ITRM930544A1 - PROCEDURE FOR DETERMINING THE SIZES THAT CHARACTERIZE THE BEHAVIOR OF A VEHICLE DURING RUNNING. - Google Patents

Description

DESCRIPTION

accompanying a patent application for an invention entitled: "Procedure for determining the quantities that characterize the behavior of a vehicle while driving".

The invention relates to a process for the determination of quantities characterizing the running behavior, according to the premabulum of claim 1

A linear model of a vehicle is known, in which the height of the center of gravity of the vehicle is neglected.

In this way, in this approximation the center of gravity of the vehicle is moved in the plane of the support points of the wheels. Since? in this way the pitching and rolling movements are excluded, in this model the wheels of an axis can be united in a wheel in the center of the axis itself. This model ? described for example in the German book:

Zomotor, Adam: Fahrwerktechnik, Fahrverhalt en, Edited by Jornsen Reimpell, Wiirzburg: Vogel 1987, ISBN 3-8023-0774-7 on pages 29 to 116.

From this publication you can not? detect coin? the variables characterizing the running behavior can be determined as a function of the measured variables.

From publication DE 36 08 420 C2? known to measure, the quantities such as the speed? longitudinal of the vehicle, its transverse acceleration and speed? yaw angle and use it to calculate a drift angle. A vehicle model is used for the calculation, which takes into account the properties? of the vehicle.

The task of the invention? that of providing a method for the determination of quantities characterizing the running behavior in such a way that a measurement accuracy that is as good as possible can be obtained, with as little expenditure as possible of the necessary hardware.

This task is solved in such a method for determining the quantities characterizing the running behavior of a vehicle with the characteristics indicated in the characterizing part of claim 1, while the characteristics of the dependent claims characterize embodiments and further advantageous developments.

The method according to the invention has advantages consisting in the fact that no input quantities must be known in the form of control inputs. - it is disturbing, - which is not - necessary! - vehicle parameters and that drift angles can be evaluated: both small and large.

The present invention relates to a method for the determination of quantities characterizing the driving behavior of vehicles, in which sensors are incorporated in the vehicle, which directly measure the longitudinal acceleration and the transverse acceleration a of the vehicle in the center of gravity, the speed? yaw angle j / 2. , as well? the speed? of the vehicle in the longitudinal direction v. From these values can be detected the speed? of the vehicle in the transverse direction v ^ and / or the angle of de-. shore . In this case the equation holds:

Below is a model in which the speed is detected? of the vehicle in the transverse direction v. From there? can you? then measure the drift angle according to equation (l). This model is based on the fact that the components of speed? are coupled through the speeds? of rotation around the longitudinal, vertical and transverse axis.

According to DIN 70000, the following differential equations characterizing the movement result:

dv / dt _ + _JLrv -? - ': v_ _ = .F / m (2) - yJ.- -y? z- z? y- x

dv / dt? a F fra. (3) y ^ - z- x? -a "V

X? ydv / dt.? 2- - ?? - V - ?. - "- v = F / m

X-. ? -y x- -z - U)

i - "- d ^ 7 * (5)

-v- / dt (i-z.z-- iy-y-) *? _ 2.y -._._ J? .2-.z- = Mx-I * dft / dt (I I (6)? y-y-- y-- ?? - --ZZ?) - * Q-. M.

X

-? -? - rd? 2 / dt (I I M (7) In these equations the quantities F ^, F and F ^ indicate the forces acting in the direction corresponding to the index, the quantities M, M and M indicate the torques around the axes indicated by indices, the quantities I, I and I indicate the moments of inertia _ xx_ yy - z.z- - - with respect to the axes indicated by indices and the magnitude m? the mass of the vehicle.

To simplify the further mathematical calculation, a linear state model is now proposed. In this case, it is assumed that the speeds? of rotation can be measured exactly. In rap? matrix presentation we thus obtain a system of differential equations:

the? ~!

0 -? 2.

2 ~ y ??

d / dt? iv 1 / m F (8) i ~ y ~ z o

??

-to. ~~ v- a_ X- _ V! F

2 ^ -L 1 last addend of equation (8) (F / m,

'y: n?

L i F / m) pu? be expressed by means of the measured acceleration signal? (a- a ~ a ~) - as well as? from the earth's acceleration g:

- sin (? ~) 7

1 / m F cos (J ~) - * sin (?)

- y- y- - s (9)

? 7

a) * COS (?)

z-In this way we obtain a differential equation of linear state relative to the velocity components? (v, v, v):

? x - y- Z- ?? a -sin (|)

X 1 o- to Z- ?? y rv-x- jf _--? X>? d / dt V 0 il I V \ a - cos (?) * sin (^) (10)

- -y-? -yv | ia! : cos (?) '"Cos (<^) j

-z i- - * --_ -i

The angles J (Pitch), ^ (Roll) and ??? (yaw) are gimbal position angles and describe the transformations of the geodetic coordinate system into the coordinate system fixed to the vehicle

Other simplifications of the aforesaid model are obtained by assuming that the vehicle is on a g al plane (meaning that cardanic position angles are negligible), when the components v and v are

_ x- y_-treated as velocity? angular and speed? transverse (i.e. when the influence of the corners of the superstructure is neglected). When no pitch or roll movements of the vehicle are recorded, the terms i> 2- * v, i2:; v,? 2? 'V, i2 "~ v are

_ y_ z v z _ x_ z_ x_ y

therefore all equal to 0. The system of equations (10) is therefore simplified to:

Y-o -SI .1 a-_

x - (11) djdt

-U2 - o- v- - 1I? -Ad-L yj. Lur- 'z 5yi L yJ

Mainly? it is possible to obtain the magnitudes_ of. state (_v v) from the equation (_LL) medianie_L_lin.t_e-.grazione. Due to the instability of the equation

_ (_ L1.) _ However, errors may occur

For the fact that the speed? in the nal longitudinal direction y? measurable- The speed? in transverse direction _v _? _ observable.?

Y

Here below is indicated or .schema of ... observe-_ zxone for _y.

The differential equation (1Jjj_ha_la. Following spatial representation _ general. Of state: _

dx / dt = A (t) x u (t) _ _ _. (12) for the corresponding measurement equation the following applies: _ y = cT * x (t) = (1 0) Tx (t) _ = v _ _ (13). This general setting of a system of equations corresponds in the present _ model: _

- (- V AfirtJ (14)

jVf? 2 -1-Ui t ^ - = - ^

i a of

By transforming for s? note in the normal observation form we obtain from equations (12) and (13) the complete observer of the form: dx / dt - (A (t) -k (t) * c (t)) x k (t) ':; -y u (t) (15) with the measurement equation:

c ^ * x (t) = (1 O) ^ x (t) = v (16)! In it, the vectors below!, Ineat - refer to the representation in the normal form of observation. The value k (t) - (k ^ k ^) Writing the equation (l5) explicitly, we obtain:

dx./dt - x k 'Ky-x) a (17) ?? ^. X-? -? Z? ?? z * '? X- ?? -1 --- - x ?? ?? ???

dx / dt = x k * (y-x) a (18)? ?2-? ? -? -1? z? Z? ?? 1 ...-- y- _ - The determination of the observer's reinforcement k (t) belongs to the state of the art as a method of Prof. 0. Fdllinger: "Entwurf zeitvar ianter Systeme durch Polvorgabe". This method? represented in the International Journal of Control, 1983 Volume 38 No. 2, pages 419 to 431 in the article by Bestie and Zeitz: "Canonical forni observer design for non? linear t ime-var iable systems"; see in particular page 421. From this bibliography results the so-called Luebberger observer of the form:

.P0- (of? / Dt). ". 7. -1

* (d / dt) (19) z

p -.- of> ^ / dt -d / dt

i- l z

In this case the quantities p_and p can be chosen pleasantly as the coefficient of the characteristic pplinome.

In other words, as much as above, it is possible to determine the reinforcement of the observer by means of a Kalman filter. Such a method? described in the book of Br anime r / Sif f ling: "Kalman-Bucy-Filter" of the series "Methoden der Regelungstechnik", Publisher R._ 01-denbourg in Munich, Vienna of the year 1985? The result is the following system of equations, -consistent -of equations (20), (21), (22), (23): dp? A ^ ^ ?? ^ 2.z / dt-p ^ _ / R? ^ + _ Q ^ L. (20)

dp2j / dt- -P22? d ^ z / dt + Pll -;: - d ^ 7 / dt - P? ^ P? 2 / Rn

(21) Qk-2 -? - (22) _? P2-2 Z ^ 2 ^ P .2,2 ^ P iZ L? ILi_l_Qk22 ^

-1

2-1-: ?? (23)

22

The values of the coefficients of the covarian- matrix ,? ? - I O = 0.3, 0 = 1 as well as? the value? -? k2L --..__ L ..? wk2.2_. _ _

R = 0.5- Initial values (0) = 0, p21 (0) = 0

(0)

as well? p 0.

2.2.?

In an arapiaraento of the model, the angles of gimbal position can also be compensated in their action, ci? that ? been neglected in the previous considerations. In this regard will come? first described a subsystem 1, in which O. ^ and v ^ are equal to 0. We then obtain the following equation?

neither :

dv / dt = a sin (P) "-g (24?). _ x__ x_

The means as a function of time of the quantity sin (P) * - g can be? then delete from the difference of dv / dt and a, if SL and v are equal to 0.

_ x__ x__ z_ z_

By means of a second subsystem, the quantities v and y can then be determined using the __gr aridity _sen _ (_?) "* G determined with? 2 0. This subsystem therefore presents the equations. Dv / dt =? 2 * -v a H sen_ {_ r _) _ -g (25) x..? z y x ~

dv / dt = -52. -'It goes

\ y z 'x 5 _ (26) _d _ = 0_ _ _ _ (27) In this case they are not necessary. * sen (?) - "- g. ^ An observer or a Kalman filter is then used for this subsystem.

Alternatively? It is also possible to consider as an error all expressions, which contain at least one of the corners! or ? and broaden the order of the system. We thus obtain, for example, the following system of equations, which can? be treated equally again by means of a Kalman filter: dv / dt - v & i-I a e? (28) - x- y- z- x-- 1

dv / dt -v * iTi a e (29) - y- - x- z- -y-- 2-de ^ / dt 0 (30) de / dt = 0 (31) 2

y = v (32).

x-An example of embodiment of the invention? illustrated schematically in the drawing and will be? now described more? close.

In the drawings:

Figure 1 shows the block diagram of an observer, in which pitch and roll angles have been neglected in the model taken as a base

And

Figure 2 represents an arrangement of sensors, with which the measured quantities are detected, which form the basis of the models.

As can be seen from the block diagram shown in Figure 1, velocity is used as measurement quantities. of the vehicle in the direction of longitude le v, the longitudinal acceleration a ^, the transverse acceleration a ^, as well as? the speed? yaw angle. X circles represent addition points, in the rectangles with the point the input quantities are multiplied with each other. Supplements and amplifiers describe themselves.

The block diagram according to Figure 1? an illustration of equations (17) and (18).

Figure 2 shows certain signals, which are transmitted by the sensors themselves? known to a 407 computer device? The measurement quantities, which correspond to the signals 401, 402, .403, 404, 405 and 406: are shown in Figure 4? In the calculating device, for example on the basis of the method described above, the speed of the vehicle in the transverse direction is determined and emitted as a signal 408. From this_signal can? then be calculated in the calculator unit 409 for example by means of the equation _ (1) _ the angle of drift. This value is then emitted as a signal 410.

Claims (2)

RESELL CAZI? NI _ 1. Procedure for the determination of the quantities and characteristics of behavior of vehicles in the field, _ with a computed device_ (407), _ a1_ which signals a1i_ (401 402, 403, 406) are transmitted, which represent the measured quantities of the speed longitudinal (v) of the vehicle, of the longitudinal acceleration (a ^) of the transverse acceleration (a) and of the speed? yaw angle _ (?) and in which at least one other quantity is derived on the basis of these measured quantities, characterized by the fact that the derivation of the other quantity takes place with the use of the measured quantities and equations of state and by the fact that the drift angle (J3) is detected and emitted as a derived quantity. Method according to claim 1, characterized in that the equations of state are transformed into the normal observer form and in that at least one other quantity (408, 410) is derived by means of a complete observer. 3 - Method according to Claim 1, characterized in that the observer reinforcement (17, 18) is derived by means of a Kalman filter 4 Method according to claims 1, 2, or. 3 characterized by the fact that in the distance equations the pitch and roll movements of the vehicle are performed in their action 404- 405