Abstract:
A method for determining an optimal steering angle in understeer situations of a vehicle is described. To assist a driver in reliably stabilizing the vehicle during an understeer situation while driving, a model-based driving traction coefficient factor, a model-based kinematic factor, and a float angle are taken into account in the determination of a steering angle. A limited steering angle δ v,lim  at which a maximum lateral force is set, is determined by addition of the driving traction coefficient factor, the kinematic factor, and the float angle. A system suitable for implementation of the method is also described.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is the U.S. national phase application of PCT International Application No. PCT/EP2007/054125, filed Apr. 26, 2007, which claims priority to German Patent Application No. DE102006020279.1, filed Apr. 27, 2006 and German Patent Application No. DE102007020169.0, filed Apr. 26, 2007, the contents of such applications being incorporated by reference herein in their entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a device and method for determining an optimum steering angle in understeer situations of a vehicle. 
     2. Description of the Related Art 
     Modern vehicles use electronically controllable motors in the steering train in order, on the one hand, to selectively influence the steering torque to be applied by the driver (power steering systems) and, on the other hand, to selectively set steering angles independently of the driver (superimposition steering systems). In addition to these steering systems which act on the front axle of the vehicle, modern chassis control systems, for example global chassis control (GCC) also use rear axle steering systems for controlling the vehicle dynamics. 
     In order to influence the steering torque which is to be applied by the driver, various closed-loop and open-loop control structures which are respectively aimed at the specific driving situation are known. For example in the case of oversteering driving situations, closed-loop control on the basis of a yaw rate reference is used (WO 2005/054039 A1) and in the case of braking on μ split open-loop control on the basis of ABS wheel information is used (WO 2005/054040 A1). In the case of understeering driving situations, the steering angle which is present when the situation is detected is “frozen”, i.e. by means of a torque control is to be recommended to the driver that he should not increase the steering angle and as a result make the situation worse. A disadvantage with this concept is that the driver is not provided with any feedback about the maximum possible lateral force. 
     It would therefore be desirable if the driver could be assisted in such a way that he can set a maximum lateral force at the wheels. 
     DE 10 2005 036 708 A1 discloses stabilizing means which actuate the steering means as a function of a lateral force coefficient of at least one of the steered wheels in order to set a steering angle which stabilizes the vehicle, in which case the stabilizing means set a slip angle of the steered wheels in such a way that the lateral force coefficient does not substantially exceed the region of the maximum. 
     SUMMARY OF THE INVENTION 
     The invention relates to improving a method of the type mentioned previously in such a way that during an understeering driving situation the driver is reliably assisted in stabilizing the vehicle. 
     The invention makes available a method for determining an optimum steering angle in understeering situations of a vehicle, in which method a first portion which represents the adhesion coefficient in the lateral direction is taken into account in the determination, in which method a second portion which represents a kinematic portion is taken into account, and in which method a third portion which represents the attitude angle is taken into account, and in which method the steering angle δ v,lim  is determined by adding the portion of the adhesion coefficient, the kinematic portion and the attitude angle. 
     The kinematic portion comprises the proportional velocities from the rotation of the vehicle referred to the velocity of the center of gravity. 
     The system for controlling electronically controllable motors in the steering train advantageously permits the driver to set the maximum lateral force value in understeering situation by means of power steering. This assistance during steering allows the vehicle to be stabilized in critical driving situations. All wheel steering systems are taken into account here. 
     During the understeering, the attitude angle can advantageously be estimated according to the relationship β≈0, since the attitude angle is approximately zero at the start of the understeering driving situation. 
     The coefficient of friction of the underlying surface is advantageously determined at the axles and the center of gravity of the vehicle. The coefficient of friction {circumflex over (μ)} 0 =max(μ VA ,μ CoG ,μ HA ) of the underlying surface is determined according to at least one of the relationships, 
     utilizing the adhesion for the front axle 
                 µ   VA     =             (       a   x     -       l   V     ⁢       ψ   .     2         )     2     +       (       a   y     +       l   V     ⁢     ψ   ¨         )     2         g       ,         
or
 
utilizing the adhesion at the center of gravity of the vehicle
 
                 µ   CoG     =           a   x   2     +     a   y   2         g       ,         
or
 
using the adhesion at the rear axle
 
     
       
         
           
             
               µ 
               HA 
             
             = 
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             a 
                             x 
                           
                           - 
                           
                             
                               l 
                               H 
                             
                             ⁢ 
                             
                               
                                 ψ 
                                 . 
                               
                               2 
                             
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             a 
                             y 
                           
                           + 
                           
                             
                               l 
                               H 
                             
                             ⁢ 
                             
                               ψ 
                               ¨ 
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
                 g 
               
               . 
             
           
         
       
     
     The optimum steering angle is advantageously calculated in a model in which the steering angle is determined in terms of absolute value according to the relationship 
     
       
         
           
             
               δ 
               
                 V 
                 , 
                 lim 
               
             
             = 
             
               
                 
                   
                     l 
                     V 
                   
                   
                     v 
                     x 
                   
                 
                 ⁢ 
                 
                    
                   
                     ψ 
                     . 
                   
                    
                 
               
               + 
               
                 
                   2 
                   
                     C 
                     α0 
                   
                 
                 ⁢ 
                 
                   
                     
                       µ 
                       ^ 
                     
                     0 
                   
                   . 
                 
               
             
           
         
       
     
     The steering angle δ v,lim  or a steering angle δ v,lim  which is multiplied by a factor k is used as a setpoint value for a steering angle control means or a steering torque control means. 
     Furthermore, there is advantageously provision that a steering torque control means is activated according to the relationship δ v,lim &lt;|δ v | 
     or deactivated according to the relationship δ v,lim &lt;|δ v |. 
     Furthermore, the invention makes available an advantageous device for carrying out the method according to aspects of the invention. 
     The device for determining an optimum steering angle in understeering situations of a vehicle is based on a determining unit for determining a stabilizing steering angle taking into account a model-based portion of the adhesion coefficient, a model-based kinematic portion and an attitude angle. 
     These and other aspects of the invention are illustrated in detail by way of the embodiments and are described with respect to the embodiments in the following, making reference to the Figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is best understood from the following detailed description when read in connection with the accompanying drawing. Included in the drawing are the following figures: 
         FIG. 1  is a block circuit diagram with an overview of a control system of an electric power steering system for determining a steering torque, 
         FIG. 2  is a block circuit diagram with an overview of a control system of a superimposition steering system for determining a steering torque, 
         FIG. 3  shows a refinement of the controller illustrated in  FIGS. 1 and 2 , with the controller portions which relate to the steering, 
         FIG. 4  shows an embodiment of a block of the block circuit diagram which is illustrated in  FIG. 2  and which determines a steering torque, 
         FIG. 5  shows a first embodiment of a block of the block circuit diagram which is illustrated in  FIG. 2  and has the purpose for determining an additional steering angle, 
         FIG. 6  shows an embodiment of a block for applying interference variables for the torque controller, 
         FIG. 7  shows an illustration of the reference variables on a vehicle with the models for the determination of the slip angle and the attitude angle, and 
         FIG. 8  shows a characteristic curve of the adhesion coefficient in the lateral direction. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The description is based on a two-axle, four-wheel motor vehicle having steerable wheels on at least one front axle  10  and, if appropriate, also on a rear axle  12 .  FIG. 1  is a schematic illustration of a vehicle having a steering actuator. A steering wheel  20  which is attached to a steering column  18  is connected via a steering gear  22  to the steered wheels  24 ,  26  of the vehicle. The steering gear  22  is preferably embodied as a toothed rack steering system which has a pinion (not illustrated), which is connected to the steering column in a rotationally fixed fashion. A torque sensor  14 , which determines the driver&#39;s steering request here by means of a manual steering toque M H  is arranged on the steering column. An electrical EPS servomotor  16  (EPS=Electric Power Steering) applies an additional steering torque M DSR  to the steering train during conventional operation, which steering torque M DSR  increases the steering torque M H  applied by the driver. 
     In order to set an additional steering torque request M DSR  (DSR=Driver Steering Recommendation) to assist the driver, the electric power steering system is used, said electric power steering system being actuated here by a, for example, GCC controller  28  (GCC=Global Chassis Control), for example via an interface with the CAN bus of the vehicle. The steering wheel angle δ L  which is set by the driver and the rear axle steering angle δ H , which are measured with steering angle sensors  30 ,  32  which are arranged on the steering column  18  and on the rear axle  12 , and the manual steering torque M H  which is determined by the torque sensor  14  are made available to the controller  28  as input variables. Furthermore, the controller  28  is provided with additional variables from the vehicle dynamics controllers and/or driver assistance controllers, as described in more detail in the applications mentioned previously. The controller  28  determines the additional steering torque M DSR  by means of the information which is made available. The EPS servomotor  16  serves here as an actuator which applies the steering torque M DSR  (DSR=Driver Steering Recommendation) to the steering train in correlation with the manual steering torque M H  via the transmission  34 . Furthermore, the controller  28  calculates a rear axle steering angle δ H,soll , which is transmitted to the rear axle via a rear axle steering unit  36 . 
     However, in a similar way, the invention can also be used in vehicles with other steering systems such as, for example, steering systems with hydraulic power steering with an external torque interface (for example APS, Active Power Steering) or a separate torque actuator (for example IPAS, Intelligent Power Assisted Steering). 
       FIG. 2  shows a power steering system with two steering actuators. Identical components and identical blocks have the same reference symbols here. In addition, compared to the embodiment according to  FIG. 1 , a superimposition transmission  40  is arranged on the steering column  18 . The superimposition transmission is generally embodied as a planetary gear mechanism and divides the steering column into two sections  18   a  and  18   b . By means of the superimposition transmission  40  it is possible to superimpose a further steering angle on the steering wheel angle δ L  measured by the steering wheel angle sensor  32 . The composite steering angle δ v  is measured by the steering angle sensor  42  which is arranged on the section  18   b  of the steering column. The superimposition transmission  40  is driven by a steering wheel motor  44 . The steering wheel motor  44  is controlled by the controller  28  whose reference variable is the correction steering wheel angle Δδ soll . For this purpose, the steering angle δ v  which is measured by the front axle steering wheel sensor  42  is made available to the controller  28 . As in the control system described in  FIG. 1 , the controller  28  is provided with further variables from vehicle dynamics controllers and/or driving assistance controllers. 
     The wheel steering angle of the front axle δ v  is included in the additional steering torque M DSR  according to the relationship 
                     δ   V     =       δ   L       i   L               (   2.1   )               
where i L  is the steering transmission ratio. The steering transmission ratio is constant or, in the case of a superimposition steering system, it can also depend on further variables such as, for example, the velocity of the vehicle.
 
     In the case of a steering angle control, the wheel steering angle of the front axle is measured directly. 
     In the case of the servomotors  16  which are illustrated in  FIGS. 1 and 2 , the servomotor is preferably required to receive a setpoint steering torque from the GCC controller and to control it independently in the manner of an “intelligent actuator”. The current manual steering torques M H  are acquired by the torque sensor  14  and fed back to the GCC controller  28 . The torque sensor  14  is optional, an IPAS does not contain a torque sensor. The presence of a rear axle steering system is not absolutely necessary for the method. However, the further statements assume that the vehicle is equipped with a rear axle steering unit (for example ARK, Active Rear Axle Kinematics). The method for calculating the maximum steering angle is also suitable for pure superimposition steering as per  FIG. 2 , in order to apply this value independently of the value specified by the driver. 
     The components and interfaces of the GCC controller  28  are represented in  FIG. 3 . Only the portions which relate to the steering are illustrated. Controller portions for other actuators such as, for example a brake, internal combustion engine, stabilizer etc. are not illustrated. The steering angle controller  50  and the steering torque controller  52  are either alternatively present or are present together for steering systems as illustrated in  FIG. 2 . The steering angle controller  50  generates steering angle setpoint values Δδ soll , δ H,soll  for the front axle  10  and the rear axle  12 . The steering torque controller  52  generates the additional steering torque M DSR  which, as a driver steering recommendation (DSR, Driver Steering Recommendation), constitutes a haptic feedback for the driver. The following variables are made available as input variables to the steering wheel controller  50  and the steering torque controller  52 :
     a x  longitudinal acceleration, measured with a longitudinal acceleration sensor or estimated from wheel speed signals   p B  brake pressure, measured with a pressure sensor (1× driver) or estimated at the wheel brakes of the respective wheels  24 ,  26  or in a model for the four wheel brakes of the wheels  24 ,  26     dψ/dt yaw rate   a y  lateral acceleration   v x  velocity of vehicle, estimated from wheel speed signals   δ L  steering wheel angle   δ v  wheel steering angle front axle   δ H  wheel steering angle rear axle   

     In addition, the driver manual torque M H  which is determined by the torque sensor  14  is also supplied as an input variable to the steering torque controller  52 . If the steering angle controller  50  is also present, the change in setpoint in the wheel steering angle Δδ soll  is additionally fed as an input variable to the steering torque controller  52 . 
     An exemplary embodiment of the steering torque controller  52  in understeering situations is illustrated in  FIG. 4 . An exemplary embodiment of the steering angle controller  50  in understeering situations is shown by  FIG. 5 . 
     Both controller  50 ,  52  have the following basic design of the steering train control system for determining the steering torque request M DSR  or the steering angle request Δδ soll . Driving situations in which an understeering driving state of the vehicle is present are detected in the blocks  60  and  62 . Said blocks make use, in particular, of information which is made available by a vehicle dynamics controller. The driving state controller can be, for example, an ESP system and/or an ABS system. Critical driving situations in which the vehicle understeers are preferably detected in the block  60  by means of an ESP understeering detection means. As an alternative, understeering of the vehicle is detected in the block  62  by means of a slip angle understeering detection means. 
     The detection of an understeering situation is carried out here at both controllers  50 ,  52  according to two alternatives. An understeering detection means which is expanded with the rear axle steering portion and consists in the ESP uses the linear steady-state single-track model. 
     
       
         
           
             
               
                 
                   
                     ψ 
                     . 
                   
                   = 
                   
                     
                       
                         v 
                         x 
                       
                       
                         l 
                         + 
                         
                           EGv 
                           x 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             δ 
                             V 
                           
                           - 
                           
                             δ 
                             H 
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   3.1 
                   ) 
                 
               
             
           
         
       
     
     The model (3.1) supplies a reference for the front axle steering angle in the form 
     
       
         
           
             
               
                 
                   
                     δ 
                     
                       V 
                       , 
                       ref 
                     
                   
                   = 
                   
                     
                       
                         l 
                         
                           v 
                           x 
                         
                       
                       ⁢ 
                       
                         ψ 
                         . 
                       
                     
                     + 
                     
                       EGa 
                       y 
                     
                     + 
                     
                       
                         δ 
                         H 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   3.2 
                   ) 
                 
               
             
           
         
       
     
     Understeering is detected if the difference
 
|δ V |−|δ V,ref   |&gt;S   δ   (3.3)
 
exceeds a predefined threshold value S δ . The second possible way of detecting understeering is based on the slip angle at the front axle.
 
                     α   V     =       -     δ   V       +   β   +         l   V       v   x       ⁢       ψ   .     .                 (   3.4   )               
and the slip axle at the rear axle, cf.  FIG. 7 ,
 
     
       
         
           
             
               
                 
                   
                     α 
                     H 
                   
                   = 
                   
                     
                       - 
                       
                         δ 
                         H 
                       
                     
                     + 
                     β 
                     - 
                     
                       
                         
                           l 
                           H 
                         
                         
                           v 
                           x 
                         
                       
                       ⁢ 
                       
                         
                           ψ 
                           . 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.5 
                   ) 
                 
               
             
           
         
       
     
     The detection requires not only the individual slip angles but also the difference 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     α 
                   
                   = 
                   
                     
                       
                         α 
                         V 
                       
                       - 
                       
                         α 
                         H 
                       
                     
                     = 
                     
                       
                         δ 
                         H 
                       
                       - 
                       
                         δ 
                         V 
                       
                       + 
                       
                         
                           l 
                           
                             v 
                             x 
                           
                         
                         ⁢ 
                         
                           
                             ψ 
                             . 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.6 
                   ) 
                 
               
             
           
         
       
     
     Understeering is detected as a function of a threshold value for the difference (3.6) between the slip angle and the sign of the yaw rate if the following is true
 
 dψ/dt&gt; 0 and Δα&lt;− S   α 
 
or
 
 dψ/dt&lt; 0 and Δα&gt; S   α 
 
     The threshold value S α  is between 2 and 10 degrees, and is preferably 5 degrees. If an understeering situation is detected in one of the blocks  60 ,  62  from the upward transgression of the threshold values S δ  or S α , the understeer flag  64 , which is the output signal of the block  60  or  62 , is set to the value 1. The understeer flag is reset from the value 1 to the value 0 if the aforesaid conditions are no longer met. However, relatively small threshold values are preferably used as the basis so that the control is steadied by a hysteresis. 
     The threshold values may be dependent on further variables of the vehicle dynamics such as, for example, the velocity v x  of the vehicle or the coefficient of friction μ of the underlying surface. As the velocity decreases, the threshold values are increased, and as the coefficient of friction of the underlying surface decreases they are correspondingly decreased. 
     The blocks  60 ,  62  are connected via an OR element  66  to an activation logic  68  for activating the control system. The wheel steering angle δ v  of the front axle, the limited wheel steering angle δ v,lim  of the front axle, the determination of which will be described later, and the understeer flag  64  are input into the activation logic  68  as the input signal. 
     If the following conditions are met
 
δ V,lim &lt;|δ V |
         and understeer flag=1
 
the steering torque control  52  is activated by an understeer active flag, which represents the output signal of the activation logic  68 , being set to the value 1.
       

     The torque control  52  is terminated and the output signal understeer active flag of the activation logic  68  is set to 0 if the following conditions apply: 
     δ V,lim &gt;|δ V | 
     
         
         
           
             or understeer flag=0
 
or after termination conditions which provide for a termination after a predetermined time has expired.
 
           
         
       
    
     Each of the controllers  50 ,  52  contains a determining unit  70  for limiting the steering angle, to which determining unit  70  the yaw rate dΨ/dt, the longitudinal acceleration a x , the lateral acceleration a y , and the velocity v x , of the vehicle are added as input variables. 
     The limitation of the steering angle serves to determine a limitation of the wheel steering angle at the front axle. For this purpose the following polynomial model of the lateral force is used 
     
       
         
           
             
               
                 
                   
                     F 
                     y 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 - 
                                 
                                   ( 
                                   
                                     
                                       
                                         C 
                                         
                                           a 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           0 
                                         
                                       
                                       ⁢ 
                                       
                                         F 
                                         z 
                                       
                                       ⁢ 
                                       α 
                                     
                                     - 
                                     
                                       sign 
                                       ⁢ 
                                       
                                         ( 
                                         α 
                                         ) 
                                       
                                       ⁢ 
                                       
                                         
                                           
                                             C 
                                             
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                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               0 
                                             
                                             2 
                                           
                                           ⁢ 
                                           
                                             F 
                                             z 
                                             2 
                                           
                                         
                                         
                                           4 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             μ 
                                             0 
                                           
                                           ⁢ 
                                           
                                             F 
                                             z 
                                           
                                         
                                       
                                       ⁢ 
                                       
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                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   1 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         
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                                           x 
                                         
                                         
                                           
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                                             z 
                                           
                                         
                                       
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                             , 
                           
                         
                         
                           
                             
                                
                               α 
                                
                             
                             &lt; 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   μ 
                                   0 
                                 
                               
                               
                                 C 
                                 
                                   α 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 - 
                                 
                                   sign 
                                   ⁡ 
                                   
                                     ( 
                                     α 
                                     ) 
                                   
                                 
                               
                               ⁢ 
                               
                                 μ 
                                 0 
                               
                               ⁢ 
                               
                                 F 
                                 z 
                               
                               ⁢ 
                               
                                 
                                   1 
                                   - 
                                   
                                     
                                       ( 
                                       
                                         
                                           F 
                                           x 
                                         
                                         
                                           
                                             μ 
                                             0 
                                           
                                           ⁢ 
                                           
                                             F 
                                             z 
                                           
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                               
                             
                             , 
                           
                         
                         
                           
                             
                                
                               α 
                                
                             
                             ≥ 
                             
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   μ 
                                   0 
                                 
                               
                               
                                 C 
                                 
                                   α 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   0 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.7 
                   ) 
                 
               
             
           
         
       
     
     If the lateral force F y  is related to the vertical force F z , the characteristic curve of the adhesion coefficient in the lateral direction which is illustrated in  FIG. 8  is obtained from the model (3.7). The adhesion coefficient reaches its maximum value at the slip angle 
     
       
         
           
             
               
                 
                   
                     α 
                     lim 
                   
                   = 
                   
                     
                       μ 
                       0 
                     
                     ⁢ 
                     
                       2 
                       
                         C 
                         
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           0 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.8 
                   ) 
                 
               
             
           
         
       
     
     The steering angle corresponding to the maximum adhesion coefficient can be determined, from (3.4) using (3.8), as 
     
       
         
           
             
               
                 
                   
                     
                       δ 
                       V 
                     
                     ⁢ 
                     
                       ❘ 
                       
                         
                           α 
                           V 
                         
                         = 
                         
                           α 
                           lim 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         
                           l 
                           V 
                         
                         
                           v 
                           x 
                         
                       
                       ⁢ 
                       
                         ψ 
                         . 
                       
                     
                     - 
                     
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             α 
                             V 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         μ 
                         0 
                       
                       ⁢ 
                       
                         2 
                         
                           C 
                           
                             α 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                     
                     + 
                     
                       β 
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   3.9 
                   ) 
                 
               
             
           
         
       
     
     The coefficient of friction μ 0  of the underlying surface and the attitude angle β cannot be acquired economically in terms of measuring technology in the vehicle. In the case of understeering, the following applies approximately to the attitude angle
 
β≈0.  (3.10)
 
     An estimation of the coefficient of friction of the underlying surface on the basis of the accelerations of the center of gravity of the vehicle (CoG Center of Gravity) or of the front and rear axles yields
 
{circumflex over (μ)} 0 =max(μ VA ,μ CoG ,μ HA ),  (3.11)
 
using the adhesion for the front axle
 
                       μ     V   ⁢           ⁢   A       =             (       a   x     -       l   V     ⁢       ψ   .     2         )     2     +       (       a   y     +       l   v     ⁢     ψ   ¨         )     2         g       ,           (   3.12   )               
using the adhesion at the center of gravity of the vehicle
 
                     μ   CoG     =           a   x   2     +     a   y   2         g             (   3.13   )               
and using the adhesion at the rear axle
 
     
       
         
           
             
               
                 
                   
                     μ 
                     HA 
                   
                   = 
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   a 
                                   x 
                                 
                                 + 
                                 
                                   
                                     l 
                                     H 
                                   
                                   ⁢ 
                                   
                                     
                                       ψ 
                                       . 
                                     
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   a 
                                   y 
                                 
                                 - 
                                 
                                   
                                     l 
                                     H 
                                   
                                   ⁢ 
                                   
                                     ψ 
                                     ¨ 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                       g 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   3.14 
                   ) 
                 
               
             
           
         
       
     
     Taking into account the relationship of the signs of the slip angle and lateral acceleration
 
sign(α lim )=−sign( a   y )  (3.15)
 
the aimed-at limitation of the wheel steering angle at the front axle is obtained, in terms of absolute value, as
 
     
       
         
           
             
               
                 
                   
                     δ 
                     
                       V 
                       , 
                       lim 
                     
                   
                   = 
                   
                     
                       
                         
                           l 
                           v 
                         
                         
                           v 
                           x 
                         
                       
                       ⁢ 
                       
                          
                         
                           ψ 
                           . 
                         
                          
                       
                     
                     + 
                     
                       
                         2 
                         
                           C 
                           
                             α 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                       ⁢ 
                       
                         
                           μ 
                           ^ 
                         
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.16 
                   ) 
                 
               
             
           
         
       
     
     The parameter C ∞  may be dependent on the coefficient of friction of the underlying surface and has to be applied in the driving trial. 
     A small attitude angle is assumed for the calculation of the limitation of the steering angle according to (3.10). It has to be assumed that the vehicle initially veers in and the attitude angle therefore increases. For this reason, the limitation should be performed only for a certain time (preferably 4 s). In a haptic system, the increase in the steering torque should then be cancelled. In a superimposition steering system, the additional steering angle is reduced again after this time. 
     The limited wheel steering angle δ v,lim  which is calculated in accordance with 3.16 is made available to the activation logic  68  which activates or terminates the steering torque control  52  on the basis of the previously described conditions. 
     In order to control the steering torque or steering angle, the current wheel steering angle δ v  of the front axle passes with reversed sign through a transmission element  72  with a dead zone. The dead zone is defined between the positive and negative values of the current limitation for the wheel steering angle (3.16). The output variable of the dead zone transmission element  72  is the control error 
     
       
         
           
             
               
                 
                   
                     e 
                     δ 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               - 
                               
                                 δ 
                                 V 
                               
                             
                             - 
                             
                               δ 
                               
                                 V 
                                 , 
                                 lim 
                               
                             
                           
                         
                         
                           
                             f 
                             ⁢ 
                             
                               u 
                               ¨ 
                             
                             ⁢ 
                             r 
                           
                         
                         
                           
                             
                               - 
                               
                                 δ 
                                 V 
                               
                             
                             ≥ 
                             
                               δ 
                               
                                 V 
                                 , 
                                 lim 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             f 
                             ⁢ 
                             
                               u 
                               ¨ 
                             
                             ⁢ 
                             r 
                           
                         
                         
                           
                             
                               - 
                               
                                 δ 
                                 V 
                               
                             
                             &gt; 
                             
                               - 
                               
                                 δ 
                                 
                                   V 
                                   , 
                                   lim 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               - 
                               
                                 δ 
                                 V 
                               
                             
                             + 
                             
                               δ 
                               
                                 V 
                                 , 
                                 lim 
                               
                             
                           
                         
                         
                           sonst 
                         
                         
                           
                               
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3.17 
                   ) 
                 
               
             
           
         
       
     
     Within the dead zone, the control error is zero, and outside it said value is the value of the wheel steering angle δ v  which is reduced by the value of the limitation. The control error e δ  is fed to a controller  74 . The controller  74  can be embodied as a simple P controller or as a dynamic controller. If a superimposition steering system ( FIG. 5 ) is present, the set point change Δδ soll  in the wheel steering angle cannot be used as a pilot control in the sense of applying different variables for the steering torque control of the steering torque controller  52 , in accordance with the illustration in  FIG. 6 . The controller output variable u M  or u Δδ  is, if appropriate, restricted in terms of its value and its increase by the limiting element  76 . The parameters of the controller  74  and of the limiting element  76  should be set as a function of the vehicle. A limitation taking into account the current manual torque of the driver is also possible. 
     While preferred embodiments of the invention have been described herein, it will be understood that such embodiments are provided by way of example only. Numerous variations, changes and substitutions will occur to those skilled in the art without departing from the spirit of the invention. It is intended that the appended claims cover all such variations as fall within the spirit and scope of the invention. 
     LIST OF REFERENCE SYMBOLS 
     
         
         a x  Longitudinal acceleration, if appropriate estimated from wheel speed signals 
         p B  Brake pressure, 1× driver, 4× wheels, if appropriate estimated dΨ/dt, Ψ Yaw rate 
         a y  Lateral acceleration 
         v x  Velocity of vehicle, estimated from wheel speed signals 
         δ L  Steering wheel angle 
         δ v  Wheel steering angle, front axle 
         δ v,lim  Limitation of wheel steering angle, front axle 
         δ v,ref  Reference value wheel steering angle, front axle 
         Δδ soll  Setpoint wheel steering angle change, front axle 
         δ H  Wheel steering angle, rear axle 
         δ H,soll  Setpoint wheel steering angle, rear axle 
         M H  Driver&#39;s manual torque on steering wheel 
         M DSR  Setpoint steering torque 
         β Attitude angle 
         α Slip angle 
         α lim  Slip angle at maximum angle of lateral force or maximum value of adhesion coefficient 
         Δα Difference in slip angle between front axle and rear axle α v -α H    
         F y  Lateral force 
         F z  Vertical force 
         μ 0  Coefficient of friction of underlying surface 
         μ y  Adhesion coefficient in lateral direction 
         μ y,max  Maximum value of cohesion of adhesion coefficient 
         C α0  Initial rise in adhesion coefficient/slip angle curve 
         EG Intrinsic steering gradient 
         I Wheel base 
         I v  Distance between center of gravity of vehicle and front axle 
         I H  Distance between center of gravity of vehicle and rear axle
 
e δ  Control error