CN111694366A - Motorcade cooperative braking control method based on sliding mode control theory - Google Patents

Motorcade cooperative braking control method based on sliding mode control theory Download PDF

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CN111694366A
CN111694366A CN202010650385.1A CN202010650385A CN111694366A CN 111694366 A CN111694366 A CN 111694366A CN 202010650385 A CN202010650385 A CN 202010650385A CN 111694366 A CN111694366 A CN 111694366A
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CN111694366B (en
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高振宇
郭戈
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Northeastern University Qinhuangdao Branch
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Abstract

The invention provides a motorcade cooperative braking control method based on a sliding mode control theory, and relates to the technical field of isomorphic motorcade control. The method constructs a three-order dynamics model of the fleet, ensures that vehicles can be rapidly and stably stopped at an appointed parking position while keeping reasonable inter-vehicle distance of each vehicle in the fleet, designs a controller of a leading vehicle and a cooperative controller of a following vehicle respectively, designs a terminal sliding mode surface, and improves the sliding mode surface in order to analyze the stability of the fleet. The method analyzes the convergence of the motorcade by using the Lyapunov method, and analyzes the string stability of the motorcade by using the transfer function method. The simulation result verifies the effectiveness of the method.

Description

Motorcade cooperative braking control method based on sliding mode control theory
Technical Field
The invention relates to the technical field of isomorphic fleet control, in particular to a fleet cooperative braking control method based on a sliding mode control theory.
Background
The reasonable inter-vehicle distance of the motorcade is always kept in the braking process, the operation of the motorcade is adversely affected when the inter-vehicle distance is too large or too small, and meanwhile, the fact that each vehicle in the motorcade can stop to a specified stop position (TSP) rapidly and stably is ensured, and the stability of the motorcade queue is ensured. In recent years, there has been little and no research on braking control of a vehicle fleet. In terms of fleet cooperative braking control, Liu and Xu propose a distributed linear control protocol based on dual integrators to bring each vehicle in a fleet to a desired TSPs during braking. Liu et al then further analyzed the convergence of fleet cooperative braking control with distributed linear feedback dynamics, taking into account fleet internal virtual forces and external braking forces. Xu et al proposed a cooperative braking control method based on nonlinear feedback, which studied the impact of communication topology on fleet safety. Li et al propose a fleet integral sliding mode cooperative braking control method, which proves the fleet queue stability while analyzing the fleet convergence. A review of the literature to date indicates that challenges in fleet braking control stem from interactions between vehicles in the fleet.
However, the linear control strategy proposed by the above research cannot sufficiently describe the dynamics of the vehicles, and cannot completely capture the tracking interaction between the vehicles in the fleet. Meanwhile, the control strategy proposed by Liu, Xu and the like cannot ensure that the distance between every two vehicles in the fleet is consistent.
Since the second-order fleet model is adopted in the above documents, the second-order fleet model does not capture the dynamic characteristics of the interior of the vehicle well compared to the third-bound model. At the same time, it is also crucial to analyze and prove fleet stability, i.e., so that fleet spacing does not scale up from lead to tail.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a motorcade cooperative braking control method based on a sliding mode control theory, which is used for constructing a motorcade three-order dynamic model, ensuring that vehicles can be stopped to an appointed parking position quickly and stably while keeping reasonable inter-vehicle distance of each vehicle in the motorcade, and strictly deducing and proving the stability of a motorcade queue.
The technical scheme adopted by the invention is as follows:
a motorcade cooperative braking control method based on a sliding mode control theory comprises the following steps:
step 1, constructing a fixed time interval strategy according to self information of vehicles in a fleet, including position information, speed information and acceleration information, and establishing a longitudinal dynamic model of the vehicles by adopting a bidirectional communication structure;
the longitudinal dynamics model of the vehicle is characterized in that the error between the ith vehicle and the (i-1) th vehicle is set as ei(t)：ei(t)＝pi-1(t)-pi(t)-ds-L, i ═ 1, 2.., n, where d issIs the desired car-to-car distance, L is the vehicle length, pi(t) the ith vehicle position information at the moment t, and t is time;
the dynamical model of the ith vehicle is described as the following nonlinear differential equation:
Figure BDA0002574711220000021
wherein v isi(t)、ai(t) speed and acceleration of the ith vehicle, respectively; c. Ci(t) is the actuator input, the nonlinear function fi(vi，ai) Is of the formula:
Figure BDA0002574711220000022
Figure BDA0002574711220000023
where σ is the air mass constant, τiIs the engine time constant, Ai,
Figure BDA0002574711220000024
And miRespectively the cross-sectional area, the resistance coefficient, the mechanical resistance and the quality of the ith vehicle, and linearizing the kinematic model to obtain a feedback linearization control law as follows:
Figure BDA0002574711220000025
the following linearized models were generated:
Figure BDA0002574711220000026
wherein u isiIs an additional control input signal;
disturbance term ξ is introduced due to communication interference between vehicles and external environment disturbancei(t), the linearization model is of the form:
Figure BDA0002574711220000027
wherein
Figure BDA0002574711220000028
ξ i(t) and
Figure BDA0002574711220000029
respectively disturbance ξiLower and upper bounds of (t).
Step 2, setting the whole fleet to be composed of 1 leading vehicle and n-1 following vehicles, and respectively constructing controllers of the leading vehicle and the following vehicles without the condition that two vehicles run side by side;
the controller of the lead car is shown as the following formula:
Figure BDA0002574711220000031
wherein p is0(t) and v0(t) position and speed of the lead vehicle at time t, q0(t) is a designated parking position TSP, F of the lead vehicle0b(-) is the braking force of the lead vehicle during braking,
Figure BDA0002574711220000032
to gain lead car controller and
Figure BDA0002574711220000033
the controller for obtaining the lead vehicle is as follows:
Figure BDA0002574711220000034
wherein
Figure BDA0002574711220000035
Firstly, designing a sliding mode surface for a following vehicle, and then designing a cooperative controller:
the design formula of the sliding mode surface of the following vehicle is as follows:
Figure BDA0002574711220000036
wherein c is1，c2Constant, sgn (. cndot.) is a sign function α1，α2Is constant and satisfies the following condition:
α2＞2
α1＝(α2-2)/α2
the sliding mode surface is modified into the following form:
Figure BDA0002574711220000037
due to si(t) convergence of ei(t) approaches zero, but string stability cannot be guaranteed, so the slip-form face is designed to:
Figure BDA0002574711220000038
where q is constant and q ≠ 0, yielding: s (t) ═ qs (t);
wherein s (t) ═ s1(t) s2(t) … sn(t)]T,S(t)＝[S1(t) S2(t) … Sn(t)]T，
Figure BDA0002574711220000041
Since Q ≠ 0 is a constant, the matrix Q is irreversible, given that:
Figure BDA0002574711220000042
wherein:
Figure BDA0002574711220000043
wherein
Figure BDA0002574711220000044
And
Figure BDA0002574711220000045
other than
Figure BDA0002574711220000046
Andξ ian upper and lower bound of (t);
Figure BDA0002574711220000047
and
Figure BDA0002574711220000048
the maximum value of the disturbance upper bound estimation and the disturbance lower bound estimation is distinguished; and
Figure BDA0002574711220000049
are respectively
Figure BDA00025747112200000410
Andξ ian upper and lower bound of (t);
Figure BDA00025747112200000411
and
Figure BDA00025747112200000412
maximum values of the disturbance upper bound estimation and the disturbance lower bound estimation are respectively;
since the last vehicle is not a following vehicle, when i ═ n, the following vehicle controller is designed to:
Figure BDA00025747112200000413
Figure BDA00025747112200000414
and
Figure BDA00025747112200000415
the adaptive law of (2) is designed into the following form:
Figure BDA00025747112200000416
η thereini> 0, i ═ 1,2,. ang, n, and μiIs defined as:
Figure BDA00025747112200000417
step 3, constructing a differential equation aiming at the driving data of the lead vehicle, and verifying the convergence of the lead vehicle;
Figure BDA0002574711220000051
wherein p is0(t) is the position of the lead vehicle at time t, q0(t) is the designated parking position TSP of the lead vehicle,
Figure BDA0002574711220000052
to gain lead car controller and
Figure BDA0002574711220000053
the solution to the equation is:
Figure BDA0002574711220000054
wherein p is0' (t) is a special solution which,
Figure BDA0002574711220000055
is a general solution, C is a constant solution, and the following is deduced:
Figure BDA0002574711220000056
Figure BDA0002574711220000057
the speed of the lead car is:
Figure BDA0002574711220000058
obtained by combining the above formulas
Figure BDA0002574711220000059
Step 4, designing a self-adaptive rate, and selecting a Lyapunov function to verify the convergence of the following vehicle;
under the cooperative braking controller of the sliding mode of the motorcade terminal, if the parameter satisfies c1＞0，c2> 0, then the fleet is lyapunov stable, resulting in:
Figure BDA00025747112200000510
lyapunov function V1(t) the following:
Figure BDA00025747112200000511
the derivation of which is:
Figure BDA00025747112200000512
wherein
Figure BDA0002574711220000061
And ξiIs a fixed upper boundary and a fixed lower boundary, there are
Figure BDA0002574711220000062
The method comprises the following steps of 2:
Figure BDA0002574711220000063
the derivation is as follows:
Figure BDA0002574711220000064
where k is the follower controller gain, therefore there are:
Figure BDA0002574711220000065
because of the fact that
Figure BDA0002574711220000066
So V1(t) is a non-increasing function, V1(t)≤V1(0) And < ∞, the following components are:
Figure BDA0002574711220000067
ξ thereini(t)，
Figure BDA0002574711220000068
And
Figure BDA0002574711220000069
because of V1(t)∈R∞，R∞Is a positive real number field, Si(t)∈R∞Has a si(t)，si+1(t)∈R∞Because ei(t)，
Figure BDA00025747112200000610
Figure BDA00025747112200000611
And sgn (S)i(t)∈R∞Therefore have ui(t)∈R∞，
Figure BDA00025747112200000612
Therefore, the temperature of the molten metal is controlled,
Figure BDA00025747112200000613
are consistently continuous; according to the formula
Figure BDA00025747112200000614
Figure BDA00025747112200000615
Figure BDA00025747112200000616
Wherein Q is reversible, following the equivalence of S ═ 0 and S ═ 0; get s when t → ∞ timesi＝0，si+1＝0；
Step 5, verifying the queue stability of the fleet and finishing cooperative braking control on the whole fleet;
if ei(0) 0 < | q | < 1, then under the terminal sliding mode control controller TSM, the string stability of the fleet is guaranteed, i.e.:
||Gi(s)||＝||Ei+1(s)/Ei(s)||≤1
where Gi(s) is the error transfer function and Ei(s) is the error ei(t) laplace transform;
obtaining S according to step 4i(t)＝qsi(t)-si+1(t) convergence to zero, let Si(t) ═ 0, with:
Figure BDA0002574711220000071
laplace transforms the above equation:
Figure BDA0002574711220000072
Figure BDA0002574711220000073
finally, the following is obtained:
Figure BDA0002574711220000074
because 0 < α1< 1, so when 0 < | q | < 1, | | | Gi(s)||≤1。
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
the invention provides a sliding mode control theory-based fleet cooperative braking control method, and aims at a fleet model which is two-order and is adopted in cooperative braking control of traditional interconnected vehicles, and a three-order linearized fleet dynamics model is established on the basis. Compared with a second-order fleet model, the third-order model can better capture dynamic characteristics inside the vehicle.
Aiming at the condition that disturbance exists in the environment of a homogeneous fleet system, the invention respectively designs a controller of a leading vehicle and a cooperative controller of a following vehicle, and designs a terminal sliding mode surface, so that the sliding mode surface is improved in order to analyze the queue stability of the fleet. The method analyzes the convergence of the motorcade by using the Lyapunov method, and analyzes the string stability of the motorcade by using the transfer function method. The simulation result verifies the effectiveness of the method.
Drawings
FIG. 1 is a flow chart of a fleet cooperative braking control method based on a sliding mode control theory according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an isomorphic fleet and communication topology used in embodiments of the present invention;
FIG. 3 is a simulation diagram of a driving distance of a vehicle according to an embodiment of the present invention;
wherein graph (a) -total distance traveled by vehicles in straight lane (no disturbance), (b) -total distance traveled by vehicles in straight lane (disturbance of lead car), (c) -total distance traveled by vehicles in straight lane (disturbance of all vehicles),
FIG. 4 is a simulation diagram of the driving speed of a vehicle according to an embodiment of the present invention;
in which graph (a) -speed (no disturbance), (b) -speed (disturbance of lead vehicle), (c) -speed (disturbance of all vehicles)
FIG. 5 is a vehicle spacing simulation of an embodiment of the present invention;
in which graph (a) -inter-vehicle distance (no disturbance), graph (b) -inter-vehicle distance (disturbance on lead vehicle), and graph (c) -inter-vehicle distance (disturbance on all vehicles)
FIG. 6 is a vehicle spacing error simulation diagram in accordance with an embodiment of the present invention;
in which graph (a) -spacing error (no disturbance), graph (b) -spacing error (disturbance of lead vehicle), graph (c) -spacing error (disturbance of all vehicles)
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
A fleet cooperative braking control method based on a sliding mode control theory, as shown in FIG. 1, includes the following steps:
step 1, constructing a fixed time interval strategy according to self information of vehicles in a fleet, including position information, speed information and acceleration information, and establishing a longitudinal dynamic model of the vehicles by adopting a bidirectional communication structure;
let the i-th vehicle and the i-1 st vehicle have an inter-vehicle distance error of ei(t)：ei(t)＝pi-1(t)-pi(t)-ds-L, i ═ 1, 2.., n, where d issIs the desired car-to-car distance, L is the vehicle length, pi(t) the ith vehicle position information at the moment t, and t is time;
the dynamical model of the ith vehicle is described as the following nonlinear differential equation:
Figure BDA0002574711220000081
wherein v isi(t)、ai(t) speed and acceleration of the ith vehicle, respectively; c. Ci(t) is the actuator input, the nonlinear function fi(vi，ai) In the form:
Figure BDA0002574711220000091
where σ is the air mass constant, τiIs the time constant of the engine and,
Figure BDA0002574711220000092
and miRespectively the cross-sectional area, the resistance coefficient, the mechanical resistance and the quality of the ith vehicle, and linearizing the kinematic model to obtain a feedback linearization control law as follows:
Figure BDA0002574711220000093
the following linearized models were generated:
Figure BDA0002574711220000094
wherein u isiIs an additional control input signal.
The disturbance term ξ is introduced to take account of communication interference between vehicles and unavoidable external environment disturbancei(t), the linearization model is rewritten as follows:
Figure BDA0002574711220000095
wherein
Figure BDA0002574711220000096
ξ i(t) and
Figure BDA0002574711220000097
respectively disturbance ξi(t) a lower bound and an upper bound;
step 2, setting the whole fleet to be composed of 1 leading vehicle and n-1 following vehicles, and respectively constructing controllers of the leading vehicle and the following vehicles without the condition that the two vehicles run side by side, wherein fig. 2 is a schematic diagram of an isomorphic fleet and a communication topology used in the embodiment;
the controller of the lead car is shown as follows:
Figure BDA0002574711220000098
wherein p is0(t) and v0(t) position and speed of the lead vehicle at time t, q0(t) is a designated parking position TSP, F of the lead vehicle0b(-) is the braking force of the lead vehicle during braking,
Figure BDA0002574711220000099
to gain leadership controller and
Figure BDA00025747112200000910
the controller of the finally obtained leader vehicle is as follows:
Figure BDA00025747112200000911
wherein
Figure BDA0002574711220000101
Aiming at the following vehicle, firstly, the design of a sliding mode surface is carried out, and then a cooperative controller is designed:
the design formula of the sliding mode surface of the following vehicle is as follows:
Figure BDA0002574711220000102
wherein c is1，c2Is a constant, sgn (·) is a sign function α1，α2Are also all constants and satisfy the following condition:
α2＞2
α1＝(α2-2)/α2
the sliding mode surface is modified into the following form:
Figure BDA0002574711220000103
due to si(t) convergence of ei(t) approaches zero, but string stability cannot be guaranteed, so the slip-form face is designed to:
Figure BDA0002574711220000104
where q is constant and q ≠ 0, yielding: s (t) ═ qs (t);
wherein s (t) ═ s1(t) s2(t) … sn(t)]T,S(t)＝[S1(t) S2(t) … Sn(t)]T，
Figure BDA0002574711220000105
Since Q ≠ 0 is a constant, so the matrix Q is irreversible, giving:
Figure BDA0002574711220000106
wherein:
Figure BDA0002574711220000111
wherein
Figure BDA0002574711220000112
And
Figure BDA0002574711220000113
are respectively
Figure BDA0002574711220000114
Andξ ian upper and lower bound of (t);
Figure BDA0002574711220000115
and
Figure BDA0002574711220000116
are respectively a disturbanceThe maximum value of the dynamic upper bound estimation and the disturbance lower bound estimation; and
Figure BDA0002574711220000117
are respectively
Figure BDA0002574711220000118
Andξ ian upper and lower bound of (t);
Figure BDA0002574711220000119
and
Figure BDA00025747112200001110
maximum values of the disturbance upper bound estimation and the disturbance lower bound estimation are respectively;
since the last vehicle is not following the vehicle, when i ═ n, the controller is designed to:
Figure BDA00025747112200001111
Figure BDA00025747112200001112
and
Figure BDA00025747112200001113
the adaptive law of (2) is designed into the following form:
Figure BDA00025747112200001114
η thereini> 0, i ═ 1,2,. ang, n, and μiIs defined as:
Figure BDA00025747112200001115
step 3, constructing a differential equation aiming at the lead vehicle, and proving the convergence of the lead vehicle;
Figure BDA00025747112200001116
the solution to the equation is:
Figure BDA00025747112200001117
wherein p is0' (t) is a special solution which,
Figure BDA00025747112200001118
is a general solution, C is a constant solution, and the following is deduced:
Figure BDA00025747112200001119
further obtaining:
Figure BDA0002574711220000121
and the speed of the lead car is:
Figure BDA0002574711220000122
combining the above formula, we can get:
Figure BDA0002574711220000123
step 4, designing a self-adaptive rate, and selecting a Lyapunov function to prove the convergence of the following vehicle;
under the cooperative braking controller of the sliding mode of the motorcade terminal, if the parameter satisfies c1＞0，c2> 0, the fleet is Lyapunov stable and available:
Figure BDA0002574711220000124
defining the Lyapunov function V1(t) the following:
Figure BDA0002574711220000125
derivation of this can yield:
Figure BDA0002574711220000126
because of the fact that
Figure BDA0002574711220000127
Andξ iis a fixed upper bound and a fixed lower bound, so there are
Figure BDA0002574711220000128
The method comprises the following steps of 2:
Figure BDA0002574711220000129
further derived are:
Figure BDA00025747112200001210
k is the follower controller gain, so there are:
Figure BDA0002574711220000131
because of the fact that
Figure BDA0002574711220000132
So V1(t) is a non-increasing function, which can be deduced as V1(t)≤V1(0) And < ∞. And:
Figure BDA0002574711220000133
ξi(t)，
Figure BDA0002574711220000134
and
Figure BDA0002574711220000135
because of V1(t)∈R∞，R∞Is a positive real number domain, therefore Si(t)∈R∞. Thus, there is si(t)，si+1(t)∈R∞. In addition, because ei(t)，
Figure BDA0002574711220000136
And sgn (S)i(t)∈R∞Therefore have ui(t)∈R∞. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002574711220000137
based on the above discussion, there are
Figure BDA0002574711220000138
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002574711220000139
are consistently continuous.
In addition, there are:
Figure BDA00025747112200001310
according to the above formula, obtain
Figure BDA00025747112200001311
Thus, there are
Figure BDA00025747112200001312
Also provided are
Figure BDA00025747112200001313
Thus, there are
Figure BDA00025747112200001314
Because Q is reversible, it follows the equivalence of S ═ 0 and S ═ 0 accordingly; get s when t → ∞ timesi＝0，si+1When it is 0, the certification is finished.
Step 5, proving the queue stability of the fleet and finishing cooperative braking control on the whole fleet;
if ei(0) 0 < | q | < 1, then under the terminal sliding mode control controller TSM, the string stability of the fleet is guaranteed.
Namely:
||Gi(s)||＝||Ei+1(s)/Ei(s)||≤1
wherein G isi(s) is the error transfer function, Ei(s) is the error ei(t) Laplace transform.
Obtaining S according to step 4i(t)＝qsi(t)-si+1(t) convergence to zero, let Si(t) ═ 0, with:
Figure BDA0002574711220000141
laplace transform of the above equation gives:
Figure BDA0002574711220000142
from the above formula, one can obtain:
Figure BDA0002574711220000143
finally, the following is obtained:
Figure BDA0002574711220000144
because 0 < α1< 1, so when 0 < | q | < 1, | | | Gi(s) | | is less than or equal to 1, and the certification is finished.
In order to verify the effectiveness of the fleet cooperative braking control method based on the sliding mode control theory, matlab is adopted to carry out simulation experiment verification, and detailed description is given.
The isomorphic fleet model provided by the embodiment comprehensively considers actuator faults and external interference, adopts a terminal differential sliding mode technology, and designs the cooperative controller, so that the fleet can realize the convergence of each vehicle in the whole braking process, and the queue stability of the whole fleet is realized.
Example 1: assuming that a leading vehicle and 3 following vehicles run on a lane in a straight line, three conditions are considered for researching and analyzing the influence of disturbance on performance: no disturbance, disturbance of lead vehicles, and disturbance of all vehicles of the fleet. The sampling interval is set to 0.01 s. Initial position is set to p (0) [51,35,19,3 ]]Tm, initial velocity v (0) [ [15,15,15,15]Tm/s and TSP of lead vehicle is set to q0＝100m。
Disturbance ξi(t) can be specifically classified into the following three forms:
case 1: without disturbance
ξi(t)＝0，i＝0,...n.
Case 2: the lead car is disturbed
ξi(t)＝0.3sin(2πt)e-t/5，t≥3s，i＝0.
Case 3: all vehicles being disturbed
ξi(t)＝0.3sin(2πt)e-t/5，t≥3s，i＝0,...,n.
In the simulation, the initial estimation of the upper and lower disturbance bounds are respectively
Figure BDA0002574711220000151
And
Figure BDA0002574711220000152
the fleet dynamics parameters were set as follows: time constant of engine (tau)i0.1), air mass constant (σ 1.2 kg/m)3) Cross sectional area of ith vehicle (A)i＝2.2m2) Coefficient of resistance (c)di0.35), mass (m)i1500kg), mechanical resistance (d)mi5.5N). The desired separation distance of adjacent vehicles is set to ds1 m. The values of the relevant parameters of the controller are set to
Figure BDA0002574711220000153
c1＝0.3，c2＝0.35，α1＝0.5，α2＝3.2，q＝0.8，k＝32，ηi0.02 and 0.5.
In the simulation, the length of the vehicle was ignored.
Based on the parameters, simulation verification is performed on the fleet cooperative braking control method based on the sliding mode control theory, which is provided by the invention, as shown in fig. 3-6.
Where figure 3 shows the position change under the proposed control. As can be seen from FIG. 3, the lead vehicle can smoothly reach its TSP (i.e., q)0＝100)。
FIG. 4 shows the speed variation of the vehicle; it can be seen from fig. 3 that the vehicles in the platoon slowly converge smoothly from the initial speed to zero. This process takes approximately 25s or so.
Fig. 5 shows the variation of the inter-vehicle distance in the platoon. It can be seen from fig. 5 that in the three cases of considering the presence or absence of disturbance, other vehicles can converge to their designated positions, and the distance of the vehicles always keeps a reasonable safe distance, thereby avoiding the occurrence of rear-end accidents.
Fig. 6 shows that there is no negative pitch error during fleet braking and that the maximum pitch error does not exceed 0.14 m. This is because the following interaction between the vehicles is considered. Further, the pitch error converges to 0 around 25s, with the magnitude of the pitch error decreasing as the vehicle index increases in the fleet. The method for controlling the cooperative braking of the motorcade based on the sliding mode control theory not only can ensure the stability of each vehicle, but also can ensure the stability of the motorcade. Also, the TSM controller is robust to disturbances.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (3)

1. A motorcade cooperative braking control method based on a sliding mode control theory is characterized by comprising the following steps: the method comprises the following steps:
step 1, constructing a fixed time interval strategy according to self information of vehicles in a fleet, including position information, speed information and acceleration information, and establishing a longitudinal dynamic model of the vehicles by adopting a bidirectional communication structure;
step 2, setting the whole fleet to be composed of 1 leading vehicle and n-1 following vehicles, and respectively constructing controllers of the leading vehicle and the following vehicles without the condition that two vehicles run side by side;
step 3, constructing a differential equation aiming at the driving data of the lead vehicle, and verifying the convergence of the lead vehicle;
Figure FDA0002574711210000011
wherein p is0(t) is the position of the lead vehicle at time t, q0(t) is the designated parking position TSP of the lead vehicle,
Figure FDA0002574711210000012
to gain lead car controller and
Figure FDA0002574711210000013
the solution to the equation is:
Figure FDA0002574711210000014
wherein p is0' (t) is a special solution which,
Figure FDA0002574711210000015
is a general solution, C is a constant solution, and the following is deduced:
Figure FDA0002574711210000016
Figure FDA0002574711210000017
the speed of the lead car is:
Figure FDA0002574711210000018
obtained by combining the above formulas
Figure FDA0002574711210000019
Step 4, designing a self-adaptive rate, and selecting a Lyapunov function to verify the convergence of the following vehicle;
under the cooperative braking controller of the sliding mode of the motorcade terminal, if the parameter satisfies c1＞0，c2> 0, then the fleet is lyapunov stable, resulting in:
Figure FDA00025747112100000110
lyapunov function V1(t) the following:
Figure FDA00025747112100000111
the derivation of which is:
Figure FDA0002574711210000021
wherein
Figure FDA0002574711210000022
Andξ iis a fixed upper boundary and a fixed lower boundary, there are
Figure FDA0002574711210000023
The method comprises the following steps of 2:
Figure FDA0002574711210000024
the derivation is as follows:
Figure FDA0002574711210000025
where k is the follower controller gain, therefore there are:
Figure FDA0002574711210000026
because of the fact that
Figure FDA0002574711210000027
So V1(t) is a non-increasing function, V1(t)≤V1(0) And < ∞, the following components are:
Figure FDA0002574711210000028
ξ thereini(t)，
Figure FDA0002574711210000029
And
Figure FDA00025747112100000210
because of V1(t)∈R∞，R∞Is a positive real number field, Si(t)∈R∞Has a si(t)，si+1(t)∈R∞(ii) a Because ei(t)，
Figure FDA00025747112100000211
And sgn (S)i(t)∈R∞Therefore have ui(t)∈R∞，
Figure FDA00025747112100000212
Is provided with
Figure FDA00025747112100000213
Therefore, the temperature of the molten metal is controlled,
Figure FDA00025747112100000214
are consistently continuous; according to the formula
Figure FDA00025747112100000215
Figure FDA00025747112100000216
Figure FDA00025747112100000217
Wherein Q is reversible, following the equivalence of S ═ 0 and S ═ 0; get s when t → ∞ timesi＝0，si+1＝0；
Step 5, verifying the queue stability of the fleet and finishing cooperative braking control on the whole fleet;
if ei(0) 0 < | q | < 1, then under the terminal sliding mode control controller TSM, the string stability of the fleet is guaranteed, i.e.:
||Gi(s)||＝||Ei+1(s)/Ei(s)||≤1
where Gi(s) is the error transfer function and Ei(s) is the error ei(t) laplace transform;
obtaining S according to step 4i(t)＝qsi(t)-si+1(t) convergence to zero, let Si(t) ═ 0, with:
Figure FDA0002574711210000031
laplace transforms the above equation:
Figure FDA0002574711210000032
Figure FDA0002574711210000033
finally, the following is obtained:
Figure FDA0002574711210000034
because 0 < α1< 1, so when 0 < | q | < 1, | | | Gi(s)||≤1。
2. The sliding-mode control theory-based fleet cooperative braking control method according to claim 1, wherein the longitudinal vehicle dynamics model in step 1 sets the distance error between the ith vehicle and the (i-1) th vehicle as ei(t)：ei(t)＝pi-1(t)-pi(t)-ds-L, i ═ 1, 2.., n, where d issIs the desired car-to-car distance, L is the vehicle length, pi(t) the ith vehicle position information at the moment t, and t is time;
the dynamical model of the ith vehicle is described as the following nonlinear differential equation:
Figure FDA0002574711210000035
wherein v isi(t)、ai(t) speed and acceleration of the ith vehicle, respectively; c. Ci(t) is the actuator input, the nonlinear function fi(vi，ai) Is of the formula:
Figure FDA0002574711210000041
Figure FDA0002574711210000042
where σ is nullGas mass constant, τiIs the engine time constant, Ai,
Figure FDA0002574711210000043
And miRespectively the cross-sectional area, the resistance coefficient, the mechanical resistance and the quality of the ith vehicle, and linearizing the kinematic model to obtain a feedback linearization control law as follows:
Figure FDA0002574711210000044
the following linearized models were generated:
Figure FDA0002574711210000045
wherein u isiIs an additional control input signal;
disturbance term ξ is introduced due to communication interference between vehicles and external environment disturbancei(t), the linearization model is of the form:
Figure FDA0002574711210000046
wherein
Figure FDA0002574711210000047
ξ i(t) and
Figure FDA0002574711210000048
respectively disturbance ξiLower and upper bounds of (t).
3. The method for controlling cooperative braking of a fleet of vehicles based on the sliding-mode control theory according to claim 1, wherein the controller of the lead vehicle in step 2 is as follows:
Figure FDA0002574711210000049
wherein p is0(t) and v0(t) position and speed of the lead vehicle at time t, q0(t) is a designated parking position TSP, F of the lead vehicle0b(-) is the braking force of the lead vehicle during braking,
Figure FDA00025747112100000410
Figure FDA00025747112100000411
to gain lead car controller and
Figure FDA00025747112100000412
the controller for obtaining the lead vehicle is as follows:
Figure FDA00025747112100000413
wherein
Figure FDA00025747112100000414
Firstly, designing a sliding mode surface for a following vehicle, and then designing a cooperative controller:
the design formula of the sliding mode surface of the following vehicle is as follows:
Figure FDA0002574711210000051
wherein c is1，c2Constant, sgn (. cndot.) is a sign function α1，α2Is constant and satisfies the following condition:
α2＞2
α1＝(α2-2)/α2
the sliding mode surface is modified into the following form:
Figure FDA0002574711210000052
due to si(t) convergence of ei(t) approaches zero, but string stability cannot be guaranteed, so the slip-form face is designed to:
Figure FDA0002574711210000053
where q is constant and q ≠ 0, yielding: s (t) ═ qs (t);
wherein s (t) ═ s1(t) s2(t) … sn(t)]T,S(t)＝[S1(t) S2(t) … Sn(t)]T，
Figure FDA0002574711210000054
Since Q ≠ 0 is a constant, the matrix Q is irreversible, given that:
Figure FDA0002574711210000055
wherein:
Figure FDA0002574711210000056
wherein
Figure FDA0002574711210000057
And
Figure FDA0002574711210000058
are respectively
Figure FDA0002574711210000059
Andξ ian upper and lower bound of (t);
Figure FDA00025747112100000510
and
Figure FDA00025747112100000511
maximum values of the disturbance upper bound estimation and the disturbance lower bound estimation are respectively; and
Figure FDA0002574711210000061
are respectively
Figure FDA0002574711210000062
Andξ ian upper and lower bound of (t);
Figure FDA0002574711210000063
and
Figure FDA0002574711210000064
maximum values of the disturbance upper bound estimation and the disturbance lower bound estimation are respectively;
since the last vehicle is not a following vehicle, when i ═ n, the following vehicle controller is designed to:
Figure FDA0002574711210000065
Figure FDA0002574711210000066
and
Figure FDA0002574711210000067
the adaptive law of (2) is designed into the following form:
Figure FDA0002574711210000068
η thereini> 0, i ═ 1,2,. ang, n, and μiIs defined as:
Figure FDA0002574711210000069
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