FR2694808A1 - Method for determining the characteristic quantities of the running behavior of a vehicle - Google Patents

Abstract

The invention relates to a method for determining quantities characterizing the running behavior of a vehicle. In the method, a calculation device (407) is used, which receives signals (401, 402, 403, 406) representing the measured quantities of the longitudinal vehicle speed (vx), of the longitudinal acceleration (ax), transverse acceleration (ay) and angular rate of turn (OMEGAz) and then, in relation to these measured quantities, the calculation device established, using a vehicle model, at least one other quantity, which may represent at least the float angle beta.

Description

The present invention relates to a method for the determination of

  variables characterizing the running behavior of a vehicle, comprising a computing device, to which signals are applied, which represent the measured magnitudes of the longitudinal vehicle speed, the longitudinal acceleration, the transverse acceleration and the speed angle of gyration, and in which one obtains, with the aid of these measured quantities, at least one other

magnitude.

  It is known a linear single-track model of a vehicle, in which the height of the center of gravity of the vehicle is neglected. Thus, in this approximation, the center of gravity of the vehicle is shifted in the plane of the wheel support points. Because in this way pitching and rolling movements are excluded, it is possible with this model to join the wheels of an axle in the form of a wheel located in the middle of the axle. This model has been described for example. in the German book: Zomotor, Adam: Fahrwerktechnik, Fahrverhalten, (Transportation Technology, Running Behavior), Hrsg Jornsen Reimpell, W rzburg: Vogel 1987, ISBN 3-8023-0774-7, to

pages 99 to 116.

  However, it is not possible to deduce from this document how it is possible to determine the data characterizing the running behavior as a function of

measured quantities.

  From DE 36 08 420 C 2, it is known to measure the quantities constituted by the longitudinal vehicle speed, the vehicle transverse acceleration and the angular rate of gyration and to use them for the calculation of an angle For calculation purposes, a vehicle model

  intrinsically account for the properties of the vehicle.

  An object of the invention is to create a method for determining the quantities characterizing the behavior in operation so that a measurement accuracy can be obtained that is as good as possible with as little expense as possible in the necessary materials. This problem is solved for a method of the aforementioned type used for determining the quantities characterizing the behavior in operation, according to the invention in that the obtaining of the other quantity is carried out using the measured quantities and equations. of state and that, as a result of

  the less the floating angle is determined and transmitted.

  According to other characteristics of the method: the state equations will be transformed into the normal form of observation and said other quantity at least obtained will be determined by means of a complete observer. the observer is produced by means of a filter

of Kalman.

  in the state equations, pitching motions and roll motions of the vehicle are

compensated in their action.

  The method according to the invention has advantages in that it does not have to know input variables in the form of control inputs and parasitic inputs, no parameter relating to the vehicle is necessary and that it is possible to estimate

  both small and large floating angles.

  The present invention relates to a method for determining the quantities characterizing the behavior in operation, whereby sensors are installed in the vehicle so as to directly measure the longitudinal acceleration ax and the transverse acceleration ay of the vehicle at the center of gravity, the speed In this respect, the angular velocity z and the velocity of the vehicle in the longitudinal direction vx. From these magnitudes, the velocity of the vehicle in the transverse direction v Y and / or the angle of repose can then be determined. the following relation is applied: = arctg (vy / Vx) (1) In the following will be defined a model where the vehicle velocity in the transverse direction v is Y determined We can deduce, according to the equation (1 ), the floating angle This model is based on the fact that speed components are combined with rotational speeds around the axis

  longitudinal axis, the vertical axis and the transverse axis.

  According to the DYN 70000 standard, we obtain the following differential equations which characterize the motion: dvx / dt + y * vz z * y V = Fx / m (2) dvy / dt + Qz * vx Qx * Vz = Fy / m (3) dvz / dt ± Qx * Vy y * vx = Fz / m (4) zj X yyz and ex x zz) * 2 y * Qz = (5) Ixx * d Qx / dt + (Izz Iyy) * Qy * z = Mx (6) yy * dy / dt + (_XX Izz) * n X * Qz = My (6)

Iyy * d Qy / dt -

  Izz * d Qz / dt + (Iyy Ixx) * Qy * QX = Mz (7) In these equations, the quantities Fx 'Fy and F are the forces acting in the direction corresponding to the index, the magnitudes Mx, My and Mz are the moments produced around the axes designated by the index and the quantities Ixx, Iyy and Izz are the moments of inertia with respect to the axes defined by the indices, the

  magnitude m designating the mass of the vehicle.

  In order to simplify the continuation of the mathematical treatment, a linear state model has now been proposed. It has been admitted that the angular velocities can be measured exactly. In the matrix representation, a system of Differential equations:

Vl -f Qzf O lv F-

  d / dt Ivy = ç O -Q 1 vx + 1 / m Fy (8) Ly x L z It is possible to express the last sum term involved in equation (8), that is to say (Fx / m, Fy / m, Fz / m) T, by means of the measured acceleration signal y (ax, ay, az) as well as by the acceleration of the gravity xyz g: 1 / m F t y cos (r) * sin (5) * g (9) z Z Lzi = Li Lcos (r) * cos () We thus obtain a differential equation of state which is linear with respect to the components of T velocity (vx, vy, vz): VX O -Qzf 2 v a-in) d / dt vy Qz o Z v X + a cos (r) * sin (f) * g Z_y IX Za cos (r) * cos (

(10)

  The angles r (pitch), (roll) and Jt (gyration) are cardan position angles and define the transformation of the geodesic coordinate system in the integral coordinate system of the

vehicle.

  Other simplifications of the above-mentioned model will be obtained if it is assumed that the vehicle is on a plane (that is to say that the cardan positions angles are negligible), when the components v X and vy are considered as a longitudinal speed and a transverse speed (ie when the influence of the body angle is neglected). When no pitching or rolling motion occurs in the vehicle, the

  terms SI y * vz, a * v, ri * v 12 x * v are all equal to 0.

  The system of equation (10) then simplifies in the form d / dt EV 3 Qo Lx + La 3 (It is in principle possible to obtain the state quantities (vx, v) T from the equation (11) by integrating With the instability of equation (11), there may be some

errors.

  Since the velocity in the longitudinal direction v X can be measured, the velocity in the transverse direction vy can be observed.

  indicate in the following the observer arrangement for vy.

  The differential equation (11) is in the following general form

dx / dt = A (t) x + u (t) (12).

  In this respect, the corresponding measurement equation is in the form:

y = c * x (t) = (1 O) Tx (t) = (13).

  This general arrangement of a system -6- equation corresponds in the existing model to the following form: X YT u (t) = (ax, ay) T x = (vx, Vy) = a, a (t) = Z r (14). Thanks to the transformation intrinsically known in the normal form of observation, one obtains from equations (12) and (13) the complete observer having the following form: d_ / dt = (A (t) -k (t) * c T (t)) x + k (t) * y + u (t) with the measurement equation: y = c T * x (t) = (10) Tx (t) V = (16) A In this respect, the vectors underlined by lines refer to the representation in the normal form of observation. The magnitude k (t) corresponds to the observer amplification k (t) = (k 1 k 2) T. the equation (15 S) explicitly, we obtain: dxl / dt = x 2 z + kl * (y-xl) + ax (17)

  dx 2 / dt = -Xl * Qz + k 2 * (Y-Xl) + a (18).

  The determination of the observer amplification k (t) corresponds in the prior art to the method of Professor OF Llinger: "Entwurf zeitvarianter System durch Polvorgabe" This method has been described in the document "International Journal of Control", 1983, Volume 38, No. 2, pages 419 to 431, in the article by Bestle and Zeitz: "Canonical form observer design for non-linear time-variable systems"; in particular referring to page 421 We can deduce from this technical literature what is called the observer of Luebberger which is in the form: -7- k = So (d Q / dt) 2 (d 2 z / In this respect, the quantities p 0 and P1 can be freely chosen as the values of the parameters p0 and p1. coefficients of the characteristic polynomial. Alternatively, it is also possible to determine observer amplification by means of a Kalman filter. A method of this kind has been described in the Brammer / Siffling book: "Kalman-Bucy-Filter" in the series of "Technical regulation methods", R Oldenbourg, Munich, Vienna editions in 1985 The following system of equations is then obtained consisting of equations (20), (21), (22), (23): dpll / dt = - 2 * P 21 * d Qz / dt P 21 / Rl + Qkll (20) dp 21 / dt = -P 22 * d Qz / dt + Pll * d Qz / dt P 21 * P 22 / Rll + Qk 21 (21 ) dp 22 / dt 2 P 22 dz / dt = 2 * P 22 P 22 / R 11 + Qk 22 (22) and

-1

  k = 21 * R (23) 2 J In these equations, the values of the coefficients of the covariance matrix are as follows:

  Qkll = 1 Qk 21 = 0.3, Qk 22 = 1 and Rl is 0.5.

  As initial values, we have: Pll (0) = 0, P 21 (O) = O and

P 22 (0) = 0.

  In an extension of the model, it is also possible to compensate the cardan position angles in their effects, which have been neglected in the above discussion. In this respect, a subsystem 1 will initially be defined in which are equal to 0 On zz then gets the following equation:

dvx / dt = ax + sin (r) * g (24).

  The temporal average of the quantity sin (r) * g can thus be calculated from the difference between

  dvx / dt and ax, when -iz and vz are 0.

  By means of a second subsystem, it is possible to determine, using the quantity sin (r * g

  determined for A z = 0, the quantities vx and vy This sub-

  The system then contains the following equations: dvx / dt = Qz * Vy + ax + sin (r) * g (25) dvy / dt = -z * Vx + ay + (26)

dg / dt = O (27).

  In this respect, uf x and y will then not be necessary. The quantity p will be taken into consideration in a particular way and it will correspond to the expression -cos (r) * sin () * g. system, we will then use either an observer

a Kalman filter.

  Alternatively in this respect, it is also possible to consider all the expressions which contain at least one of the angles r or i as errors and to extend the order of the system. For example, the following system of equations is obtained. can again be processed using a Kalman filter: dvx / dt = vy * Qz + ax + e 1 (28) d Vy / dt = -VX * Qz + ay + 2 (29) del / dt = O (30) of 2 / dt = O (31) and

y VX (32).

  Other features and advantages of the invention will be highlighted later in the

  description, given by way of non-limiting example, in

  Referring to the accompanying drawings, in which Figure 1 shows the block diagram of an observer, o in the basic model, the pitch and roll angles r and 4 have been neglected and Figure 2 shows a sensor arrangement. , with which the measured variables are determined

which are at the base of the models.

  As shown in the block diagram shown in FIG. 1, the vehicle speed in the longitudinal direction vx is used as the measuring variables, the longitudinal acceleration axi the acceleration

  transversal ay and the angular rate of gyration -lz.

  In this case, the circles represent summation zones and in the rectangles provided with the point, the input quantities will be multiplied together. The integrators and the amplifiers explain themselves. The block diagram of Figure 1 is a

  representation of equations (17) and (18).

  FIG. 2 shows specific signals which are applied by intrinsically known sensors to a computing device 407 The measurement quantities, which correspond to the signals 401, 402, 403, 404, 405 and 406, are represented in FIG. computing device, for example with application of the method described above, the vehicle speed in the transverse direction vy is determined and produced in the form of the output signal 408. From this signal, it is possible to calculate subsequently in calculation unit 409 the floating angle @ for example by means of equation (1) This value will then be transmitted under

form of an output signal 410.

-10-

Claims (4)

  A method for determining the characteristic variables of the running behavior of a vehicle, comprising a computing device (407), to which signals (401, 402, 403, 406) are applied, which represent the measured magnitudes of the longitudinal speed of the vehicle. vehicle (vx), the longitudinal acceleration (ax), the transverse acceleration (ay) and the angular rate of turn (r) i and in which, using these measured quantities, at least another size, characterized in that the obtaining of the other quantity is carried out using the measured quantities and the equations of state and in that, as the quantity obtained, at least the floating angle (g) is determined and transmitted.   Method according to claim 1, characterized in that the state equations will be transformed into the normal form of observation and in that said other at least one obtained magnitude (408, 410) will be determined at means of a complete observer.   Process according to Claim 1, characterized in that the observer (17, 18) is produced by means of a Kalman filter.   4 Process according to one of claims 1, 2 or   3, characterized in that, in the state equations, pitch motions and roll movements of the   vehicle are compensated in their action (404, 405).