GB2269571A

GB2269571A - Process for determining quantities characterising vehicle travel behaviour.

Info

Publication number: GB2269571A
Application number: GB9314918A
Authority: GB
Inventors: Avshalom Suissa
Original assignee: Daimler Benz AG
Current assignee: Daimler Benz AG
Priority date: 1992-08-13
Filing date: 1993-07-19
Publication date: 1994-02-16
Anticipated expiration: 2013-07-19
Also published as: SE9302610D0; FR2694808B1; GB2269571B; SE513553C2; ITRM930544A0; DE4226749C2; FR2694808A1; DE4226749A1; IT1261511B; SE9302610L; ITRM930544A1; GB9314918D0

Abstract

Signals 401, 402, 403, 406 which represent the longitudinal acceleration ax, the vehicle velocity in the longitudinal direction Vx, the transverse acceleration ay and the yaw angular velocity OMEGA z, are fed to a computer 407 and at least one further quantity 408, 410 comprising at least the floating angle is derived on the basis of these measured quantities in the computing device 407, using a vehicle model. The floating angle beta is defined by beta = - arctan (Vy/Vx). <IMAGE>

Description

22695707 1 Process for the determination of auantities characterising the

travel behaviour The invention relates to a process for the determination of quantities characterising the travel behaviour of a vehicle, with a computing device, to which signals are fed, which signals represent measured quantities of the vehicle longitudinal velocity (vx), of the longitudinal acceleration (ax), of the transverse acceleration (a y) and of the yaw angular velocity (n.), and in which at least one further quantity is derived on the basis of these measured quantities.

A linear single track model of a vehicle is known, in which the height of the centre of gravity of the vehicle is disregarded. Accordingly, in this approximation the centre of gravity of the vehicle is displaced into the plane of the points of support of the wheels. Since, accordingly, roll and pitch movements are excluded, when using this model the wheels of one axle can be combined to form a wheel at the centre of the axle. This model is described, for example, in the German book: Zomotor, Adam: Fahrwerktechnik, Fahrverhalten [Chassis technology, travel behaviour] published by Jbrnsen Reimpell, Wfirzburg: Vogel 1987,, ISBN 38023-0774-7 on pages 99 to 116.

It cannot be inferred from this presentation how quantities characterising the travel behaviour can be determined as a function of measured quantities. - It is known, from DE 3,608,420 C2, to measure the quantities vehicle longitudinal velocity, vehicle transverse acceleration and yaw angular velocity, and to utilise these quantities for the computation of a floating angle. For the computation, a vehicle model taking into consideration the properties of the vehicle per se is utilised.

The present invention seeks to refine a process for the determination of quantities characterising the travel behaviour in such a manner that the best possible accuracy 2 of measurement can be achieved with the lowest possible expenditure on required hardware.

According to the present invention there is provided a process for the determination of quantities characterising the travel behaviour of a vehicle, with a computing device, to which signals are fed, which signals represent measured quantities of the vehicle longitudinal velocity (vx), of the longitudinal acceleration (ax), of the transverse acceleration (a y) and of the yaw angular velocity (nz), and in which at least one further quantity is derived on the basis of these measured quantities, wherein the derivation of the further quantity takes place with the use of the measured quantities and of equations of state, and at least the floating angle (B) is determined as derived quantity and output.

Preferably, the equations of state are transformed into the observation standard form, and the at least one further quantity is derived by means of a complete observer. The observer gain may be derived by means of a Kalman filter. Preferably, roll movements and pitch movements of the vehicle are compensated in their action in the equations of state.

The process according to the invention shows advantages to the effect that input quantities do not need to be known in the f orm of control inputs and disturbance inputs, that no vehicle parameters are required, and that both small and large floating angles can be estimated.

A preferred embodiment of the present invention is a process for the determination of quantities characterising the travel behaviour, in which process sensors are incorporated in the vehicle, which sensors directly measure the longitudinal acceleration ax and the transverse acceleration a y of the vehicle at the centre of gravity, the yaw angular velocity nz as well as the vehicle velocity in the longitudinal direction vx. From these quantities, it is the possible to determine the vehicle velocity in the transverse direction VY and/or the floating angle B. In this 3 case, the following relation is applicable:

B arctan(v y /vx) In the text which follows, a model is set forth, in which the vehicle velocity in the transverse direction vy is determined. From this, it is then possible to determine the floating angle B in accordance with equation (1). This model is based on the concept that the velocity components are coupled via the speeds of rotation about the longitudinal, vertical and transverse axes.

According to DIN 70000, the following differential equations characterising the movement are obtained:

dvx/dt + n y V z - nzvy = FxIn (2) dv y /dt + nzvx - nxvz = F y /m (3) dvz/dt + nxvy - nyvx = Fz/m (4) and Ixxdnx/dt + (Izz - I yy)n y nz = Mx (5) I yy dn y /dt + (Ixx - Izz)nxnz = MY (6) izzdnz/dt + (I yy - IM) fly ú2x = Mz (7) In this case, the quantities Fx, F y and FZ are the forces which act in the direction corresponding to the index, the quantities Mx, MY and MZ are the moments about the axes designated by the index, the quantities IMP, Iyy and Izz are the moments of inertia with respect to the axes designated by the indices and the quantity m is the vehicle mass.

In order to simplify the further mathematical treatment, a linear model of state is now proposed. In this case, it is presumed that the speeds of rotation n can be accurately measured. In matrix representation, the result is thus a system of differential equations:

v X 0 -0 z - 0 y v X X d/dt v 0 0 n v + l/= F VY -Q z 0 0 X VY FY Z_ - Y X - - Z_ Z_ The last summand of the equation (FX/M, F Y/M1 Fz/a)l can be expressed by the measured acceleration signal 4 (a., ayl az)l as well as the acceleration due to gravity g:

F a X -sin (r) 1/M FX a cos (1-) sin (fl g FY ay cos (1-) cos (9) Z_ Z_ This thus gives a differential equation of state which is linear with respect to the velocity components (vX1 VY ' v Z) T v X 0 -()z _oy v X -a X- -sin(r) d/dt vy QZ 0 Q X v y + a y - cos(r)sin( ) g (10) v z -n Q X 0 v z a z COSW)COSM y The angles r (pitch), (roll) and 7r (yaw) are cardan setting angles and describe the transformation of the geodetic coordinate system into the coordinate system which is fixed relative to the vehicle.

Further simplifications of the above model are obtained if it is assumed that the vehicle is situated on a plane (i.e., that the cardan setting angles are negligible), if the components vx and VY are considered as the -longitudinal and transverse velocity (i.e., if the influence of the structural angles is disregarded). If no pitch or roll movements of the vehicle occur, then the terms ny vz" n y V X 11xvZ1 11xVY are all equal to 0. The system of equations (10) is then simplified as follows:

-11] 0Z [v d/dt vx ayx] [VVYX1 [no Y] + [a it is in principle possible to obtain the variables of state (vx, V' from the equation (11) by integration. As a result of the instability of the equation (11), errors may arise, however.

As a result of the f act that the velocity in the longitudinal direction vx is measurable, the velocity in the transverse direction vy is observable. In the text which follows, the formulation of the observer for v y is indicated.

The differential equation (11) has the following general spatial representation of state:

dx/dt = A(t)x + u(t) (12) in this case, the following is applicable for the associated measurement equation:

y = &X (t) = (1 O)Tx(t) = vx (13) The following corresponds to this general statement of a system of equations, using the present model:

= (vx, vy) T 01 AM [o 0 u(t) = (a., a) T y (14) As a result of the transformation, known per se, into the observation standard form, the complete observer is obtained from the equations (12) and (13) in the following form:

(IX/dt = (A(t)-k(t)cl(t))X + k(t)y + u(t) (15) with the measurement equation y = CTX(t) = (1 O)Tx(t) = VX (16) In this case, the underlined vectors relate to the presentation in the observation standard form. The quantity k(t) is the observer gain k(t) = (ki k2)" If the equation (15) is written in explicit form, the following is obtained:

dAl/dt = x2nz + kl(y..xl) + ax (17) dX2/dt = --x-lnz + k2(y__Ki) + a y (18) The determination of the observer gain k(t) is prior art as the method of Prof. 0. F61linger: 11Entwurf zeitvarianter Systeme durch Polvorgabell ["Formulation of Time-Variant Systems through Specification of Poles"]. This method is presented in the International Journal of Control, 1983 Volume 38 No. 2, pages 419 to 431 in the article by

6 Bestle and Zeitz: Canonical form observer' design for nonlinear timevariable systems; therein, especially, on page 41. This literature reference reveals the so-called.Luebberger observer of the form:

p0 (do /dt)2 (do z /dt)-1 (19) p 1 dn z /CA - dt Q Z/dt12 In this case, the quantities po and p, are freely selectable as coefficients of the characteristic polynomial.

As an alternative to thist it is possible to determine the observer gain by means of a Kalman filter. Such a method is described in the book by Brammer/Siffling: 11Kalman-Bucy Filter" in the series 11Methoden der RegelungstechnikIl P'Methods of automatic control technology"] in the R. Oldenbourg publishing house in Munich, Vienna dating back to 1985. In this case, the following system of equations is obtained, comprising the equations (20), (21), (22), (23):

dpll/dt = -2 P21 dnz/dt - P211/R11 + Qk11 (20) dP21/dt = _P22 dnz/dt + p,, dnz/dt - P21P22/R11 + Qk21 (21) dP22/dt = 2 P22 dnz/dt - P22'/R11 + Qk22 (22) and k = [PP2]l R 11-1 2 2 (23) in this case, the values of the coefficients of the covariance matrix are Qk11 = 1, Qk21 = 0.3, Qk22 1 and the value R 11 = O.S. The initial values are p,,(-0) 01 P21(0) 0 and P22(0) = 0.

In an extension of the model, 'it is also possible to compensate the cardan setting angles in their action; in the earlier consideration of the system, these were disregarded.

7 To this end, in the first instance a subsystem 1 is described in which subsystem n. and v. are equal to 0. The following-equation is then obtained:

dvx/dt = ax + sin(r)g (24) Accordingly, the time average of the quantity sin(r)g may be computed from the difference of dvx/dt and ax, when nz and vz are equal to 0.

By means of a second subsystem, it is then possible to determine the quantities vx and VY using the quantity sin(r)g determined at nz = 0. In these circumstances, this subsystem has the equations:

dvx/dt = nzvy + ax + sin(r)g (25) dv y /dt = -nzvx + a y + 11 (26) dbt/dt = 0 (27) In this case, nx and n y are then not required. In this case, the quantity g is separately considered and corresponds to the expression cos(r)sin(95)g. For this subsystem, either 'an observer or a Kalman filter is then employed.

As an alternative to this, it is also possible to interpret all expressions which include at least one of the angles r or 0 as errors and to expand the order of the system. The result is then, for example, the following system of equations, which system can likewise again be processed by means of a Kalman filter:

dvx/dt = vynz + ax + ei (28) dv y /dt = -vxnz + ay + e2 (29) del/dt = 0 (30) de2/dt = 0 (31) and Y = Vx (32) An illustrative embodiment of the invention is diagrammatically shown in the drawing and it described in greater detail hereinbelow. In the drawing: Fig. 1: shows the block circuit diagram of an observer, in the case of which the pitch and roll angles r and were disregarded in the basic model, and 8 Fig. 2: shows an arrangement of sensors by which the process variables which form the basis of the models are determined.

As is evident from the block circuit diagram shown in Fig. 1, the vehicle velocity in the longitudinal direction vX# the longitudinal acceleration axi the transverse acceleration a y and the yaw angular velocity n z are employed as measured variables. In this case, the circles represent summation stations and at the rectangles with the dot the input variables are multiplied by one another. The integrators and amplifiers are selfexplanatory.

The block circuit diagram according to Fig. 1 is a representation of the equations (17) and (18).

Fig. 2 shows specific signals which are fed from sensors known per se to a computing device 407. The measured variables which correspond to the signals 401, 402, 403, 404, 405 and 406 are shown in Fig. 2. In the computing device, by way of example, the vehicle velocity in the transverse direction vy is determined on the basis of the initially described process and is output as signal 408. From this signal, it is then possible to compute the floating angle B in the computing unit 409 for example by means of the equation (1). This value is then output as signal 410.

9 claims 1. A process for the determination of quantities characterising the travel behaviour of a vehicle, with a computing device, to which signals are fed, which signals represent measured quantities of the vehicle longitudinal velocity (vx), of the longitudinal acceleration (ax), of the transverse acceleration (a y) and of the yaw angular velocity (nz), and in which at least one further quantity is derived on the basis of these measured quantities, wherein the derivation of the further quantity takes place with the use of the measured quantities and of equations of state, and at least the floating angle (B) is determined as derived quantity and output.

Claims

2. A process according to Claim 1, wherein the equations of state are

transformed into the observation standard form, and the at least one further quantity is derived by means of a complete observer.

3. A process according to Claim 1, wherein the observer gain is derived by means of a Kalman filter.

4. A process according to Claim 1, 2 or j, wherein roll movements and pitch movements of the vehicle are compensated in their action in the equations of state.

5. A process for the determination of quantities characterising the travel behaviour of a vehicle, substantially as described herein with reference to and as illustrated in the accompanying drawing.