WO1997010983A1

WO1997010983A1 - Process for finding data for the control of rail vehicles

Info

Publication number: WO1997010983A1
Application number: PCT/DE1996/001631
Authority: WO
Inventors: Martin Witte
Original assignee: Siemens Aktiengesellschaft
Priority date: 1995-09-21
Filing date: 1996-09-02
Publication date: 1997-03-27
Also published as: DE19535122C1

Abstract

Data for controlling the running behaviour of rail vehicles (Fi) are found by measuring the acceleration curve (ai(vi)) for each vehicle, deriving speeds (vi(t)) therefrom and storing them. Changes in the 'normal curve' (ai(vi)) in speed approximation intervals ([vi1, vi1+1]) are approximated by approximation factors (pi1) in which the causes of the changes are taken into account, in that the approximation factors (pi1) are linked to the acceleration curve (ai(vi)) in the relevant speed approximation interval ([vi1, vi1+1]). It is thus unnecessary to resolve each time the speed differential equations and the rail vehicle (Fi) can be rapidly controlled.

Description

description

Method for determining data for regulating track-bound vehicles

When regulating track-bound vehicles and networks of track-bound vehicles, the fast and sufficiently precise calculation of the driving dynamics behavior of the individual vehicles is a central problem.

The driving dynamic behavior, possibly including the energy requirement of the individual track-bound vehicles, must be calculated in advance in order to be able to calculate optimal driving curves both in terms of energy and time. This is particularly important in automatic vehicles from a safety-technical point of view, that is to say, for example, the determination of the braking distance or also the determination of data for precise braking.

It is known to piece the route traveled by the track-bound vehicles and to linearize the movement of the track-bound vehicle with the assumption of constant acceleration for each section of the route to be traveled. The movement data is then calculated successively along the route to be traveled (turning, driving dynamics, transpress VΞ3 Verlag für Verkehrswesen, Berlin, 2nd edition, ISBN 3-344-00363-1, 1990, pp. 15 to 17).

The method leads to high computing times, which is a considerable disadvantage of the method described. Another disadvantage of this method is that initial errors in the data determination relate to the errors in the determination of the movement data when the distances are distant. impact sections, whereby the errors accumulate.

The invention is based on the problem of specifying a method with which movement data for regulating track-bound vehicles are determined, the determination of the data should be able to be carried out more quickly than is possible with the known method.

In the method according to the invention, the acceleration is measured as a function of the speed of a vehicle. Using this differential motion equation, the speed behavior is determined as a function of time. From this all further equations of motion, e.g. the acceleration, depending on the time, or the distance traveled, depending on the time, determines.

These equations are only solved once for each track-bound vehicle.

Changes that e.g. by changing the roadway or by changing the mass of the vehicle, e.g. B. caused by loading or by admitting passengers are taken into account in approximation factors and summarized. The approximation factors are easily determinable and are each determined for arbitrarily small selectable speed intervals or also for several speed intervals. For selectable parts of the speed intervals, the approximation factor is now linked to the originally determined motion equations, so that an approximated equation of motion arises. The approximated equations of motion approximate the "normal solution" very well, taking into account the changes described above.

It can be seen from this that the main advantage of the method is that the changes in the driving A very approximating solution, which takes into account, can be determined very quickly, thus enabling fast and reliable control of the vehicles.

Further developments of the invention result from the dependent claims.

Some typical exemplary embodiments are shown in the figures and are described in more detail below.

FIG. 1 shows a flow chart describing individual method steps of the method according to the invention;

FIG. 2 shows a sketch in which the various possibilities for forming the approximation integrals described below are shown;

Figure 3 is a sketch showing various ways of forming the approximation factors.

The method is explained further with reference to FIGS. 1 to 3.

In Figure 1, the process is shown in its individual process steps in the form of a flow chart.

In a first step 1, movement variables ai (v) are determined for track-bound vehicles Fi. A first index i clearly identifies a vehicle type with the same driving characteristics. The index i is an arbitrary natural number.

The motion variables ai (v), which in each case depend on the acceleration behavior of the track-bound vehicles Fi describe gig of all possible speeds v _{λ of} the various track-bound vehicles F _x , measured.

This is usually done on the basis of the examination of an empty, that is to say unloaded, track-bound vehicle F _x on a flat, straight, windless route, taking into account the driving resistance that occurs.

Further resistances, such as the inclination of the route or the payload, are taken into account in further steps, as will be described below.

Movement differential equations are used to determine speeds v ₂ (t) of the individual track-bound vehicles F _x , depending on a time t

v _χ (t) = a _χ (v)

of the individual track-bound vehicles F _λ solved (step 2).

The result obtained is the dependence of the speed v _x (t) of the track-bound vehicles F _x on the time t, thus the speed profile of the respective track-bound vehicle F _x when the track-bound vehicle F _x starts with an initial speed vo = 0 at an initial time t ₀ = 0.

The determined speeds v _x (t) of the track-bound vehicles F _λ are stored in a memory of a computer (step 3).

From these velocities v _x (t) further equations of motion can be determined, for example by differentiating the velocities v _x (t) an acceleration a ± (t) of the respective track-bound vehicle F _λ depending on the Time t at the start of the track-bound vehicle F _x with the starting speed vo = 0 at the starting point in time to = 0.

The determination of the further movement equations takes place as a function of the information required to control the track-bound vehicles F _x and differs from case to case.

Further movement equations, such as the dependence of the path s _x (t) on the time t at the start of the track-bound vehicles F _λ with the initial speed vo = 0 at the initial time tn = 0, are also to be calculated. A further equation of motion represents the dependence of the path s _x (v) on the speeds v _x , ie the acceleration path of the track-bound vehicle F _x , which is required for an acceleration from an initial acceleration ao = 0 to the respective speed v _x becomes.

Also, the acceleration tent t _x (v), which for the acceleration of the track-bound vehicles F _λ of a Anfangsge ^¬ speed V _Q = 0 on the respective speed v -, _ is needed, provides such a motion equation represents.

The motion differential equations a _x (v) are given, for example, in the form of n support points. These support points form the speed intervals [v ₁ - ₎ , V- _L -J + I.], Which are determined in accordance with the required accuracy of the approximation (step 4), as will be described below.

Here again, the first index I denotes the respective vehicle type F _λ and em second index j denotes a polygon course, that is to say unambiguously, a speed interval. The polygons in the respective speed interval have the form c ₁ - _] v ₁ + d _η , so they are linear. The constants c- _j and d- _j are general constants for solving differential equations. Furthermore, the motion differential equations a _x (v) can be represented not only in m polygon courses, but also in the form of an explicit function or m in the form of so-called splmes, i.e. m in the form of quadratic polynomials, which smooth the motion differential equations a _η (v ) at the n support points.

In the following, however, the exemplary embodiment is only explained further on the basis of speed intervals which are represented in polygon courses, in order to simplify the illustration. However, the further steps of the method can also be carried out unchanged when using splmes to represent the motion differential equations a _x (v) or an explicit representation.

In the following derivation, the first index I is omitted, since the solution is explained using only one track-bound vehicle F- _L . Of course, this does not in any way limit the generality of the following formulas.

In the event that the constant Cη is not equal to 0, the solution to the equation of motion differential a (v) is:

This results from simple integration, differentiation or by using movement equations for each other for the further movement equations:

^k ic _n td _{η 2} s (t) = - ^ e ³ - ^ t + k ^ ^c 3 ^c 3 ³

The equation of motion v (s) cannot be represented explicitly, but must be determined numerically from the equation of motion s (v). The Newton method described in (J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Springer Verlag, ISBN 0-387-90420-4, pp. 244-252, 1980) can be used, for example. Other possible methods are also given in this reference.

The constants k ¹ and k ^ are successively determined from the initial values:

The times tη are the times at which the track-bound vehicle reaches the speed V _η . This happens at a point s ₃ .

If the constant c-, equals 0, there is another solution for the motion equations:

v (t! d ₃ t ₊ k ^

t (v: v ^d D

The constants k 3 and k4 are in turn successively derived from the

Initial values determined in the following way:

^k j ³ = ^V D - (^ j)

s

The total motion equations are then composed of the solutions of the equations of motion in the respective speed intervals.

This method described in the above only has to be determined once for each movement quantity a _x (v) of a track-bound vehicle F _λ . Since these are very complex in the solution method described above, the method according to the invention, as will be described in the following, enables the method to be carried out very quickly, since it is always based on the variables determined in the previous, that are stored in a memory of the computer performing the method can be stored (step 3), can be used.

If the actual driving behavior of the track-bound vehicles F _λ changes, this change is determined by approximation factors p _{x are} taken into account. If the approximation factors p _x are determined with sufficient accuracy so that they reproduce the actual changes sufficiently well, then the new lots of the motion differential equations that are actually always necessary can be avoided.

This is understandable, because if, for example, the speeds v _x (t) are solutions of the differential motion equations dv _x / dt = a _x (v), then obviously v _x (t, p _x ): = v _x (t • p _x ) Solutions of the motion differential equations dv _x / dt = p _x • a _x (v). These are independent of the special form of the motion differential equations a _x (v).

In this case, the following also applies to the other equations of motion:

^a ι (t 'Pi) = Pi * a _x (t ^• p _x )

_/ , _\ a ₁ (t »p) Pi

t (v _χ ) t (v _{1 / Pl} )

This "global approximation factor p _x " considered up to now is, of course, considered when looking at speed intervals [v _{1 ±} , v _{lx + 1} ] to approximation factors p _x χ, each for each speed approximation interval [v _x χ, v _x χ ₊ χ] be recalculated.

The approximation factors p _xl are each for freely selectable approximation speed intervals [v _lx , v _x ] _ ₊ χ] determined. The speed approximation intervals [v _xl , ^v ιl + l] do not have to match the speed intervals [v _x - _j , v _X η ₊₁ ] described above. They can differ from one another in any way and overlap.

Em index 1 is any natural number and uniquely identifies each speed approximation interval I ^v ιl- ^v ιl + ll.

There are the Approximationsfaktoren p _xl formed which 'the manner ^ιn with a change in movement Great a _x (v) m motion Great ^a ιll ^(v, the actual change in the Bewegungs¬ a large _x (v) approximated that:

Pil • ^a ι ( ^v ) ~ ^a ιll ( ^v ) ^ιn the respective speed approximation interval [v _xx , v _x χ + ι].

The speed approximation interval [v _xx , v _x ] _ _{+ x} ] can be subdivided further and further depending on the required goodness of the approximation. In this way, explicit access to the driving dynamics variables of interest is gained and there is no need for iterative approximations. The lower the speed approximation intervals [v _xl , v _{xl + I} ], the more precise the approximation will of course be. However, this also increases the computing time required for the computers required to determine α approximation.

Different possibilities are used to form the approximation factors p _xx m different variants of the exemplary embodiment.

A first possibility is that the approximation factors p _lx are formed in such a way that the respective average acceleration m corresponds to the approximation of speed. tion interval [v _xl , v _{lx + 1} ] remains the same (see FIGS. 3, 31, 32). This is equivalent to the following:

Here, the term a _x n (v _x ) denotes actual movement variables m the respective speed approximation interval [v _lx , v _{xx + x} ], which differ from the movement variables (a _x (v _x )) in the following way:

* ιll v _π fι (v _χ ) * a ₁ (v ₁ ) + q _x (vj,

the variables f _x (v _x ) and q _x (v _x ) are dependent on physical variables in the speed approximation interval [v _x j_, v _{xx +} ι], which have an influence on the changed acceleration behavior of the track-bound vehicles F _x .

In this particular case, f _x (v _x ) is assumed to be constant and is designated f _x .

In this case, step 7 can be used to determine the approximation factors p _x χ in the following way (see FIGS. 5, 7, 21, 31):

_Pll + (v ₁ ) dv ₁

In particular, the polynomial q _x (v _x ) can be formed by a linear approximation

q ₁ (v- _L ) = bχv ₁ + b2 where again constants b _x and b2 each describe the changes in the acceleration behavior of the respective track-bound vehicle Fi. In this case, the approximation factors PÜ are simplified to:

Pil ( ^v il + l - + v _n ) + b ₂ y

The polynomial qi (vi) = K is constant for the very simple case that occurs particularly in the case of track inclinations or changes in the weight of the track-bound vehicles Fi.

The constant K is also dependent on the application. In this case, the formation of the approximation factors pü can be simplified to:

Pil ( ^v il + l - v _n ) κ

Approximation integral AIÜ appearing in all the above equations

In each case, since they are not directly dependent on the changes, they can be calculated in advance and, for example in tabular form, stored in step 6 for the initial speed vo = 0 and in each case fixed speeds vi. This further accelerates the implementation of the method according to the invention.

The special values for the polynomial q _x (v _x ) and the factor f _x depend on the respective causes of the changes in the acceleration behavior of the individual track-bound vehicles F _x and are described, for example, in (Wende, Fahr¬ dynamik, transpress VEB Verlag für Verkehrswesen, Berlin, 2nd edition, ISBN 3-344-00363-1, 1990, pp. 31 to 56).

The approximation factors p _xl are stored according to step 8 in a memory of the computer used for the approximation.

From the stored velocities v _x (t) of the differential equations of motion

v _χ (t) = a _λ (v)

and the approximation factor p _xl is in each case an approximate solution AL _{XX of} the motion differential equations

v, v

determined for each speed approximation interval [v _xl , ^v ιl + ll according to step 9 m as follows:

ALil = _Pll • a ₁ (v ₁ ) «a _lll (v ₁ )

The approximated solutions AL _1X are now used according to step 10 in order to regulate the driving properties of the individual track-bound vehicles F _x . B. the speed of the individual track-bound vehicles F _x . This will achieve a better flow of traffic. In a second exemplary embodiment, the criterion for forming the approximation factors p _x χ is the minimization of the quadratic error when the acceleration behavior of the individual track-bound vehicles F _{x changes} .

So the following applies:

^v ιl + l

.Pil • a- v _η - aiil vι)) ² dv _3rd -> mm

Vll

For the general formula for the formation of the approximation factors p _{xx it} follows:

v ll + l ^v ιl + l

Pi l J (a _x (v _χ)) _dv: J a ₁ (v ₁₎ a _III dv ₁ ^'33: vil ^v ιl

By the same procedure as in the previous in the first embodiment, correspondingly more complicated formulas for this embodiment are obtained if the actual change a _xll (v) is actually approximated.

Again, however, there is the possibility of calculating and storing the approximation integrals AI _X1 a priori. In this exemplary embodiment, these then have the following structure:

In a third exemplary embodiment, the individual changes are additionally m different with the weighting function in the speed approximation interval [v _x χ, v _{11 + 1} ]. weighted g _x μ (v). In this case, the following results for the formation of the approximation _factors p _ιx :

The index μ uniquely denotes each weighting function g _X μ (v) and is any natural number. The intervals at which each weighting function g _X μ (v) is valid are again completely independent of the speed approximation intervals [v _x χ, v _{xl + 1} ] and the speed intervals [v _X η, V _χ η +] J.

_ll (v ₁ ) g _lμ (v ₁ ) dv- ^' 34 ^'

Again there is the possibility of calculating and storing the approximation integral AI _X1 a priori. In the third exemplary embodiment, these have the following structure:

AIil ^'23:

V ^v ιl

The weighting of the changes between the movement quantities a _x (v _x ) and the changed movement quantities a _x n (v ₁ ) m at the respective speed approximation intervals [v _x χ, v _{11 + 1} ] is carried out in such a way that, for example, errors m in the acceleration phase be weighted more heavily at low speeds.

Linear functions are generally sufficient as weighting functions gμ (v).

In special application cases, for example, it is possible to further improve the regulation of driving dynamics for light rail vehicles or freight trains by familiarizing them with the special The peculiarities of the different vehicle types are taken into account when determining the approximation factors p _xx .

Even if the regulation in the exemplary embodiments was only explained explicitly for the case of the acceleration of the vehicles, it is possible that the same procedure also applies to the case of braking of the track-bound vehicles F _x , since braking is nothing other than eme negative acceleration and thus the method does not require any changes in this case, which is implicitly contained in the exemplary embodiments.

Claims

claims

1. Method for determining data for regulating the travel of track-bound vehicles F _x , where ι = l..n denotes a vehicle type with the same driving characteristics,

at the movement variables a _x (v), which describe the acceleration behavior of the track-bound vehicles F _{x as a} function of possible speeds v _{x of} the respective vehicle types, (1),

- at which speeds v _x (t) are determined as a function of time t from the motion quantities containing a _x (v)

Motion differential equations v ₁ (t) = a _x C ^v ) of ^the track-bound vehicles F _x (2), - in which the speeds v _x (t) are stored (3),

at which the possible speeds v _x m are divided into any number of speed intervals [v _X η, v ₁₁₊ χ], where j = 0..m (4),

- where for all movement sizes a _x (v) for speed approximation intervals [v _xl , v _{xx + 1} ] each em

Approximation integral AI _{XX is} formed, where 1 = 1 .. k

(5),

- in which the approximation integrals AI _X1 are stored

(6), - in which, for each track-bound vehicle F _x m to be controlled, all speed approximation intervals [v _xl , v _{xl + 1} ], each approximation _factor p _ιx is determined and stored (7, 8),

- at which from the stored speeds v _x (t) of the differential motion equations v -_ (t)

and the

Approximation factor p _xx each approximated solution

AL _{X1 of} the motion differential equations v _α (t) = a ₁ (v) for the respective speed approximation interval [v _xl , v _x χ ₊ χ] is determined (9), and - in which the approximated solution AL _{X1 is used} to control the travel of the vehicles F _x (10).

2. The method according to claim 1, - in which at least one of the approximation _integrals AI _xj _ (24) is formed by:

- in which at least one of the approximation factors p _lx (32) is formed by:

Pil ιll V, dv 1 '

where a term a _x χι (v _x ) denotes actual movement quantities m the respective speed _interval [v _xι , v _{11 + i} ], which differ from the movement quantities a _x (v _x ) m in the following way:

a _lll (v ₁ ) = f _χ (v _χ ) * a ₁ (v ₁ ) + q _x (v _λ ),

the variables f _x (v _x ) and q _x (v _x ) are dependent on physical variables in each case m the speed interval [v _xl , v _{11 + i} ], which have an influence on the changed acceleration behavior of the track-bound vehicles F _x .

3. The method according to claim 1 or 2,

- in which at least one of the approximation integrals AI _X1 (22) is formed by:

in which at least one of the approximation _factors p _xl (33) is formed by:

Pil _x v- ^l ιll v, dv 1 '

where a term a _x u (v _x ) actual movement quantities m denote the respective speed _{approximation interval} [v _xx , v ₁ ι +] _], which differ from the movement quantities a _x (v) m as follows:

^l ιll> ι <= ^f ι ( ^v ι) * ^a ι ( ^v ι) + qι ( ^v ι) '

where the variables f _x (v _x ) and q _x (v _x ) are dependent on physical variables in each case m the speed approximation interval [v _lx , v _xx -ι-] J, which have an influence on a changed acceleration behavior the track-bound vehicles F _x .

4. The method according to any one of claims 1 to 3,

- With at least one of the approximation integrals AI _XX

(23) is formed by:

AIil

^v ιl

where a weighting function g _x (v _x ) weights the movement quantities a _x (v _x ) m the different speed approximation interval [v _x χ, v _x ι ₊ ι], and where at least one of the approximation factors p _lx (34) is formed by:

Pil iil. v. ^ζ fiμ V- dv-

where a term a _xx ι (v _x ) denotes actual movement quantities m the respective speed approximation interval [v _lx , v _x ] _ +] _], which differ from the movement quantities a _x (v _x ) m as follows:

a _lll (v ₁ )

a ₁ (v ₁ ) + q _x (vj,

where the variables f _x (v _x ) and q _x (v _x ) are dependent on physical variables in each case m the speed approximation interval [v _xl , v _xl +] _], which have an influence on the changed acceleration behavior of the track-bound vehicles F _x .

5. The method according to one of claims 1 to 4, in which further equations of motion with the aid of the at least one

Approximation integral AI _1X and / or with the aid of at least one approximation factor p _x χ can be determined.