CN107390517A - Robust adaptive non-singular terminal sliding-mode control for train ATO systems - Google Patents
Robust adaptive non-singular terminal sliding-mode control for train ATO systems Download PDFInfo
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Abstract
The present invention discloses a kind of robust adaptive non-singular terminal sliding-mode control for train ATO systems, including：S1, analysis Train's Longitudinal Movement carry out stressing conditions, establish the Train's Longitudinal Movement kinetic equation for including unknown parameter, uncertainty and external disturbance；S2, position tracking error, speed tracing error and acceleration tracking error are defined, construct non-singular terminal sliding-mode surface；S3, the adaptive law of each unknown parameter estimate of design and non-singular terminal sliding-mode surface control strategy；S4, the control strategy substitution Train's Longitudinal Movement kinetic equation by non-singular terminal sliding-mode surface, the adaptive law of each unknown parameter estimate and non-singular terminal sliding-mode surface, non-singular terminal sliding formwork closed-loop control equation is obtained, is controlled using non-singular terminal sliding formwork closed-loop control equation.The present invention can enable the tracking error of the position and speed of train ATO systems reach slidingsurface in finite time, and in Finite-time convergence to zero.
Description
Technical field
The present invention relates to Train Control Technology field.It is adaptive more particularly, to a kind of robust for train ATO systems
Answer non-singular terminal sliding-mode control.
Background technology
Modern railways traffic system adheres to target that is fast-developing and meeting great demand, pursues higher train speed
It is very urgent and inevitable.Current train automatically controls (ATC) system and is mainly made up of following three subsystems, that is, arranges
Car automatic running (ATO) system, time interval between to trains (ATP) system and train automatic monitoring (ATS) system.Wherein, train ATO
System can control all stages of train operation, such as automatic start, accelerate, and cruise, braking, accurate parking, interim between standing
Parking, auto-returned etc..Therefore, train ATO systems play vital effect in the performance of ATC trains, by theory
With the great attention of the researcher of engineering field, the discovery of many efficient algorithms, such as Self Adaptive Control, Fuzzy Control are promoted
System, robust control etc..
However, the uncertainty of model and do not model caused external disturbance, up/down car passenger, weather condition (strong wind and
Shower), and the key factor of train operation, such as slope are deeply paid close attention to.Therefore, it is necessary to moved with reference to longitudinal train
Mechanics develops a kind of control method for the robustness and other performances for being adapted to ensure that above-mentioned factor.
On the other hand, it is well known that sliding formwork control has to Parameters variation, and system model is uncertain and disturbs insensitive
The characteristics of.And many documents have been presented for being related to some important process and achievement of sliding formwork control.In the past few decades
In, sliding mode control strategy is largely applied in systems in practice, such as robotic manipulator, gyroscope and power system.
And the shape of sliding surface determines whether the dynamic property of corresponding System with Sliding Mode Controller is good.Phadke proposes linear slide face
Although controller can ensure the final stable convergence of system in equalization point, but be in Infinite Time, so in order to overcome
This shortcoming of linear sliding mode, it is proposed that Nonlinear Sliding face controls.In recent years, the TSM with Nonlinear Sliding surface is controlled
It may insure that the state of resulting closed-loop system can be in Finite-time convergence to equalization point, therefore received greatly
Concern.However, its singularity problem may be drawn in the case where not providing primary condition suitably, do not have also particularly
The correlative study achievement of robust NTSM control problems in the case of Train Parameters and the normal bounded of sliding surface parameter.
Accordingly, it is desirable to provide a kind of robust adaptive non-singular terminal sliding-mode control for train ATO systems.
The content of the invention
It is an object of the invention to provide a kind of robust adaptive non-singular terminal sliding formwork control for train ATO systems
Method, to solve the position of train ATO systems and speed under the influence of unknown parameter, model uncertainty and external disturbance
Tracking control problem.
To reach above-mentioned purpose, the present invention uses following technical proposals：
A kind of robust adaptive non-singular terminal sliding-mode control for train ATO systems, comprise the following steps：
S1, analysis Train's Longitudinal Movement carry out stressing conditions, establish comprising unknown parameter, uncertainty and external disturbance
Train's Longitudinal Movement kinetic equation；
S2, position tracking error, speed tracing error and acceleration tracking error are defined, construct non-singular terminal sliding formwork
Face；
S3, the adaptive law of each unknown parameter estimate of design and non-singular terminal sliding-mode surface control strategy；
S4, by non-singular terminal sliding-mode surface, the adaptive law of each unknown parameter estimate and non-singular terminal sliding-mode surface
Control strategy substitutes into the Train's Longitudinal Movement kinetic equation for including unknown parameter, uncertainty and external disturbance, obtains nonsingular
Terminal sliding mode closed-loop control equation, the robust for train ATO systems is carried out using non-singular terminal sliding formwork closed-loop control equation
Adaptive non-singular terminal sliding formwork control.
Preferably, train of the foundation comprising unknown parameter, uncertainty and external disturbance established in step S1 is longitudinally transported
Dynamic kinetic equation is：
Wherein, m is unknown train gross mass；For the speed of train；For the acceleration of train；U is unknown train
Required longitudinally controlled power；c0、cvAnd caFor the unknown coefficient for wearing dimension equation；θ is the gradient of train operation track；And meetD represents outside
Interference, Δ m, Δ ca、ΔcvM, c are represented respectively with Δ coa, cvAnd coUncertainty, b0>0, b1>0, b2>0, b3>0 and b0、b1、
b2And b3It is unknown parameter.
Preferably, step S2 detailed process is：
Defining site error, velocity error and acceleration error is：
E=x-xr
Wherein, xr、WithThe respectively desired locations of train operation, desired speed and expectation acceleration.
Design non-singular terminal sliding-mode surface：
Wherein, β is positive parameter to be designed；P and q is respectively positive odd number, and is met
Preferably, step S3 detailed process is：
Design the adaptive law of each unknown parameter estimate：
Wherein, km、ko、kvAnd kaIt is positive parameter to be designed；
Design the control strategy of non-singular terminal sliding-mode surface：
U=u1+u2+u3+u4
Wherein, ks2For normal number to be designed；WithRespectively unknown parameter co、cυ、caWith estimating for m
Evaluation；
Preferably, the non-singular terminal sliding formwork closed-loop control equation obtained in step S4 is：
Beneficial effects of the present invention are as follows：
1st, the present invention can effectively eliminate singularity caused by the TSM control with Nonlinear Sliding face.
2nd, the present invention is capable of the influence of effective compensation unknown parameter, model uncertainty and external disturbance
3rd, the present invention can apply enables the tracking error of the position and speed of train ATO systems having in train ATO systems
Interior arrival slidingsurface in limited time, and in Finite-time convergence to zero.
Brief description of the drawings
The embodiment of the present invention is described in further detail below in conjunction with the accompanying drawings；
Fig. 1 shows the flow chart of the robust adaptive non-singular terminal sliding-mode control for train ATO systems.
Fig. 2 shows that displacement curve schematic diagram it is expected in train operation.
Fig. 3 shows displacement error response curve schematic diagram.
Fig. 4 shows velocity error response curve schematic diagram.
Fig. 5 shows the schematic diagram of control input.
Fig. 6 shows unknown parameter co、cυ、caWith m estimate schematic diagram.
Embodiment
In order to illustrate more clearly of the present invention, the present invention is done further with reference to preferred embodiments and drawings
It is bright.Similar part is indicated with identical reference in accompanying drawing.It will be appreciated by those skilled in the art that institute is specific below
The content of description is illustrative and be not restrictive, and should not be limited the scope of the invention with this.
As shown in figure 1, the robust adaptive non-singular terminal sliding formwork control side disclosed by the invention for train ATO systems
Method, comprise the following steps：
S1, analysis Train's Longitudinal Movement carry out stressing conditions, establish comprising unknown parameter, uncertainty and external disturbance
Train's Longitudinal Movement kinetic equation；
S2, position tracking error, speed tracing error and acceleration tracking error are defined, construct non-singular terminal sliding formwork
Face；
S3, the adaptive law of each unknown parameter estimate of design and non-singular terminal sliding-mode surface control strategy；
S4, by non-singular terminal sliding-mode surface, the adaptive law of each unknown parameter estimate and non-singular terminal sliding-mode surface
Control strategy substitutes into the Train's Longitudinal Movement kinetic equation for including unknown parameter, uncertainty and external disturbance, obtains nonsingular
Terminal sliding mode closed-loop control equation, the robust for train ATO systems is carried out using non-singular terminal sliding formwork closed-loop control equation
Adaptive non-singular terminal sliding formwork control.
Wherein,
Step S1 detailed process is：
Consider due to complex state caused by a variety of causes possibility in train travelling process, therefore train ATO systems are realized
Be extremely complex nonlinear Control problem.The stressing conditions of Train's Longitudinal Movement are analyzed based on this, establish train longitudinal direction
The kinetic equation of motion：
Wherein, m is the unknown train gross mass for including passenger mass in train body quality and train；X is train
Position；For the speed of train；For the acceleration of train；V is the longitudinal velocity of train；U is the longitudinal direction needed for unknown train
Controling power；
f1For by rolling machine resistance fmWith aerodynamic resistance faThe train running resistance of composition, it can be described as：
f1=fm+fa
Wherein, c0、cvAnd caFor the unknown coefficient for wearing dimension equation；
f2For the slope resistance as caused by slope, can be described as：
f2=mgsin θ
Wherein, g represents acceleration of gravity, and θ is the gradient of train operation track.
Consider the uncertainty and external disturbance of unknown parameter, the kinetic equation of Train's Longitudinal Movement is described as：
Wherein, d represents external disturbance；Δm、Δca、ΔcvWith Δ coM, c are represented respectivelya, cvAnd coUncertainty.It is logical
Cross definitionAnd meet following condition：
Wherein, b0>0, b1>0, b2>0, b3>0 and b0、b1、b2And b3It is unknown parameter.
Therefore, the kinetic equation of the Train's Longitudinal Movement comprising unknown parameter, uncertainty and external disturbance is：
Step S2 detailed process is：
Defining site error, velocity error and acceleration error is：
E=x-xr
Wherein, xr、WithThe respectively desired locations of train operation, desired speed and expectation acceleration.
Design non-singular terminal sliding-mode surface：
Wherein, β is positive parameter to be designed；P and q is respectively positive odd number, and is met
Step S3 detailed process is：
Design the adaptive law of each unknown parameter estimate：
Wherein, km、ko、kvAnd kaIt is positive parameter to be designed；
Design the control strategy of non-singular terminal sliding-mode surface：
U=u1+u2+u3+u4
Wherein, ks2For normal number to be designed；WithRespectively unknown parameter co、cυ、caWith estimating for m
Evaluation；
The non-singular terminal sliding formwork closed-loop control equation obtained in step S4 is：
Non-singular terminal sliding formwork closed loop control disclosed by the invention is proved below by Lyapunov (Liapunov) function
The validity of equation processed.
Construct following Lyapunov functions：
Wherein,
Over time, V2It can derive as following form:
Designed control strategy u and Self Adaptive Control rate are substituted into above formula, can be obtained：
By the way that the adaptive law of design is included in above formula, it can be deduced that conclusion：
The position tracking error e and speed tracing error of train ATO systemsCan Finite-time convergence to zero and
Sliding surface is reached under arbitrary primary condition.
In order to verify the robust adaptive non-singular terminal sliding-mode control disclosed by the invention for train ATO systems
Validity, using MATLAB carry out emulation experiment checking, describe in detail it is as follows.
In emulation experiment, total travel distance 41.991km, train gross mass m=5 × 105Kg, gravity acceleration g=
9.8N/kg, Davis's coefficient co=m × 0.01176N/kg, ca=1.6 × 10-5N·s2/(m2Kg), cv=m × 7.7616
×10-4Ns/ (mkg), disturbance d meet following expression：
dωe+ωs+ωr
Wherein, ωr、ωsAnd ωeResistance due to curvature, tunnel resistance and other resistances are represented respectively.
ωr、ωsValue it is as follows：
ωr=10.5 αrmg/(1000lr)
ωs=0.00013lsmg/103
Wherein, ls=1000m is length of tunnel, lr=200m is length of curve,It is the central angle of curve.It is false
Determine ωe=sin ((0.01+0.1*rand) t.It is assumed that road slopeParameter uncertainty Δ m=1000*
Rand, Δ co=200*rand, Δ ca=0.2*rand, Δ cvWhat=30*rand. wherein rand were represented is the random of [0,1]
Value.
The purpose of the present invention is that the suitable control algolithm of design meets that train physical location and speed can track required position
The requirement with speed is put, as shown in Figure 2.When carrying out emulation experiment, the original state of setting is x (0)=[2.5 0]T.Control
Device parameter is ks2=107, H0=105.The parameter of sliding surface is β=1.6, p=77, q=79.With reference to the Parameter uncertainties of setting
Property and external disturbance numerical value can calculate
b0=104,b1=30, b2=0.2, b3=103.And select km=1, k0=10, kv=0.1, ka=0.01, δ1=2,
δ2=8.5
Based on above-mentioned parameter and the desired positions of Fig. 2 and speed tracing curve, control strategy proposed by the present invention is entered
Go checking, draw Fig. 3-6 simulation result.What wherein Fig. 3 and Fig. 4 was shown respectively is in designed controller and adaptive law
The displacement of lower control and velocity error track, and demonstrate the validity of control measurement proposed by the invention；Fig. 5 shows system
Control input curve；Fig. 6 is shown to unknown parameter co、cυ、caWith m estimation.Analogous diagram 3-6 shows that the present invention discloses
The robust adaptive non-singular terminal sliding-mode control for train ATO systems validity.
Obviously, the above embodiment of the present invention is only intended to clearly illustrate example of the present invention, and is not pair
The restriction of embodiments of the present invention, for those of ordinary skill in the field, may be used also on the basis of the above description
To make other changes in different forms, all embodiments can not be exhaustive here, it is every to belong to this hair
Row of the obvious changes or variations that bright technical scheme is extended out still in protection scope of the present invention.
Claims (5)
1. a kind of robust adaptive non-singular terminal sliding-mode control for train ATO systems, it is characterised in that including such as
Lower step：
S1, analysis Train's Longitudinal Movement carry out stressing conditions, establish the train for including unknown parameter, uncertainty and external disturbance
Lengthwise movement kinetic equation；
S2, position tracking error, speed tracing error and acceleration tracking error are defined, construct non-singular terminal sliding-mode surface；
S3, the adaptive law of each unknown parameter estimate of design and non-singular terminal sliding-mode surface control strategy；
S4, the control by non-singular terminal sliding-mode surface, the adaptive law of each unknown parameter estimate and non-singular terminal sliding-mode surface
Strategy substitutes into the Train's Longitudinal Movement kinetic equation for including unknown parameter, uncertainty and external disturbance, obtains non-singular terminal
Sliding formwork closed-loop control equation, carried out using non-singular terminal sliding formwork closed-loop control equation adaptive for the robust of train ATO systems
Answer non-singular terminal sliding formwork control.
2. the robust adaptive non-singular terminal sliding-mode control according to claim 1 for train ATO systems, its
It is characterised by, the Train's Longitudinal Movement power that the foundation established in step S1 includes unknown parameter, uncertainty and external disturbance
Equation is：
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b2And b3It is unknown parameter.
3. the robust adaptive non-singular terminal sliding-mode control according to claim 2 for train ATO systems, its
It is characterised by, step S2 detailed process is：
Defining site error, velocity error and acceleration error is：
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4. the robust adaptive non-singular terminal sliding-mode control according to claim 3 for train ATO systems, its
It is characterised by, step S3 detailed process is：
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2
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