Patent Publication Number: US-2022212514-A1

Title: System and method for controlling the stability of a vehicle provided with a semi-active suspension

Description:
TECHNICAL FIELD 
     This invention relates to a system and a method for controlling the stability of a vehicle, specifically a system and a method for controlling the stability of a vehicle equipped with semi-active suspension. 
     BACKGROUND ART 
     Suspension systems have a large impact on the driveability and safety of a vehicle, as well as on the driver&#39;s comfort on a rough road surface. 
     Modern stability control systems mainly involve two types of suspensions: electronic pneumatic suspensions and semi-active suspensions. 
     The difference between the two types of suspensions lies in the fact that electronic pneumatic suspensions are active and capable of applying forces, whilst semi-active suspensions are passive and the resistance of the suspensions to contraction and extension can be adjusted. 
     Semi-active suspensions, however, have the advantage of having a higher control frequency and being less cumbersome in terms of weight and space and less energy-intensive insofar as they are passive. 
     Control methods known to date implement algorithms of the skyhook type, which are designed to limit as much as possible the dynamics of the damped mass that is, the vehicle body compared to the substantially undamped mass which is in contact with the ground that is, the wheels. 
     Based on the vertical speeds of the body and wheels, measured by specific sensors, skyhook algorithms calculate an ideal damping level that the dampers have to apply to ensure an optimal driving quality. 
     Most of the suspension control methods developed are based on mathematical models of the vehicle angles so as to locally attenuate the shocks caused by the irregularities of the road surface. 
     These systems, however, fail to control the general dynamics of the vehicle which affect vehicle stability and driving pleasure, such as, for example, the rolling and pitching dynamics determined by the steering, braking and acceleration commands given by the driver. 
     To control these dynamics, the prior art teaches the use of hierarchical systems where low-level controllers are used to handle individual vehicle dynamics and high-level controllers are used to determine which low-level controller is to have priority, based on predetermined logic. 
     Suspension control is thus managed in a sub-optimal manner since one control system takes priority over the others, whose commands are therefore ignored. 
     Thus, when a higher priority is assigned to the rolling and pitching control system, the commands issued by the system that controls the damping of road surface irregularities are ignored, and vice versa. 
     These priority-based control systems, therefore, do not ensure total, simultaneous control of vehicle dynamics, which reflects negatively on the driving comfort and road holding capability of the vehicle. 
     Consequently, a particularly strongly felt need in the field of vehicle stability control is that of providing total systems: that is to say, systems capable of simultaneously handling road surface irregularities and general vehicle dynamics. 
     Aim of the Invention 
     In this context, the main aim of the invention is to overcome the above-mentioned drawbacks. 
     Specifically, the aim of this disclosure is to propose a system for controlling the stability of a vehicle equipped with semi-active dampers and which allows simultaneously handling the oscillations caused by road surface irregularities and the vehicle rolling and pitching dynamics due to the driver&#39;s manoeuvres. 
     According to an aspect of this disclosure, the system for controlling the stability of a vehicle equipped with semi-active dampers comprises:
         a plurality of actuators configured to continuously regulate the damping level of the semi-active dampers;   a first group of sensors configured to detect at least one dynamic parameter of the vehicle;   a second group of sensors configured to capture the input from the vehicle driver;   a high-level control unit configured to calculate a nominal damping parameter, through a model, as a function of the quantities detected by the two groups of sensors;   at least one mid-level control unit configured to calculate, as a function of the quantities detected by the first group of sensors, the damping level to be applied by the high-level control unit to each damper through a parameterized algorithm;   at least one low-level control unit, configured to send drive signals to the actuators of the dampers.       

     According to another aspect, this disclosure relates to a method or controlling the stability of a vehicle, comprising the steps of capturing dynamic parameters of the vehicle, capturing the input entered by the driver, executing an algorithm for calculating the optimum damping level to be applied to each damper the vehicle is provided with and, lastly, implementing the damping levels calculated. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further features and advantages of this invention are more apparent in the non-limiting description of a preferred but non-exclusive embodiment of a system for controlling the stability of a vehicle, as illustrated in the accompanying drawings, in which: 
         FIG. 1  shows a schematic side view of a vehicle equipped with the stability control system of this patent specification; 
         FIG. 2  schematically illustrates a detail of the stability control system of  FIG. 1 ; 
         FIG. 3  illustrates through a greyscale map the match between the dynamic parameters of the vehicle and the damping level. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION 
     With specific reference to the drawings, the numeral  100  denotes a system for controlling the stability of a vehicle  1 . 
     As illustrated, the vehicle  1  has a vehicle body  2  and a plurality of wheels  3 , which are the points where the vehicle touches the ground. 
     Preferably, the vehicle  1  has four wheels  3 . 
     The vehicle  1  also has a longitudinal axis of extension x, a transverse axis of extension y and a vertical axis of extension z. 
     The vehicle  1  further comprises at least one semi-active damper  4  for each wheel  3  the vehicle  1  is provided with; for simplicity, reference is hereinafter made only to one damper  4 , since the semi-active dampers  4  are preferably all technically the same for each wheel. 
     The damper  4  is interposed between the respective wheel  3  and the vehicle body  2  and is configured to damp the oscillations of the vehicle body  2  along the vertical axis of extension z of the vehicle  1 . 
     Preferably, the damper  4  has a damping level C ref  which is adjustable continuously between a minimum damping level C min  and a maximum damping level C max . 
     In other words, the number of possible damping levels C ref  is not finite and predetermined but settable as required within the range defined by C min  and C max . 
     Advantageously, compared to traditional skyhook systems having a finite number of adjustment levels, the fact that the damping level C ref  can be regulated continuously allows the system  100  to have practically infinite possibilities of setting the damping level, with obvious advantages in terms of stability and driving pleasure of the vehicle  1 . 
     In a preferred but non-limiting embodiment, the semi-active damper  4  is a magnetorheological damper: that is to say, a type of damper where the resistance to oscillations is regulated by applying a magnetic field in order to modify the fluid dynamic properties of a liquid included in the damper  4  itself. 
     In another embodiment, the semi-active damper  4  is an electrorheological or electrohydraulic damper. 
     A stability system  100  for the vehicle  1  is responsible for controlling and driving the damper  4  of the vehicle  1 , in order to limit the oscillations of the vehicle body  2  along the vertical axis of extension z, thus ensuring optimum comfort for the driver of the vehicle  1 . 
     As illustrated in  FIG. 2 , the system  100  comprises at least one actuator  5  configured to continuously regulate a damping level C ref  of the damper  4 . 
     Preferably, each damper  4  the vehicle  1  is provided with is associated with an actuator  5  responsible for driving the respective damper  4 . 
     The actuator  5  transduces the control signal into a mechanical, electrical or magnetic stimulus for continuously modifying the physical properties of the semi-active damper  4  which condition its response to the oscillations along the vertical axis of extension z of the corresponding wheel  3  and/or of the vehicle body  2 . 
     The system  100  comprises at least a first sensor  6 D, configured to measure at least one dynamic parameter of the vehicle  1  and send at least a first signal S 1  containing an information item regarding the dynamic parameter. 
     Preferably, the at least first sensor  6 D comprises at least one of the following:
         an accelerometer  10  configured to measure an acceleration of the vehicle body  2  in proximity to one of the wheels  3  along a direction parallel to the vertical axis of extension z;   a potentiometer  11  configured to measure the compression of the damper  4  along its axis of extension;   a GPS sensor, configured to capture the position of the vehicle  1 .       

     Also as illustrated, the system  100  comprises at least a second sensor  6 C configured to capture an input entered by a driver of the vehicle  1  and to send at least a second signal S 2  containing an information item regarding that input. 
     Preferably, the at least second sensor  6 C comprises at least one of the following:
         a steering angle sensor  12  configured to measure the steering angle δ determined by a steering wheel  13 ;   an accelerator sensor  14  configured to measure an action applied through a command from the accelerator  15 ;   a brake sensor  16  configured to measure an action applied through a command from the brake  17 .       

     In other words, the second sensor  6 C monitors the behaviour of the driver, whose actions are reflected (after a response interval) on the translational and oscillational movement of the vehicle  1 , which is then monitored by the first sensor  6 D. 
     Advantageously, the use of two different types of sensors, one to monitor the movement of the vehicle  1  and one to monitor the actions of the driver, allows predicting, through a model, the future dynamics of the vehicle  1 , specifically the longitudinal and lateral accelerations the vehicle  1  is about to be subjected to. 
     The possibility of predicting the future dynamics of the vehicle  1  also ensures that the system  100  can preventively adapt the state of the damper  4  in order to guarantee driving comfort for the driver and, at the same time, good road holding. 
     Also as illustrated, the system  100  comprises a high-level control unit  8 H in communication with the first sensor  6 D and with the second sensor  6 C. 
     The high-level control unit  8 H is configured to calculate a nominal damping parameter C nom  as a function of the first signal S 1  and of the second signal S 2 . 
     The nominal damping parameter C nom  represents the damping level that the damper  4  must apply when the vehicle body  2  or the respective wheel  3  is not subjected to oscillations along the vertical axis of extension z of the vehicle  1 . 
     Advantageously, dependence on the second signal S 2  received from the second sensor  6 C allows the high-level control unit  8 H to calculate the nominal damping level C nom  also on the basis of the driver&#39;s actions, making it possible to anticipate and thus improve the response of the system  100  to the dynamics of the vehicle  1 . 
     The system  100  further comprises a mid-level control unit  8 M, in communication with the high-level control unit  8 H and with the first sensor  6 D. 
     The mid-level control unit  8 M is configured to receive the nominal damping parameter C nom  from the high-level control unit  8 H and to calculate, through an algorithm or calculation routine A, a damping level C ref  as a function of the first signal S 1  received from the first sensor  6 D. 
     In other words, the mid-level control unit  8 M is in communication with the high-level control unit  8 H, which parameterizes the algorithm A responsible for calculating the damping level C ref  to be applied at the level of the damper  4 . 
     The term parameterization of an algorithm is thus used to mean calculating a parameter which, when applied as input to an algorithm, influences the result of the algorithm in substantially the same way as an independent input variable (in our case, the signal S 1 ). 
     The term algorithm is used to mean any calculation routine which, through a finite number of steps performed according to finite set of rules, allows obtaining the value for an output variable as a function of the input variables and/or of the input parameters. 
     In an embodiment, the system  100  comprises a mid-level control unit  8 M for each damper  4  the vehicle  1  is provided with, so each mid-level control unit  8 M is responsible for calculating the damping level C ref  of a single damper  4 . 
     Preferably, the high-level control unit  8 H sends to the mid-level control unit  8 M the nominal damping level C nom , which constitutes an input variable in the algorithm A. 
     Thus, the algorithm A calculates the damping level C ref  as a function of the first signal S 1  received from the first sensor  6 D and of the nominal damping parameter C nom  received from the high-level control unit  8 H. 
     Specifically, each mid-level control unit  8 M executes the respective algorithm A to calculate, independently of the other mid-level control units  8 M, the optimum damping level C ref  for the damper  4  associated with it. 
     Advantageously, the presence of a mid-level control unit  8 M for each damper  4  the o the vehicle  1  allows each damper  4  to execute the respective algorithm A differently and distinctly from the others. 
     The nominal damping level C nom , calculated by the high-level control unit  8 H, is sent to all the mid-level control units  8 M. 
     In an embodiment, the same nominal damping level C nom  is sent to the mid-level control units  8 M and thus constitutes an input variable common to all the algorithms A, which are then executed independently by each mid-level control unit  8 M to calculate the optimum damping level C ref  for the damper  4  that each is associated with. 
     In another embodiment, a distinct and specific nominal damping level C nom  is sent to each mid-level control unit  8 M and constitutes an input variable of the respective algorithm A, which is thus executed independently of the other algorithms of the other mid-level control units  8 M to calculate the optimum damping level C ref  for the damper  4  that it is associated with. 
     The system  100  comprises a low-level control unit  8 L, in communication with the mid-level control unit  8 M and with the actuator  5  and configured to send a drive signal to the actuator  5 . 
     More precisely, the low-level control unit  8 L is configured to receive from the mid-level control unit  8 M an information item containing the desired damping level C ref  and to generate a corresponding drive signal for the actuator  5 . 
     Preferably, the system  100  comprises a low-level control unit  8 L for each actuator  5  the vehicle  1  is provided with, so each low-level control unit  8 L is responsible for driving a single actuator  5 . 
     In a preferred embodiment, the system  100  comprises a computerized calculation unit  7  in communication with the first sensor  6 D, the second sensor  6 C, the high-level control unit  8 H and the mid-level control unit  8 M. 
     The unit  7  is configured to process the first signal S 1  from the first sensor  6 D and the second signal S 2  from the second sensor  6 C. 
     The unit  7  is also configured to send at least one derived signal to the high-level control unit  8 H and mid-level control unit  8 M. 
     In other words, the unit  7  receives as input the raw data captured by the first sensor  6 D and from the second sensor  6 C and processes them, by filtering or integration, to derive other quantities used to calculate the damping level C ref  to be applied to each damper  4  present in the vehicle  1 . 
     In an embodiment comprising at least one accelerometer  10  and at least one potentiometer  11 , the computerized calculation unit  7  processes the first signal S 1  containing the information item from the accelerometer  10  and from the potentiometer  11  included in the system  100 , to obtain a vertical speed of the vehicle body z c  in proximity to the wheels  3  and a damper compression speed z d . 
     In other words, from the accelerations captured by the accelerometer  10  and from the movements captured by the potentiometer  11 , the computerized calculation unit  7  derives the vertical speed z c  of the vehicle body in proximity to the wheel  3  and the compression speed z d  of the damper by integration and differentiation (and filtrations, if necessary), respectively. 
     Described below is a preferred embodiment, illustrated in  FIG. 2 , where the damping level C ref  of the damper  4  is calculated by the respective mid-level control unit  8 M through the algorithm A as a function of the vertical speed z c  of the vehicle body and the compression speed z d  of the damper. 
     According to the convention adopted in this preferred embodiment, z c  is defined as positive when the vehicle body  2  moves downwardly along the vertical axis of extension z and z d  is defined as positive when the reference damper  4  is compressed. 
     In this embodiment, the algorithm A, executed by the respective mid-level control unit  8 M, is defined as follows 
     
       
         
           
             
               
                 C 
                 ref 
               
               = 
               
                 
                   sat 
                   
                     
                       C 
                       
                         r 
                         ⁢ 
                         e 
                         ⁢ 
                         f 
                       
                     
                     ∈ 
                     
                       [ 
                       
                         
                           C 
                           min 
                         
                         , 
                         
                           C 
                           max 
                         
                       
                       ] 
                     
                   
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         K 
                         
                           s 
                           ⁢ 
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                           ⁢ 
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                       ⁢ 
                       
                         z 
                         c 
                       
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                         n 
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                   ) 
                 
               
             
             , 
           
         
       
     
     where C min  and C max  are, respectively, a minimum value and a maximum value for the damping level C ref  applicable to the damper  4 , sat is a saturation function which restricts the dynamics of C ref  to the range [C min ,C max ] and where K sky  is a parameter representing a gain of the algorithm A. 
     In other words, the function sat keeps the value C ref  unchanged when K sky z c z d +C nom  falls within the range [C min , C max ] but applies C ref =C max  when K sky z c z d +C nom  is greater than C max  and C ref =C min  when K sky z c z d +C nom , is greater than C min . 
     Preferably, the gain K sky  is selectable by the driver of the vehicle  1  from a finite number of values, corresponding to different vehicle attitude configurations. 
     The preferred embodiment of the system  100  illustrated in  FIG. 2  comprises, in addition to the high-level control unit  8 H, four mid-level control units  8 M, four low-level control units  8 L and four actuators  5  (one for each wheel  3  of the vehicle  1 ). 
     In this embodiment, the high-level control unit  8 H and the four mid-level control units  8 M calculate, respectively, the nominal damping levels C nom,i  and the damping levels C ref,i  (where i is a whole number from 1 to 4) independently for each wheel  3 . 
     Advantageously, in this embodiment, the independence between the different values of nominal damping C nom,i  and damping C ref,i  allow optimum adjustment of the attitude of the vehicle  1 . 
     Advantageously, use of the algorithm A allows regulating the damping level C ref  more uniformly, for added comfort, compared to traditional skyhook algorithms with two stages. 
     In effect, traditional skyhook algorithms calculate the damping level C ref  as a function of the vertical speed z c  of the vehicle body and of the speed of compression z d  of the damper as follows 
     
       
         
           
             
               C 
               ref 
             
             = 
             
               { 
               
                 
                   
                     
                       C 
                       min 
                     
                   
                   
                     
                       
                         
                           se 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
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                           ⁢ 
                           
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                         0 
                       
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                       max 
                     
                   
                   
                     
                       
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                         ⁢ 
                         
                             
                         
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                           d 
                         
                       
                       &gt; 
                       0. 
                     
                   
                 
               
             
           
         
       
     
     This way of handling damper operation causes unwanted jolting when the speeds involved are almost zero, since minor variations, for example caused by sensor noise, result in numerous changes between the two states allowable by the damping level. 
     In the embodiment proposed and illustrated in  FIG. 3  in the configuration where C nom =0, small variations in the speed values z c  and z d  cause only slight variations in the damping value C ref , thus cancelling the jolts caused by the changes of state in the traditional implementations of skyhook algorithms. 
     Advantageously, the use of this more uniform variant of a skyhook algorithm ensures a wider variety of adjustments of the damping level C ref  of the damper  4  (which can adapt better to the jolts of the vehicle  1 ), thus improving the driving comfort for the driver. 
     The parameter C nom  is calculated by the high-level control unit  8 H as a function of the first signal S 1  and second signal S 2  (if necessary, processed by the computerized calculation unit  7 ) and transmitted to the mid-level control unit  8 M. 
     As described above, the nominal damping parameter C nom  is a damper parameter to be applied to the dampers when there are no oscillations (that is, when z c =0 or z d =0). 
     Again in accordance with the preferred embodiment, the nominal damping parameter C nom  is obtained by the high-level control unit  8 H through the following relation 
         C   nom   =C   0   +C   lat   +C   long , 
     where C 0  is a default nominal damping level, applied when there are no longitudinal or lateral accelerations of the vehicle  1 , and where C lat  and C long  are, respectively, a first additive factor and a second additive factor, both calculated by the high-level control unit  8 H as a function of the first signal S 1  and of the second signal S 2 . 
     The first additive factor C lat  and the second additive factor C long  which take into account the dynamics of lateral acceleration and longitudinal acceleration of the vehicle  1 , respectively. 
     Preferably, the default nominal damping level C 0  is selectable by the driver of the vehicle  1  from a finite number of values, corresponding to different attitude configurations of the vehicle  1 . 
     More specifically, in this preferred embodiment, the first additive factor C lat  is calculated by the high-level control unit  8 H as follows 
         C   lat   =K   lat   A   y,HP , 
     where K lat  is an adjustable gain factor and A y,HP  is a version, filtered preferably by a high pass band filter, of the quantity 
     
       
         
           
             
               
                 A 
                 y 
               
               = 
               
                  
                 
                   
                     
                       v 
                       2 
                     
                     ⁢ 
                     δ 
                   
                   
                     
                       
                         K 
                         us 
                       
                       ⁢ 
                       
                         v 
                         2 
                       
                     
                     + 
                     L 
                   
                 
                  
               
             
             , 
           
         
       
     
     where v is a speed of movement of the vehicle  1 , K us  is a steering reference coefficient and L is a model parameter describing the length of the wheelbase of the vehicle  1 . Preferably, the speed of movement v is derived by the computerized calculation unit  7  by processing at least a first signal S 1  captured and sent by the GPS sensor the vehicle  1  is provided with. 
     Again in accordance with the preferred embodiment the second additive factor C long  is calculated by the high-level control unit  8 H as follows 
         C   long   =K   long   A   x,HP , 
     where K long  is an adjustable gain factor and A x,HP  is a version, filtered preferably by a high pass band filter, of the quantity 
     
       
         
           
             
               
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                 x 
               
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                       ⁢ 
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                       ⁢ 
                       
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                         2 
                       
                     
                     
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                       ⁢ 
                       
                           
                       
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     where ρ is an air density, S is a front surface of the vehicle  1 , C x  is an aerodynamic friction coefficient of the vehicle  1 , m is a mass of the vehicle  1 , v is the speed of movement of the vehicle  1 , k bk  is a braking efficiency, P bk  is a pressure on the brake control  17  measured by the brake sensor  16 , k pos  is a first model parameter describing the efficiency of the propelling unit, k neg  is a second model parameter describing the efficiency of the propelling unit, T eng,pos  is a positive parameter describing a positive torque of the engine, T eng,neg  is a negative parameter describing a negative torque of the engine and ω eng  is a parameter describing a number of revolutions of the engine of the vehicle  1 . 
     Preferably, when T eng,neg  is greater than 0, then T eng,neg  is equal to 0 and when T eng,neg  is less than 0, then T eng,neg  is equal to 0, respectively. In other words, it is impossible for both of the last two addends in the preceding equation to contribute simultaneously to the calculating of A x . 
     Advantageously, the presence of the first additive factor C lat  and of the second additive factor C long  allows the stability control system  100  to take into account the rolling and pitching dynamics of the vehicle  1 , respectively. 
     Still more advantageously, the fact that the nominal damping level C nom  (thus calculated by adding the first additive factor C lat  and the second additive factor C long ) parameterizes the algorithm A allows driving comfort and road holding to be managed simultaneously in the presence of both rolling and pitching dynamics. 
     In effect, the addition of the nominal damping level C nom  calculated by the high-level control unit  8 H, allows the mid-level control unit  8 M to execute the algorithm A with a vehicle attitude previously optimized as a function of the second signal S 2 , that is, as a function of the inputs entered by the driver. 
     Also defined according to the invention is a method  200  for controlling the stability of a vehicle  1  having a longitudinal axis of extension x, a transverse axis of extension y and a vertical axis of extension z and comprising a body  2 , a plurality of wheels  3  and, for each wheel  3 , at least one semi-active damper  4  interposed between the respective wheel  3  and the body  2 . 
     The method  200  comprises a first step of measuring  201 , for capturing a dynamic parameter of the vehicle  1 . 
     The first step of measuring  201  for capturing a dynamic parameter of the vehicle  1  comprises at least one of the following sub-steps:
         measuring at least one acceleration of the body  2  in proximity to the wheels  3  along a direction parallel to the vertical axis z of the vehicle  1 ;   measuring at least one compression of the dampers  4  along a direction nearly parallel to the vertical axis z.       

     Preferably, in an embodiment comprising at least the measuring of the acceleration of the vehicle body  2  and the measuring of the compression of the dampers  4 , the first step of measuring  201  comprises at least one sub-step of processing the dynamic parameters of the vehicle  1  to calculate a vertical speed z c  of the vehicle body in proximity to the wheels  3  and a speed of compression z d  of the dampers. 
     After the first step of measuring  201 , the method  200  comprises a second step of measuring  202  for capturing an input entered by the driver of the vehicle  1 . 
     Preferably, the second step of measuring  202  for capturing an input entered by the driver of the vehicle  1  comprises at least one of the following sub-steps:
         measuring the steering angle δ determined by a steering wheel  13 ;   measuring an action of acceleration applied through a command from the accelerator  15 ;   measuring an action of braking applied through a command from the brake  16 .       

     Next, the method  200  comprises a step  203  of executing an algorithm A to calculate a damping level C ref  for the damper  4  as a function of the dynamic parameter captured in the first step of measuring  201  and of the input captured in the second step of measuring  202 . 
     In a preferred embodiment comprising at least the measuring of the acceleration of the vehicle body  2 , the measuring of the compression of the dampers  4 , and the sub-step of processing the dynamic parameters of the vehicle  1 , the step  203  of executing comprises executing the algorithm A defined as 
     
       
         
           
             
               
                 C 
                 ref 
               
               = 
               
                 
                   sat 
                   
                     
                       C 
                       
                         r 
                         ⁢ 
                         e 
                         ⁢ 
                         f 
                       
                     
                     ∈ 
                     
                       [ 
                       
                         
                           C 
                           min 
                         
                         , 
                         
                           C 
                           max 
                         
                       
                       ] 
                     
                   
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         K 
                         
                           s 
                           ⁢ 
                           k 
                           ⁢ 
                           y 
                         
                       
                       ⁢ 
                       
                         z 
                         c 
                       
                       ⁢ 
                       
                         z 
                         d 
                       
                     
                     + 
                     
                       C 
                       
                         n 
                         ⁢ 
                         o 
                         ⁢ 
                         m 
                       
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     where C min  and C max  are, respectively, a minimum value and a maximum value for the damping level C ref , sat is a saturation function which restricts the dynamics of C ref  to the range [C min , C max ] and where K sky  and C nom  are two adjustable parameters representing, respectively, a gain of the algorithm A and a nominal damping level in the absence of vertical body speed z c  or damper compression speed z d . 
     Preferably, the nominal damping level C nom  is calculated as a function of the dynamic parameters of the vehicle  1  captured during the first step of measuring  201  and of the input captured during the second step of measuring  202 .