Process for steering a road vehicle with front and rear wheel steering.

The invention relates to a method for steering a road vehicle with front and rear wheel steering.

When driving road vehicles such as cars, trucks, buses and the like, the driver is currently expected to master the dynamic behavior of the vehicle under different operating conditions, such as loading, road conditions, driving speed, etc., and to adjust his driving style accordingly. The assessment of borderline situations, such as black ice, tight corners will always remain the responsibility of the driver; Even before such limits are reached, there are considerable differences between an experienced driver and a beginner, and between different vehicles.

The difficulties that arise when unexpected yawing movements of the vehicle occur, such as on rainy roads, sudden evasive maneuvers, driving into a crosswind on a forest edge or behind a bridge, etc. are known. Incorrect steering reactions in such situations can then result Yaw motions are even amplified.

Many traffic accidents are due to driver errors and are based in particular on incorrect assessments of vehicle dynamics at different speeds, with different road conditions and different loads. The existing vehicle steering systems provide the driver with very little, if any, support.

So far, a steering angle that has been kept constant has been converted into a stationary circular arc travel with a constant radius and associated yaw rate. Which stationary value that is and how the transient process proceeds depends on the changing operating conditions.

Steering is often servo-assisted in vehicles on the market today; however, there is always a mechanical connection from the steering wheel to the front wheels, ie the steering wheel position commands the steering angle of the front wheels with a slight delay.

In experimental vehicles and also in the literature, such as in "Mechatronics for cars: integrating machines and electronics to prevent skidding on icy roads", by Y. Hossam EI-Deen and Ali Seireg in Computers in Mechanical Engineering, 1987, Stn. 10th to 22, the possibility of a so-called "drive-by-wire" system has already been investigated; Here, the steering wheel angle is measured, for example by means of a potentiometer tap, which is then a reference variable of an electrical control circuit with sensors and a control law implemented in a microcomputer, by means of which an electric or hydraulic motor is actuated to adjust the front wheels. The measured steering angle is compared with a target value, the so-called command variable.

Although the introduction of the "drive-by-wire" system to a large extent still precludes safety concerns, such as those that were brought up against the corresponding "fly-by-wire" system in aircraft 20 years ago, the main reasons for its introduction are the positive experiences in aviation with "fly-by-wire" systems, the introduction of the "drive by wire" for rear wheel steering and future development opportunities, such as automatic tracking, such as those examined in Europe in the so-called Prometheus program, as well as in the USA and Japan.

Additional rear wheel steering was first introduced by Japanese manufacturers. For example, Honda uses a mechanical connection through which the rear wheels are steered only depending on the steering wheel angle, in the same direction at smaller angles or in opposite directions at larger angles. Mazda has, for example, implemented a "drive-by-wire" system for the rear wheels, the ratio of the steering angles at the front and rear being changed as a function of the vehicle speed. Nissan and Mitsubishi also use a pressure measurement from the front wheel power steering in their "drive-by-wire" system for the rear wheel steering.

In a Ford test vehicle, the yaw rate r is measured with a gyroscope and introduced into the rear wheel steering system. The yaw rate r is considered an additional control variable, ie a fictitious yaw rate r is made from the steering wheel angle and driving speed_son calculated, and the difference (r_soh- r) is applied to the rear wheel steering via a vehicle-specific controller (see B. Los A. Matheis, JE Nametz and RE Smith, design and development of a vehicle with microprocessor-controlled all-wheel steering, VDI report No. 650, Düsseldorf 1987 No. 239 -257).

The idea of ​​a fictitious yaw rate r_son to use appears in various other publications. Here, however, quite contradictory information about the calculation or the determination of the value r_son made, which is determined empirically or theoretically from the stationary cycle.

The object of the invention is therefore to provide a method for steering road vehicles with front and rear wheel steering, in which the effects of yaw movements on the lateral movement of the front axle are automatically and completely compensated for and at the same time intrinsic values ​​of the yaw movements can be defined according to specifications. According to the invention, this is achieved in a method for steering road vehicles with front wheel and rear wheel steering by the features in the characterizing part of claim 1.

In the steering method according to the invention for road vehicles with front and rear wheel steering, the steering wheel angle no longer directly commands the steering angle as before, but advantageously the yaw rate. Compared to other systems in which a gyroscope is also used to measure the yaw rate, the often dubious estimate of a fictitious target yaw rate (r_son), which is derived from the driving speed and the steering wheel angle according to different criteria.

When using the steering method according to the invention, the driver only has to take over, as before, the path planning and the compensation of lateral deviations of the front axle of the vehicle from the planned path. According to the invention, this is made considerably easier for him by the fact that the yaw movement, which is dependent on variable parameters, no longer has any effect on the lateral movement of the front axle. When using the steering method according to the invention, the driver no longer has to worry about the yaw movement of the vehicle; it is always stable and can be dampened by constructive measures.

The particular advantage of the method according to the invention is that the required control no longer has to be designed specifically for the vehicle or changed depending on the operating state, since it is a simple, robust control in which, according to the invention, the yaw rate is given via the gyro feedback to an integrating actuator becomes.

Furthermore, according to the invention, since the vehicle has an additional rear wheel steering, eigenvalues ​​of the yaw movement can be set as desired via this rear wheel steering; on top of that, these eigenvalues ​​can even be designed to be switchable in adaptation to different driver requests, for example whether a more sporty or comfortable driving style is preferred.

The components that are required to set up a steering system designed according to the method according to the invention, such as gyroscopes, integrating motors or actuators and the like. are commercially available and therefore available because they are already used and used in vehicle construction for other purposes, but have not yet been interconnected to a steering system according to the method according to the invention.

The gyros that are required for series use in road vehicles must be reliable and inexpensive. In contrast, the requirements for their measurement accuracy and for a low drift, ie requirements which otherwise make the gyroscope expensive, are only low. Examples of possible uses for the steering method according to the invention are: Vibratory gyroscopes, such as those manufactured by Robert Bosch GmbH, Berlin, and for example at the DGON Symposium Gyro Technology, 1990 in Stuttgart by Kaiser, Boruschewitz, Hamisch, Gärtner, Pfaff in " Development of a low cost gyro based on an vibrating piezoelectric plate ", from British Aerospace, Plymouth manufactured vibration gyro (" Solid state vibrating shell gyro ", or Vibratory gyroscope manufactured by GEC Ferranti, Edinburgh.

Likewise, hydraulic actuators (without position feedback) have already been used for automatic tracking, as described, for example, by W. Darenberg in "Automatic Tracking of Motor Vehicles", automobile industry 1987, pages 155 to 159. By using better magnetic materials, electric servomotors can also be used for vehicle steering. Both the hydraulic actuators and the electric actuators have an integrating behavior.

In the following, the invention is explained in detail using a preferred embodiment with reference to the attached drawings. Show it:<ul id="ul0001" list-style="none"><li>1 shows a schematic representation of a single-track vehicle model when cornering;</li><li>2 shows a block diagram in which the relationship between different sizes of a status display and measures for steering is illustrated only by means of front wheel steering;</li><li>3 shows a block diagram equivalent to FIG. 2, in which other state variables are used to derive the control law;</li><li>4 shows a simplified representation of the block diagram of FIG. 3, and</li><li>5 shows a block diagram of a compensator for the pole specification of a yaw movement.</li></ul>

The theory on which the invention is based is first dealt with and then illustrated with the aid of block diagrams shown in FIGS. 2 to 4, in which the structure of a steering system according to the invention is made up of commercially available components and its mode of operation is illustrated.

A linearized, mathematical model is used for the vehicle dynamics during the steering movement. This is a single-track model, which is dealt with by P. Riekert and TE Schunk in the publication "On vehicle mechanics of rubber-tired motor vehicles" in Ing. Archiv 1940, the movements being described in the degrees of freedom yaw and swim. From A. Zomotor are used in the book "Fahrwerktechnik" published by Vogel-Verlag, Würzburg in 1987 in the chapter "driving behavior" the size designations also entered in Fig. 1, as follows:<ul id="ul0002" list-style="none"><li>ℓv v = distance from center of gravity to front axle</li><li>ℓ h = distance from center of gravity to rear axle</li><li>v = driving speed</li><li>ß = float angle (between the v-vector and the vehicle's longitudinal axis)</li><li>ψ = yaw rate (between the vehicle's longitudinal axis and an inertial reference system)</li><li>δ_v = Steering angle (front)</li><li>δ_H = Steering angle (rear)</li><li>SP = focus</li></ul>

Changing parameters of the vehicle and the road surface are:<ul id="ul0003" list-style="none"><li>Cy, C_H = Slip resistance at the front or rear</li><li>mg = vehicle mass</li><li>Ig_e.g. = Moment of inertia.</li></ul>

As equations of motion for the single-track model with steering only the front wheels, ie δ_v = δ and δ_H ≡0, then result according to Zomotor in the specified textbook (Ste.101):<maths id="math0001" num=""><img file="EP0474130A2_D0001.tif" /></maths><maths id="math0002" num=""><img file="EP0474130A2_D0002.tif" /></maths><maths id="math0003" num=""><img file="EP0474130A2_D0003.tif" /></maths>

If a variable r = ψ (= dψ / dt) is introduced for the yaw rate, the equations (1) and (2) can be written as:<maths id="math0004" num=""><img file="EP0474130A2_D0004.tif" /></maths><maths id="math0005" num=""><img file="EP0474130A2_D0005.tif" /></maths>or in matrix notation as a state model<maths id="math0006" num=""><img file="EP0474130A2_D0006.tif" /></maths>with the coefficients<maths id="math0007" num=""><img file="EP0474130A2_D0007.tif" /></maths><maths id="math0008" num=""><img file="EP0474130A2_D0008.tif" /></maths><maths id="math0009" num=""><img file="EP0474130A2_D0009.tif" /></maths><maths id="math0010" num=""><img file="EP0474130A2_D0010.tif" /></maths><maths id="math0011" num=""><img file="EP0474130A2_D0011.tif" /></maths><maths id="math0012" num=""><img file="EP0474130A2_D0012.tif" /></maths>

Two simplifying assumptions are made for the drafting of the control law: (1) The mass distribution in the longitudinal direction of the vehicle is equivalent to two concentrated masses on the front and rear axles, which gives the vehicle moment of inertia<maths id="math0013" num=""><img file="EP0474130A2_D0013.tif" /></maths>and the position of the center of gravity and thus the distances between the center of gravity and the front and rear axles ℓ_v andt_H, do not change with the vehicle mass mg. (2) The skew stiffness has a common factor µ that describes the adhesion with the road surface, ie<maths id="math0014" num=""><img file="EP0474130A2_D0014.tif" /></maths>where: µ = 1.0 for dry roads and µ = 0.5 for wet roads. This factor can be used to "normalize" the mass, ie the normalized mass can be defined as follows:<maths id="math0015" num=""><img file="EP0474130A2_D0015.tif" /></maths>

With these assumptions, the coefficients of the state model are (4):<maths id="math0016" num=""><img file="EP0474130A2_D0016.tif" /></maths>

The mathematical model manipulated in this way describes the influence of the unsafe operating parameters µ (vehicle mass / adhesion coefficient) and the driving speed v on the dynamics of the single-track model for steering. There are deviations from this model for an extremely changed mass distribution in the longitudinal direction of the vehicle, for example with full load in the trunk, and for extremely different adhesion factors on the front and rear wheels, such as when driving over a small icy area Derivation of the regulatory law with regard to the information provided are not taken into account here.

The interrelationship between the quantities β, r and δ according to Eq. (4) is illustrated by a block 10 in FIG.

According to the invention, the yaw angular velocity r is measured with a gyroscope 1. The associated setpoint r_son is tapped from the steering wheel angle by a potentiometer 2, for example. A control deviation u = (r_should - r) controls an integrating actuator 4 directly, ie with gain one and without dynamic compensation. In FIG. 2, in addition to the coefficients specified and defined in Eq. (4), which are represented by blocks a₁₁, a₁₂, a21, a₂₂, bi and b₂ are reproduced, integrating elements 5 and 6 and further adders 7 to 9 are shown.

The actuator 4 shown in FIG. 2 is, for example, a commercially available hydraulic or electric servomotor for the steering angle δ, in which the input signal u is integrated, so that:<maths id="math0017" num=""><img file="EP0474130A2_D0017.tif" /></maths>

An alternative embodiment is to use a conventional power steering with position feedback within the actuator. This can be done by the following differential equation<maths id="math0018" num=""><img file="EP0474130A2_D0018.tif" /></maths>or the transfer function<maths id="math0019" num=""><img file="EP0474130A2_D0019.tif" /></maths>with a time constant T_a describe. By using a PI controller with the transfer function<maths id="math0020" num=""><img file="EP0474130A2_D0020.tif" /></maths>an integrating behavior is again obtained. Summarized with Eq. (10 ') we get:<maths id="math0021" num=""><img file="EP0474130A2_D0021.tif" /></maths>ie the same behavior as with the servomotor (see G1.9) is achieved without feedback.

The steering angle δ is included in the state model (4) as a further state variable:<maths id="math0022" num=""><img file="EP0474130A2_D0022.tif" /></maths>

To derive the control law, another state variable is introduced instead of the float angle β, namely the lateral acceleration a_v on the front axle. According to Eq. (3) the lateral force F_c at the focus SP:<maths id="math0023" num=""><img file="EP0474130A2_D0023.tif" /></maths>and with that the lateral acceleration a_sp at the focus SP: a_sp = v (ψ + β). With the state model (13) the lateral acceleration a_sp at the focus SP:<maths id="math0024" num=""><img file="EP0474130A2_D0024.tif" /></maths>

On the front axle there is the influence of yaw acceleration<maths id="math0025" num=""><img file="EP0474130A2_D0025.tif" /></maths>so that the following then applies:<maths id="math0026" num=""><img file="EP0474130A2_D0026.tif" /></maths>and with Eqs. (13) and (14) we get:<maths id="math0027" num=""><img file="EP0474130A2_D0027.tif" /></maths>

The coefficients a_ij and b_i according to Eq. (8), so that:<maths id="math0028" num=""><img file="EP0474130A2_D0028.tif" /></maths>With<maths id="math0029" num=""><img file="EP0474130A2_D0029.tif" /></maths>

The relationship between the new and the old state vector is then:<maths id="math0030" num=""><img file="EP0474130A2_D0030.tif" /></maths><maths id="math0031" num=""><img file="EP0474130A2_D0031.tif" /></maths>and the state equation (13) takes the form after a few intermediate calculations:<maths id="math0032" num=""><img file="EP0474130A2_D0032.tif" /></maths>with the coefficients<maths id="math0033" num=""><img file="EP0474130A2_D0033.tif" /></maths><maths id="math0034" num=""><img file="EP0474130A2_D0034.tif" /></maths><maths id="math0035" num=""><img file="EP0474130A2_D0035.tif" /></maths><maths id="math0036" num=""><img file="EP0474130A2_D0036.tif" /></maths><maths id="math0037" num=""><img file="EP0474130A2_D0037.tif" /></maths><maths id="math0038" num=""><img file="EP0474130A2_D0038.tif" /></maths>

Crucial for the draft of the regulation law is the fact that the coefficients d₁₃ = 0 and d₁₂ = are. This is emphasized by the following notation:<maths id="math0039" num=""><img file="EP0474130A2_D0039.tif" /></maths>

According to the invention, a return is used for all vehicles and operating conditions<maths id="math0040" num=""><img file="EP0474130A2_D0040.tif" /></maths>used, the size r_son which is the target value for the yaw angular velocity r specified by the steering wheel, for example via a potentiometer tap. An insertion of the rule law (22) in Eq. (21) then yields:<maths id="math0041" num=""><img file="EP0474130A2_D0041.tif" /></maths>

This is referred to as a canonical form of the state representation for the splitting of the system into an observable and an unobservable subsystem. From Eq. (23) it can be seen that from the initial quantity<maths id="math0042" num=""><img file="EP0474130A2_D0042.tif" /></maths>from, the subsystem with the states r and δ is not observable. This means that its dynamics, which depend on changing operating conditions, are not included in the transfer function from the steering wheel to the lateral acceleration of the front axle. This transfer function results from the controllable and observable subsystem<maths id="math0043" num=""><img file="EP0474130A2_D0043.tif" /></maths>to<maths id="math0044" num=""><img file="EP0474130A2_D0044.tif" /></maths>with the time constant<maths id="math0045" num=""><img file="EP0474130A2_D0045.tif" /></maths>

The block diagram in FIG. 3 shows the relationship between the variables a_v, r, 0 and u in Eq. (21) in a particularly clear manner. In addition to the coefficients specified and defined in Eq. (20), which are represented by blocks d₁₁, d₂₁, d₂₂, d₂₃ and c are shown, the gyroscope 1, the potentiometer 2, integrating elements 4 'to 6' and addition elements 3 and 7 'to 9' are shown.

The inner connection in vehicle model 10 ′ marked with o in FIG. 3 is canceled by the feedback of the yaw angular velocity r measured with the gyro 1. FIG. 4 shows a simplified block diagram from which it can be seen that there is now no coupling from the yaw angular velocity r to the lateral acceleration a_v the front axle is more. However, since the block diagram of FIG. 4 corresponds exactly to the system in FIG. 3, the corresponding elements are also designated with the same reference numerals A steering command r_son acts on the two subsystems only coupled in one direction according to FIG. 4, so that their dynamics can now be examined individually. It can be seen that, on the one hand, a lateral acceleration a_v on the front axle according to Eq. (26) builds up, while on the other hand a control deviation δ = r_should- r arises, which leads to a constant steering angle δ and thus to s = 0 with a stable control loop in the stationary state, so that a deviation is thereby completely corrected.

The stability of the circle can be examined using its characteristic polynomial P (s):<maths id="math0046" num=""><img file="EP0474130A2_D0046.tif" /></maths>

When driving forward, both coefficients are c_H(ℓ_v + ℓ_H) / mvℓ_v and c_H/ m _v always positive and the control loop is therefore stable. When reversing, the vehicle movement with and without a gyro feedback is unstable and must therefore be stabilized by the driver.

From the driver's point of view, the following difference then results from a conventional steering at constant speed. In the conventional steering of the front wheels, a fixed steering angle corresponds to a smaller or larger stationary arc, depending on the load on the vehicle and the slickness of the road. According to the invention, the driver commands a yaw rate which is independent of the operating conditions and corresponds to a fixed, stationary circular arc.

Yaw motions, which are not triggered by a driver command, but, for example, by cross wind or due to the nature of the road, are now automatically compensated; This leads to increased safety if, for example, the vehicle drives into a strong cross wind from a forest.

The yaw rate can be measured, for example, using a commercially available gyro. Since only a feedback has to be implemented without a further control algorithm, the gyro can also be integrated mechanically or fluidically into the servomotor for the steering, for example. The target yaw rate can also be reconstructed from the measurements of two accelerometers.

In a vehicle with additional rear wheel steering, the dynamics of the yaw movement can be changed as desired. First, Eq. (28), which in this form only applies to front wheel steering, with the aid of a damping variable D and a natural frequency ω_n rewritten, ie with the expression<maths id="math0047" num=""><img file="EP0474130A2_D0047.tif" /></maths>compared. The result is:<maths id="math0048" num=""><img file="EP0474130A2_D0048.tif" /></maths><maths id="math0049" num=""><img file="EP0474130A2_D0049.tif" /></maths>

In terms of design, the damping D can be achieved with a long wheelbase ℓ_H+ ℓ_v, a small vehicle mass m, a center of gravity SP far ahead, ie a small distance from the center of gravity of the front axle ℓ _v as well as a large rear slip resistance c_H increase. This then also becomes the natural frequency ω_n made as big as possible.

When implementing these design considerations, however, conflicts can arise, so that alternative ways of increasing the damping are of interest. Since the type of yaw movement is perceived or desired differently by different drivers, it is quite interesting if it is possible to switch between a "sporty" and "comfortable" driving style. These possibilities are given in vehicles with an additional rear wheel steering by the steering method according to the invention.

In Eq. (1) for the lateral movement must take into account Eq. (6) the steering term -C_vδ are replaced by the expression (-C_v• δ_v-C_H• δ_H), and in Eq. (2) for the yaw movement, the steering term -C_v ℓ_v δ replaced by the expression (-C_v ℓ_v δ_v + C_H ℓ_H δ_H ), where δ_v and δ_H are the front and rear steering angles. The status display (4) thus becomes:

<maths id="math0050" num=""><img file="EP0474130A2_D0050.tif" /></maths><maths id="math0051" num=""><img file="EP0474130A2_D0051.tif" /></maths><maths id="math0052" num=""><img file="EP0474130A2_D0052.tif" /></maths>Instead of Eq. (9) there are now two integrating servomotors, so that the following applies:<maths id="math0053" num=""><img file="EP0474130A2_D0053.tif" /></maths>

The equation of state or model (13) then becomes:<maths id="math0054" num=""><img file="EP0474130A2_D0054.tif" /></maths>

Eqs. (14) and (15) then widen<maths id="math0055" num=""><img file="EP0474130A2_D0055.tif" /></maths><maths id="math0056" num=""><img file="EP0474130A2_D0056.tif" /></maths>

However, the following applies:<maths id="math0057" num=""><img file="EP0474130A2_D0057.tif" /></maths>so that Eq. (16) with δ = δ_v applies unchanged and thus also Eqs. (18) and (19). From Eq. (21) will however:<maths id="math0058" num=""><img file="EP0474130A2_D0058.tif" /></maths>

The return from r to u_v according to Eq. (22) then causes:<maths id="math0059" num=""><img file="EP0474130A2_D0059.tif" /></maths>

The subsystem with the state variables r, δ_v and δ_H is then not of a_v from observable. A return of a_v would have no influence on its dynamics. The subsystem is (due to the value -1 from the gyro feedback) of u_H taxable; thus its eigenvalues ​​can be set arbitrarily by a state vector feedback. The states r (which are obtained by gyroscopes) and the quantities δ_v and δ_Hwhich are obtained from front and rear steering angle sensors can be measured, so that the state vector feedback can be implemented.

The subsystem is now used to execute the pole specification:<maths id="math0060" num=""><img file="EP0474130A2_D0060.tif" /></maths>With<maths id="math0061" num=""><img file="EP0474130A2_D0061.tif" /></maths>examined. Through a state vector feedback<maths id="math0062" num=""><img file="EP0474130A2_D0062.tif" /></maths>the system receives the characteristic polynomial P (s):<maths id="math0063" num=""><img file="EP0474130A2_D0063.tif" /></maths>

Conversely, for a given, characteristic polynomial P (s) from Eq. (43), the state vector feedback required for this can be obtained<maths id="math0064" num=""><img file="EP0474130A2_D0064.tif" /></maths>With<maths id="math0065" num=""><img file="EP0474130A2_D0065.tif" /></maths>or<maths id="math0066" num=""><img file="EP0474130A2_D0066.tif" /></maths><maths id="math0067" num=""><img file="EP0474130A2_D0067.tif" /></maths><maths id="math0068" num=""><img file="EP0474130A2_D0068.tif" /></maths>with the pole specification matrix<maths id="math0069" num=""><img file="EP0474130A2_D0069.tif" /></maths>

In driving tests it must then be found out which position of the eigenvalues ​​of the yaw movement is perceived by drivers as pleasant.

According to the invention, the front steering angle need not be measured. Rather, an electronic integrator is used in the rear wheel steering. Together with a servomotor, ie a mechanical integrator, a second-order compensator can be constructed, as shown in a block diagram in FIG. The upper part of FIG. 5 corresponds to the simplified form of the block diagram shown in FIG. 4, to which only an additional adder 11 has been added. In the lower part of FIG. 5, in addition to a setpoint generator 12 for the rear steering, additional adders 13 and 14 and a further integrator 15 and an integrating servomotor 16 in addition to the coefficient blocks do, di, eo, ei and b₂₂ intended.

The transfer function of the compensator for the y_c open control loop is:<maths id="math0070" num=""><img file="EP0474130A2_D0070.tif" /></maths>

Additional input variables of the compensator can be set by a setpoint generator from the variables r_son and v are generated, the overall control has no influence on the eigenvalues ​​of the yaw movement. Rather, these eigenvalues ​​result from the interconnection of the compensator in accordance with the transfer function (48) with the subsystem with the input value y_c and the initial value r. Its state model results from Eq. (40) as follows:<maths id="math0071" num=""><img file="EP0474130A2_D0071.tif" /></maths>

Only the input y = b is used for the pole specification of the yaw movement₂₂ δ_H used and the corresponding transfer function is then:<maths id="math0072" num=""><img file="EP0474130A2_D0072.tif" /></maths>

The characteristic polynomial of the yaw movement follows from the closing condition of the circle via the compensator:<maths id="math0073" num=""><img file="EP0474130A2_D0073.tif" /></maths>

The coefficient comparison with a default polynomial<maths id="math0074" num=""><img file="EP0474130A2_D0074.tif" /></maths>gives the system of equations<maths id="math0075" num=""><img file="EP0474130A2_D0075.tif" /></maths>

The coefficients d₂₂, d₂₃ and b₂₂ given and the compensator coefficients do, di, eo and ei result in:<maths id="math0076" num=""><img file="EP0474130A2_D0076.tif" /></maths>

The desired eigenvalues ​​can be specified for the controlled system "yaw dynamics", so that the characteristic polynomial (52) is then also specified and the compensator coefficients do, di eo and ei according to (54) provide the required compensator setting.

After the stability of a vehicle is reliably guaranteed when the method according to the invention is applied, further requirements regarding the steering of the rear wheels can be realized without compromise and thus also without any effects on the stability. The compensator shown in the block diagram in FIG. 5 offers two intervention options for a setpoint generator which, for example, specifies the setpoint yaw rate r specified by the driver_should as well as the driving speed v processed. Such a typical requirement would be that yaw angular velocity and lateral acceleration at the driver's seat, as the two motion quantities actually perceived by the driver, have the same phase delay. The orientation of the vehicle's longitudinal axis relative to the curve tangent could also be influenced.