CN116560227B - Lu Bangxian stable vehicle team longitudinal control method based on generalized extended state observer - Google Patents
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Abstract
The application discloses a Lu Bangxian stable motorcade longitudinal control method based on a generalized extended state observer, which comprises the following steps: constructing a fleet longitudinal dynamics model based on the following model; and designing a composite controller based on the generalized extended state observer, and acquiring a stable fleet input-state chord by combining the fleet longitudinal dynamics model. The application discloses a vehicle team longitudinal following control method based on a generalized extended state observer and linear state feedback, which is used for processing external interference, uncertain parameters and vehicle-to-vehicle communication faults existing in a vehicle team system; by means of the input-state chord stability definition, it has been theoretically demonstrated that the designed control algorithm can guarantee input-state chord stability for fleet systems with non-zero initial state, parameter uncertainty and external disturbances. To improve the control effect of vehicle formation.
Description
Technical Field
The application belongs to the field of intelligent automobile fleet longitudinal following control, and particularly relates to a Lu Bangxian stable fleet longitudinal control method based on a generalized extended state observer.
Background
In recent years, fleet system control is becoming a hot research object in the intelligent traffic field, and can control vehicles on the same lane to run in a desired inter-vehicle distance array as small as possible under the condition of ensuring safety, so that the air resistance of the vehicles is reduced, the energy consumption is reduced, the traffic jam is relieved, the traffic force of a road network is improved, the environmental pollution is reduced to a certain extent, and the driving comfort is improved.
However, currently, techniques exist that demonstrate that anti-interference control of fleet systems is not effective in dealing with external disturbances, uncertain parameters, and vehicle-to-vehicle communication failures when these problems are present in the fleet system at the same time. When there is a vehicle-to-vehicle communication failure in the fleet, the acceleration of the front vehicle cannot be obtained, and at this time, the acceleration of the front vehicle appears as a non-matching disturbance in a state space model of the fleet system, and if the processing is poor, the performance of the system will be reduced. The current efforts on fleet longitudinal control are not directly used to solve this problem. For this purpose, a composite controller based on a generalized extended state observer and linear state feedback is designed. External disturbances, uncertain parameters and vehicle-to-vehicle communication faults present in fleet systems are handled. By means of the input-state chord stability definition, it has been theoretically demonstrated that the designed control algorithm can guarantee input-state chord stability for fleet systems with non-zero initial state, parameter uncertainty and external disturbances. To improve the control effect of vehicle formation.
Disclosure of Invention
The application aims to provide a Lu Bangxian stable vehicle team longitudinal control method based on a generalized extended state observer, which improves the control effect of vehicle formation.
To achieve the above object, the present application provides a Lu Bangxian stable fleet longitudinal control method based on a generalized extended state observer, comprising the steps of:
constructing a fleet longitudinal dynamics model based on the following model;
and designing a composite controller based on the generalized extended state observer, and acquiring a stable fleet input-state chord by combining the fleet longitudinal dynamics model.
Optionally, the fleet longitudinal dynamics model includes a bilayer structure controller;
the double-layer structure controller comprises an upper layer controller and a lower layer controller;
the upper controller is used for controlling the following behavior of each vehicle in the motorcade by adjusting the distance and the speed difference between two adjacent vehicles in the motorcade;
the lower controller is used for adjusting the actual acceleration of the vehicle to be the acceleration for realizing the following behavior.
Optionally, the method for designing the upper layer controller includes: with a fixed time-interval strategy, the desired head space is calculated as follows,
wherein the method comprises the steps of，Is the desired head spacing of vehicle i at time t, v i (t) represents speed, < >>Representing a predefined fixed time interval, l i Representing the head space of the vehicle i when stationary;
deviation deltas of vehicle i from desired head spacing i (t) speed difference Deltav with preceding vehicle of vehicle i i (t) is calculated as follows,
Δv i (t)＝v i-1 (t)-v i (t)
wherein s is i And (t) is the actual head space between the vehicle i and the preceding vehicle.
Optionally, the method for designing the lower layer controller includes:
wherein a is i (t) is the actual acceleration of the vehicle i at time t, u i (t) is the desired acceleration, and,the ratio at which the desired acceleration can be achieved for vehicle i, is->For the lag time of the actuator to achieve the desired acceleration, delta i (t) including parameter uncertainty and external disturbances.
Optionally, the method for constructing a state space model based on the upper layer controller and the lower layer controller includes:
wherein,
C o ＝[1 0 0]
wherein for vehicle i, x is defined i (t)＝[Δs i (t)，Δv i (t)，a i (t)] T 、For state, measured output vector and controlled output vector, a i-1 And (t) is the acceleration of the front vehicle.
Optionally, the generalized extended state observer based composite controller includes feedforward compensation and linear state feedback adjustment based on the generalized extended state observer estimate.
Optionally, the method of feedforward compensation and linear state feedback adjustment based on the generalized extended state observer estimate includes:
designing generalized extended state observer to estimate lumped disturbance and acceleration a of preceding vehicle i-1 (t) comprises:
wherein the method comprises the steps ofAnd->Respectively x i (t) and d i Estimate of (t)/(t)>Is an observer gain matrix to be designed;
the state estimation error and the interference estimation error are respectively as follows:
wherein e i (t)＝[e xi (t) T ，e di (t) T ] T ，
Optionally, the method for obtaining the stable fleet input-state chord comprises the following steps: the dynamic of X (t) is
Wherein,
presence ofClass function ψ, ->Class functions Λ and σ, and normal number c 1 ，c 2 And c 3 For an initial condition x satisfying the following formula i (0) Estimation error e i (t), disturbance d i (t) is expressed as:
and meets the conditions
A stable fleet input-state chord is obtained.
The application has the technical effects that: the application discloses a Lu Bangxian stable motorcade longitudinal control method based on a generalized extended state observer, which is used for treating external interference, uncertain parameters and vehicle-to-vehicle communication faults existing in a motorcade system; by means of the input-state chord stability definition, it has been theoretically demonstrated that the designed control algorithm can guarantee input-state chord stability for fleet systems with non-zero initial state, parameter uncertainty and external disturbances. To improve the control effect of vehicle formation.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
FIG. 1 is a fleet system for driving on a level road;
FIG. 2 is a functional block diagram of a controller of the generalized extended state observer as designed;
FIG. 3 is a plot of pilot vehicle acceleration;
FIG. 4 shows the estimation error (a) a i-1 (t) estimation error (b) delta i (t) estimating an error;
FIG. 5 is a graph of a pitch error performance comparison (a) a controller of a generalized extended state observer (b) a linear state feedback section and a communication-based feedforward compensation section (c) a linear state feedback control;
FIG. 6 is a relative velocity performance comparison of (a) a controller of a generalized extended state observer (b) a linear state feedback section and a communication-based feedforward compensation section (c) a linear state feedback control;
FIG. 7 is a graph of acceleration performance comparison (a) a controller of a generalized extended state observer (b) a linear state feedback section and a communication-based feedforward compensation section (c) a linear state feedback control;
FIG. 8 is a graph showing a comparison of head space error root mean square, relative velocity root mean square, and acceleration root mean square performance;
FIG. 9 a i (t) estimating an error;
FIG. 10 is a graph of pitch error performance comparison (a) controller of a first generalized extended state observer (b) controller of a second generalized extended state observer;
FIG. 11 is a relative velocity performance comparison of (a) a controller of a first generalized extended state observer (b) a controller of a second generalized extended state observer;
FIG. 12 is a graph comparing acceleration performance (a) a controller of a first generalized extended state observer (b) a controller of a second generalized extended state observer;
FIG. 13 is a graph showing the root mean square of head space error, root mean square of relative velocity, root mean square of acceleration performance comparison;
fig. 14 is a schematic flow chart of a fleet longitudinal following control method based on a generalized extended state observer and linear state feedback according to an embodiment of the present application.
Detailed Description
It should be noted that, without conflict, the embodiments of the present application and features of the embodiments may be combined with each other. The application will be described in detail below with reference to the drawings in connection with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
As shown in fig. 1 to 14, the method for controlling the longitudinal direction of the Lu Bangxian stable motorcade based on the generalized extended state observer is provided in the present embodiment, and includes the following steps:
in the first step, a dynamics model description of a motorcade system is given based on a following model, and the dynamics model description specifically comprises the following steps:
a fleet system for driving on level roads is shown in fig. 1, which includes a lead vehicle and N following vehicles. In order to solve the problem of longitudinal following control of a motorcade under the conditions of uncertain parameters and external interference, the control system adopts a double-layer structure control, and comprises an upper-layer controller and a lower-layer controller. The upper layer controller controls the following behavior of each vehicle in the motorcade by adjusting the distance and the speed difference between two adjacent vehicles in the motorcade, and the lower layer controller adjusts the actual acceleration of the vehicle to be the acceleration for realizing the following behavior of the upper layer under the condition that the system has uncertainty and external interference. Next, the design of the two-layer structure controller will be described in detail.
Upper layer controller design
Given that the fixed-time-interval strategy is more tolerant of external disturbances than the fixed-time-interval strategy, where the fixed-time-interval strategy is employed, it is desirable that the head-to-head spacing can be expressed by the following equation
Wherein the method comprises the steps ofIs the desired head space of the vehicle i at time t. v i And (t) represents the speed.Representing a predefined fixed time interval. l (L) i Representing the head space when the vehicle i is stationary. Thus, for vehicle i, the deviation Δs from the desired head space i (t) speed difference Deltav with its preceding vehicle i (t) can be expressed as respectively
Δv i (t)＝v i-1 (t)-v i (t)#(3)
Wherein s is i And (t) is the actual head space between the vehicle i and the preceding vehicle.
Lower level controller design
For the underlying controllers, a general longitudinal dynamics equation of the vehicle is used to describe the nonlinear dynamics of the vehicle. In particular, based on a vehicle longitudinal dynamics modeling process, vehicle longitudinal dynamics characteristics can be approximately characterized by a first order differential equation
Wherein a is i (t) represents the actual acceleration of the vehicle i at time t. u (u) i And (t) represents a desired acceleration.The ratio of the required acceleration can be achieved for the vehicle i.Indicating the lag time of the actuator to achieve the desired acceleration. Delta i (t) represents unknown but bounded uncertainties present in the system, including parameter uncertainties and external disturbances. Note that to facilitate the composite controller design here, the parameter uncertainty and external disturbance are treated as a whole as a lumped disturbance δ i (t)。
Note that lumped disturbance is a broad concept, widely used in the field of active disturbance rejection control. It may include external disturbances, parameter uncertainties, complex nonlinear dynamics, etc.
State space model
For vehicle i, define x i (t)＝[Δs i (t)，Δv i (t)，a i (t)] T 、For the state, the measured output vector and the controlled output vector. Considering acceleration a of preceding vehicle when communication is faulty i-1 (t) unavailable conditions, combining equations (2) - (4), the state space model of the entire fleet system may be summarized as
Wherein the method comprises the steps of
C o ＝[1 0 0]
Step two, a design and analysis process of the composite controller based on the generalized expansion state observer is provided, and the method specifically comprises the following steps:
the fleet system with uncertainty and external disturbances is described above. The controller is designed for the motorcade system under the working condition of vehicle-to-vehicle communication failure, and the following two aims are achieved: 1) Output of fleet systemsCan track the desired output +.>2) The stability of the input-state strings of the whole motorcade system is ensured. For this purpose, a composite controller based on a generalized extended state observer and linear state feedback is designed. The composite controller comprises a feedforward compensation part and a linear state feedback adjustment part which are based on the estimation value of the generalized extended state observer.
Design and analysis of generalized extended state observer
Before the generalized extended state observer design, the following settings are given
Setting unknown lumped disturbance delta i (t) is continuously differentiable with respect to time t.
Setting d i (t) satisfying the conditionlim t→∞ d i (t)＝κ 2 Wherein kappa is 1 And kappa (kappa) 2 Is a positive constant.
Will d i (t) as a new state of expansion, the following expansion state equation is obtained in combination with (5):
wherein the variables are
Matrix array
From the following componentsThe state of the augmentation system (6) is easily known to be fully observable. Then for the augmentation system (6) the following generalized extended state observer may be designed to estimate the lumped disturbance and acceleration a of the preceding vehicle i-1 (t)：
Wherein the method comprises the steps ofAnd->Respectively x i (t) and d i An estimate of (t).Is the view to be designedA detector gain matrix.
For brevity, the state estimation error and the interference estimation error are defined as respectively
Substituting (6) and (7) into (8) to obtain
Wherein e i (t)＝[e xi (t) T ，e di (t) T ] T ，
Before proving that the observer estimation error is bounded, the following settings are given:
setting upIs Hulviz, then there is a scalar Γ > 0 such that +.> This is true.
Based on the above settings and the previously designed generalized extended state observer, the following conclusions can be drawn:
if the fleet system meets the first two settings of (6), selecting the observer gain vector L in (7) i So that A is ei In case of a Huwz matrix, the observer estimates the error e i (t) is bounded and can be adjusted by adjusting L i To reduce errors.
To find the upper part, first, to solve the linear time-invariant differential equation (9), it is rewritten as
Both sides are multiplied by matrix index exp (-A) ei t) to obtain
Rewriting (11) to be based on the integral criterion and the nature of the matrix index
Integrating (12) over the interval 0 to t
Then has
Further, both sides (14) are multiplied by exp (A) ei t) according to the matrix index property
For simplicity, without loss of generality, assume thatAnd->If the observer gain L in (7) is selected i So that A is ei Is Hertzian, then by setting, equation (15) can be written as
Wherein the fourth inequality is represented by the assumption thatAnd (10) the previous settings. As can be seen from (16), by selecting the appropriate parameter L i Can obtain proper ρ (A) ei ) To reduce the estimation error.
As can be seen from (15), L can be adjusted i To obtain a desired exponential convergence rate. The exponential convergence rate can ensure that the observer has good transient performance, which is of great significance in engineering implementation. In some cases, delta i (t) and a i-1 (t) may be a constant value in steady state. In this case, error e i (t) asymptotically converges to zero at an exponential rate.
Design and analysis of a composite controller
To achieve the control objective described above, the system (5) is designed with the following generalized extended state observer-based controller in combination with the above estimation values obtained with the generalized extended state observer
Wherein the method comprises the steps ofFor feedback control of gain vector +.>The gain vector is compensated for the disturbance. A functional block diagram of a controller of a generalized extended state observer designed in connection with fig. 2.
To determine k xi And k di Substituting the control law (17) into the system (5) there is the following closed loop system:
wherein A is fi ＝A i +B i k xi ，Obviously, the gain vector k can be controlled by selecting an appropriate feedback xi So that A is fi Is helvetz. From d i (t) to->Is G yd (s)＝C o (sI-A fi ) -1 (D+B i k di ). To eliminate d i (t) influence on output, taking lim into account t→∞ d i (t)＝κ 2 According to the final value theorem, conditions To be satisfied, then k di Can be given as
Using a derivation similar to (10) - (15), it is possible to obtain
Due to e i (t) and d i (t) is bounded, so x can be obtained i (t) is exponentially bounded.
When delta i (t) and a i-1 (t) all in steady stateWhen constant, error e i (t) asymptotically converges to zero at an exponential rate. Thus, x i (t) also asymptotically receives rose to zero at an exponential rate, which in turn means the head space error Δs i (t) asymptotically converges to zero at an exponential rate.
Note that the proposed controller method of the generalized extended state observer is shown in a as compared to the conventional scheme i The relevant information of (t) is also applicable and valid in case it is not available. In this case, becauseCan pass through a i The control law is designed by estimation of (t), wherein +.>
For the traditional scheme, the selected state variable is x i (t)＝[α i (t)，β i (t)，γ i (t)] T And sliding the variable sigma in the equation i Substituting into the equation as the control input, it is easy to see that the controller in the conventional scheme is equivalent to a composite controller constructed based on linear state feedback and feedforward compensation based on disturbance observations. However, the control algorithm in the conventional scheme can only solve the matching interference, and the control algorithm can solve not only the matching interference but also the non-matching interference. The control algorithm presented here is a generalization of the control algorithm in the conventional scheme.
Compared with the existing vehicle team longitudinal following control algorithm which needs to obtain the front vehicle acceleration through vehicle-vehicle communication, the controller algorithm of the generalized extended state observer is designed to consider the working condition of communication faults in the vehicle team, consider the front vehicle acceleration as external interference and uniformly estimate the lumped interference in the system. In addition, no vehicle-to-vehicle wireless communication is required, and the designed control algorithm is suitable for the situation that part of vehicles in a vehicle team are manually driven vehicles without broadcasting functions. From this point of view, the controller method of the generalized extended state observer has wider application scenes.
Queue chord stability analysis
For simplicity, noteAndis the aggregate of all following vehicles in the fleet. Then the dynamics of X (t) can be expressed as
Wherein the method comprises the steps of
Definition if presentClass function ψ, ->Class functions Λ and σ, and normal number c 1 ，c 2 And c 3 For an initial condition x satisfying the following formula i (0) Estimation error e i (t), disturbance d i (t)
All have
If true, the fleet system is said to be input-state chord stable.
The main conclusion is given below
If the fleet system (5) meets the two previous settings of (6), the observer gain matrix L in (7) i And (17)Vector k xi Respectively make A ei And A fi ＝A i +B i k xi Is helvetz, the entire fleet system is input-state chord stable under the influence of the designed compound control law (17).
The upper part, like (10) - (15), proves that the solution of (20) can be obtained as follows
Calculation of Euclidean norms for X (t)
Because A is fi Is a helvetz, so a matrixAlso a helvetz matrix. According to (10) the front is provided with
R= I r= | gamma, then (21) in the previous definitionClass functions Λ and σ may be chosen as
And
at the same timeThe class function ψ may be selected as
Note that as known from (25), the parameter k can be adjusted xi And L i To obtain a smaller X (t) and thus a smaller head space error Deltas i (t). From the practical point of view, this can improve the traffic of road network.
Step three, carrying out case analysis, specifically:
the effectiveness and superiority of the controller algorithm of the proposed generalized extended state observer and the correctness of the theoretical analysis are illustrated here by numerical simulations. For this purpose, a fleet system consisting of six vehicles is considered, comprising a pilot vehicle and five following vehicles. To illustrate the superiority of the proposed control algorithm, the comparative algorithm in the simulation is a known conventional algorithm. In the following simulations, the pilot vehicle acceleration trajectory was reconstructed using MATLAB software using the data provided as known. The reconstructed acceleration trajectory is shown in connection with fig. 3. The horizontal axis represents time, and the vertical axis represents acceleration. Fixed time interval in fixed time interval strategySet to 1s. The system parameters in the simulation are set to known system parameters, i.e.>In the simulation, a trigonometric function is adopted to simulate lumped interference delta i (t), i.e. delta 1 (t)＝0.025sint，δ 2 (t)＝0.02sint+0.01，δ 3 (t)＝0.015sin(2t)+0.03，δ 4 (t)＝0.01sin(5t)+0.03，δ 5 (t) =0.028 sint. To ensure the stability of the fleet of the whole fleet systemQualitative and queue chord stability, linear state feedback gain is selected to be k xi ＝[0.78，0.91，-0.05]. To ensure that the generalized extended state observer can converge, the pole of the generalized extended state observer is set to be p geso ＝[-10.5，-10.4，-10.3，-10.2，-10.1] T . Without loss of generality, it is assumed that the initial value of the observer is zero.
Known control law u i (t)＝k i x i (t)+k Fi a i-1 (t). Which includes a linear state feedback portion and a communication-based feedforward compensation portion. The parameters are set as
k i ＝[0.78，0.91，-0.05]And k Fi =0.32. When a vehicle-to-vehicle communication failure occurs in a fleet system, a i-1 (t) when not available, the known control method is degraded to a so-called linear state feedback control algorithm. When the algorithm is evaluated, the root mean square of the head space error, the relative speed and the acceleration is used as an evaluation index. The results of the relevant simulation are shown in fig. 4 to 8. In fig. 4 to 6, the horizontal axis in fig. 7 represents time. The vertical axis of FIG. 4 (a) represents a i-1 The estimation error of (t), while the vertical axis of FIG. 4 (b) represents delta i The estimation error of (t). The vertical axis of fig. 5 represents pitch error. The vertical axis of fig. 6 represents the relative velocity. The vertical axis of fig. 7 represents acceleration.
It is obvious from the simulation that when there are parameter uncertainty, external interference and vehicle-to-vehicle communication faults in the system, the controller algorithm of the generalized extended state observer designed here can ensure that each vehicle in the fleet follows the preceding vehicle better, see fig. 5 (a). In addition, its performance is comparable to the linear state feedback part and the communication-based feedforward compensation part methods. The reason behind the performance difference is that the generalized extended state observer estimates a i-1 (t) there is a very small amplitude estimation error. In some cases, a i-1 (t) is a constant value in a steady state. In this case, the estimation error converges exponentially to zero, at which time there is substantially no difference in the behavior of the two control algorithms. It is noted that, when the system fails in vehicle-to-vehicle communication, the front vehicle acceleration a i-1 (t) presentation in a state space model of a systemFor the mismatch interference, the satisfactory simulation results in the figure illustrate that the controller control algorithm of the generalized extended state observer is insensitive to the mismatch interference. In addition, as shown in fig. 7, under the action of the controller control algorithm of the generalized extended state observer, the root mean square index of the first vehicle in the fleet system is larger than that of the following vehicles, that is, the root mean square of the head space error, the relative speed and the acceleration is decreasing along the direction of the fleet, which means that the controller control algorithm of the generalized extended state observer designed herein can ensure the chord stability of the queue.
As expected, both the controller of the generalized extended state observer and the linear state feedback control algorithms can reduce the pitch error caused by the acceleration of the external pilot vehicle. As can be seen from fig. 3 and 7, when the pilot vehicle starts to change acceleration, the first vehicle immediately following it also starts to change acceleration. Then, along the fleet direction, the acceleration of each vehicle in the fleet begins to change in turn. Although both control algorithms can reduce the pitch error, it is apparent that the controller algorithm of the generalized extended state observer presented herein can significantly reduce the pitch error and perform better. As can be seen from fig. 8, the root mean square of the spacing error can be reduced by at least 40% under the control algorithm of the generalized extended state observer. At the same time, the root mean square of the relative velocity is reduced by at least 12%. In addition, the root mean square of the acceleration is reduced by 0.6-15%. It should be noted that when the parameter k in the controller algorithm of the generalized extended state observer is di When set to zero, the controller algorithm of the generalized extended state observer also degenerates to a linear state feedback control algorithm. From this, it can be concluded that the disturbance observer based feedforward control term can significantly improve the performance of the system.
Whereas acceleration obtained by deriving the velocity may introduce noise to the system in view of the high cost of the acceleration sensor, in practical applications a i (t) may not be available. In this working condition becauseWherein the method comprises the steps ofWe can estimate a using a generalized extended state observer i (t). Then, use the estimatedDesigning a composite controller to obtain-> Next, we will verify the controller algorithm of the designed generalized extended state observer through numerical simulation at a i (t) availability when not available. The selection of the controller and observer parameters is the same as a i (t) available operating conditions. Will carry a i Controller and band of (t)>Is denoted as the controller of the first generalized extended state observer and the controller of the second generalized extended state observer, respectively. Simulation results are shown in fig. 9 to 12 and fig. 13. FIG. 9 a i From the estimation error of (t), it can be seen that a i The estimation error of (t) converges to a small neighborhood of the origin. The vertical axis of fig. 10 represents pitch error. The vertical axis of fig. 11 represents the relative velocity. The vertical axis of fig. 12 represents acceleration. As shown in fig. 10 to 13, the performance of the controller algorithm of the second generalized extended state observer can be compared to the controller algorithm of the first generalized extended state observer. This illustrates that the controller algorithm of the generalized extended state observer is at a i The same applies when (t) is not available.
The problem of stable longitudinal following control of the robust chord of the motorcade under the condition of vehicle-vehicle communication failure is studied, and a controller control algorithm of the generalized extended state observer is designed to overcome the adverse effects of parameter uncertainty, external interference and vehicle-vehicle communication failure on system performance. It is worth noting that most existing works assume that the initial operating conditions of the system are zero when analyzing the stability of the fleet system chord. Different from the existing achievements, the patent adopts input-state chord stability definition, fully considers the non-zero initial state, communication fault, parameter uncertainty and external disturbance existing in the motorcade system, and theoretically proves that the controller algorithm of the designed generalized extended state observer can ensure the chord stability of the whole motorcade system. Numerical simulation results show that when a motorcade system encounters a failure of vehicle-to-vehicle communication, the controller algorithm of the designed generalized extended state observer can ensure that each vehicle in the motorcade safely and stably follows a front vehicle and can improve the traffic force of a road network; the controller algorithm of the designed generalized extended state observer has better performance than the control algorithm in the traditional scheme.
The present application is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present application are intended to be included in the scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims (2)
1. Lu Bangxian stable motorcade longitudinal control method based on generalized extended state observer is characterized by comprising the following steps:
constructing a fleet longitudinal dynamics model based on the following model;
designing a composite controller based on a generalized extended state observer, and acquiring a stable fleet input-state chord by combining the fleet longitudinal dynamics model;
the fleet longitudinal dynamics model comprises a double-layer structure controller;
the double-layer structure controller comprises an upper layer controller and a lower layer controller;
the upper controller is used for controlling the following behavior of each vehicle in the motorcade by adjusting the distance and the speed difference between two adjacent vehicles in the motorcade;
the lower controller is used for adjusting the actual acceleration of the vehicle to be the acceleration for realizing the following behavior;
the method for designing the upper layer controller comprises the following steps: with a fixed time-interval strategy, the desired head space is calculated as follows,
wherein,is the desired head spacing of vehicle i at time t, v i (t) represents speed, < >>Representing a predefined fixed time interval, l i Representing the head space of the vehicle i when stationary;
deviation deltas of vehicle i from desired head spacing i (t) speed difference Deltav with preceding vehicle of vehicle i i (t) is calculated as follows,
Δv i (t)＝v i-1 (t)-v i (t)
wherein s is i (t) is the actual head space between vehicle i and the preceding vehicle;
the method for designing the lower controller comprises the following steps:
wherein a is i (t) is the actual acceleration of the vehicle i at time t, u i (t) is the desired acceleration, and,is practical for vehicle iThe ratio of the acceleration required is now +.>For the lag time of the actuator to achieve the desired acceleration, delta i (t) including parameter uncertainty and external disturbances;
the composite controller based on the generalized extended state observer comprises feedforward compensation and linear state feedback adjustment based on the estimation value of the generalized extended state observer;
the method for feedforward compensation and linear state feedback adjustment based on the generalized extended state observer estimation value comprises the following steps:
designing generalized extended state observer to estimate lumped disturbance and acceleration a of preceding vehicle i-1 (t) comprises:
wherein the method comprises the steps of And->Respectively x i (t) and d i Estimate of (t)/(t)>Is an observer gain matrix to be designed;
the state estimation error and the interference estimation error are respectively as follows:
wherein e i (t)＝[e xi (t) T ,e di (t) T ] T ,
The method for acquiring the stable fleet input-state chord comprises the following steps: the dynamic of X (t) is
Wherein,
presence ofClass function ψ, ->Class functions Λ and σ, and normal number c 1 ,c 2 And c 3 For an initial condition x satisfying the following formula i (0) Estimation error e i (t), disturbance d i (t) is expressed as:
and meets the conditions
A stable fleet input-state chord is obtained.
2. The method of Lu Bangxian stable fleet longitudinal control based on a generalized extended state observer according to claim 1, wherein the method of constructing a state space model based on the upper layer controller and the lower layer controller comprises:
wherein,
C o ＝[1 0 0]
wherein for vehicle i, x is defined i (t)＝[Δs i (t),Δv i (t),a i (t)] T 、For state, measured output vector and controlled output vector, a i-1 And (t) is the acceleration of the front vehicle.
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