CN110244747B - Heterogeneous fleet fault-tolerant control method based on actuator fault and saturation - Google Patents

Heterogeneous fleet fault-tolerant control method based on actuator fault and saturation Download PDF

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CN110244747B
CN110244747B CN201910712070.2A CN201910712070A CN110244747B CN 110244747 B CN110244747 B CN 110244747B CN 201910712070 A CN201910712070 A CN 201910712070A CN 110244747 B CN110244747 B CN 110244747B
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郝立颖
李平
郭戈
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Abstract

The invention provides a heterogeneous fleet fault-tolerant control method based on actuator faults and saturation, which comprises the following steps: carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a longitudinal dynamic model of the vehicle under the fault and saturation of the actuator by combining the fault and saturation models of the actuator; constructing a time interval-variable strategy with fault information and saturation indexes according to the self information of the vehicle; establishing a proportional-integral-derivative sliding mode surface and a coupling sliding mode surface based on a constructed variable time interval strategy; and selecting a proper Lyapunov function, designing a fault-tolerant controller and a self-adaptive update rate, and proving the limited time stability of the system. Compared with the traditional variable time interval strategy, the variable time interval strategy with the fault information and the saturation index can solve the problem of non-zero initial interval error and can increase the critical traffic capacity.

Description

Heterogeneous fleet fault-tolerant control method based on actuator fault and saturation
Technical Field
The invention relates to the technical field of heterogeneous fleet control, in particular to a fault-tolerant control method for a heterogeneous fleet based on actuator faults and saturation.
Background
In the last years, the longitudinal control of the autonomous motorcade is deeply studied, and aiming at the autonomous motorcade under the influence of a communication network, Yuei et al fully considers motorcade and communication network induction factors (such as quantification, delay and packet loss), establishes a hybrid motorcade control model under the influence of the motorcade communication network induction factors, perfects the existing motorcade control system model to a great extent, and further designs a controller for overcoming the interference of leading vehicles, so that not only can the stable operation control of the motorcade be realized, but also the motorcade control effect is greatly improved. And the peak and the like analyze and research the queue stability and the control method of the automatic fleet based on a vehicle longitudinal hysteresis dynamic model, and respectively analyze the queue stability of the two controllers according to a queue stability judgment criterion based on a sliding mode controller and proportional-integral-derivative control of a fixed time interval strategy to obtain a conclusion that the proportional-integral-derivative controller has stronger hysteresis robustness. Most of the literature does not consider the case of actuator failure. In an actual fleet control system, the performance of the system is reduced and even unstable due to the occurrence of an actuator fault, so that the Guo Xianggui et al provides self-adaptive fuzzy fault-tolerant control based on a high-speed train by using a compensation control law of self-adaptive gain, a fuzzy approximation technology and a sliding mode control method, and the fault-tolerant control method can also ensure the stability of a single train and the stability of a queue when the actuator has a fault. On the other hand, due to the physical limitation of the actuator and the consideration of passenger safety, actuator saturation is inevitable in a practical system, and the dynamic performance of the system is generally reduced due to the actuator saturation, and even the system is unstable. To remove this assumption, Guo Xiang Gui et al studied the actuator saturation problem with unknown nonlinear characteristics, combined the REF neural network approximation technique with the sliding mode control method, and compensated the effect of unknown nonlinear saturation by using the adaptive compensation technique, the designed adaptive control can not only ensure the stability of the bicycle, but also ensure the queue stability. By establishing the Lyapunov function, the limited time stability of the vehicle and the queue stability of the fleet are proved. Finally, the simulation proves the effectiveness of the method.
In the above-described study, the simultaneous occurrence of the actuator failure and the actuator saturation is not considered, and therefore the present invention is made to study the simultaneous occurrence of the actuator failure and the actuator saturation. In addition, Gu Xiang Gui et al uses a fixed time interval strategy that, while ensuring queue stability, does not ensure traffic flow stability. Moreover, in the research of Guxianggui et al, all vehicles assume the same specification, which significantly reduces the technical difficulty and also limits the practical application, so the invention will carry out research on heterogeneous fleet control.
Disclosure of Invention
According to the above-mentioned prior art, the simultaneous occurrence of actuator failure and actuator saturation is not considered, and the prior art uses a fixed time interval strategy, which can ensure queue stability but cannot ensure traffic flow stability, but provides a variable time interval strategy with failure information and saturation index, which can not only solve the problem of non-zero initial interval error, but also increase critical traffic capacity compared with the conventional variable time interval strategy.
The technical means adopted by the invention are as follows:
a heterogeneous fleet fault-tolerant control method based on actuator faults and saturation comprises the following steps:
s1, carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a longitudinal dynamic model of the vehicle under the fault and saturation of the actuator by combining the fault and saturation models of the actuator;
s2, constructing a time interval-variable strategy with fault information and saturation index according to the information of the vehicle;
s3, establishing a proportional-integral-derivative sliding mode surface and a coupling sliding mode surface based on the variable time interval strategy constructed in the step S2;
s4, selecting a proper Lyapunov function based on the proportional-integral-derivative sliding mode surface and the coupling sliding mode surface established in the step S3, designing a fault-tolerant controller and a self-adaptive update rate, and proving the limited time stability of the system.
Further, the step S4 is followed by:
and S5, based on the time-interval-variable strategy with the fault information and the saturation index in the step S2, the stability of the traffic flow is proved.
And S6, based on the proportional integral derivative sliding mode surface and the coupling sliding mode surface in the step S3, proving the queue stability of the fleet.
Further, the specific process of step S1 is as follows:
s11, defining a dynamic model of the leading vehicle, as follows:
Figure BDA0002154115580000031
wherein x is0(t)、v0(t)、a0(t) represents the position, speed, acceleration of the lead car, and a0(t) is a given function of time;
s12, carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a vehicle longitudinal dynamic model under the condition of actuator failure and saturation:
Figure BDA0002154115580000032
Figure BDA0002154115580000033
Figure BDA0002154115580000034
wherein sat (u)ai(t)) is the actuator input with fault and saturation characteristics, wi(t) is unknown external interference, fi(vi,aiT) is a non-linear function whose function is expressed as follows:
Figure BDA0002154115580000035
wherein, tauiIs the engine time constant, upsilon is the air mass constant, mi，Ai，CdiAnd dmiMass, cross-sectional area, drag coefficient and mechanical drag of vehicle i, respectively;
s13, the considered actuator fault model is specifically as follows:
uai(t)＝ρi(t，tρi)ui(t)+ri(t，tri)
wherein u isai(t) is the control input at actuator failure, ρi(t,tρi) Representing a failure in the efficiency of the actuator, ri(t,tri) Representing a bias failure of the actuator, tρiAnd triRespectively representing the times when the efficiency fault and the bias fault occur;
and substituting the actuator fault model into the vehicle longitudinal dynamic model, and further obtaining the vehicle longitudinal dynamic model as follows:
Figure BDA0002154115580000041
Figure BDA0002154115580000042
Figure BDA0002154115580000043
wherein x isi(t),vi(t),ai(t) position, velocity, acceleration of the ith vehicle, respectively;
s14, the actuator saturation model to be considered is specifically:
Figure BDA0002154115580000044
wherein u isr,imax> 0 and ul,imin< 0 represents the maximum value and the minimum value of the control torque which can be output by the actuating mechanism respectively; br,i> 0 and bl,i< 0 represents the amplitude of the actuator; gr,i(ui(t)) and gl,i(ui(t)) is an unknown non-linear function; sat (u)i(t)) is a saturation function, sat (u) is the saturation functioni(t)) may be expressed as:
sat(ui(t))＝χui(t)ui(t)
then there are:
Figure BDA0002154115580000045
wherein, χui(t)∈(0,1]The saturation exponent representing the ith control component exists at a sufficiently small parameter χlMake 0 < χl＜χui(t) < 1, when xuiWhen (t) is 0, it means that the actuator is almost completely saturated; when xuiWhen (t) is 1, the actuator is not saturated at all;
and bringing the actuator saturation model into the vehicle longitudinal dynamics model, and further obtaining the vehicle longitudinal dynamics model as follows:
Figure BDA0002154115580000046
Figure BDA0002154115580000047
Figure BDA0002154115580000048
further, the specific process of step S2 is as follows:
s21, defining displacement tracking error as follows:
Figure BDA0002154115580000051
wherein, deltai(t) is the inter-vehicle distance error between the ith vehicle and the (i-1) th vehicle, γiIs a normal number, LiIs the length of vehicle i, Δi-1,iIs the safety distance between two vehicles, h represents the delay time of the fleet control system, σ represents the safety factor, AmIs the maximum acceleration, pi0Lower bound, χ, representing actuator failurelIs the lower bound of the saturation index, so that it can be derived:
Figure BDA0002154115580000052
the initial value representing the variable time spacing strategy proposed by the present invention is zero in any case;
s22, defining an ideal workshop distance as follows:
Figure BDA0002154115580000053
further, the specific process of step S3 is as follows:
s31, in order to make deltai(t) inApproaching to infinite and approaching to 0 in limited time and ensuring consistent stability of the queue, and constructing a proportional-integral-derivative sliding mode surface:
Figure BDA0002154115580000054
wherein, Kp,Ki,KdRespectively representing proportional, integral and differential coefficients;
s32 according to transfer function GiDefinition of(s), construction of δi(t) and δi+1(t) defining a coupling sliding mode surface:
Figure BDA0002154115580000055
wherein λ is a coupling sliding mode surface si(t) and si+1(t) normal; when s isi(t) when it reaches the slip form surface, si(t) also reaches the slip-form surface;
s33, performing nonlinear processing by using an RBF neural network function, wherein the function expression is as follows:
Figure BDA0002154115580000056
wherein the content of the first and second substances,
Figure BDA0002154115580000057
an ideal weight vector representing a radial basis function neural network, wherein
Figure BDA0002154115580000058
Representing a real matrix, and M represents a network summary point number; ziRepresenting a network input vector; xi (Z)i) A basis function representing a neural network; in the form of a gaussian function, namely:
Figure BDA0002154115580000061
wherein phi iskAs the central vector of the kth node of the network, bkFor the base width parameter of the kth node of the network,
Figure BDA0002154115580000062
representing an approximation error, satisfies
Figure BDA0002154115580000063
Wherein
Figure BDA0002154115580000064
Is an unknown normal number.
Further, the specific process of step S4 is as follows:
s41, designing a fault-tolerant controller:
Figure BDA0002154115580000065
wherein 1 is less than or equal to 1/rhoi0≤Λi，
Figure BDA0002154115580000066
And ζiRepresents a normal number, ki1Representing the gain of the controller, Zi(t) is expressed as:
Figure BDA0002154115580000067
Figure BDA0002154115580000068
s42, designing a self-adaptive error, specifically:
Figure BDA0002154115580000069
Figure BDA00021541155800000610
in the formula (I), the compound is shown in the specification,
Figure BDA00021541155800000611
is thetai *The error of the estimation of (2) is,
Figure BDA00021541155800000612
is etai *The estimation error of (2);
s43, designing a self-adaptive updating law, specifically:
Figure BDA00021541155800000613
Figure BDA00021541155800000614
s44, in order to prove the system to be bounded, constructing a Lyapunov function, wherein the function expression of the Lyapunov function is as follows:
Figure BDA00021541155800000615
and (3) carrying out derivation on the Lyapunov function, and substituting the distance error, the coupling sliding mode surface, the self-adaptive update rate and the control law into a formula after the derivation of the Lyapunov function to obtain:
Figure BDA0002154115580000071
and obtaining that all signals in the closed-loop system are finally and consistently bounded according to the Lyapunov stabilization theory, wherein:
Figure BDA0002154115580000072
Figure BDA0002154115580000073
further, the specific process of step S5 is as follows:
s51, based on the time-varying interval strategy with fault information and saturation index in step S2, assuming the interval S of the ith following vehicle in a stable statequad,i(t)＝Squad(t) and velocity vi(t) ═ v (t), Γ in a stable statei(t) ═ 0, yielding:
Figure BDA0002154115580000074
traffic density:
Figure BDA0002154115580000075
s52, defining flow rate:
Figure BDA0002154115580000076
s53, calculating queue stability of the whole fleet
Figure BDA0002154115580000077
Reissue to order
Figure BDA0002154115580000078
Calculating the critical traffic density:
Figure BDA0002154115580000079
s54, using the same method as the steps S51-S53, the critical traffic density of the traditional time-space-variable strategy is obtained:
Figure BDA0002154115580000081
s55, comparing the critical traffic density calculated in steps S53 and S54, it is proved that the critical traffic density can be improved based on the variable time interval strategy with the fault information and the saturation index in step S2.
Further, the specific process of step S6 is as follows:
because of Si(t)＝λsi(t)-si+1(t) tends to approach the vicinity of the 0 domain indefinitely in a finite time, the relationship can be derived as follows:
Figure BDA0002154115580000082
laplace transform is performed on both sides of the above equation to obtain:
Figure BDA0002154115580000083
therefore, the following can be obtained: gi(s)＝δi+1(s)/δi(s) ═ λ, if 0 < λ ≦ 1, queue stability for the entire fleet will be satisfied.
Further, the step S6 is followed by:
s7, carrying out simulation verification research on the vehicle longitudinal dynamics model, the proportional-integral-derivative sliding mode surface, the coupling sliding mode surface, the fault-tolerant controller and the self-adaptive update rate under the condition of actuator faults and saturation by adopting the heterogeneous fleet fault-tolerant control scheme based on the actuator faults and saturation, and comparing with the conventional means to further verify the effectiveness and superiority.
Compared with the prior art, the invention has the following advantages:
1. considering that the fixed interval strategy can cause the queue of the system to be unstable, and the fixed time interval strategy can cause the traffic flow to be unstable, the variable time interval strategy provided by the invention can not only ensure the queue stability, but also ensure the traffic flow stability;
2. aiming at the fleet control system, the invention simultaneously considers the conditions of actuator failure and actuator saturation, so that the fleet control system can normally operate under the conditions of actuator failure and actuator saturation;
3. most of the research, the designed controller requires that the nonlinear characteristic of the actuator is known, which is undoubtedly a harsh assumption, and the invention removes the assumption;
4. since the system is more unstable due to the fact that the actuator fault and the actuator occur simultaneously, the system may generate larger control force to compensate the influence of the actuator fault and the actuator, and therefore the variable time interval strategy with fault information and saturation indexes is provided, compared with the traditional variable time interval strategy, the variable time interval strategy not only removes the assumption of zero initial interval error, but also can increase the critical traffic capacity.
Based on the reasons, the method can be widely popularized in the fields of heterogeneous motorcades and the like.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a heterogeneous fleet of vehicles according to an embodiment of the present invention.
Fig. 3 is a diagram illustrating a pitch error simulation according to an embodiment of the present invention.
Fig. 4 is a diagram of a location simulation provided in an embodiment of the present invention.
Fig. 5 is a velocity simulation diagram provided by the embodiment of the present invention.
Fig. 6 is an acceleration simulation diagram provided in the embodiment of the present invention.
Fig. 7 is a drawing of a slip film surface simulation provided by an embodiment of the present invention.
Fig. 8 is a simulation diagram of saturated input according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1, the present invention provides a heterogeneous fleet fault tolerance control method based on actuator failure and saturation, which includes the following steps:
s1, carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a longitudinal dynamic model of the vehicle under the fault and saturation of the actuator by combining the fault and saturation models of the actuator;
s2, constructing a time interval-variable strategy with fault information and saturation index according to the information of the vehicle;
s3, establishing a proportional-integral-derivative sliding mode surface and a coupling sliding mode surface based on the variable time interval strategy constructed in the step S2;
s4, selecting a proper Lyapunov function based on the proportional-integral-derivative sliding mode surface and the coupling sliding mode surface established in the step S3, designing a fault-tolerant controller and a self-adaptive update rate, and proving the limited time stability of the system.
And S5, based on the time-interval-variable strategy with the fault information and the saturation index in the step S2, the stability of the traffic flow is proved.
And S6, based on the proportional integral derivative sliding mode surface and the coupling sliding mode surface in the step S3, proving the queue stability of the fleet.
Example 1
The specific process of step S1 is as follows:
s11, defining a dynamic model of the leading vehicle, as follows:
Figure BDA0002154115580000101
wherein x is0(t)、v0(t)、a0(t) represents the position, speed, acceleration of the lead car, and a0(t) is a given function of time;
s12, carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a longitudinal dynamic model of the vehicle under the fault:
Figure BDA0002154115580000111
Figure BDA0002154115580000112
Figure BDA0002154115580000113
wherein, sat (u)ai(t)) is the actuator input with fault and saturation characteristics, wi(t) is unknown external interference, fi(vi,aiT) is a non-linear function whose function is expressed as follows:
Figure BDA0002154115580000114
wherein, tauiIs the engine time constant, upsilon is the air mass constant, mi，Ai，CdiAnd dmiMass, cross-sectional area, drag coefficient and mechanical drag of vehicle i, respectively;
s13, the considered actuator fault model is specifically as follows:
uai(t)＝ρi(t，tρi)ui(t)+ri(t，tri)
wherein u isai(t) is the control input at actuator failure, ρi(t,tρi) Representing a failure in the efficiency of the actuator, ri(t,tri) Representing a bias failure of the actuator, tρiAnd triRespectively representing the times when the efficiency fault and the bias fault occur;
and substituting the actuator fault model into the vehicle longitudinal dynamic model, and further obtaining the vehicle longitudinal dynamic model as follows:
Figure BDA0002154115580000115
Figure BDA0002154115580000116
Figure BDA0002154115580000117
wherein x isi(t),vi(t),ai(t) position, velocity, acceleration of the ith vehicle, respectively;
s14, the actuator saturation model to be considered is specifically:
Figure BDA0002154115580000118
wherein u isr,imax> 0 and ul,imin< 0 represents the maximum value and the minimum value of the control torque which can be output by the actuating mechanism respectively; br,i> 0 and bl,i< 0 represents the amplitude of the actuator; gr,i(ui(t)) and gl,i(ui(t)) is an unknown non-linear function; sat (u)i(t)) is a saturation function, sat (u) is the saturation functioni(t)) may be expressed as:
sat(ui(t))＝χui(t)ui(t)
then there are:
Figure BDA0002154115580000121
wherein, χui(t)∈(0,1]The saturation index representing the ith control component exists at a sufficiently small parameter χlMake 0 < χl＜χui(t) < 1, when xuiWhen (t) is 0, it means that the actuator is almost completely saturated; when xuiWhen (t) is 1, the actuator is not saturated at all;
and bringing the actuator saturation model into the vehicle longitudinal dynamics model, and further obtaining the vehicle longitudinal dynamics model as follows:
Figure BDA0002154115580000122
Figure BDA0002154115580000123
Figure BDA0002154115580000124
example 2
On the basis of embodiment 1, the specific procedure of step S2 is as follows:
s21, defining displacement tracking error as follows:
Figure BDA0002154115580000125
wherein, deltai(t) is the inter-vehicle distance error between the ith vehicle and the (i-1) th vehicle, γiIs a normal constant, LiIs the length of vehicle i, Δi-1,iIs the safe distance between two vehicles, h represents the delay time of the fleet control system, σ represents the safety factor, AmIs the maximum acceleration, ρi0Lower bound, χ, representing actuator failurelIs the lower bound of the saturation index, so that it can be derived:
Figure BDA0002154115580000131
the initial value representing the variable time interval strategy proposed by the present invention is zero in any case;
s22, defining an ideal workshop distance as follows:
Figure BDA0002154115580000132
example 3
On the basis of embodiment 2, the specific procedure of step S3 is as follows:
s31, in order to make deltai(t) approaching infinite to 0 in finite time and ensuring consistent stability of the queue, constructing a proportional-integral-derivative sliding mode surface:
Figure BDA0002154115580000133
wherein, Kp,Ki,KdRespectively representing proportional, integral and differential coefficients;
s32 according to transfer function GiDefinition of(s)Construction of deltai(t) and δi+1(t) defining a coupling sliding mode surface:
Figure BDA0002154115580000134
wherein λ is a coupling sliding mode surface si(t) and si+1(t) normal; when s isi(t) when it reaches the slip form surface, si(t) also reaches the slip-form surface;
s33, performing nonlinear processing by using an RBF neural network function, wherein the function expression is as follows:
Figure BDA0002154115580000135
wherein the content of the first and second substances,
Figure BDA0002154115580000136
an ideal weight vector representing a radial basis function neural network, wherein
Figure BDA0002154115580000137
Representing a real matrix, and M represents a network summary point number; ziRepresenting a network input vector; xi (Z)i) A basis function representing a neural network; in the form of a gaussian function, namely:
Figure BDA0002154115580000138
wherein phi iskAs the central vector of the kth node of the network, bkFor the base width parameter of the kth node of the network,
Figure BDA0002154115580000139
representing an approximation error, satisfies
Figure BDA00021541155800001310
Wherein
Figure BDA00021541155800001311
Is an unknown normal number.
Example 4
On the basis of embodiment 3, the specific procedure of step S4 is as follows:
s41, designing a fault-tolerant controller:
Figure BDA0002154115580000141
wherein 1 is less than or equal to 1/rhoi0≤Λi，
Figure BDA0002154115580000142
And ζiRepresents a normal number, ki1Representing the gain of the controller, Zi(t) is expressed as:
Figure BDA0002154115580000143
Figure BDA0002154115580000144
s42, designing a self-adaptive error, which specifically comprises the following steps:
Figure BDA0002154115580000145
Figure BDA0002154115580000146
in the formula (I), the compound is shown in the specification,
Figure BDA0002154115580000147
is thetai *The error of the estimation of (2) is,
Figure BDA0002154115580000148
is etai *The estimation error of (2);
s43, designing a self-adaptive updating law, specifically:
Figure BDA0002154115580000149
Figure BDA00021541155800001410
s44, in order to prove the system to be bounded, constructing a Lyapunov function, wherein the function expression of the Lyapunov function is as follows:
Figure BDA00021541155800001411
and (3) carrying out derivation on the Lyapunov function, and substituting the distance error, the coupling sliding mode surface, the self-adaptive update rate and the control law into a formula after the derivation of the Lyapunov function to obtain:
Figure BDA00021541155800001412
and obtaining that all signals in the closed-loop system are finally and consistently bounded according to the Lyapunov stabilization theory, wherein:
Figure BDA0002154115580000151
Figure BDA0002154115580000152
example 5
On the basis of embodiment 4, the specific procedure of step S5 is as follows:
s51, based on the time-varying interval strategy with fault information and saturation index in step S2, assuming the interval S of the ith following vehicle in a stable statequad,i(t)＝Squad(t) and velocity vi(t) ═ v (t), Γ in a stable statei(t) ═ 0, yielding:
Figure BDA0002154115580000153
traffic density:
Figure BDA0002154115580000154
s52, defining flow rate:
Figure BDA0002154115580000155
s53, calculating queue stability of the whole fleet
Figure BDA0002154115580000156
Reissue to order
Figure BDA0002154115580000157
Calculating the critical traffic density:
Figure BDA0002154115580000158
s54, using the same method as the steps S51-S53, the critical traffic density of the traditional time-space-variable strategy is obtained:
Figure BDA0002154115580000159
s55, comparing the critical traffic density calculated in steps S53 and S54, it is proved that the critical traffic density can be improved based on the variable time interval strategy with the fault information and the saturation index in step S2.
Example 6
On the basis of embodiment 5, the specific procedure of step S6 is as follows:
because of Si(t)＝λsi(t)-si+1(t) tends to approach the vicinity of the 0 domain indefinitely in a finite time, the relationship can be derived as follows:
Figure BDA0002154115580000161
laplace transform is performed on both sides of the above equation to obtain:
Figure BDA0002154115580000162
therefore, the following can be obtained: gi(s)＝δi+1(s)/δi(s) ═ λ, if 0 < λ ≦ 1, queue stability for the entire fleet will be satisfied.
Example 7
On the basis of the embodiments 1-5, the method further comprises the following steps:
s7, performing simulation verification research on a vehicle longitudinal dynamic model, a proportional-integral-derivative sliding mode surface, a coupling sliding mode surface, a fault-tolerant controller and a self-adaptive update rate under the condition of actuator faults and saturation by adopting a heterogeneous fleet fault-tolerant control scheme based on actuator faults and saturation, and comparing the simulation verification research with a conventional means to further verify effectiveness and superiority.
In order to verify the effectiveness of the heterogeneous fleet fault-tolerant control method with actuator faults and actuator saturation provided by the embodiment, matlab is adopted to perform simulation experiment verification, and detailed description is given.
As shown in fig. 2, the heterogeneous fleet model provided in this embodiment comprehensively considers actuator faults, actuator saturation and external interference, and adopts a sliding mode technique and an RBF neural network approximation technique to design a fault-tolerant control method for a heterogeneous fleet, so that a closed-loop system is stable in a limited time, and has good position, speed and acceleration tracking performance, a certain robustness for actuator faults, and good suppression for external interference.
Specifically, in this embodiment, assuming that there are one leading vehicle and six following vehicles traveling straight on the lane, the acceleration trajectory of the leading vehicle is defined as:
Figure BDA0002154115580000171
defining a model of actuator saturation:
Figure BDA0002154115580000172
in addition, a safety distance Δ is set in the simulationi-1,i7m, 0.08s delay time h, 0.2 safety factor sigma, maximum acceleration Am＝3.5m/s2Air mass constant u 1.2kg/m3Cross sectional area A of vehiclei＝2.2m2Coefficient of drag force Cdi0.35, mechanical drag dmi5N; taking into account interference wi(t) 0.1sin (t), actual input u for actuator failureai＝ρi(t)ui(t)+ri(t) wherein ρi(t)＝0.75+0.25sin(0.1it)，ri(t) ═ 0.1sin (t), assuming a lower bound ρ of the faulti0Using this relationship 1 ≦ 1/ρ, 0.5i0≤ΛiCan obtain ΛiNot less than 2. Mass m of another six following vehiclesiAre [1500, 1600, 1550, 1650, 1500, 1400 respectively]Time constant of engine τiAre respectively [0.1, 0.3, 0.2, 0.4, 0.25, 0.4 ]]Length of vehicle LiAre respectively [4, 4.5, 5, 5, 4.5, 3.5 ]]；
Finally, in the simulation, the initial state of the entire fleet of vehicles including a leading vehicle and six following vehicles was as follows: initial position xi(0)(m)＝[150，135，125.5，112.5，99.5，87，75.5](ii) a Initial velocity vi(0)(m/s)＝[1，4，2，0，5，3，1]Initial acceleration ai(0)(m/s2)＝[0，1，5，2，1，3，1]. Selecting a Gaussian function as a radial basis function of the neural network:
Figure BDA0002154115580000173
wherein phi isk∈[-1.5,1.5]，bk＝2。
Based on the parameters, simulation verification is carried out on the heterogeneous fleet fault-tolerant control method with actuator fault and saturation, which is provided by the invention, as shown in fig. 3-8. Wherein the pitch error curve of fig. 3 shows that the pitch error converges to around 0 in a limited time, which indicates that the controller has good dynamic performance; FIG. 4 illustrates the following vehicle following the lead vehicle displacement, each vehicle completely avoiding the fleet collision problem; FIG. 5 shows a velocity tracking curve, following a lead vehicle to a desired velocity; FIG. 6 shows acceleration tracking curves, with the acceleration of the following vehicle gradually tending towards the acceleration of the lead vehicle; fig. 7 shows that the sliding mode curve gradually approaches near 0 and eventually the buffeting almost completely disappears; fig. 8 shows a plot of actuator saturation input. The above simulation results show the effectiveness of the proposed spacing strategy.
The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
In the above embodiments of the present invention, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to related descriptions of other embodiments.
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; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. A heterogeneous fleet fault-tolerant control method based on actuator faults and saturation is characterized by comprising the following steps:
s1, carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a longitudinal dynamic model of the vehicle under the fault and saturation of the actuator by combining the fault and saturation models of the actuator;
s2, constructing a time interval-variable strategy with fault information and saturation index according to the information of the vehicle;
s3, establishing a proportional-integral-derivative sliding mode surface and a coupling sliding mode surface based on the variable time interval strategy constructed in the step S2;
s4, selecting a Lyapunov function based on the proportional-integral-derivative sliding mode surface and the coupling sliding mode surface established in the step S3, designing a fault-tolerant controller and a self-adaptive update rate, and proving the limited time stability of the system;
the specific process of step S4 is as follows:
s41, designing a fault-tolerant controller:
Figure FDA0003473383230000011
wherein k isi,λ,bi,kdIs represented by an arbitrary normal number, Si(t) denotes a sliding mode surface, h denotes a delay time of a control system, χ1Lower bound value representing saturation index, σ represents safety factor, vi(t) represents the speed of the ith vehicle, AmRepresenting the absolute value of the maximum possible deceleration, pi0A lower bound value representing a fault factor,
Figure FDA0003473383230000012
representing an unknown parameter thetai *The error of the estimation of (2) is,
Figure FDA00034733832300000110
is representative of xiiThe transpose of (a) is performed,
Figure FDA0003473383230000013
is representative of xiiSquare of (d), muiAnd
Figure FDA0003473383230000014
represents a small constant, 1 ≦ 1/ρi0≤Λi，
Figure FDA0003473383230000015
And ζiRepresents a normal number, ki1Representing the gain of the controller, Zi(t) is expressed as:
Figure FDA0003473383230000016
Figure FDA0003473383230000017
wherein, KpThe scale factor is expressed in terms of a scale factor,
Figure FDA0003473383230000018
representing the pitch error deltaiDerivative of, KiRepresenting the integral coefficient, ai(t) represents the acceleration of the ith vehicle,
Figure FDA0003473383230000019
is expressed as gammaiThe second derivative of (d);
s42, designing a self-adaptive error, specifically:
Figure FDA0003473383230000021
Figure FDA0003473383230000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003473383230000023
is thetai *Is estimated byDifference, thetai *Denotes an unknown constant, pi0A lower bound value representing a fault factor,
Figure FDA0003473383230000024
denotes thetai *Is determined by the estimated value of (c),
Figure FDA0003473383230000025
is etai *Of the estimated error, ηi *It is shown that the unknown constant is,
Figure FDA0003473383230000026
expression ηi *An estimated value of (d);
s43, designing a self-adaptive updating law, specifically:
Figure FDA0003473383230000027
Figure FDA0003473383230000028
wherein alpha isi,λ,Kd,biWhich represents an arbitrary normal number of the components,
Figure FDA0003473383230000029
is representative of xii(Zi) Xi. transposition of1iXi and xi2iRepresents an arbitrary bounded continuous function;
s44, in order to prove the system to be bounded, constructing a Lyapunov function, wherein the function expression of the Lyapunov function is as follows:
Figure FDA00034733832300000210
and (3) carrying out derivation on the Lyapunov function, and substituting the distance error, the coupling sliding mode surface, the self-adaptive update rate and the control law into a formula after the derivation of the Lyapunov function to obtain:
Figure FDA00034733832300000211
wherein alpha isiAnd betaiRepresents any normal number;
and obtaining that all signals in the closed-loop system are finally and consistently bounded according to the Lyapunov stabilization theory, wherein:
Figure FDA00034733832300000212
Figure FDA00034733832300000213
wherein alpha isiAnd biWhich represents an arbitrary normal number of the components,
Figure FDA00034733832300000214
representing a smaller constant.
2. The heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S4 is followed by further comprising:
s5, based on the time-interval-variable strategy with the fault information and the saturation index in the step S2, the stability of the traffic flow is proved;
and S6, based on the proportional integral derivative sliding mode surface and the coupling sliding mode surface in the step S3, proving the queue stability of the fleet.
3. The heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S1 is performed as follows:
s11, defining a dynamic model of the leading vehicle, as follows:
Figure FDA0003473383230000031
wherein x is0(t)、v0(t)、a0(t) represents the position, speed, acceleration of the lead car, and a0(t) is a given function of time;
s12, carrying out stress analysis on the longitudinal motion of the vehicle, and establishing a vehicle longitudinal dynamic model under the condition of actuator failure and saturation:
Figure FDA0003473383230000032
Figure FDA0003473383230000033
Figure FDA0003473383230000034
wherein, sat (u)ai(t)) is the actuator input with fault and saturation characteristics, wi(t) is unknown external interference, fi(vi,aiT) is a non-linear function whose function is expressed as follows:
Figure FDA0003473383230000035
wherein, tauiIs the engine time constant, upsilon is the air mass constant, mi，Ai，CdiAnd dmiMass, cross-sectional area, drag coefficient and mechanical drag of vehicle i, respectively;
s13, the considered actuator fault model is specifically as follows:
uai(t)＝ρi(t，tρi)ui(t)+ri(t，tri)
wherein u isai(t) is the control input at actuator failure, ρi(t,tρi) Representing a failure in the efficiency of the actuator, ri(t,tri) Representing a bias failure of the actuator, tρiAnd triRespectively representing the times when the efficiency fault and the bias fault occur;
and substituting the actuator fault model into the vehicle longitudinal dynamic model, and further obtaining the vehicle longitudinal dynamic model as follows:
Figure FDA0003473383230000041
Figure FDA0003473383230000042
Figure FDA0003473383230000043
wherein x isi(t),vi(t),ai(t) position, velocity, acceleration of the ith vehicle, respectively;
s14, the actuator saturation model to be considered is specifically:
Figure FDA0003473383230000044
wherein u isr,imax> 0 and ul,imin< 0 represents the maximum value and the minimum value of the control torque which can be output by the actuating mechanism respectively; br,i> 0 and bl,i< 0 represents the amplitude of the actuator; g is a radical of formular,i(ui(t)) and gl,i(ui(t)) is an unknown non-linear function; sat (u)i(t)) is a saturation function, sat (u) is the saturation functioni(t)) may be expressed as:
sat(ui(t))＝χui(t)ui(t)
then there are:
Figure FDA0003473383230000045
wherein, χui(t)∈(0,1]The saturation exponent representing the ith control component exists at a sufficiently small parameter χlMake 0 < χl＜χui(t) < 1, when xuiWhen (t) is 0, it means that the actuator is almost completely saturated; when xuiWhen (t) is 1, the actuator is not saturated at all;
and bringing the actuator saturation model into the vehicle longitudinal dynamics model, and further obtaining the vehicle longitudinal dynamics model as follows:
Figure FDA0003473383230000046
Figure FDA0003473383230000047
Figure FDA0003473383230000048
4. the heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S2 is performed as follows:
s21, defining displacement tracking error as follows:
Figure FDA0003473383230000051
Figure FDA0003473383230000052
Figure FDA0003473383230000053
wherein, deltai(t) is the inter-vehicle distance error between the ith vehicle and the (i-1) th vehicle, xi(t) represents the position of the i-th vehicle, vi(t) represents the speed of the i-th vehicle, γiIs a normal number, LiIs the length of vehicle i, Δi-1,iIs the safe distance between two vehicles, h represents the delay time of the fleet control system, σ represents the safety factor, AmIs the maximum acceleration, pi0Lower bound, χ, representing actuator failurelIs the lower bound of the saturation index, so that it can be derived:
Figure FDA0003473383230000054
the initial value representing the variable time spacing strategy proposed by the present invention is zero in any case;
s22, defining an ideal workshop distance as follows:
Figure FDA0003473383230000055
5. the heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S3 is performed as follows:
s31, in order to make deltai(t) approaching infinite to 0 in finite time and ensuring consistent stability of the queue, constructing a proportional-integral-derivative sliding mode surface:
Figure FDA0003473383230000056
wherein, Kp,Ki,KdRespectively representing proportional, integral and differential coefficients; deltai(τ) represents a pitch error;
s32, according to transfer function GiDefinition of(s), construction of δi(t) and δi+1(t) defining a coupling sliding mode surface:
Figure FDA0003473383230000057
wherein λ is a coupling sliding mode surface si(t) and si+1(t) normal; when si(t) when it reaches the slip form surface, si(t) also reaches the slip-form surface;
s33, performing nonlinear processing by using an RBF neural network function, wherein the function expression is as follows:
Figure FDA0003473383230000061
wherein the content of the first and second substances,
Figure FDA0003473383230000062
an ideal weight vector representing a radial basis function neural network, wherein
Figure FDA0003473383230000063
Representing a real matrix, and M represents a network summary point number; ziRepresenting a network input vector; xi (Z)i) A basis function representing a neural network; in the form of a gaussian function, namely:
Figure FDA0003473383230000064
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003473383230000065
as the central vector of the kth node of the network, bkFor the base width parameter of the kth node of the network,
Figure FDA0003473383230000066
representing an approximation error, satisfies
Figure FDA0003473383230000067
Wherein
Figure FDA0003473383230000068
Is an unknown normal number.
6. The heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S5 is performed as follows:
s51, based on the time-varying interval strategy with fault information and saturation index in step S2, assuming the interval S of the ith following vehicle in a stable statequad,i(t)＝Squad(t) and velocity vi(t) ═ v (t), Γ in a stable statei(t) ═ 0, resulting in:
Figure FDA0003473383230000069
wherein L represents the length of the ith vehicle, h represents the delay time of the control system, sigma represents the safety factor, AmRepresenting the absolute value of the maximum possible deceleration, pi0A lower bound value representing a fault factor;
traffic density:
Figure FDA00034733832300000610
s52, defining flow rate:
Figure FDA00034733832300000611
s53, calculating queue stability of the whole fleet
Figure FDA00034733832300000612
Reissue to order
Figure FDA00034733832300000613
Calculating the critical traffic density:
Figure FDA00034733832300000614
s54, using the same method as the steps S51-S53, the critical traffic density of the traditional time-space-variable strategy is obtained:
Figure FDA0003473383230000071
s55, comparing the critical traffic density calculated in steps S53 and S54, it is proved that the critical traffic density can be improved based on the variable time interval strategy with the fault information and the saturation index in step S2.
7. The heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S6 is performed as follows:
because of Si(t)＝λsi(t)-si+1(t) tends to approach the vicinity of the 0 domain indefinitely in a finite time, the relationship can be derived as follows:
Figure FDA0003473383230000072
wherein S isiRepresenting the slip form face, KpDenotes the proportionality coefficient, KiDenotes the integral coefficient, KdRepresenting the differential coefficient, δiRepresenting the distance error of the ith vehicle and the (i-1) th vehicle; laplace transform is performed on both sides of the above equation to obtain:
Figure FDA0003473383230000073
therefore, the following can be obtained: gi(s)＝δi+1(s)/δi(s) ═ λ, if 0 < λ ≦ 1, queue stability for the entire fleet will be satisfied.
8. The heterogeneous fleet fault tolerance control method according to claim 1, wherein said step S6 is followed by further comprising:
s7, carrying out simulation verification research on the vehicle longitudinal dynamic model, the proportional-integral-derivative sliding mode surface, the coupling sliding mode surface, the fault-tolerant controller and the self-adaptive update rate under the condition of actuator fault and saturation by adopting the heterogeneous fleet fault-tolerant control scheme based on the actuator fault and saturation, and verifying the effectiveness and superiority.
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