DE2339600A1 - Steering control for articulated vehicle - prevents undesired motion of trailer during vehicle reversing by wheel angle adjustment - Google Patents

Abstract

The steering angles of the steerable wheels of the tractor vehicle are so continuously adjusted according to a control rule in relation to the position of the vehicle trailer train that a predetermined required condition is attained and maintained stable. Th vehicle position is described in relation to the angle between the projected longitudinal axes of the tractor and trailer in the case of a single-axle trailer. When a double-axled trailer is used the position is described by the angle between the longitudinal axis of the tractor and trailer shaft and the angle between the trailer shaft and the longitudinal axis of the trailer. The control rule for the steering angle of a front steered tractor vehicle is given by specified equations.

Description

Rainer Hofmann 7 Stuttgart 1 Wartbergstrasse

Steering control to make it easier for car trains to reverse

The invention relates to a control device that when reversing from Wagon trains., Which consist of a. The towing vehicle and trailer exist, prevent that the trailer runs in an undesired direction and finally turns sideways.

So far there has been the problem of reversing with such car trains already a lot of suggestions. But they see all the special features of the structure such as B. an additional, independent steering option for the trailer before. Because of the effort involved, most of the wagon trains have them not using such devices and reversing is only possible in this case if continuously on the steering wheel of the towing vehicle an incipient instability of the trailer is appropriately corrected, which is especially true in the case of a two-axle trailer and a nimble one Driver rarely succeeds.

The invention is based on the object by means of a control device only to steer the towing vehicle so that the entire train of cars when reversing stably in the direction desired by the driver and over a The direction to be specified moves.

This object is achieved according to the invention in that the steering angle of the towing vehicle via a suitable control law depending on the current situation of the towing vehicle and trailer Continuously adjusts the train control system in such a way that a desired target state is reached and maintained.

To clarify the question of how to steer in such a case, describes the behavior of the wagon train controlled system by a mathematical

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matic model, which is based on the components necessary for the regulation is limited. Such a model is shown in FIG. 1 for the initially assumed case of a two-axle trailer. It means:

a - center distance of the towing vehicle

b - Distance of the trailer coupling from the rear axle of the towing vehicle

c - Length of the trailer drawbar from the attachment point to the front axle of the trailer

d - center distance of the trailer

ν - driving speed of the towing vehicle, assumed to be positive when reversing

Oi - steering angle of the towing vehicle

TP - perpendicularly projected angle between . The imaginary centerline of the towing vehicle and the trailer drawbar extended to the rear

Ti / - perpendicularly projected angle between The imaginary trailer drawbar and trailer center line extended to the rear (steering angle of the trailer).

Hints:

As indicated in Figure 1, let all angles be positive if the car train as a whole is set to the right-hand bend when reversing and looking in the direction of travel. Often double axes are used instead of one. In this In the case one thinks of a reduced axis in the middle between the two and determines the distances a to d accordingly. Towing vehicles generally have Axle steering, so that both front wheels would have to have different steering angles when cornering and with exact steering geometry. The angle to be taken as α is the same with turntable steering Curve radius would result. This can be achieved if one looks at α more appropriately Place of the steering transmission linkage measures, for example in steering wheel turns. Often, however, the front wheels are also used with a stub axle steering

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led in parallel, so that this difficulty is eliminated.

Most trailers have turntable steering. With stub axle steering the above applies.

A clever embodiment of the invention is that for identification of the position state the angles y and y are used because as generalized coordinates, these form the smallest set of parameters that fully describe the state.

The towing vehicle can now have front, rear or all-wheel drive. As will be shown later, the Pail is the most unfavorable for the settlement Rear wheel drive. Therefore, if one assumes that the towing vehicle is connected to the center of the axle via a differential gear on the rear wheels constant speed ν, taking into account the kinematic constraints (no "erasing" of the wheels on the road) the equations of motion:

-V = siny- (- + - cozy) tana

^{v Y a a Y} (D

c * c foe

- ψ = - sin y + - cos ψ sin Tf / + - (cos V ⁺ j "siny siny) tan OL '

₉ m

where y and 1 // mean the time derivatives.

One recognizes immediately that the equilibrium positions of this differential equation systems, i.e. singular solutions of the form

Ot = ^a ₀ = const., Y = y = const., Ψ = γ = const, through the relationships

_{tan α} = (2)

ο c + b cos V

and

d sin y _o

sm

= r—. .

b + c cos y> (3)

Marked are.

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In order to avoid unnecessary diversity, one can rely on the practically possible cases

Yy

limit, where Ot means the maximum steering angle. In this

Area, the equilibrium positions are stable when driving forwards and unstable when driving backwards. If you take z. B. the particularly characteristic case of straight-ahead travel & ⁼ "] f - Ύ = o, when reversing even the smallest disturbance will be sufficient to cause ever greater deviations from this position. Now it is no longer sufficient, a Forward travel must be kept constant at the value (X = ο , but rather one must continuously set OL as a function of y and V / in such a way that disturbances are corrected again immediately.

Assuming that the wagon train is already in a straight line and only small deviations from it occur, the system of equations (1) can be linearized. With the linear combination

OC = Ky - JUL γ ( iC, JbL... Const.)

The linearized system of equations that is valid for small y and "ψ then results as a simple rule law:

with the characteristic equation

2v, b + Cv _/ .b _/ . c ..., ν, 2, c .. cc b + c *. .

ca & y dca * dda

From this, according to the Hurwitz criterion, the stability conditions LL > r ~ - fC + τ- (1 + -j) for v> o (4)

U> -rr-K - I for v ^ o (5)

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FIG. 2 shows the stability relationships in the 4C, U plane. In order to determine from the multitude of possible stable settings those which can be expected to have a favorable control course, a comparison is made with the general characteristic equation of a 2nd order system p ² + 2 OCJ ρ + CJ ² = ο

OO

and is given as the degree of damping

b + c α. b _Λ c

K + - U - 1L- -

a a ^ d

D =

c c_ b + c j *

J d "d * a

as well as the related natural angular frequency of the undamped system

cc. b + c Af

d ~ d a

In FIG. 2, the curves D = const and the straight lines = const are also shown. A useful setting is obtained for D> 0.5 if Xl is not too large. Too small Ώ. only does one

^& ο ο

very slow correction of disturbances, too large Ώ. causes a reaction may be too fast, which may lead to instability due to the non-linearities if larger deviations from the target position must be adjusted.

In order to also be able to drive curves, one has to expand the control law by a further part

α - Ky-jJLy + XG, (6)

where 0 "represents the target value for the curve position and X is a constant factor that is only used for adaptation, but has no influence on the stability.

Is z. B. a certain curve position OL = (X, y = y> and ψ = "ψ desired, where α, ¹ W and Ij / form a state of equilibrium,

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which is defined by equations (2) and (3), one must (5 " to the fixed value

to adjust. If one assumes, as before, when driving straight ahead, that the wagon train is already in this state of equilibrium and the control initially only has the task of correcting small deviations Δ "ψ and Δ W , with CT being kept constant, then one can use the differential equation system ( 1) linearize again around this state of equilibrium

a = oil + Aa, γ = γ + Ay, ψ = γ + Ay

and note that QT has been set so that

^a o ⁼ * y _o -ßjo ^{+ λο} Ό

applies, it follows from the regulation law (6) for deviations from the target position

Δα = HAy -

A more detailed study of the stability of the for all possible equilibrium positions linearized system (1) shows that a setting that is stable when driving straight ahead is generally also stable when cornering.

Figure 3 shows the relationship between (ΞΓ and TJ /, as it is derived from the equations (2) and (3) and the control law (6) results. This one is clear in the same direction and quite useful.

All previous stability considerations are based on linearized equations and small deviations ^ y and Δ W from the equilibrium position considered in each case. In practice, however, there are also large deviations. Would you like B. change from sharp cornering to straight ahead and if you set GT abruptly to the value (y = ο, then the target position is straight ahead while the wagon train is currently cornering, i.e. large deviations from the target position.

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shows. In this case, the previous stability conditions (4) and (5) are necessary, but no longer sufficient; rather, because of the non-linearities, the stability can depend on the initial conditions y (o) and y / (o) in addition to ü and JH . So it is z. B. It is quite possible that despite a stable setting of iC and Jl, instability occurs if the deviations Δγ or Δ * ψ are too large. The steering angle restriction jctj Sf Oi <- = y- also plays a decisive role. It can now happen that the expression

will. In this case, at best, you can

CC = OC sgn ( -Ky -MY + && )

meet because steering angles greater than the maximum possible are not set can be. Taking this restriction into account, this is the final form of the rule law

'Itf (7)

oil. = α sgn ( icy - juy + X (S) for \% y- juiy + X & \ > (X

A computer simulation and practical investigations show that, in general, no difficulties arise if O * is changed so slowly that the control system can easily follow. This is understandable because in this case the linear theory holds with good accuracy. However, if you want to abruptly move from z. B. change extreme left curve to extreme right curve, then y will initially increase in amount and can either hit a limit or get outside the stable range, especially if

tan ² a <-Τ — τ2
mc ^ - b

To avoid these undesirable effects, one can take the following measures consider:

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-δ-1. According to FIG. 3, the factor X is determined in such a way that when Q = + (T

o- max

only sufficiently weak curves are possible, and make sure that the starting positions are within this permissible range. In most use cases this will be sufficient.

2. Try a rule setting with a smaller £ 1 .

3. The driver is warned by an acoustic or visual signal before changing from CT too quickly if this threatens to make the angle y too large in terms of magnitude.

4. One extends the rule law to

(χ = Ky-juy + XG + v% for \ ay -juf + λ, σ + v% \ = <*

m or

(X = OL sgn ( KV- ΜΨ ⁺ λ & + VX) for \ iCy ~ MW + / LG> + VJC \> (X

with

^ l (IyI - yj ^s s ⁿ v ^for IyI > v ₀

where IP is a fixed angle and V is a constant factor. If, as a result of strong changes in GT, the angle y is larger than W, the control law (8) uses % to compensate for the change caused by G " , thus making a further increase in \ y \ more difficult.

The last, somewhat complicated, explanations are only intended for the sake of completeness explain certain marginal phenomena. For the vast majority of cases that occur in practice, however, one can summarize determine the following:

The control law (7) is completely sufficient if one does not value too sharp cornering and -K and JU can according to the linearized stability conditions (4) and (5) as well as according to the

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Figure 2 to be drawn up for the individual case can be determined. The cheapest Adjustment can then be tried on a case-by-case basis within the framework of these guidelines.

To set the steering angle (K to the value prescribed by the regulation law, there are now essentially two options in addition to a theoretically conceivable mechanical transmission by means of rods or cables:

1. In the automatic embodiment of the invention, an internal position control is used. For this purpose, the expression Δ = fty-jH * ¹ ? + & G - (X is formed in the controller and controls a servomotor with this signal via a power amplifier in the sense that Δ disappears or becomes very small in terms of its magnitude.

If the towing vehicle already has power steering, then the servomotor available for this purpose can also be expediently used for setting the steering angle.

Since the steering linkage is not interrupted, it rotates With this version, the steering wheel turns itself and the driver only gives backwards to drive right, left or straight ahead a setpoint, e.g. B. via a joystick before. In this case, reversing will hardly be more difficult than that Drive forward. To drive forward, the entire control device is then switched off again and the power steering works again normal.

2. In the semi-automatic embodiment of the invention, the rotates Driver himself at the steering wheel, always in such a way that it was indicated to him on a display instrument or in some other way Setpoint

^{σ =} k * - l ^{f +} fy ■

as it results from the rule law, adjusts to the desired value. If C becomes too large, it must decrease cn , and vice versa.

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Single axle trailer

The situation is simpler with a wagon train consisting of a towing vehicle with a single-axle trailer. According to FIG. 1, the controlled system of the wagon train is given by the one differential equation - Kp = sin iff - (- + - cos 1p ) tan α

ν ^J ~ aa ^J

whose equilibrium positions, i.e. singular solutions of the form OC = OC = const., ψ = y = const., are described by the relationship

_tan

ο c + b cos ip

given are. Here, too, one restricts oneself to the area

It is known that these equilibrium positions are unstable when reversing if Oc is merely kept constant at the value OC-OC . In order to stabilize it, the linear combination can be used as a rule law

ex = icy -% <o

use, where 6 * means the setpoint for the direction of travel. If one linearizes here as well to travel straight ahead as a particularly characteristic equilibrium position, then for small angles y> results

c
* + V = o with T = -

vM- + - / TI -

and thus as a stability condition for reversing:

a
K >

b + c

The larger IC is selected, the faster a disturbance will be corrected because the time constant T becomes smaller. Do larger deviations from the desired target position have to be corrected or do you have χ

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- ii -

Chosen very large, so can also be done here

will. However, since greater than the maximum steering angle is not set can be, as an embodiment of the invention, the rule law at best

ϊϋτ \ κγ-
or a = e * _m sgn (icy-λσ) for \ χγ-

to be fulfilled.

If one also admits the case b <o, as it z. B. with some articulated lorries occurs, but assumes that c> | b | , what in. is always true in general, a precise stability analysis of the nonlinear differential equation shows that a setting that is stable when driving straight ahead is also stable when cornering. If in addition

tan of> - -,

m δ. δ

c - b

so the stability is complete, otherwise it still depends on the initial condition ip (o). However, if in the latter case you do not want to drive narrower curves when driving backwards than is possible when driving forwards with (X = + (χ) , make sure that the initial condition "ψ (o) is also within the range given by + ψ so there will be no trouble.

The relationship between the setpoint (5 and the state angle V

ο ·> ο

in the state of equilibrium one obtains from equation (2) and the control law (9) too

K 1, a sin \ p

t J ο

arctan
%

c + b cos TP

JO

with the unambiguous and unidirectional "course" shown in FIG.

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The adjustment of the steering angle can also be done either internally Position control can be carried out with a servo motor or by the driver. The previous ones The statements apply accordingly. Theoretically, a mechanical implementation of the rule law is of course also conceivable here.

In all previous considerations, among other things, the stability was only depends on the sign of the driving speed ν. It has been shown that a stable setting when driving backwards when driving forwards {where the Control is switched off anyway) would work the wrong way. But if you consider that apart from a mechanical transmission, every steering angle setting ,, whether it is carried out by a position control or by the driver, is associated with a certain time delay and that On the other hand, if the state angles change more rapidly with increasing driving speed, it is clear that the driving speed is the only way It may be great that the rule of law is still fulfilled at any given moment can be. Should now only a constant state of equilibrium are observed, the state angles change only slowly and it can be driven faster than in the cases where a new one Equilibrium must first be reached ..: "

You can also see immediately that rear-wheel drive has a more unfavorable effect than front-wheel drive, because the front wheels are then used when cornering of the towing vehicle, higher speeds occur, which in turn results in faster changes in the state angle. In any case however, stability can always be achieved if the vehicle is driven slowly enough.

The advantages achieved by the invention are that the driver of wagon trains, especially in the case of the automatic configuration, reversing is no more difficult than driving forward. The operation is extremely simple and is done by the driver alone

_ 13 _

Pahrerplatz from. Even the smallest deviations are eliminated by the regulation corrected from the desired direction faster and better than a driver can. So is z. B. extremely accurate straight-ahead driving backwards possible.

The scheme can be applied to all towing vehicles commonly used today with simple means and trailers can be added without any changes to the structure required are. In addition, the geometrical links are adhered to, so that the wheels are not "erased" on the road. Finally, the invention can in principle also be applied to towing vehicles with several single-axle or two-axle trailers or with certain Special vehicles, if the regulation law to the new conditions

sizes is added accordingly.

The technical execution can be done in different ways. Conceivable are mechanical, electrical, electrohydraulic or a combination thereof. It should be most useful when measuring the state variables as well as the steering angle and the setpoint is made electrically in a suitable manner and the processing in the controller takes place electronically in known analog computing technology. For internal position control of the steering angle, a servomotor that is already present in power steering is suitable.

However, the invention is essentially a method that is based on a specific embodiment is not bound.

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Claims (8)

Rainer Hofmann 7 Stuttgart 1 Wartbergstrasse 18 λ) Steering control to make it easier for car trains to reverse Patent claims: C Yj Steering control for reversing car trains consisting of the towing vehicle and trailer, characterized in that the steering angle of the steerable wheels of the towing vehicle is continuously adjusted according to a control law, depending on the position of the car train, so that a predetermined target state is reached and maintained in a stable manner. 2. Steering control according to claim 1, characterized in that in a wagon train consisting of a towing vehicle and a single-axle trailer, the angle y> projected vertically into the roadway plane is used between the rearwardly extended traction vehicle center line and the trailer center line to describe the situation. 3. Steering control according to claim 1, characterized in that in a wagon train consisting of a towing vehicle and a two-axle trailer, to describe the state of the position of the perpendicularly projected angle y in the plane of the road between the traction vehicle center line extended to the rear and the trailer drawbar and perpendicular to the Carriageway plane projected angle Tf / between trailer drawbar extended to the rear and trailer center line is used. 4. Steering control according to claims 1 and 2, characterized in that the combination (9) as a control law for the steering angle α of a towing vehicle steered at the front 509807/0232 α = icy _ λσ for \ κ · φ - _m or «= α sgn {A ^ - ^ S ¹ ) for \ Χγ - Λ, & 1 > α is used, where Ä and λ are constant factors, <G "means the target state and cc the amount of the maximum possible steering angle. OL , y and G" are assumed to be positive "if the wagon train as a whole makes a right turn when driving backwards and in the direction of travel describes. 5. Steering control according to claims 1 and 3, characterized in that the combination (7) is used as the control law for the steering angle OC of a front-steered towing vehicle a = Ky -jtf * X <5 m _r \ xy-jif '+ &&! · £ a respectively, · a = α sgn ( icy -jty + Xv | mv \% y-jif +% ® \> a is used, where ü, JUL and Λ are constant factors, <3 means the target state and OC means the maximum possible steering angle. OL, * ψ, 'ψ and G "are assumed to be positive if the wagon train as a whole describes a right-hand bend when driving backwards and in the direction of travel. 6. Steering control according to claims 1 and 3, characterized in that to avoid instability in extremely sharp cornering as a control law for the steering angle € L of a front-steered towing vehicle, the extended combination (8) et = yjyχ _v \% fjy% \ α = α · sgn (icy-juy + X (5% + y) f _or \ icy- g (yjy% ) \ cyβψ # | with O:. " ' for p for is used, "where iC, Ji; X and V are constant factors, 0 the SoH state, Ot the maximum possible steering angle and - ip 509807/0232 A fixed positive limit angle means that is to be selected smaller than the value that the state angle y may assume in terms of its absolute value. OC, y>, iv and <ö are assumed to be positive, as in claim 5, if the wagon train as a whole describes a right-hand curve when driving backwards and in the direction of travel. 7. Steering control according to claims 1 to 6, characterized in that an internal position control is used to set the steering angle OC to the value prescribed by the control law at any moment, expediently in the presence of a power steering, the servo motor already built in for this purpose is also used for steering angle adjustment will. 8. Steering control according to claims 1 to 6, characterized in that for setting the steering angle CC to the value prescribed by the control law at any given moment, the driver himself rotates the steering wheel of the towing vehicle, always in such a way that it moves in a suitable manner set the displayed setpoint 6 "to the value he wants. 509807/0232 Leeward