DE19535122C1 - Data calculation method for control of rail-bound traffic - Google Patents

Abstract

A method for calculation of data in order to control rail- borne vehicles, in which movement magnitudes (ai(v)) describing the acceleration behaviour of the vehicle are measured. Time-dependent speeds (vi(t)) are determined from movement differential equations of the track-bound vehicle. The speeds are stored. The possible speeds (vi) in an arbitrary number of speed intervals are sub-divided, and an approximation integral (AIil) is formed for all the movement magnitudes (ai(v)) for the speed approximation intervals. The approximation integral is then stored. An approximation factor (pil) is calculated, for each track vehicle (Fi) to be controlled, in all the speed approximation intervals. An approximated solution (ALil) of the movement differential equations for the speed approx. intervals is derived from the stored speeds (vi(t)) for the movement differential equations and the approximation factor.

Description

The invention relates to a method for determining data for regulating the travel of spurge tied vehicles.

When controlling track-bound vehicles and networks track-bound vehicles is quick and adequate accurate calculation of the driving dynamics behavior of the individual Vehicles a key problem.

The dynamic behavior, possibly incl sive of the energy requirements of the individual track-bound vehicles ge, are calculated in advance in both energetic and also calculate optimal driving curves in terms of time can. This is particularly the case with automatic vehicles important from a safety point of view, for example as the determination of the braking distance or determination of Data for precise braking.

It is known that commanded by the track-bound vehicles segment and to be used for each section moving route the movement of the track-bound vehicle linearize with the assumption of constant acceleration. Then successively along the to be driven Route calculates the movement data (turning, driving dynamics, transpress VEB Verlag für Verkehrswesen, Berlin, 2nd edition, ISBN 3-344-00363-1, 1990, pp. 15 to 17).

The process leads to high computing times, which is quite a challenge Chen disadvantage of the method described. Of another disadvantage of this method is that Initial errors in the data acquisition on the errors in the Determination of the movement data with a distant distance ken sections affect, which accumulates the error ren.

The invention is based on the problem of starting a method with which movement data for the control of track-bound Vehicles are determined, the determination of the data should be feasible faster than with the known Procedure is possible.

In the method according to the invention, the acceleration measured depending on the speed of a vehicle. Using this differential motion equation, the Ge speed behavior determined depending on the time. Dar from all other equations of motion, z. B. the Be acceleration, depending on the time or the return put away depending on the time, determined.

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

Changes, e.g. B. by changes in the roadway or by changing the mass of the vehicle, e.g. B. by Zu cargo or by taking passengers, who caused are taken into account in approximation factors and to summarized. The approximation factors are easy to determine bar, and are each for arbitrarily small selectable speed intervals or for several speeds tervalle determined. For selectable parts of the speed The approximation factor with the original Lich certain equations of motion linked so that a approximated equation of motion arises. The approximated Equations of motion approximate the "normal solution" very good observation of the changes described above on.

It can be seen from this that, above all, in the process The advantage to be seen is that the changes in driving behavior Very considerate, very approximating solution can be determined quickly and thus a quick and reliable regulation of the vehicles is made possible.  

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 flowchart that writes individual process steps of the inventive method;

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

Fig. 3 is a sketch in which different possibilities for forming the approximation factors are shown.

Referring to Figs. 1 to 3, the method is further tert erläu.

In Fig. 1 in the form of a flowchart of the method is shown in its individual method steps.

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

The movement variables a _i (v), which each describe the acceleration behavior of the track-bound vehicles F _i depending on all possible speeds v _{i of} the various track-bound vehicles F _i , are measured.

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

The consideration of further resistances, such as the inclination of the route or the payload takes place as in further described in further steps.

To determine speeds v _i (t) of the individual track-bound vehicles F _i , depending on a time t, who the motion differential equations

_i (t) = a _i (v)

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

As a result, the dependence of the speed v _i (t) of the track-bound vehicles F _i on the time t is obtained, thus the speed curve of the respective track-bound vehicle F _i at a start of the track-bound vehicle F _i with an initial speed v₀ = 0 to one Start time t₀ = 0.

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

From these speeds v _i (t), further equations of motion can be determined, for example by differentiating the speeds v _i (t) an acceleration a _i (t) of the respective track-bound vehicle F _i depending on the time t when the track-bound vehicle F starts _i with the initial speed v₀ = 0 at the initial time t₀ = 0.

The determination of the further equations of motion takes place as a function of the information required to control the track-bound vehicles F _i and is different from case to case.

Further equations of motion, such as the dependence of the path s _i (t) on the time t at the start of the track-bound vehicles F _i with the initial speed v₀ = 0 at the starting point t₀ = 0, are also to be calculated. Another equation of motion represents the dependence of the path s _i (v) on the speeds v _i , i.e. the acceleration path of the track-bound vehicle F _i , which is required for an acceleration from an initial acceleration a₀ = 0 to the respective speed v _i .

The acceleration time t 1 (v), which is for the acceleration supply of track-bound vehicles F₁ from an initial ge speed v₀ = 0 according to the respective speed v₁ such an equation of motion is required.

The differential equations of motion a 1 (v) are, for example, given in the form of n bases. These interpolation points form the speed intervals [v _ÿ , v _{ÿ + 1} ], 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 designates the respective vehicle type F _i and a second index j designates a polygon, ie a speed interval unambiguously. The polygons in the respective speed interval have the form c _ÿ · v _i + d _j , so they are linear. The constants c _j and d _j are general constants for solving differential equations.

Furthermore, the motion differential equations a _i (v) can be represented not only in polygon lines, but also in the form of an explicit function or in the form of so-called splines, i.e. in the form of quadratic polynomials, which smooth the motion differential equations a _i (v) enable the n bases.

In the following, however, the exemplary embodiment is only further explained on the basis of speed intervals which are represented in polygon lines. However, the further steps of the method can also be carried out unchanged when using splines to represent the differential motion equations a _i (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 _i . Of course, this does not limit the general validity of the following formulas in any way.

In the event that the constant c _{j is} not equal to 0, the solution to the motion differential equation a (v) is:

This results from simple integration, differentiati on or by inserting equations of motion into each other for the other equations of motion:

The equation of motion v (s) cannot be shown explicitly must be numerically from the equation of motion s (v) be determined. For example, this is applicable Newton method described in (J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Springer Verlag, ISBN 0-387-90420-4, Pp. 244-252, 1980). Other possible procedures are in this Literature also given.

The constants k _j ¹ and k _j ² are successively determined from the initial values:

With

t₀ = 0; s₀ = 0; t _j = t (v _j ); s _j = (t _j ).

Here, the times t _j are the times at which the track-bound vehicle reaches the speed v _j . This happens at a point s _j .

If the constant c _j is 0, there is another solution for the equations of motion:

The constants k _j ³ and k _j ⁴ are again successively determined from the initial values in the following way:

The total equations of motion then consist of the Lö solutions of the equations of motion in the respective speeds intervals.

This method described in the above only has to be determined once for each movement quantity a _i (v) of a track-bound vehicle F _i . Since these methods are very complex in the solution 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 above that are stored in a memory of the computer performing the method can be used (step 3).

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

This is understandable because if, for example, the speed v _i (t) is a solution to the motion differential equations dv _i / dt = a _i (v), then obviously v _i (t, p _i ): = v _i (t · _p i) Solutions of the motion differential equations dv _i / dt = p _i · a _i (v). These are independent of the special form of the motion differential equations a _i (v).

In this case, further motions continue to apply equations the following:

a _i (t, p _i ) = p _{ia i} (tp _i )

v _i (s _i , p _i ) = v _i (s _i · p _i )

This previously considered "global approximation factor p _i" is, of course, when considering each of speed intervals [v _{il, il} v _{+ 1]} p _il to Approximationsfaktoren that are [v _{il, il} v _{+ 1]} respectively for each Geschwindigkeitsapproximationsintervall recalculated.

The approximation factors p _il will therefore be determined for freely selectable speed approximation intervals [v _il , v _{il + 1} ]. The speed approximation intervals [v _il , v _{il + 1} ] do not have to match the speed intervals [v _ÿ , v _{ÿ + 1} ] described above. They can differ from one another and overlap in any way.

An index l is an arbitrary natural number and uniquely identifies each speed approximation interval [v _il , v _{il + 1} ].

There are the Approximationsfaktoren p _il formed which approximate the actual change with a change in movement variables a _i (v) in a movement variables _IL1 (v) in the manner of the motion parameters a _i (v), that:

p _il · a _i (v) ≈ a _il1 (v) in the respective speed approximation _interval [v _il , v _{il + 1} ].

The speed approximation interval [v _il , v _{il + 1} ] can be subdivided depending on the required quality of the approximation. This gives you explicit access to the interesting vehicle dynamics and does not rely on iterative approximations. The smaller the speed approximation intervals [v _il , v _{il + 1} ] are selected, the more accurate the approximation will of course be. However, this also increases the computing time required for the computers required to determine the approximation.

Different possibilities for forming the approximation factors p _{il are used} in different variants of the exemplary embodiment.

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

The term a _il1 (v _i ) denotes actual movement variables in the respective speed _{approximation interval} vall [v _il , v _{il + 1} ], which differ from the movement variables (a _i (v _i )) in the following way:

a _il1 (v _i ) = f _i (v _i ) _* a _i (v _i ) + q _i (v _i ),

the quantities f _i (v _i ) and q _i (v _i ) are dependent on physical quantities in each case in the speed approximation interval [v _il , v _{il + 1} ], which have an influence on a changed acceleration behavior of the track-bound vehicles F _i .

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

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

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

q _i (v _i ) = b₁v _i + b₂,

where again constants b₁ and b₂ each describe the changes in the acceleration behavior of the respective track-bound vehicle F _i . In this case, the formation of the approximation factors p _{il is} simplified to:

The polynomial q _i (v _i ) = 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 F _i .

The constant K also depends on the application. In this case, the formation of the approximation factors p _{il can be} simplified to:

Approximation ink grale AI _il appearing in all the above equations

can each, since they are not directly dependent on the changes, be calculated in advance and, for example, in table form, can be stored in step 6 for the initial speed v₀ = 0 and in each case specific speeds v _i .

As a result, the method according to the invention is carried out rens accelerated even further.

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

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

From the stored speeds v _i (t) of the differential equations of motion

_i (t) = a _i (v)

and the approximation factor p _il becomes an approximated solution AL _{il of} the differential equations of motion

_i (t) = a _i (v)

determined for each speed approximation interval [v _il , v _{il + 1} ] according to step 9 in the following manner:

AL _{il il} = p · a _i (v _i) ≈ a _il1 (v _i).

The approximated solutions AL _il are now used according to step 10 in order to regulate the driving properties of the individual track-bound vehicles F _i . B. the speed of the individual track-bound vehicles F _i . This will result in a better flow of traffic.

In a second exemplary embodiment, the criterion for forming the approximation factors p _{il is} the minimization of the quadratic error when the acceleration behavior of the individual track-bound vehicles F _{i changes} .

So the following applies:

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

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 _il1 (v) is actually approximated.

Again, however, there is the possibility of calculating and storing the approximation integral AI _il prior. In this embodiment, these then have the following construction:

In a third exemplary embodiment, the individual changes are additionally weighted differently in the speed approximation interval [v _il , v _{il + 1} ] with weighting functions g _iµ (v). In this case, the following results for the formation of the approximation factors p _il :

The index µ _clearly denotes each weighting function g _iµ (v) and is any natural number. The intervals in which a weighting function g _iµ (v) is valid are in turn completely independent of the speed approximation intervals [v _il , v _{il + 1} ] and the speed intervals [v _ÿ , v _{ÿ + 1} ].

Again, there is the possibility of calculating and storing the approximate ink grale AI _il prior. In the third exemplary embodiment, these have the following structure:

The weighting of the changes between the movement _variables a _i (v _i ) and the changed movement _variables a _il1 (v _i ) in the respective speed _{approximation intervals} [v _il , v _{il + 1} ] is carried out in such a way that, for example, errors in the acceleration _{phase for small ones} Speed should be weighted more heavily.

Linear functions are generally sufficient as weighting functions g _µ (v).

In special applications, for example, it is possible to further improve the control of driving dynamics for light rail vehicles or freight trains by taking into account the special, known peculiarities of the various vehicle types when determining the approximation factors p _il .

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 the track-bound vehicles F _i , since braking is nothing more than a negative one Acceleration and thus the procedure does not require any changes in this case, which is implicitly contained in the exemplary embodiments.

Claims (5)

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

• - at which motion quantities a _i (v), which describe the acceleration behavior of the track-bound vehicles F _i depending on possible speeds v _{i of} the respective vehicle types, are measured (1),
• - t are determined at the speeds v _i (t) depending on a time from the movement variables a _i (v) containing motion differential equations _i (t) = a _i (v) the spurge-bound vehicles F _i (2)
• - at which the speeds v _i (t) are stored (3),
• - in which the possible speeds v _i in any number of speed intervals [v _il , v _{il + 1} ], where at j = 0. . . m, can be divided (4),
• - In which an approximation integral AI _{il is} formed for all movement variables a _i (v) for speed approximation intervals [v _il , v _{il + 1} ], where l = 1. . . k (5),
• - in which the approximation integrals AI _il are stored (6),
• - an approximation factor p _{il is} determined and stored for each track-bound vehicle F _i to be controlled in all speed approximation intervals [v _il , v _{il + 1} ] (7, 8),
• - In the case of the stored speeds v _i (t) of the differential motion equations _i (t) = a _i (v) and the approximation factor p _il , an approximate solution AL _{il of} the differential motion equations _i (t) = a _i (v) for the respective one Speed approximation interval [v _il , v _{il + 1} ] is determined (9), and
• - in which the approximated solution AL _{il is used} to regulate the travel of the vehicles F _i (10).

2. The method according to claim 1,

• - in which at least one of the approximation integrals AI _il (24) is formed by: and
• - in which at least one of the approximation factors p _il (32) is formed by: where a term a _il1 (v _i ) _denotes actual movement _variables in the respective speed interval [v _il , v _{il + 1} ], which differ from the movement variables a _i (v _i ) in the following way: a _il1 (v _i ) = f _i (v _i ) _* a _i (v _i ) + q _i (v _i ), the quantities f _i (v _i ) and q _i (v _i ) being dependent on physical quantities in each case in the speed interval [v _il , v _{il + 1} ], which have an influence on a changed acceleration behavior of the track-bound vehicles F _i .

3. The method according to claim 1 or 2,

• - in which at least one of the approximation integrals AI _il (22) is formed by:
• - in which at least one of the approximation factors p _il (33) is formed by: where a term a _il1 (v _i ) _denotes actual movement _variables in the respective speed _{approximation interval} [v _il , v _{il + 1} ], which differ from the movement _variables a _i (v) in the following way: a _il1 (v _i ) = f _i (v _i ) _* a _i (v _i ) + q _i (v _i ), the quantities f _i (v _i ) and q _i (v _i ) being dependent on physical quantities in each case in the speed approximation interval [v _il , v _{il + 1} ], which have an influence on a changed acceleration behavior of the track-bound vehicles F _i .

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

• - in which at least one of the approximation integrals AI _il (23) is formed by: wherein a weighting function g _i (v _i ) weights the movement quantities a _i (v _i ) in the different speed approximation intervals [v _il , v _{il + 1} ], and
• - in which at least one of the approximation factors p _il (34) is formed by: where a term a _il1 (v _i ) _denotes actual movement _variables in the respective speed _{approximation interval} [v _il , v _{il + 1} ], which differ from the movement _variables a _i (v _i ) in the following way: a _il1 (v _i ) = f _i (v _i ) _* a _i (v _i ) + q _i (v _i ), the quantities f _i (v _i ) and q _i (v _i ) being dependent on physical quantities in each case in the speed approximation interval [v _il , v _{il + 1} ], which have an influence on a changed acceleration behavior of the track-bound vehicles F _i .

5. The method according to any one of claims 1 to 4, in which further equations of motion are determined using the at least one approximation integral AI _il and / or using the at least one approximation factor p _il .