CN109375510A - A kind of adaptive sliding mode fault tolerant control method for bullet train - Google Patents
A kind of adaptive sliding mode fault tolerant control method for bullet train Download PDFInfo
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Abstract
The embodiment of the invention discloses a kind of adaptive sliding mode fault tolerant control methods for bullet train, are related to bullet train control field, can extenuate the problem of bullet train actuator uncertainty.The present invention includes: according to train runing parameters collected, and selection matches the train model of the train runing parameters from train model set.Obtain the corresponding sliding formwork fault-tolerant controller of selected train model and adaptive law.Selected train model is loaded onto the corresponding sliding formwork fault-tolerant controller and the adaptive law.Using the sliding formwork fault-tolerant controller and the adaptive law, according to current time collected quantity of state tracking expectation displacement and desired speed.The present invention is suitable for coping with the adaptive sliding mode faults-tolerant control of bullet train actuator uncertainty and failure.
Description
Technical field
The present invention relates to bullet train control field more particularly to a kind of fault-tolerant controls of adaptive sliding mode for bullet train
Method processed.
Background technique
Between nearly 20 years, Chinese High-sped Trains are advanced by leaps and bounds.Bullet train is because its speed is fast, load-carrying is big, punctual
Feature, it has also become one of most important vehicles.Since the requirement to train speed and safety increases, controller is as high speed
The design of the core component of train, fault detection and faults-tolerant control causes the pass of more and more researchers and engineer
Note.
Uncertainty, including model uncertainty and disturbance, are widely present in actual physics system, therefore consider control
Various uncertainties in design, fault detection and Fault-tolerant Control Design are vital.Especially bullet train is in reality
There are some inside and outside are uncertain in operation.In existing all controllers and faults-tolerant control for High-Speed Train Design
For device, the external disturbance for being modeled as system model additional signal has been widely studied, however in system differential dynamical equation
In be modeled as state or input/actuator is probabilistic internal uncertain, be but seldom considered.
Therefore, for coping with the scheme of bullet train actuator uncertainty and failure, the emphasis studied in the industry has been known as it.
Summary of the invention
The embodiment of the present invention provides a kind of adaptive sliding mode fault tolerant control method for bullet train, can extenuate height
The problem of fast train actuator uncertainty.
In order to achieve the above objectives, the embodiment of the present invention adopts the following technical scheme that
According to train runing parameters collected, selection matches the column of the train runing parameters from train model set
Vehicle model.
Obtain the corresponding sliding formwork fault-tolerant controller of selected train model and adaptive law.
Using the sliding formwork fault-tolerant controller and the adaptive law, the phase is tracked according to current time collected quantity of state
Hope displacement and desired speed.
Specifically, the train model set includes at least: health model, parametrization fault model, imparametrization failure
Model and the unknown fault model of interference limit.
The invention discloses with the uncertain bullet train adaptive sliding mode faults-tolerant control scheme of actuator, in actuator
Under condition of uncertainty, the Longitudinal Dynamic Model of bullet train is proposed；For the uncertain health with external disturbance of actuator
System devises a kind of novel sliding mode controller, can drive tracking error dynamical system to preset cunning in finite time
In die face, and sliding formwork movement is kept hereafter；Respectively for known fault boundary, unknown failure boundary and imparametrization event
The train model of barrier proposes NEW ADAPTIVE sliding formwork fault-tolerant controller, thus alleviate bullet train trailer system actuator failures and
Uncertain problem.
Detailed description of the invention
It to describe the technical solutions in the embodiments of the present invention more clearly, below will be to needed in the embodiment
Attached drawing is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for ability
For the those of ordinary skill of domain, without creative efforts, it can also be obtained according to these attached drawings other attached
Figure.
Fig. 1 a is trailer system operation principle schematic diagram provided in an embodiment of the present invention；
Fig. 1 b is the schematic diagram of method flow provided in an embodiment of the present invention；
Fig. 2 is displacement and the speed tracing figure of train health system provided in an embodiment of the present invention；
Fig. 3 a is that the tracking of the segmented model of train health system known disturbances containing boundary provided in an embodiment of the present invention misses
Difference figure；
Fig. 3 b is the tracking of the parametrization fault model of train system known disturbances containing boundary provided in an embodiment of the present invention
Error；
Fig. 3 c be train system known disturbances containing boundary provided in an embodiment of the present invention imparametrization fault model with
Track error；
Fig. 3 d is the tracking of the parametrization fault model of train system unknown disturbances containing boundary provided in an embodiment of the present invention
Error.
Specific embodiment
Technical solution in order to enable those skilled in the art to better understand the present invention, with reference to the accompanying drawing and specific embodiment party
Present invention is further described in detail for formula.Embodiments of the present invention are described in more detail below, the embodiment is shown
Example is shown in the accompanying drawings, and in which the same or similar labels are throughly indicated same or similar element or has identical or class
Like the element of function.It is exemplary below with reference to the embodiment of attached drawing description, for explaining only the invention, and cannot
It is construed to limitation of the present invention.Those skilled in the art of the present technique are appreciated that unless expressly stated, odd number shape used herein
Formula " one ", "one", " described " and "the" may also comprise plural form.Those skilled in the art of the present technique are appreciated that unless another
Outer definition, all terms (including technical terms and scientific terms) used herein have with it is common in fields of the present invention
The identical meaning of the general understanding of technical staff.It should also be understood that those terms such as defined in the general dictionary should
It is understood to have a meaning that is consistent with the meaning in the context of the prior art, and unless defined as here, it will not
It is explained in an idealized or overly formal meaning.
The embodiment of the present invention provides a kind of adaptive sliding mode fault tolerant control method for bullet train, as shown in Figure 1 b,
Include:
S1, according to train runing parameters collected, selection matches the train runing parameters from train model set
Train model.
S2, the corresponding sliding formwork fault-tolerant controller of selected train model and adaptive law are obtained.
Wherein, adaptive sliding mode controller and its adaptive law are designed for the actuator of train health system, guarantees to close
The stability and displacement state amount of loop system can track desired value.When actuator failures occur in the process of running for train
When, for segmentation dynamic model and actuator the parametrization fault model design adaptive failure compensation control of train fault system
Device structure and its adaptive law.
In practical applications, the train generic failure that actuator occurs in the process of running, for actuator imparametrization
Fault model designs adaptive sliding mode fault-tolerant controller structure and its adaptive law in the present embodiment.If interference limit is unknown,
It need to estimate the boundary of interference.For the situation that interference limit is unknown, adaptive sliding mode fault-tolerant controller is designed.
S3, using the sliding formwork fault-tolerant controller and the adaptive law, according to current time collected quantity of state with
Track expectation displacement and desired speed.
Specifically, the displacement of train and speed signal are to obtain in real time during train operation.Current time adopts
The quantity of state collected can be understood as in train travelling process, the intermediate variable of internal system, characterize system motion state, be to use
The differential equation describes the mode of a control system.
Train model set includes: health model, parameterizes fault model, imparametrization fault model, interference limit not
The fault model known.
Health model are as follows:
Wherein, x1(t) be train displacement,x2(t) be train the speed of service,It is that the operation of train adds
Speed, a, b and c are the resistance coefficients of Davis equation.
Trailer system generates tractive force, can be considered the actuator of bullet train, by inverter, rectifier, PWMs (pulsewidth tune
System), the composition such as traction electric machine and relevant mechanical transmission mechanism.Consider that actuator is uncertain, tractive force Ft(t) dynamic mathematics
Model is Ft(t)=(1+ Δ f (t)) F (t)+Δ F (t).There is input saturation and dead zone phenomenon in actuator in bullet train.
Since braking system is in running order when trailer system starts, when engine work, tractive force is applied to train, can
To avoid input dead zone.In addition, the maximum speed allowed determines maximum drawbar pull and trailer system redundancy.And bullet train is not
It can work under input saturation, therefore the formula can indicate that most of actuator is uncertain.F (t) is the power that motor provides, Δ F (t)
It is to indicate the uncertain time-varying function of trailer system with Δ f (t).Δ F (t) and Δ f (t) bounded, boundary by maximum drawbar pull and
Mechanical device obtains.
The Longitudinal Dynamic Model of bullet train can be described as
Train weight is believed that is at each station
Different, and remained unchanged between two continuous stations, train weight can be described asM (t) is by arranging
The constant that vehicle load determines, Δ M (t) are constant between two stations, and are only stopping station change.Δ M (t) bounded and it can be estimated
Meter.D (t) simulates weather condition or rail conditions (ramp, tunnel
Road, curvature etc.) generate external disturbance.Since slope and warp rail can cause additional friction, for the high speed row for realizing train
It sails, railroad track need to be smooth, and the angle of gradient and curvature are smaller.Therefore, slope and bending resistance can be considered interference d (t),Δ m (t) andMeet 0≤Δ m (t)≤mb< m,mbWith dbIt is
Know constant and db> 0.
Tracking error e1(t), e2(t) are as follows:
e1(t)=x1(t)-yd(t)
e2(t)=x2(t)-xd(t)
Wherein, e1(t) be train displacement tracking error, e2(t) be train speed tracing error, x1It (t) is train
Displacement, xdIt (t) is desired speed, ydIt (t) is expectation displacement.Tracking error dynamic is obtained by train health model and tracking error
Equation are as follows:
Design sliding-mode surface is δ (e1,e2)=ke1(t)+e2(t), wherein k > 0 is design parameter.Health model sliding formwork control
Device structure are as follows:
WhereindbMeet
L (t) is non-negative time-varying gain, is met
Due to
Meet accessibility, therefore sliding formwork control ratio can drive system mode arrival predetermined in finite time when fault-free
Sliding-mode surface.Controller can guarantee healthy train system tracking error asymptotic convergence.
Parameterize fault model are as follows:
Wherein, x3It (t) is that train occurs to parameterize the displacement under fault condition,x4It (t) is that train parameterizes
The speed of service under fault condition,It is that train occurs to parameterize the operation acceleration under fault condition, wherein v (t) is to be
System input signal, kvFor remaining healthy amount controller, and meetξ andIt is to describe holding for fault type
Row device fault parameter. Wherein i=1 ..., n.Vector ξ can be with
Fault progression and change, but be in a certain time interval it is fixed, | | ξ | |2≤ξ0, ξ0It is known constant.It is by basis
The vector of signal composition,Basis letter
Number riρ(t) known.kν, ξ andIt determines which actuator has occurred failure and what type of failure occurs: breaking down
Before, kν=n, ξ=0；When actuator breaks down, kν, ξ is unknown constant.Indicate interference.
Displacement tracking error is e3(t):
e3(t)=x3(t)-yd(t)
e4(t)=x4(t)-xd(t)
Wherein, e3It (t) is that train occurs to parameterize the displacement tracking error under fault condition, e4It (t) is that speed tracing misses
Difference.x3It (t) is that train occurs to parameterize the displacement under fault condition, xdIt (t) is desired speed, ydIt (t) is expectation displacement.By arranging
Vehicle parameter fault model and displacement tracking error can obtain:
The parameter
Change fault model and controls signal ν1(t) are as follows:
Wherein,WithIt is respectivelyWithEstimated value, l (t) is non-negative time-varying gain.
0≤Δm(t)≤mb< m,
mbWith dbIt is known constant and db> 0.Failure actuator quantityMeetGain l (t) is controlled to meetWherein η > 0.
In the parametrization fault model, for arbitrary initial estimated valueWithParameterAdaptive law are as follows:
Wherein, adaptive law gainAndIt is normal number.N is the quantity of performer motor, gv(t) by
It is given below:
Wherein,
Select following Lyapunov equation:
Enable (Tp,Tp+1), p=0,1 ..., N, T0=0, it is time interval, actuator is only in time TpIt breaks down.It executes
Device fault mode be during this period of time it is fixed, this indicate ξ in t ∈ (Tp,Tp+1) be constant, and t ∈ [0, ∞) do not connect
It is continuous.To t ∈ (Tp,Tp+1), p=0,1 ..., N obtains V according to evaluated error and adaptive law2Time-derivative:
According to Lyapunov Stability Theorem, when parametrization failure occurs for actuator, closed-loop system evaluated error uniform bound.
Due to finite energy slip function
I.e.Then because control signal bounded, with and track error 0 can be converged to when t tends to be infinite.
Imparametrization fault model are as follows:
Wherein, x5(t) be train occur imparametrization fault condition under displacement,x6It (t) is that non-ginseng occurs for train
The speed of service under numberization fault condition,It is that operation acceleration under imparametrization fault condition, wherein v occur for train
It (t) is system input signal, kvFor remaining healthy amount controller, and meet n-n≤kv≤ n, ξ (t) are the events of bounded time-varying motor
Barrier.|ξ|≤ξ1, ξ1It is unknown.Indicate interference.
The imparametrization fault model controls signal ν2(t) are as follows:
Wherein, whereinL (t) is the increasing of non-negative time-varying
Benefit.WithIt is respectivelyWithEstimated value.
To initial estimation amountSignal v (t) andWithAdaptive law design are as follows:
V (t)=- r | δ (t) |
Wherein r > 0, adaptive law gain Γξ、For normal number, gv(t) it is given by:
Wherein,
Select following Lyapunov equation:
According to evaluated error and adaptive law, V is obtained3Time-derivative:
According to Lyapunov Stability Theorem, when parametrization failure occurs for actuator, controller state evaluated error unanimously has
Boundary, tracking error uniform bound.
The unknown fault model of interference limit are as follows:
Wherein, x7It (t) is that train occurs to parameterize the displacement under fault condition,x8It (t) is that train parameterizes
The speed of service under fault condition,It is that train occurs to parameterize the operation acceleration under fault condition, wherein v (t) is to be
System input signal, kvFor remaining healthy amount controller, and meetξ andIt is to describe holding for fault type
Row device fault parameter.Wherein i=1 ..., n.Vector ξ can
Change with fault progression, but be in a certain time interval it is fixed, | | ξ | |2≤ξ0, ξ0It is known constant.It is by base
The vector of plinth signal composition,
Basis signal .riρ
(t) known to.kν, ξ andDetermine which actuator has occurred failure and what type of failure occurs: before breaking down, kν
=n, ξ=0；When actuator breaks down, kν, ξ is unknown constant.Indicate interference.
The control signal ν of the interference limit unknown failure model3(t) are as follows:
Wherein,dbMeetmb< m.
Failure actuator quantityMeetL (t) is non-negative time-varying gain, is met
To initial estimation amountSignal v (t) andWithAdaptive law design are as follows:
Wherein r > 0, Γξ,For positive value, n is the quantity of performer motor, gvIt is given by:
Wherein,
Select following Lyapunov equation:
For fault mode fixed interval t ∈ (Tp,Tp+1), p=1 ..., N obtain V4Time-derivative:
According to Lyapunov Stability Theorem, when parametrization failure occurs for actuator, controller state evaluated error is unanimously steady
It is fixed, solve uniform bound.
Simulating, verifying is carried out to the fault-tolerant actuator of bullet train sliding formwork provided by the invention below:
Step 1, design train motion process, including accelerate, further accelerate, at the uniform velocity, slow down, slow down again, slow down to complete
Stop.
Train Parameters are selected as, a=8.63 × 10-3KN, b=7.295 × 10-6KNs/m, c=1.12 × 10-6KNs2/m2,Δ M (t)=20 (ton), Δ f (t)=1-e-0.05t, Δ F (t)=10sin (0.03t).
Step 2 is directed to bullet train health model, injection interference: d (t)=100sin (0.03t).
Primary condition is x (0)=[0.55 0]T, controller parameter k=8, l=0.8.
Step 3 parameterizes actuator failures model for bullet train, considers that event occurs for some motor in 16 motors
Barrier, is at the beginning constant value failure, then develop into time-varying failure, last motor stops working completely.It is given birth in failure expression formula strong
Health actuator quantity kv=15, fault parameter description are as follows:
Failure bound is ξ0=4 × 105。
Primary condition is x (0)=[0.55 0]T, parameter initial estimate is the 80% of nominal value, the gain of adaptive law
Value is 0.2, controller parameter k=8, l=1.
Step 4 is directed to bullet train imparametrization actuator failures model, considers that imparametrization time-varying failure, residue are strong
Health amount controller is kv=15, fault parameter ξ (t) is selected as ξ (t)=2 × 105sin(0.01t-30),t≥600。
Primary condition is x (0)=[0.05 0]T, parameter initial estimate is the 90% of nominal value, the gain of adaptive law
Value is 0.2, controller parameter k=12, l=2 and r=3.
Step 5 parameterizes failure and the unknown situation of interference limit for bullet train, in failure mode and step 3
Failure mode is identical:
In simulation process, the boundary of interference is unknown.Primary condition is x (0)=[0.1 0]T, parameter initial estimate is
The 90% of nominal value, the yield value of adaptive law are 0.2, controller parameter k=12, l=1 and r=2.
Obtained state-space model imported into Matlab/Simulink, and establishes in Simulink by step 6
Train traction system simulation model, when emulation, are 2000 seconds a length of.The segmented model of train health system known disturbances containing boundary
Displacement tracking figure is as shown in Figure 2.
Method of the invention can not known and failure feelings in actuator effectively known to Fig. 3 (a), (b), (c), (d)
Under condition, reach closed-loop stabilization and train progressive tracking characteristic, efficiently solves unknown parameter, imparametrization failure, interference is not
Train Fault-Tolerant Problems and its Practical problem when knowing, this and failure uncertain for solution bullet train actuator
Problem has great importance.
It is well known that input saturation, dead zone and lag are to lead to actuator not when input signal is limited and bounded
Deterministic common reason.And the internal uncertain outside that is different from is uncertain in system modelling, because system mode
Boundedness needs are guaranteed by the design of controller, are commonly used in designed controller, and cannot presuppose bounded.Although
The actuator of bullet train has input saturation and dead zone, but the uncertainty from electrical equipment and mechanical device, including one
A little dynamic characteristics still will affect input distribution matrix.On the other hand, faults-tolerant control is a kind of necessary and effective technology, can be
Guarantee the stability or certain control performances (such as progressive tracking) of system under conditions of the system failure.Although for uncertain system
Fault diagnosis or faults-tolerant control have been achieved for many achievements, but it is suitable to probabilistic research in input distribution matrix
It is limited.For failure system, fault-signal can regard unknown parameter as.In the case, adaptive technique can be used to handle unknown
Parameter simultaneously obtains ideal performance.This method is suitable for bullet train failure.
The present invention is directed to containing the uncertain bullet train with failure of unknown actuator, and it is sliding to propose a kind of NEW ADAPTIVE
Mould faults-tolerant control scheme.In addition to providing the model under train health status, while there is parametrization for bullet train and executing
Device failure, situations such as imparametrization actuator failures and interference limit is unknown, establish a variety of train models.To healthy train
System devises sliding mode controller to guarantee tracking error dynamical equation energy asymptotic convergence.Also appearance parametrization is executed simultaneously
Device failure, situations such as imparametrization actuator failures and interference limit is unknown, devise adaptive sliding mode fault-tolerant controller.This
Invention combining adaptive technology proposes adaptive sliding mode faults-tolerant control scheme while handling actuator uncertainty and failure.
Adaptive sliding mode fault-tolerant controller can be uncertain under fault condition in unknown actuator, and bullet train is made to reach closed-loop stabilization
With progressive tracking characteristic.
The invention discloses with the uncertain bullet train adaptive sliding mode faults-tolerant control scheme of actuator, in actuator
Under condition of uncertainty, the Longitudinal Dynamic Model of bullet train is proposed；For the uncertain health with external disturbance of actuator
System devises a kind of novel sliding mode controller, can drive tracking error dynamical system to preset cunning in finite time
In die face, and sliding formwork movement is kept hereafter；Respectively for known fault boundary, unknown failure boundary and imparametrization event
The train model of barrier proposes NEW ADAPTIVE sliding formwork fault-tolerant controller, thus alleviate bullet train trailer system actuator failures and
Uncertain problem.
All the embodiments in this specification are described in a progressive manner, same and similar portion between each embodiment
Dividing may refer to each other, and each embodiment focuses on the differences from other embodiments.Especially for equipment reality
For applying example, since it is substantially similar to the method embodiment, so describing fairly simple, related place is referring to embodiment of the method
Part explanation.The above description is merely a specific embodiment, but protection scope of the present invention is not limited to
This, anyone skilled in the art in the technical scope disclosed by the present invention, the variation that can readily occur in or replaces
It changes, should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claim
Subject to enclosing.
Claims (6)
1. a kind of adaptive sliding mode fault tolerant control method for bullet train characterized by comprising
According to train runing parameters collected, selection matches the train mould of the train runing parameters from train model set
Type；
Obtain the corresponding sliding formwork fault-tolerant controller of selected train model and adaptive law；
Using the sliding formwork fault-tolerant controller and the adaptive law, according to current time collected quantity of state tracking expectation position
Shifting and desired speed.
2. the method according to claim 1, wherein the train model set includes at least: health model, ginseng
Numberization fault model, imparametrization fault model and the unknown fault model of interference limit.
3. according to the method described in claim 2, it is characterized in that, the health model indicates are as follows:
Wherein:
x1(t) be train displacement,
The derivative of the displacement of train,
x2(t) be train the speed of service,
It is the operation acceleration of train,
A, b and c respectively indicate three kinds of resistance coefficients in Davis equation, and a indicates the rolling resistance of train, and rolling resistance is by going
Journey, rolling and track resistance composition；B indicates the linear resistance of train, and linear resistance is by wheel rim friction, wheel rim impact, wheel track
The wave action of rolling resistance and track forms；C indicates non-linear resistance, and non-linear resistance is by tail portion resistance, head end wind pressure, column
Turbulent flow, wind-tunnel yaw angle and the frictional force of the train side composition in workshop.
Tractive force Ft(t) dynamic mathematical models are Ft(t)=(1+ Δ f (t)) F (t)+Δ F (t),
F (t) is the power that motor provides,
Δ F (t) and Δ f (t) is to indicate the uncertain time-varying function of trailer system, wherein Δ F (t) and Δ f (t) bounded, boundary
It is obtained by maximum drawbar pull and mechanical device, Δ f (t) indicates the multiplying property disturbance of tractive force, and Δ F (t) indicates additive disturbance；
Train weight is expressed asWherein, M (t) is the constant determined by train load,Indicate empty wagons
Quality, Δ M (t) expression make the increased load quality of unladen vehicle weight, are constant between two stations,
D (t) indicates external disturbance,
Δ m (t) andMeet 0≤Δ m (t)≤mb< m,mbWith dbRespectively indicate m withBoundary be
Know constant and db> 0；
It is described that displacement and desired speed it is expected according to current time collected quantity of state tracking, comprising:
The tracking error of train is expressed as e1(t) and e2(t):
e1(t)=x1(t)-yd(t)
e2(t)=x2(t)-xd(t)
Wherein, e1(t) be train displacement tracking error, e2(t) be train speed tracing error, x1(t) be train position
It moves, x2(t) be train speed, xdIt (t) is desired speed, ydIt (t) is expectation displacement,
Tracking error dynamical equation is obtained by train health model and tracking error are as follows:
Design sliding-mode surface is δ (e1,e2)=ke1(t)+e2(t), wherein k > 0 is design parameter, then is loaded with the health model
The sliding mode controller are as follows:
Wherein,dbMeetmb< m, l (t)
It is non-negative time-varying gain, meets
4. according to the method described in claim 2, it is characterized in that, the parametrization fault model are as follows:
Wherein, x3It (t) is that train occurs to parameterize the displacement under fault condition,
It is x3(t) derivative, x4It (t) is that train occurs to parameterize the speed of service under fault condition,
It is that train occurs to parameterize the operation acceleration under fault condition,
V (t) is system input signal,
kvFor remaining healthy amount controller, and meet
ξ andIt is the actuator failures parameter for describing fault type,
Wherein,Indicate the vector being made of basis signal, kνFault mode parameter, with ξ andWhich actuator determined
Failure has occurred and what type of failure occurs.When actuator breaks down, kν, ξ is unknown constant；Before breaking down, kν=
N, ξ=0.When an error occurs, ν (t) is the control signal designed according to Fault Compensation, for guaranteeing the stability and gradually of system
Into tracking performance,Indicate interference；
It is described that displacement and desired speed it is expected according to current time collected quantity of state tracking, comprising:
The tracking error of train is expressed as e3(t):
e3(t)=x3(t)-yd(t)
e4(t)=x4(t)-xd(t)
Wherein, e3It (t) is that train occurs to parameterize the displacement tracking error under fault condition, e4It (t) is speed tracing error, x3
It (t) is that train occurs to parameterize the displacement under fault condition, xdIt (t) is desired speed, ydIt (t) is expectation displacement, by Train Parameters
Changing fault model and displacement tracking error can obtain:
The parametrization fault model controls signal ν1(t) are as follows:
Wherein,WithIt is respectivelyWithEstimated value, l (t) is non-negative time-varying gain,mbWith db
It is known constant and db> 0, failure actuator quantityMeetGain l (t) is controlled to meet
Wherein, η > 0, in the parametrization fault model, for arbitrary initial estimated valueWith
In the case where being then loaded with the parametrization fault model, signalAdaptive law are as follows:
Wherein, adaptive law gainAndIt is normal number, n is the quantity of performer motor, gv(t) by following formula
It provides:
Wherein,
5. according to the method described in claim 2, it is characterized in that, the imparametrization fault model are as follows:
Wherein, x5(t) be train occur imparametrization fault condition under displacement,
x6(t) be train occur imparametrization fault condition under the speed of service,
It is the operation acceleration under train generation imparametrization fault condition,
V (t) is system input signal,
kvFor remaining healthy amount controller, and meet
ξ (t) is bounded time-varying electrical fault, | ξ |≤ξ1, ξ1It is unknown,Indicate interference；
It is described that displacement and desired speed it is expected according to current time collected quantity of state tracking, comprising:
The tracking error of train is expressed as e5(t):
e5(t)=x5(t)-yd(t)
e6(t)=x6(t)-xd(t)
Wherein, e5It (t) is that train occurs to parameterize the displacement tracking error under fault condition, e6It (t) is speed tracing error, e5
It (t) is that train occurs to parameterize the displacement under fault condition, xdIt (t) is desired speed, ydIt (t) is expectation displacement, by Train Parameters
Changing fault model and displacement tracking error can obtain:
The imparametrization fault model controls signal ν2(t) are as follows:
Wherein,L (t) is non-negative time-varying gain,WithIt is respectivelyWithEstimated value, to initial estimation amountIt is then loaded with described
In the case where imparametrization fault model, signal v (t),WithAdaptive law design are as follows:
V (t)=- r | δ (t) |
Wherein r > 0, adaptive law gain Γξ、For normal number, gv(t) it is given by:
Wherein,
6. according to the method described in claim 2, it is characterized in that, the unknown fault model of the interference limit are as follows:
Wherein, x7It (t) is that train occurs to parameterize the displacement under fault condition,
x8It (t) is that train occurs to parameterize the speed of service under fault condition,
It is that train occurs to parameterize the operation acceleration under fault condition,
V (t) is system input signal,
kvFor remaining healthy amount controller, and meet
ξ andIt is the actuator failures parameter for describing fault type, Wherein i=1 ..., n, vector ξ can change with fault progression, but between certain time
Every it is interior be it is fixed, | | ξ | |2≤ξ0, ξ0It is known constant,
Wherein,The vector being made of basis signal, kνFault mode parameter, with ξ andWhich actuator hair determined
It has given birth to failure and what type of failure occurs.When actuator breaks down, kν, ξ is unknown constant；Before breaking down, kν=n,
ξ=0.When an error occurs, ν (t) is the control signal designed according to Fault Compensation, for guaranteeing the stability of system and progressive
Tracking performance.Indicate interference；
It is described that displacement and desired speed it is expected according to current time collected quantity of state tracking, comprising:
The control signal ν of the interference limit unknown failure model3(t) are as follows:
Wherein,dbMeetTherefore
Hinder actuator quantityMeetL (t) is non-negative time-varying gain, is metTo first
Beginning estimatorIn the case where being then loaded with the unknown fault model of the interference limit, signal v (t),WithAdaptive law design are as follows:
Wherein r > 0, Γξ,For positive value, n is the quantity of performer motor, gvIt is given by:
Wherein,
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