Abstract:
A rollover avoidance system for changing the damping characteristics of suspension dampers at each wheel of a vehicle so as to mitigate the potential for vehicle rollover. The system includes a plurality of vehicle parameter sensors for measuring vehicle parameters and providing vehicle parameter signals. The system also includes a controller for generating a damper suspension command signal for each damper using the vehicle parameter signals. The controller considers a roll control factor representing a rollover condition of the vehicle and a yaw stability control factor representing a yaw condition of the vehicle to set the damping of the dampers to mitigate the potential for vehicle rollover.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to a vehicle rollover avoidance system and, more particularly, to a vehicle rollover avoidance system that employs a roll control factor and a yaw rate stability control factor to control semi-active suspension dampers to mitigate the risk of vehicle rollover. 
     2. Discussion of the Related Art 
     It is known in the art to mitigate a potential vehicle rollover using differential braking control, rear-wheel steering control, front-wheel steering control, or any combination thereof. A vehicle rollover avoidance system may receive vehicle dynamics information from various sensors, such as yaw rate sensors, lateral acceleration sensors and roll rate sensors, to determine the proper amount of action to be taken to detect a potential vehicle rollover. A balance typically needs to be provided between estimating the vehicle roll motion and the vehicle yaw motion to provide the optimal vehicle response. Thus, it is usually necessary to detect certain vehicle conditions to provide the roll detection. To precisely identify vehicle roll stability conditions, it may be advantageous to know the vehicle&#39;s roll rate and roll angle because they are the most important states in vehicle roll dynamics. 
     Under normal driving conditions, drivers can direct the vehicle to the desired heading through the control of the steering wheel. When the vehicle is turning, there are actually three motions taking place with the vehicle. Particularly, a turning motion, or yaw, is occurring, as the vehicle body is turning around an imaginary access vertical to the ground through the so-called yaw-center of the vehicle. Also, there is subtle vehicle sliding laterally, sometimes in the direction of the turn and sometimes away from the turn, depending mainly on the vehicle speed. Further, a tilting motion or roll motion occurs as the vehicle&#39;s body is turning around an imaginary axis parallel to the ground through the so-called roll-axis of the vehicle. 
     Under normal vehicle maneuvering conditions, the tire/road contact surfaces can generate sufficient forces to sustain the desired vehicle motions, and drivers are accustomed with these motions as they occur. However, when the vehicle maneuver starts approaching limit-handling conditions, the tire/road contact surfaces can no longer sustain the desired yaw motion and side-slip motion, and the vehicle body will exhibit an increased roll motion. As a result, a discrepancy will build up between the vehicle&#39;s yaw rate and its desired yaw rate, and between the vehicle&#39;s side-slip velocity and its desired side-slip velocity. Further, if the roll motion becomes too large, the vehicle may roll over. 
     SUMMARY OF THE INVENTION 
     In accordance with the teachings of the present invention, a vehicle rollover avoidance system is disclosed that controls semi-active suspension dampers at each wheel of the vehicle in response to a vehicle yaw and roll condition so as to mitigate vehicle rollover potential. The system includes various sensors that measure vehicle parameters, such as a speed sensor, a roll rate sensor, a lateral acceleration sensor, a yaw rate sensor and a hand-wheel angle sensor. Using these measured values, the system calculates a yaw stability control factor and a roll stability indicator. The system also calculates a roll error signal between a desired roll stability indicator command for the suspension dampers and the calculated roll stability indicator. The system generates a closed-loop roll control factor based on the roll error signal and a gain signal that is based on the magnitude of the calculated roll stability indicator, where the gain signal is a function of the vehicle speed. The system adds the closed-loop roll control factor to an open-loop rollover control factor, where the open-loop roll control factor is a function of the vehicle lateral acceleration. The system determines whether the yaw stability control factor or the added roll control factor is larger, and determines a front to rear distribution of damping control commands based on a yaw rate error signal and whether the vehicle is in an understeer or oversteer condition. The system uses the front to rear distribution and the larger of the roll control factor and the yaw stability control factor to calculate the damper control signals applied to the dampers at each wheel of the vehicle. 
     Additional features of the present invention will become apparent from the following description and appended claims taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a vehicle including a vehicle rollover stability control system, according to an embodiment of the present invention; 
         FIG. 2  is a schematic block diagram of the rollover stability control system of the invention; 
         FIG. 3  is a flow chart diagram showing a process for providing damper commands to the vehicle suspension system to provide rollover mitigation, according to an embodiment of the present invention; 
         FIG. 4  is a flow chart diagram showing a process for determining a roll control factor value in the process of  FIG. 3 ; 
         FIG. 5  is a graph with lateral acceleration on the horizontal axis and damper feed-forward control on the vertical axis for determining a feed-forward control factor based on vehicle lateral acceleration; 
         FIG. 6  is a graph with vehicle speed on the horizontal axis and a gain function on the vertical axis for determining the gain function based on vehicle speed for a low roll stability indicator; and 
         FIG. 7  is a graph with vehicle speed on the horizontal axis and a gain function on the vertical axis for determining the gain function based on vehicle speed for a medium roll stability indicator. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     The following discussion of the embodiments of the invention directed to a vehicle rollover avoidance system is merely exemplary in nature, and is in no way intended to limit the invention or its applications or uses. 
       FIG. 1  is a schematic plan view of a vehicle  10  including a rollover stability controller  12 . The rollover stability controller  12  receives a hand-wheel angle signal from a hand-wheel angle sensor  14  indicative of the turning angle of a vehicle hand-wheel  16 . Further, the controller  12  receives a vehicle speed signal V x  from a speed sensor  18 , a roll rate signal R from a roll rate sensor  20 , a lateral acceleration sensor signal Ay from a lateral acceleration sensor  22  and a yaw rate signal Y from a yaw rate sensor  24 . The vehicle  10  includes a magneto-rheological (MR) damper  30  at the right front tire  32 , an MR damper  34  at the left front tire  36 , an MR damper  38  at the right rear tire  40  and an MR damper  42  at the left rear tire  44 . Passive MR dampers are well known in the vehicle suspension art that can be controlled to provide a desired ride for the vehicle. 
     The present invention proposes using semi-active MR dampers to change the stiffness of the damper in response to a potential rollover condition. As will be discussed in detail below, the rollover stability controller  12  provides a signal to the dampers  30 ,  34 ,  38  and  42  when the vehicle  10  is turning if a potential rollover condition occurs. Particularly, when suspension control is implemented for yaw rate stability control, the controller  12  commands the dampers  30 ,  34 ,  38  and  42  to redistribute the vehicle normal forces to create a lateral force difference across the vehicle axles  46  and  48 . The difference of the lateral forces at the two ends of the axles  46  and  48  creates the desired yaw moment to stabilize the vehicle  10  when it is undergoing a limit-handling condition. By achieving the desired yaw moment, the vehicle  10  could increase its roll motion. In other words, yaw and roll motions are coupled and need to be balanced in order to achieve both yaw and roll stability. 
       FIG. 2  is a schematic block diagram of a roll stability control system  50 , according to an embodiment of the present invention. The control system  50  includes a vehicle  52  that is being controlled. The speed signal V x  from the sensor  18  is provided on line  54 , the roll-rate signal R from the roll rate sensor  20  is provided on line  56 , the lateral acceleration signal Ay from the lateral acceleration sensor  22  is provided on line  58 , the yaw rate signal Y from the yaw rate sensor  24  is provided on the line  60  and the hand-wheel signal from the hand-wheel sensor  14  is provided on line  62 . 
     The system  50  includes a parameter estimation/sensor fusion processor  64  that receives the speed signal V x , the roll rate signal R, the lateral acceleration signal Ay and the yaw rate signal Y. The processor  64  uses these measurements of vehicle states to estimate other vehicle states used in the stability control. For example, the processor  64  may generate estimates of vehicle roll angle, vehicle side-slip angle, vehicle center of gravity height, etc. Processors that perform these operations based on the measured state signals are well known to those skilled in the art. 
     The estimated vehicle state signals from the processor  64  are applied to a dynamic rollover indicator processor  66 . The processor  66  employs a roll stability indicator algorithm that determines whether the vehicle  52  is in a potential rollover condition. Various systems are known in the art to provide an index or indicator of a potential vehicle rollover condition. For example, U.S. patent application Ser. No. 11/330,640, filed Jan. 12, 2006, titled Vehicle Rollover Indicator for Vehicle Rollover Control, assigned to the Assignee of this application, and herein incorporated by reference, discloses one suitable process for providing a roll stability indicator. 
     The estimate vehicle state signals from the processor  64  are applied to an understeer/oversteer processor  76 . The understeer/oversteer processor  76  calculates an understeer or oversteer condition of the vehicle  52  for reasons that will become apparent in the discussion below. Those skilled in the art will readily recognize various systems that are known that calculate vehicle understeer and oversteer. 
     The system  50  also includes a dynamic command processor  68  that receives the hand-wheel angle signal, the speed signal V x  and the state estimations from the processor  64 . The dynamic command processor  68  generates a command signal for the desired yaw rate of the vehicle  52 . Any suitable dynamic command processor can be employed for this purpose, such as the command interpreter described in U.S. Pat. No. 6,865,468, titled Method and Apparatus for Vehicle Stability Enhancement System, assigned to the Assignee of this application and herein incorporated by reference. 
     The dynamic command signal, the roll stability indicator, the understeer/oversteer condition and the estimations from the processor  64  are applied to a close-loop controller  70 . As will be discussed in detail below, the closed-loop controller  70  provides a closed-loop roll control factor that sets the stiffness of the dampers  30 ,  34 ,  38  and  42  based on the actual yaw and roll measurements of the vehicle  52  and the desired yaw and roll motion of the vehicle  52 . The controller  70  determines a distribution of the damping control commands between the front and rear axles  46  and  48 . As will be discussed in more detail below, the front to rear distribution between the axles  46  and  48  is based on a yaw rate error signal and whether the vehicle  52  is in an understeer or oversteer condition. The controller  70  can use look-up tables to determine the distribution based on these factors. 
     An open-loop controller  72  receives the roll stability indicator from the processor  66 , the vehicle speed signal V x  and the hand-wheel angle signal to provide an open-loop roll control factor for the stiffness of the dampers  30 ,  34 ,  38  and  42 . The open-loop roll control factor and the closed-loop roll control factor are added by an adder  74  and are used to control the stiffness of the dampers  30 ,  34 ,  38  and  42 . 
     The following is a discussion of the theory for calculating the closed-loop roll control factor based on vehicle dynamics, according to the invention. During cornering, the lateral load transfer unloads the inside wheels of the vehicle and increases the load on the outside wheels of the vehicle. The distribution between the outside and inside tires depends on the suspension characteristics, such as vehicle roll-stiffness, roll-damping, roll axis orientation, etc. Significant pitch motion affects the front and rear axle loads. In general, the tire lateral force F y  is a complicated non-linear function of normal force, lateral/longitudinal slip, vehicle speed, etc. 
     In the calculations below, it is assumed that the tire lateral force F y  is only a function of lateral slip and normal force as:
 
 F   y   =a (ƒ z )sin( b (ƒ z )tanh( c (ƒ z )α))  (1)
 
where α is the lateral slip, and a(ƒ z ), b(ƒ z ), c(ƒ z ) are polynomials (up to 6 th  degree) of ƒ z =F z /F z0  as defined in the following equations.
 
 a (ƒ z )=4451.85ƒ z −66.92ƒ z   2 +104.44ƒ z   3 −192.09ƒ z   4 +58.86ƒ z   5 −5.24ƒ z   6   (2)
 
 b (ƒ z )=2.75−3.20ƒ z +4.291ƒ z   2 −2.44ƒ z   3 +0.67ƒ z   4 −0.09ƒ z   5 +0.004ƒ z   6   (3)
 
 c (ƒ z )=0.08+0.18ƒ z −0.25ƒ z   2 +0.15ƒ z   3 −0.04ƒ z   4 +0.006ƒ z   5−0.00033ƒ   z   6   (4)
 
In these equations, F z  is the tire normal load and F z0  is the tire nominal load. Coefficients of such polynomials can be determined from tire test data using some fitting procedures.
 
     Alternatively, the tire lateral force F y  can be defined by a three-dimensional table. 
     A tire lateral load transfer (TLLT) function for the front of the vehicle is defined as: 
                     TLLT   Fr     =       Δ   ⁢           ⁢     F   zFr         F   zFr               (   5   )                 Δ   ⁢           ⁢     F   zFr       =       F   zL     -     F   zR               (   6   )                 F   zFr     =       F   zL     +     F   zR               (   7   )               
where F zL  is left front tire load, F zR  is the right front tire load, and F zFr  is the front total load. The TLLT for the rear of the vehicle is defined in the same manner.
 
     The TLLT causes a reduction of the lateral force by: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       F 
                       y 
                     
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                         
                           F 
                           y 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 
                                   F 
                                   zL 
                                 
                                 + 
                                 
                                   F 
                                   zR 
                                 
                               
                               2 
                             
                             , 
                             α 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         F 
                         y 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             F 
                             zL 
                           
                           , 
                           α 
                         
                         ) 
                       
                     
                     - 
                     
                       Fy 
                       ⁡ 
                       
                         ( 
                         
                           
                             F 
                             zR 
                           
                           , 
                           α 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The following semi-active suspension magneto-rheological damper (MRD) model is adopted here as: 
                       F   MDR     ⁡     (     V   ,   I     )       =       ∑     n   =   1     7     ⁢       (       ξ     0   ⁢   n       +       ξ     1   ⁢   n       ⁢   I       )     ⁢     V   n                 (   9   )               
where I is current, V is damper velocity, and ξ 1n  are constants. The following equation shows an example of this model.
 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       MRD 
                     
                     ⁡ 
                     
                       ( 
                       
                         V 
                         , 
                         I 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           1931.98 
                           + 
                           
                             852.55 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       V 
                     
                     + 
                     
                       
                         ( 
                         
                           81.57 
                           - 
                           
                             224.63 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         V 
                         2 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             - 
                             1327.95 
                           
                           - 
                           
                             451.44 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         V 
                         3 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             - 
                             91.42 
                           
                           + 
                           
                             112.95 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         V 
                         4 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           563.94 
                           + 
                           
                             206.03 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         V 
                         5 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           21.76 
                           - 
                           
                             21.10 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         V 
                         6 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             - 
                             82.27 
                           
                           - 
                           
                             31.88 
                             ⁢ 
                             I 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         V 
                         7 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The front roll moment due to MRD forces is defined as: 
                     M   Fr     =       [         F   MRD     ⁡     (       V   LF     ,     I   LF       )       -       F   MRD     ⁡     (       V   RF     ,     I   RF       )         ]     ⁢       T   Fr     2               (   11   )               
where T Fr  is the front track, LF is the left front and RF is the right front.
 
     Damper velocity can be directly measured or related to sprung mass roll velocity as:
 
 V   RF   =−V   LF   ={dot over (φ)}ρT   Fr /2  (12)
 
where {dot over (φ)} is roll velocity and ρ is the front shock lever ratio. The rear roll moment is defined in the same manner.
 
     By knowing the roll angle φ and the roll velocity {dot over (φ)}, the TLLT for the front and rear can be determined as: 
                     TLLT   Fr     =       1       T   Fr     /   2       ⁢     (             -     K   Fr       ⁢   φ     +     M   Fr         F   zFr       +     h   ⁢           ⁢   φ       )               (   13   )                 TLLT   Rr     =       1       T   Rr     /   2       ⁢     (             -     K   Rr       ⁢   φ     +     M   Rr         F   zFr       +     h   ⁢           ⁢   φ       )               (   14   )               
where K Fr  and K Rr  are the front and rear roll stiffness and h is the sprung mass center of gravity height above the roll axis.
 
     The yaw moment due to lateral load transfer is:
 
Δ M   yaw   =aΔF   y   Fr   −bΔF   y   Rr   (15)
 
where a and b are longitudinal distances between the vehicle center of gravity (CG) and the front and rear axles, respectively.
 
     In general, ΔM yaw  depends on the front and rear TLLT, slip angle, roll angle, roll velocity or damper velocities, and the amount of current at each damper. For given vehicle states, the MRD control capacity U is the maximum achievable yaw moment:
 
 U=ΔM   yaw ( I   Fr =0 ,I   Rr =max)−Δ M   yaw ( I   Fr =max, I   Rr =0)  (16)
 
In other words, the MRD control capacity U is the maximum oversteer moment minus the maximum understeer moment. It is also a function of the TLLT, slip angle, roll angle, roll velocity or damper velocities. In order to better visualize the MRD control capacity U, assume that the slip angle is a function of lateral acceleration A y  only, and such functions are determined from a steady-state cornering.
 
     Neglecting roll inertia effect, roll angle can be derived from: 
                   φ   =           M   S     ⁢   h   ⁢           ⁢     a   y       +     M   Fr     +     M   Rr           K   Fr     +     K   Rr     -       M   S     ⁢   g   ⁢           ⁢   h                 (   17   )               
where M S  is the sprung mass.
 
     Note that the tire slip angles can be estimated using available sensor information. U.S. Pat. No. 6,035,251, titled Brake System Control Method Employing Yaw Rate and Slip Angle Control, issued Mar. 7, 2000 to Hac et al., assigned to the Assignee of this application and herein incorporated by reference, shows one example of how to estimate this information. The vehicle state variables φ and {dot over (φ)} can be measured and/or estimated using other vehicle sensor information. By way of example, U.S. Pat. No. 6,179,394, titled Active Brake Balance Control Method, issued Jan. 30, 2001 to Browalski et al, assigned to the Assignee of this application and herein incorporated by reference, shows one example of how this information can be estimated through combined sensor inputs. 
     With proper distribution between the front and rear damper control currents, the desired yaw moment can be obtained through both feed-forward and feedback controls. The vehicle yaw moment can thus be controlled by changing the damping at each axle  46  and  48 . For example, if the vehicle is in an oversteer condition, the suspension controller can increase the front axle damping while reducing the rear axle damping to correct the problem. 
     The roll moment can also be controlled through similar suspension control using the equation: 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       M 
                       roll 
                     
                   
                   = 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         F 
                         zFr 
                       
                       ⁢ 
                       
                         
                           T 
                           Fr 
                         
                         2 
                       
                     
                     + 
                     
                         
                     
                     ⁢ 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         F 
                         zFr 
                       
                       ⁢ 
                       
                         
                           T 
                           Rr 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     The total roll moment is simply the sum of the roll moment from each axle  46  and  48 . Therefore, after the desired total roll moment is determined, proper distribution between the control of the front and rear axles  46  and  48  can be provided to achieve the proper yaw control without adversely affecting the roll moment control performance. 
     The rollover control algorithm of the invention characterizes the vehicle understeer/oversteer behavior by checking vehicle information, such as yaw rate, lateral acceleration, vehicle speed and steering angle. Based on this information and by calculating a yaw rate error and a side-slip error, a yaw stability control factor K Y  can be calculated as a magnitude and direction. One procedure for providing yaw stability control using semi-active suspension is disclosed in U.S. Patent Publication No. 2006/0074533 to Karaba et al., filed Sep. 20, 2005, titled Method and Apparatus for Controlling Semi-Active Suspension Components, which is assigned to the Assignee of the present invention and herein incorporated by reference. After the yaw stability control factor K Y  is calculated, the algorithm then determines the roll stability indicator (RSI) based on the roll rate measurement and roll angle estimation. If this value exceeds a predetermined threshold, which indicates a single wheel lift condition, a rollover control algorithm is implemented. Otherwise, no rollover avoidance is needed. 
       FIG. 3  is a flow chart diagram  80  showing a process for providing rollover avoidance using the yaw stability control factor K Y  and the roll stability indicator as discussed above, according to an embodiment of the present invention. The algorithm first reads the sensor inputs at box  82  including the vehicle speed signal V x , the roll rate signal R, the lateral acceleration signal A y , the yaw rate signal Y and the hand-wheel angle signal. The algorithm then calculates an understeer or oversteer indicator at box  84 . The understeer and oversteer indicator can be calculated by any suitable technique known in the art, such as the one disclosed in U.S. Patent Application Publication 2005/0222731 to Ghoneim, titled Method and Apparatus for Estimating Steering Behavior for Integrated Chassis Control, published Oct. 6, 2005, assigned to the assignee of this application and herein incorporated by reference. 
     The algorithm then calculates the yaw stability control factor K Y  at box  86 , and the roll stability indicator at box  88 . The algorithm then determines whether the roll stability indicator is greater than a first threshold RSI_th_ 1  at decision diamond  90 . If the roll stability indicator is less than the first threshold RSI_th_ 1 , then the vehicle  52  does not need rollover control and a roll control factor K R  is set to zero at box  92 . If, however, the roll stability indicator is greater than the first threshold RSI_th_ 1  at the decision diamond  90 , then the algorithm calculates the roll control factor K R  at box  94 . 
       FIG. 4  is a flow chart diagram  96  showing a process for calculating the rollover control factor K R , according to an embodiment of the present invention. The algorithm reads the roll stability indicator, the vehicle lateral acceleration signal Ay at box  98 . The roll control factor K R  consists of both a feed-forward factor K Ro  (open-loop) and a feedback factor K Rc  (closed-loop) control. The algorithm calculates the feed-forward factor K Ro  at box  100  by the equation:
   K   Ro   =C   oƒ   o ( Ay )  (19) 
Where C o  is a constant and ƒ o  is a non-linear function of vehicle speed.  FIG. 5  is a graph with lateral acceleration Ay on the horizontal axis and the function ƒ 0  on the vertical axis showing how the function ƒ 0  changes as lateral acceleration changes.
 
     The algorithm then calculates a roll error signal e R  as the difference between the desired roll stability indicator command signal from the processor  68  and the roll stability indicator from the processor  66  at box  102 . The algorithm then determines whether the roll stability indicator is greater than a second threshold RSI_th_ 2  at decision diamond  104 . If the roll stability indicator is less than the second threshold RSI_th_ 2 , meaning that the rollover condition is low, then the algorithm calculates a damper control gain G at box  106  as:
 
 G=C   1ƒ   1 ( V   x )  (20)
 
where C 1  is a constant and ƒ 1  is a non-linear function of vehicle speed.  FIG. 6  is a graph with vehicle speed V x  on the horizontal axis and the function ƒ 1  on the vertical axis showing how the function ƒ 1  changes as the vehicle speed increases.
 
     If the roll stability indicator is greater than the second threshold RSI_th_ 2  at the decision diamond  104 , then the algorithm determines whether the roll stability indicator is greater than a third threshold RSI_th_ 3  at decision diamond  108 . If the roll stability indicator is not greater than the third threshold RSI_th_ 3  at the decision diamond  108 , then the algorithm calculates the damper control gain G at box  110  as:
 
 G=C   2ƒ   2 ( V   x )  (21)
 
where C 2  is a constant and ƒ 2  is a non-linear function of vehicle speed.  FIG. 7  is a graph with vehicle speed on the horizontal axis and the function ƒ 2  on the vertical axis showing how the function ƒ 2  changes as the vehicle speed increases.
 
     When the RSI value exceeds the third threshold RSI_th_ 3  at the decision diamond  108 , it indicates that the vehicle is in imminent risk of rolling over. In this case, the control gain G for all wheels is set to the maximum allowed at box  112  as:
 
 G=C   3   (22)
 
     The closed-loop roll control factor K Rc  is then calculated at box  114  based on the following equation:
 
 K   Rc   =Ge   R   (23)
 
Where e R  is the computed error between the desired RSI value and the actual RSI value.
 
     The total roll control factor is the sum of the feed-forward and feedback factors at box  116 .
 
 K   R   =K   Ro   +K   Rc   (24)
 
     Returning to  FIG. 3 , the algorithm then determines which of the yaw stability control factor K Y  or the roll stability control factor K R  is larger at box  118 , and sets either the yaw stability control factor K Y  or the roll control factor K R  equal to a total control factor K T .
 
 K   T =MAX( K   Y   ,K   R )  (25)
 
     The next step of the control algorithm is to determine the distribution of the damping control command between the front and rear axles  46  and  48  at box  120 . The front/rear (F/R) axle distribution is based on the degree of deviation of vehicle yaw response from the desired yaw command and the vehicle understeer/oversteer behavior. As the yaw rate error increases, the distribution ratio between the front and rear axles  46  and  48  goes from a more stiff rear axle to a more stiff front axle. Table I below is an example of the F/R distribution when the vehicle exhibits an understeer condition, and Table II is an example of the F/R distribution when the vehicle exhibits an oversteer condition where the distribution is the opposite for the understeer condition. 
     
       
         
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE I 
               
             
             
               
                   
                   
               
               
                   
                 Yaw rate error 
               
             
          
           
               
                   
                 −10 
                 −5 
                 0 
                 5 
                 10 
               
               
                   
                   
               
             
          
           
               
                   
                 F/R Ratio (FR) 
                 0 
                 0.25 
                 0.5 
                 0.75 
                 1.0 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE II 
               
             
             
               
                   
                   
               
               
                   
                 Yaw rate error 
               
             
          
           
               
                   
                 −10 
                 −5 
                 0 
                 5 
                 10 
               
               
                   
                   
               
             
          
           
               
                   
                 F/R Ratio (FR) 
                 1.0 
                 0.75 
                 0.5 
                 0.25 
                 0 
               
               
                   
                   
               
             
          
         
       
     
     Once the front to rear distribution is determined, then the algorithm determines the damping command signal for the dampers  30 ,  34 ,  38  and  42  at box  122  by the following equations, where K LF  is the damping command signal for the damper  34 , K RF  is the damping command signal for the damper  30 , K LR  is the damping command signal for the damper  42  and K RR  is the damping command signal for the damper  38 .
 
 K   LF =0.5 K   T   FR   (26)
 
 K   RF   =K   LF   (27)
 
 K   LR =0.5 K   T (1− FR )  (28)
 
 K   RR   =K   LR   (29)
 
     The foregoing discussion discloses and describes merely exemplary embodiments of the present invention. One skilled in the art will readily recognize from such discussion and from the accompanying drawings and claims that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims.