that the vehicle i can achieve the required acceleration; u (u) i (t) represents a control input; omega shape i (t) represents lumped interference; a, a i (t) represents vehicle i acceleration; a, a i-1 (t) represents a front vehicle acceleration; delta i (t) represents the parameter uncertainty or external disturbance present in the system; delta i (t) is unknown but bounded and satisfies |delta i (t)|<Delta, delta is a positive constant.Representing a predefined fixed time interval; epsilon i (t) represents a head space deviation; /> and θi Is a system parameter.
Optionally, based on the vehicle longitudinal dynamics model, and using a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface, dynamically controlling the head space deviation of the target fleet under the non-zero initial deviation condition, so that the head space of the target fleet is an expected value, and meanwhile, the chord stability of the whole fleet system is ensured, and the method specifically comprises the following steps:
based on the vehicle longitudinal dynamics model, dynamically estimating lumped interference by using the limited time interference observer to obtain a lumped interference estimation result;
and according to the lumped interference estimation result, the second-order continuous sliding mode algorithm and the coupling sliding mode surface, controlling the head space deviation of the target motorcade under the non-zero initial deviation condition, and designing a composite control strategy, wherein the composite control strategy comprises the steps of enabling the head space deviation of the target motorcade to be 0 along with the time, enabling the head space of the target motorcade to be an expected value and guaranteeing the chord stability of the whole motorcade system.
Optionally, the method further comprises: the design and analysis of the controller are carried out under the non-zero initial deviation, so that the problem of large instantaneous engine/brake torque caused by the non-zero initial deviation is solved, and the method specifically comprises the following steps:
the design of the controller is carried out under non-zero initial deviation, and the setting is that:
wherein ,the virtual headstock distance deviation at the time t; epsilon i (t) is the actual head space deviation at the moment t; epsilon i (0) The head space deviation at the initial moment; />Is epsilon i An initial value of the first derivative of (t),>is epsilon i An initial value of a second derivative of (t); n is n i For the convergence rate to be designed, exp (·) represents the natural exponential function;
the finite time interference observer is designed to estimate as follows:
wherein ,ψ 1 ＝ε i (0),/>x i,0 (t),x i,1 (t),x i,2 (t) are respectively->Ω i (t),/>Is a function of the estimated value of (2); />Respectively x i,0 (t),x i,1 (t),x i,2 (t) a first derivative; />The virtual headstock distance deviation at the time t; epsilon i (t) is the actual head space deviation at the moment t; epsilon i (0) The head space deviation at the initial moment; n is n i Is the convergence rate to be designed; a, a i (t) represents vehicle i acceleration; /> and θi Is a system parameter; b is omega i Lipshitz constant of (t); m is m i0 ,m i1 ,m i2 A positive observer gain is to be designed; sign (·) is a sign function; sig (sig) c (·)＝sign(·)|·| c . Defining an estimation error as:
the dynamics of the estimated error is then obtained as:
optionally, the design composite control strategy includes ensuring chord stability of the whole fleet system while enabling the head distance of the target fleet to be a desired value for adjusting the head distance deviation to trend to 0 along with the time, and specifically includes:
the control target of the design controller is to adjust the head space deviation epsilon i (t) tends to be 0 over time while guaranteeing chord stability for the entire fleet. To make the head space deviate epsilon i (t) converging to 0, designing a slip form surfaceWherein alpha is a normal number to be designed; the following coupling slip-form surfaces are introduced to ensure chord stabilization of the entire fleet:
wherein 0 is<If beta is less than or equal to 1 as the weight coefficient, S as follows can be obtained i (t) and s i Relation of (t):
S i (t)＝Bs i (t)
wherein ,
S(t)＝col(S i (t), ian), s (t) =col(s) i (t), iN), n=1, 2, l, N is the set of following vehicles iN the fleet.
Since β+.0, B is reversible, then we get the time S i (t) when it goes to 0, s i (t) also tends to 0;
further, a composite controller may be designed as follows:
wherein ,η i1 and ηi2 Is the normal number to be designed. Under the action of the designed composite controller, the convergence to 0 can be asymptotically achieved and the entire fleet is chord stable.
If omega i (t) is conductive andthere is a Lipshitz constant b that holds when the controller parameters satisfy:
under the action of the designed controller, the head space deviation of each vehicle in the fleet system gradually converges to 0. When 0< |beta| is less than or equal to 1, the whole motorcade is chord stable;
where χ=max { βl i,2 (t)+l i+1,2 (t),βl N,2 (t)},i＝1,2,…,N-1，l i,2 (t) is e i,1 (t) upper bound of rate of change.
The invention also provides a vehicle team longitudinal composite control system based on the second-order continuous sliding mode algorithm, which comprises the following steps:
the model construction module is used for constructing a vehicle longitudinal dynamics model of the target motorcade of the actuator dynamics; the expected headstock distance dynamic change of the vehicle longitudinal dynamics model is described by using a fixed time interval strategy;
the motorcade control module is used for dynamically controlling the head space deviation of the target motorcade under the non-zero initial deviation condition by utilizing a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface based on the vehicle longitudinal dynamics model, so that the head space of the target motorcade is an expected value and the chord stability of the whole motorcade system is ensured.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a vehicle fleet longitudinal composite control method and system based on a second-order continuous sliding mode. The technical scheme can ensure limited time stability of estimation errors, and through the continuity of the realized control signals, the buffeting problem caused by discontinuous control signals is avoided, so that the performance of a longitudinal control system of a motorcade is improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a fleet longitudinal composite control method based on a second-order continuous sliding mode;
fig. 2 is a schematic diagram of a locomotive spacing deviation test based on a second-order continuous sliding mode algorithm under a non-zero initial deviation of an isomorphic fleet in the embodiment;
fig. 3 is a schematic diagram of a sliding mode surface experiment based on a second-order continuous sliding mode algorithm under non-zero initial deviation of an isomorphic motorcade in the embodiment;
fig. 4 is a schematic diagram of a control input experiment based on a second-order continuous sliding mode algorithm under non-zero initial deviation of an isomorphic motorcade in the embodiment;
fig. 5 is a schematic diagram of a simulation of the head space deviation based on a second-order continuous sliding mode algorithm under non-zero initial deviation of a heterogeneous fleet in the embodiment;
FIG. 6 is a schematic diagram of a sliding mode surface simulation based on a second-order continuous sliding mode algorithm under non-zero initial deviation of a heterogeneous fleet in the embodiment;
fig. 7 is a schematic diagram of a control input simulation test based on a second-order continuous sliding mode algorithm under non-zero initial deviation of a heterogeneous fleet in the embodiment.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a vehicle team longitudinal composite control method and system based on a second-order continuous sliding mode, which can ensure limited time stability of estimation errors, avoid buffeting caused by discontinuous control signals and improve the longitudinal control performance of the vehicle team by realizing the continuity of the control signals.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 1, the invention provides a vehicle team longitudinal compound control method based on a second-order continuous sliding mode, which comprises the following steps:
step 100: constructing a vehicle longitudinal dynamics model of a target motorcade containing actuator dynamics; the desired headway of the fleet is described using a fixed headway strategy.
Step 200: based on the vehicle longitudinal dynamics model, a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface are utilized to dynamically control the head space deviation of the target motorcade under the non-zero initial deviation condition, so that the head space of the target motorcade is an expected value, and the chord stability of the whole motorcade system is ensured.
The specific process is as follows: and dynamically estimating the lumped interference by using the limited time interference observer based on the vehicle longitudinal dynamics model to obtain an error dynamic estimation result. And according to the lumped interference estimation result, the second-order continuous sliding mode algorithm and the coupling sliding mode surface, controlling the head space deviation of the target motorcade under the non-zero initial deviation condition, and designing a composite control strategy, wherein the composite control strategy comprises the steps of enabling the head space deviation of the target motorcade to be 0 along with the time, enabling the head space of the target motorcade to be an expected value and guaranteeing the chord stability of the whole motorcade system.
Wherein, the dynamic change of the expected vehicle head distance is expressed as:
in the formula ,representing the expected head space of the vehicle i at the moment t; v i (t) represents a speed; />Representing a predefined fixed time interval; delta i Representing the head space when the vehicle i is stationary.
The head space deviation of the target motorcade is expressed as:
in the formula ,τi Indicating a lag time of the actuator to achieve the desired acceleration; kappa (kappa) i A ratio indicating that the vehicle i can achieve the required acceleration; u (u) i (t) represents a control input; omega shape i (t) represents lumped interference; a, a i (t) represents the vehicle i plusA speed; a, a i-1 (t) represents a front vehicle acceleration; delta i (t) represents the parameter uncertainty or external disturbance present in the system; delta i (t) is unknown but bounded and satisfies |delta i (t)|<δ。
On the basis of the technical scheme, the following embodiments are provided:
step one, a vehicle longitudinal dynamics model considering the dynamics of an actuator is established, and a fixed time interval strategy is selected to describe the dynamics of the expected locomotive distance.
And secondly, designing and analyzing the controller under the non-zero initial deviation, and solving the problem of large instantaneous engine/brake torque caused by the non-zero initial deviation.
And thirdly, explaining the validity of the designed control algorithm and the correctness of theoretical analysis through numerical simulation.
Further, a fixed time interval strategy is adopted in the first step, specifically:
wherein ,representing the expected head space of the vehicle i at the moment t; v i (t) represents a speed; />Representing a predefined fixed time interval; delta i Representing the head space when the vehicle i is stationary.
The method comprises the following steps of establishing a vehicle longitudinal dynamics model considering the actuator dynamics, wherein the vehicle longitudinal dynamics model comprises the following specific steps of:
in the formula ,ai (t) represents acceleration of the vehicle i at time t, τ i Indicating a lag time of the actuator to achieve the desired acceleration;κ i a ratio indicating that the vehicle i can achieve the required acceleration; u (u) i (t) represents a control input; delta i (t) represents the parameter uncertainty or external disturbance present in the system; delta i (t) is unknown but bounded and satisfies |delta i (t)|<δ。
For vehicle i, head space deviation epsilon i (t) speed difference Deltav with preceding vehicle i (t) can be expressed as:
Δv i (t)＝v i-1 (t)-v i (t) (4)
wherein pi (t) represents the actual head space between the vehicle i and the preceding vehicle.
The first derivative is obtained for both sides of (2):
further, it is possible to obtain:
substituting formula (2) into formula (6) can obtain the dynamic of the desired headstock distance as follows:
wherein ,δ i (t) is unknown but bounded and satisfies |delta i (t)|<Delta. To reduce communication, the present embodiment adopts a unidirectional communication topology in which the vehicle i obtains information of the vehicle behind it only by wireless communication, and does not communicate with the vehicle in front of it. For this purposeAcceleration a of the front vehicle i-1 (t) is considered an external disturbance. Omega is set in the design process of the following controller i (t) is considered as lumped interference.
In the second step, the design and analysis of the controller are performed under the non-zero initial deviation to solve the problem of large instantaneous engine/brake torque caused by the non-zero initial deviation, specifically:
in practice, non-zero initial deviations are unavoidable. Non-zero initial deviation is brought about when vehicles in the fleet enter or when vehicles leave the fleet. Non-zero initial deviations may result in relatively large engine or braking torque. Each vehicle in the fleet is coupled in association with each other. Deviations caused by disturbances acting on one vehicle may have adverse effects on other vehicles, propagating amplification backwards along the fleet, reducing the following performance between vehicles in the fleet, and even leading to unstable train strings. For this purpose, the design and analysis of the controller is performed with non-zero initial deviation.
Setting up
Next, a composite control algorithm based on a Finite Time Disturbance Observer (FTDO) and a second order continuous sliding mode algorithm is designed. The FTDO vs. Ω is designed as follows i (t) performing estimation:
wherein ,ψ 1 ＝ε i (0),/>m i0 ,m i1 ,m i2 a positive observer gain is to be designed; x is x i,0 (t),x i,1 (t),x i,2 (t) are respectively->Ω i (t),/>Is used for the estimation of the estimated value of (a).
The present embodiment sets an estimation error:
the observer estimation error dynamics can be obtained as:
selecting a suitable observer gain, estimating the error e i,1 (t) converge to 0 within a finite time. To adjust epsilon i (t) to 0, design slip planeWherein alpha is a positive constant to be designed, and in order to ensure the stability of the queue chord of the whole motorcade system, the following coupling sliding die surface is designed:
in the formula, 0<If beta is less than or equal to 1 as the weight coefficient, S as follows can be obtained i (t) and s i Relation of (t)
S i (t)＝Bs i (t) (13)
wherein ：
S(t)＝col(S i (t), ian), s (t) =col(s) i (t),iN),N=1, 2, l, n is the set of following vehicles in the fleet.
Since β+.0, B is reversible, then S can be taken as i (t) when it goes to 0, s i (t) also tends to be 0. And vice versa. The composite controller based on the FTDO and the second-order continuous sliding mode algorithm is designed as follows:
wherein ,
η i1 and ηi2 Is the normal number to be designed.
To this end, this embodiment can obtain:
if omega i (t) is conductive andthe Lipshitz constant b is true, and the controller parameter selection satisfies:
then in the non-zero initial deviation situation, the fleet system under the action of the composite controller, the head space deviation of each vehicle gradually converges to 0. When 0 is<When the beta is less than or equal to 1, the whole motorcade is chord stable. Where χ=max { βl i,2 (t)+l i+1,2 (t),βl N,2 (t)},i＝1,2,…,N-1，l i,2 (t) is e i,1 (t) upper bound of rate of change.
Under the condition of non-zero initial deviation, the fleet system generates the head space deviation epsilon of each vehicle under the action of a composite control law (14) based on the FTDO and second-order continuous sliding mode algorithm i (t) asymptotically converges to 0. And when beta is selected to satisfy 0<And if the beta is less than or equal to 1, the whole motorcade is chord-stable. Where χ=max { βl i,2 (t)+l i+1,2 (t),βl N,2 (t)},i＝1,2,…,N-1，l i,2 (t) is e i,1 (t) upper bound of rate of change.
In the third step, the validity of the designed control algorithm and the correctness of theoretical analysis are illustrated by numerical simulation, specifically:
consider a fleet system of 6 vehicles, including 1 lead vehicle and 5 following vehicles. Numerical simulation is carried out on isomorphic and heterogeneous fleet types by utilizing MATLAB simulation software, wherein the maneuvering process of the piloted vehicle is as follows:
in the following simulation, the constant time interval is takenn i =4+i 0.1, i=1, 2, l,5. Parameter setting kappa in isomorphic fleet simulation i ＝0.85，τ i =0.25. Delta in simulation i (t) using trigonometric functions, delta 1 (t)＝2.5sint,δ 2 (t)＝2sint+0.01,δ 3 (t)＝1.5sin(2t)+0.03,δ 4 (t)＝sin(5t)+0.03,δ 5 (t) =2.8 sint. The FTDO parameter is set to m i0 ＝3,m i1 ＝1.5,m i2 =1, i=1, 2, …,5. And the controller parameter is set to b=0.99, a= 6,h i1 ＝2.1,h i2 =11.2. When simulation is performed on a heterogeneous fleet, parameters of vehicles in the fleet are shown in table 1, and corresponding FTFO and controller parameter settings are shown in table 2. The simulation results of the fleet system under the action of the proposed control algorithm are shown in the figure, wherein the horizontal axes of the figure represent time, the vertical axes of the figure 2 represent the head space deviation, the vertical axes of the figure 3 represent the slide plane, the vertical axes of the figure 4 represent the control input, the vertical axes of the figure 5 represent the head space deviation, the vertical axes of the figure 6 represent the slide plane, and the vertical axes of the figure 7 represent the control input. From the simulation, it can be observed that under non-zero initial errors, the fleet system performs well under the proposed control algorithm.
TABLE 1 vehicle parameters
TABLE 2 simulation results
In addition, the invention also provides a vehicle team longitudinal composite control system of the second-order continuous sliding mode algorithm, which comprises:
the model construction module is used for constructing a vehicle longitudinal dynamics model of the target motorcade of the actuator dynamics; the desired head space dynamic change of the vehicle longitudinal dynamics model is described by using a fixed time interval strategy.
And the motorcade control module dynamically controls the head interval error of the target motorcade by utilizing a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface, so that the head interval of the target motorcade is an expected value and the chord stability of the whole motorcade system is ensured.
In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, so that the same or similar parts between the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the core concept of the invention; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (7)
1. The longitudinal composite control method for the motorcade based on the second-order continuous sliding mode is characterized by comprising the following steps of:
constructing a vehicle longitudinal dynamics model of a target motorcade containing actuator dynamics; the expected head space of the motorcade is described by using a fixed time interval strategy;
based on the vehicle longitudinal dynamics model, a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface are utilized to dynamically control the head space deviation of the target motorcade under the non-zero initial deviation condition, so that the head space of the target motorcade is an expected value, and the chord stability of the whole motorcade system is ensured.
2. The fleet longitudinal composite control method based on the second-order continuous sliding mode according to claim 1, wherein the desired head-to-head spacing of the target fleet is expressed as:
wherein ,representing the expected head space of the vehicle i at the moment t; v i (t) represents a speed; />Representing a predefined fixed time interval; delta i Representing the head space when the vehicle i is stationary.
3. The fleet longitudinal composite control method based on the second-order continuous sliding mode algorithm according to claim 1, wherein the head space deviation of the target fleet is expressed as:
wherein ,τi Indicating a lag time of the actuator to achieve the desired acceleration; kappa (kappa) i A ratio indicating that the vehicle i can achieve the required acceleration; u (u) i (t) represents a control input; omega shape i (t) represents lumped interference; a, a i (t) represents vehicle i acceleration; a, a i-1 (t) represents a front vehicle acceleration; delta i (t) represents the parameter uncertainty or external disturbance present in the system; delta i (t) is unknown but bounded and satisfies |delta i (t)|<Delta, delta is a positive constant.Representing a predefined fixed time interval; epsilon i (t) represents a head space deviation; /> and θi Is a system parameter.
4. The fleet longitudinal composite control method based on the second-order continuous sliding mode algorithm according to claim 1, wherein the fleet longitudinal composite control method is characterized in that based on the vehicle longitudinal dynamics model, the headstock distance deviation of the target fleet is dynamically controlled under the non-zero initial deviation condition by using a limited time interference observer, the second-order continuous sliding mode algorithm and a coupling sliding mode surface, so that the headstock distance of the target fleet is a desired value, and chord stability of the whole fleet system is ensured, and the method specifically comprises the following steps:
based on the vehicle longitudinal dynamics model, dynamically estimating lumped interference by using the limited time interference observer to obtain a lumped interference estimation result;
and according to the lumped interference estimation result, the second-order continuous sliding mode algorithm and the coupling sliding mode surface, controlling the head space deviation of the target motorcade under the non-zero initial deviation condition, and designing a composite control strategy, wherein the composite control strategy comprises the steps of enabling the head space deviation of the target motorcade to be 0 along with the time, enabling the head space of the target motorcade to be an expected value and guaranteeing the chord stability of the whole motorcade system.
5. The fleet longitudinal composite control method based on the second-order continuous sliding mode algorithm according to claim 1, further comprising: the design and analysis of the controller are carried out under the non-zero initial deviation, so that the problem of large instantaneous engine/brake torque caused by the non-zero initial deviation is solved, and the method specifically comprises the following steps:
the design of the controller is carried out under non-zero initial deviation, and the setting is that:
wherein ,the virtual headstock distance deviation at the time t; epsilon i (t) is the actual head space deviation at the moment t; epsilon i (0) The head space deviation at the initial moment; />Is epsilon i An initial value of the first derivative of (t),>is epsilon i An initial value of a second derivative of (t); n is n i For the convergence rate to be designed, exp (·) represents the natural exponential function;
the finite time interference observer is designed to estimate as follows:
wherein ,ψ 1 ＝ε i (0),/>x i,0 (t),x i,1 (t),x i,2 (t) are respectively->Ω i (t),/>Is a function of the estimated value of (2); />Respectively x i,0 (t),x i,1 (t),x i,2 (t) a first derivative; />The virtual headstock distance deviation at the time t; epsilon i (t) is the actual head space deviation at the moment t; epsilon i (0) The head space deviation at the initial moment; n is n i Is the convergence rate to be designed; a, a i (t) represents vehicle i acceleration; /> and θi Is a system parameter; b is omega i Lipshitz constant of (t); m is m i0 ,m i1 ,m i2 A positive observer gain is to be designed; sign (·) is a sign function; sig (sig) c (·)＝sign(·)|·| c . Defining an estimation error as:
the dynamics of the estimated error is then obtained as:
6. the method for longitudinal composite control of a fleet based on a second-order continuous sliding mode algorithm according to claim 4, wherein the designing the composite control strategy includes ensuring chord stability of the entire fleet system while keeping the head distance of the target fleet at a desired value for adjusting the head distance deviation to trend to 0 over time, specifically includes:
the control target of the design controller is to adjust the head space deviation epsilon i (t) tends to be 0 over time while guaranteeing chord stability for the entire fleet. To make the head space deviate epsilon i (t) converging to 0, designing a slip form surfaceWherein alpha is a normal number to be designed; the following coupling slip-form surfaces are introduced to ensure chord stabilization of the entire fleet:
wherein 0 is<If beta is less than or equal to 1 as the weight coefficient, S as follows can be obtained i (t) and s i Relation of (t):
S i (t)＝Bs i (t)
wherein ,
S(t)＝col(S i (t), ian), s (t) =col(s) i (t), i N), n=1, 2, l, N being the set of following vehicles in the fleet.
Since β+.0, B is reversible, then we get the time S i (t) when it goes to 0, s i (t) also tends to 0;
further, a composite controller may be designed as follows:
wherein ,η i1 and ηi2 Is the normal number to be designed. Under the action of the designed composite controller, the convergence to 0 can be asymptotically achieved and the entire fleet is chord stable.
If omega i (t) is conductive andthere is a Lipshitz constant b that holds when the controller parameters satisfy:
under the action of the designed controller, the head space deviation of each vehicle in the fleet system gradually converges to 0. When 0< |beta| is less than or equal to 1, the whole motorcade is chord stable;
where χ=max { βl i,2 (t)+l i+1,2 (t),βl N,2 (t)},i＝1,2,…,N-1，l i,2 (t) is e i,1 (t) upper bound of rate of change.
7. The utility model provides a vertical compound control system of motorcade based on second order continuous sliding mode algorithm which characterized in that includes:
the model construction module is used for constructing a vehicle longitudinal dynamics model of the target motorcade of the actuator dynamics; the expected headstock distance dynamic change of the vehicle longitudinal dynamics model is described by using a fixed time interval strategy;
the motorcade control module is used for dynamically controlling the head space deviation of the target motorcade under the non-zero initial deviation condition by utilizing a limited time interference observer, a second-order continuous sliding mode algorithm and a coupling sliding mode surface based on the vehicle longitudinal dynamics model, so that the head space of the target motorcade is an expected value and the chord stability of the whole motorcade system is ensured.
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