Patent Publication Number: US-2010121529-A1

Title: Method and apparatus for controlling a semi-active suspension

Description:
The present invention relates to a method and apparatus for controlling a semi-active suspension in accordance, respectively, with the preamble of claims  1  and  14 . 
     More in particular, the invention relates to a method and apparatus for controlling the dynamics of a controllable force generator in a semi-active suspension. 
     Semi-active suspensions have their application in various industrial fields, such as for example automotive, motorcycle industry, agricultural machinery, railway vehicles, household appliances and the like. 
     In the present description, the term of suspended mass refers to the chassis of a motor vehicle, whereas the term of non suspended mass refers to the wheels of a motor vehicle, that is, rim, tyre, braking system and part of the driving gears. 
     The union between suspended mass and non suspended mass is ensured by the suspension which consists of an elastic system and a damping element, also called shock absorber. 
     It is worth noting that such auto simplification also applies, with simple considerations, to any one of the industrial fields listed above. 
     As known, suspensions may be divided into the following types:
         passive: consisting of springs and shock absorbers whose parameters are selected in the design step by the manufacturer and cannot be changed; and   semi-active: consisting of springs and shock absorbers whose damping coefficient value may be changed by a control system.       

     It should be noted that, irrespective of the type of suspension selected, the purpose of suspensions is to obtain the following objects:
         driving comfort: which is strictly related to the insulation of the vehicle and thus of the driver, from road irregularities;   grip: which is strictly related to the contact force between tyre and asphalt.       

     It is important to note that comfort and grip objects are intrinsically in contrast with one another and it will therefore be necessary to make a compromise between the two. 
     In fact, as is well known to the man skilled in the art, a vehicle provided with a particularly “soft” suspension will be capable of deforming very quickly and therefore of absorbing any road irregularities, but on the other hand, it is subject to easily lose contact between wheel and asphalt reducing the vehicle grip, making it virtually undrivable. 
     On the other hand, a vehicle provided with a particularly “stiff” suspension will have excellent grip to the disadvantage of the insulation from the road, that is, to the detriment of driving comfort. 
     With reference to  FIG. 1 , wherein the acceleration spectrum of an element of a passive suspension is shown, for example of the suspended mass, a first profile  1  is noted, which corresponds to a particularly “soft” passive suspension or to a minimum damping coefficient C min , a second profile  2 , which corresponds to a particularly “stiff” passive suspension or to a maximum damping coefficient c max , and a third profile  3 , which corresponds to a compromise or standard passive suspension. 
     In particular, such third profile  3  is one of the possible compromise choices that are usually made by the manufacturers to ensure a suitable compromise between comfort and grip. 
     It is just to meet such need that semi-active suspensions have been developed, which using suitable control logics or methods, implemented by specific control apparatus, allow improving both the driving comfort and the grip at the same time, as compared to passive suspensions. 
     The main differences found between semi-active suspensions can be identified in the different control logics or in the different types of adjustable force generators (or shock absorbers) that can be used. 
     As regards the control logics or methods, they can be developed on the basis of a finite number of levels preselected by the manufacturer in the design step, for example two levels, such as an “on” level and an “off” level, or continuous. 
       FIG. 2  shows various typical profiles of the acceleration spectrum of an element of a suspension, such as the suspended mass, based on the control methods such as Sky-Hook, Acceleration-Driven-Damping (known in the prior art) and compared with profile  3 , which as described above with reference to  FIG. 1 , corresponds to a passive suspension having a compromise damping coefficient. 
     In particular, in such  FIG. 2 , a profile  4  is noted which represents a two state control profile Sky-Hook (SH), typically “on” and “off, and another profile  5  which represents another two state control method Acceleration-Driven-Damping (ADD). 
     Such control methods, Sky-Hook and/or Acceleration-Driven-Damping, in the substance envisage imposing, by suitable control systems, a control signal (for example a current piloted by a control unit) capable of varying the shock absorber damping coefficient, in particular between an “on” level and an “off” level. 
     It should be noted that the “on” level coincides with the damping coefficient c max  and the “off” level coincides with the damping coefficient c min  of the shock absorber. Such coefficients c max  and c min  are selected by the manufacturer in the design step of the suspension in relation to the type of vehicle the suspension itself is intended for. 
     As regards the different types of adjustable force generators (or shock absorbers), which have as a peculiar feature that of varying their damping coefficient according to the control signal, the following types may be distinguished:
         CDC (Continuously Damping Control) shock absorbers, whose operation is based on the variation of the size of the orifices connecting the top and bottom chamber of the shock absorber piston, that is, it is possible to change the speed at which the suspension returns to the balance position; and   Rheological shock absorbers, whose operation envisages the use of rheological fluids, that is, fluids that exhibit a variable viscosity based on a suitable electrical and/or magnetic field (also called electro-rheological or magneto-rheological shock absorbers).       

     Several patent documents are known in the art, which describe the different control logics and/or apparatus capable of controlling the dynamics of a semi-active suspension, such as for example those listed below:
         U.S. Pat. No. 6,904,344 entitled “Semi-Active Shock Absorber Control System”;   U.S. Pat. No. 6,311,110 entitled “Adaptive Off-State Control Method”;   U.S. Pat. No. 6,115,658 entitled “No-Jerk Semi-Active Skyhook Control Method and Apparatus”;   U.S. Pat. No. 5,732,370 entitled “Method for Controlling Motion Using two-stage Adjustable Damper”;   U.S. Pat. No. 5,088,760 entitled “Semi-Active Suspension Control System with Reduced Switching Frequency in Hard and Soft Suspension Characteristics”; and   U.S. Pat. No. 5,062,657 entitled “On/Off Semi-Active Suspension Control”.       

     Such patent documents are based on a “simplified” analysis of the suspension dynamics, which from the conceptual point of view is shown in  FIG. 3 . 
     Such  FIG. 3  shows a so-called “quarter car view”, that is, a partial and schematic view of the vehicle being simulated, wherein a controllable suspension system  6  is noted, capable of interconnecting the suspended mass  7  (“M”) of a vehicle with non suspended mass  8  (“m”) of such vehicle. 
     To this end, the controllable suspension  6  comprises a controllable force generator (or controllable shock absorber)  6 A and a spring  6 B capable of controlling the vertical dynamics of the non suspended mass  8 , which in the representation in  FIG. 3  is shown as running along the profile of a road  9 . 
     From  FIG. 3  it is also noted that the profile of road  9  leads the following movements to suspension  6 :
         z r  road profile  9  movement relative to a reference plane H;   z t  movement of the non suspended mass “m” of the vehicle relative to the reference plane H;   z movement of the suspended mass “M” of the vehicle relative to said reference plane H.       

     Among the patent documents listed above, documents U.S. Pat. No. 6,311,110, U.S. Pat. No. 6,115,658, U.S. Pat. No. 5,732,370, U.S. Pat. No. 5,088,760 and U.S. Pat. No. 5,062,657 have in common the measurement apparatus  10 , also schematically shown in  FIG. 3 . 
     In particular, such measurement apparatus  10  comprises an acceleration sensor  10 A mounted on the non suspended mass  8  and a linear potentiometer (also called strainmeter)  10 B, arranged between such non suspended mass  8  and that constrained  7 . 
     In patent document U.S. Pat. No. 6,904,344, as an alternative to the linear potentiometer  10 B, an acceleration sensor is provided arranged on the constrained mass (not shown in  FIG. 3 ). 
     The control methods illustrated by the patent documents mentioned above may be divided into the following three groups: 
     1 st  group: patent documents U.S. Pat. No. 6,311,110 and U.S. Pat. No. 6,115,658 are intended for improving the critical aspects of the Sky-Hook control method. However, such methods strongly depend on the specific calibration procedures of the vehicle the suspension is mounted on. 
     2 nd  group: patent documents U.S. Pat. No. 6,904,344, U.S. Pat. No. 5,732,370 and U.S. Pat. No. 5,062,657 found the control methods on a simplified calculation of the optimum force that the suspension should develop in particular conditions, such as reaching the travel end of the suspension, thus limiting their efficacy to particular events. 
     3 rd  group: patent document U.S. Pat. No. 5,088,760 describes a control method based on a processing step of signals relating to a plurality of sensors seated on the suspension; however, the performance of detection of such sensors are limited only to a portion of the characteristic frequency band of the system. 
     In view of the prior art described above, the object of the present invention is to provide a method and an apparatus for controlling an adjustable force generator in a controllable suspension system which should be capable of solving the drawbacks found in the methods and apparatus made according to the prior art. 
     In accordance with the present invention, such object is achieved by a method for controlling a controllable force generator in a controllable suspension system, in accordance with claim  1 . 
     Such object is also achieved by an apparatus for controlling a controllable force generator in a controllable suspension system, in accordance with claim  14 . 
     Thanks to the present invention it is possible to obtain a control method that, after a step of processing suitable signals of measurement of the suspension dynamics, allows optimising the suspension response in a quick and efficient manner. 
     The inventive method allows the real exploitation of the capabilities of a semi-active suspension, optimising the performance thereof, ensuring better grip, height from the ground, reacting to the external forces, controlling roll, pitch and yaw, filtering noises of various types, in a more accurate and precise manner than in the prior art. 
     Finally, but not less important, the low complexity of the control apparatus makes the implementation of the inventive method particularly advantageous. 
     In fact, the control methods developed in accordance with the known techniques provide worse results with almost always higher computation complexity. 
    
    
     
       The features and advantages of the present invention will appear more clearly from the following detailed description of some practical embodiments thereof, made by way of a non-limiting example with reference to the annexed drawings, wherein: 
         FIG. 1  shows typical profiles of the acceleration spectrum of a suspension element based on damping coefficient c min  c max  and C standard , in accordance with the prior art; 
         FIG. 2  shows typical profiles of the acceleration spectrum of a suspension element based on control methods such as Sky-Hook, Acceleration-Driven-Damping, in accordance with the prior art; 
         FIG. 3  shows a “quarter car” view in accordance with the prior art; 
         FIGS. 4 to 6  show a three possible embodiments of the method and apparatus according to the present invention; 
         FIG. 7  shows the comparison between typical profiles of the acceleration spectrum of a suspension element and the profiles obtained by the use of the control method in accordance with the present invention. 
     
    
    
     In the following description, reference is made, for simplicity of description, to a semi-active suspension in relation to the specific field of the automotive industry, but it is clear that the following description also applies to semi-active suspensions intended for being implemented on motorcycles, agricultural machines, railway vehicles, household appliances and the like. 
     With reference to the annexed  FIGS. 4 to 7 , reference numeral  11  denotes the apparatus for controlling a controllable force generator  13  in a controllable suspension system  12 . 
     The controllable suspension system  12  is interconnected between a first element  14  and a second element  15 . 
     Such controllable force generator  13  (or controllable shock absorber) in combination with a spring  16  with elastic constant k is capable of controlling the vertical dynamics of the non suspended mass “m” of the vehicle (or wheel). 
     The non suspended mass “m” is identified with the second element  15  that in the present representation is depicted by a spring  17  with elastic constant k t . 
       FIGS. 4-6  also show that the profile of road  18  leads the following movements to suspension  12 :
         z r —road profile  18  movement relative to a reference plane H;   z t  movement of the non suspended mass “m” of the vehicle relative to the reference plane H;   z movement of the suspended mass “M” of the vehicle relative to said reference plane H.       
     The control apparatus  11  comprises the following elements:
         first detection means  19  for detecting suitable physical quantities so as to generate a first S 1  and a second signal S 2  representative of said physical quantities;   control means  20  suitable for receiving said first signal S 1  and said second signal S 2  for generating a control signal S in  for controlling the dynamics of the damping of said controllable force generator  13 .       

     The detection means  19  may for example detect physical quantities such as speed, acceleration and the like induced on suspension  12  when the vehicle (not shown in the annexed figures) covers the road profile  18 . 
     In the embodiment shown in  FIG. 4 , the first signal S 1  may represent the acceleration that said first element  14  undergoes while the vehicle covers the profile of said road  18  and the second signal S 2  may represent the speed of said first element  14  while the vehicle covers the profile of said road  18 . 
     In other words, signal S 1  can be identified with the second derivative of the movement z of the suspended mass “M” while signal S 2  can be identified with the first derivative of the movement z of the suspended mass “M”, that is:
         signal S 1  can be identified with {umlaut over (z)}(t), that is, the second derivative of movement z;   signal S 2  can be identified with ż(t), that is, the first derivative of movement z.       

     The first detection means  19 , in the embodiment shown in  FIG. 4 , is an accelerometer  19 A operatively associated to said first element  14 , suitable for detecting the acceleration of said first element  14  and for generating said first signal S 1  (that is, the second derivative of movement z, that is, {umlaut over (z)}(t)) and an integration device  19 B suitable for carrying out the operation of integration of said first signal S 1  for obtaining signal S 2  (that is, the first derivative of movement z, that is, ż(t)) representative of the speed of said first element  14 . 
     Similar remarks may be made with reference to the embodiment shown in  FIG. 5 , with the exception that accelerometer  19 A is operatively associated to said second element  15 . 
     In the embodiment shown in  FIG. 5 , accelerometer  19 A is suitable for detecting the acceleration of said second element  15  for generating said signal S 1 . 
     With reference to the embodiments shown in  FIGS. 4 and 5 , the control means  20  is adapted for generating, advantageously, said control signal S in  which is a function of the ratio value between said first signal S 1  squared and said second signal S 2  squared so as to discriminate whether the elements of suspension  12  exhibit a high or low frequency behaviour. 
     More in particular, the control means  20  is suitable for generating said control signal S in  as a function of a first damping law L 1  when the relationship value between said first signal S 1  squared and said second signal S 2  squared is less than or equal to a predetermined constant, or said control means  20  is suitable for generating said control signal S in  as a function of a second damping law L 2  when the ratio value between said first signal S 1  squared and said second signal S 2  squared is more than said predetermined constant. 
     In other words, the control means  20  generates the control signal S in  based on the following function: 
         f ( t )= {umlaut over (z)} ( t ) 2 −α 2   ż ( t ) 2   [1] 
     that is, the control means  20  applies the first control law L 1  if: 
         z ( {umlaut over (t)} ) 2   /z ( {dot over (t)} ) 2 &lt;α 2   [2] 
     or, the control means  20  applies the second control law L 2  if: 
         z ( {umlaut over (t)} ) 2   /z ( {dot over (t)} ) 2 &gt;α 2   [3] 
     where 
     {umlaut over (z)}(t) is the acceleration expressed in m/s 2  of said first element  14  of the controllable suspension  12  measured at time t; 
     ż(t) is the speed expressed in m/s of said first element  14  of the controllable suspension  12  measured at time t; 
     α is the invariance frequency expressed in rad/sec, that is, the constant that represents the frequency suitable for discriminating the set of frequencies between high and low frequencies. 
     It is worth noting that a is a fixed parameter and is determined in advance during the design of the controllable suspension  12 . 
     It is also worth noting that the damping laws identified above may be alternately applied to the first element  14  (or suspended mass “M” of the vehicle) or to the second element  15  (or non suspended mass “m” of such vehicle). 
     Thus, the function f(t) identified in [1] is a function capable of discriminating between high and low frequency, that is, if f(t)&gt;0 we are in the high frequency field while if f(t)&lt;0 we are in the low frequency field. 
     In the practice, function f(t) allows discriminating whether an element of suspension  12  exhibits a behaviour in high or low frequency, that is, function f(t) is alternately applicable to the first  14  or to the second element  15 , if the first  14  or the second element  15  exhibit high or low frequency dynamics. 
     Thus, the elements of suspension  12  exhibit a high frequency behaviour if the frequency value is higher than the invariance frequency value α (see  FIGS. 1 and 2 ), or they exhibit a low frequency behaviour if the frequency value is lower than the invariance frequency value α (see  FIGS. 1 and 2 ). 
     To select the constant α in a controllable suspension capable of alternately working at high or low damping (that is, respectively c max  or c min ) it is worth noting that a working frequency typical of the suspension exists wherein it is unimportant if the adjustable force generator  13  is controlled to operate at a high or low damping coefficient. 
     In other words, even if a damping coefficient c max  or c min  is selected, the behaviour of the controllable suspension  12  does not change. 
     Such frequency is called invariance frequency and imposing such frequency value in function f(t) identified in [1], the value of the invariance frequency of the controllable suspension  12  is obtained. 
     The value of constant α can be calculated by the function described hereinafter: 
       α=√{square root over (2 k/M )} 
     that is, √{square root over (2)} times the resonance of the suspended mass M, k being the suspension stiffness. 
     Typical values for the example being discussed, that is, a semi-active suspension in relation to the specific automotive industry field, identify as a possible range of values for the constant α that comprised between 1.5 and 2.5 Hz, preferably 1.8 Hz (see  FIG. 1  and  FIG. 2 ). 
     It is worth noting that if reference is made to a semi-active suspension in relation to the specific motorcycle industry field, the possible range of values for the constant would be that comprised between 1.5 and 5 Hz, preferably 4 Hz. 
     Advantageously, in the preferred embodiment of the present invention, the first damping law L 1  to be applied to the adjustable force generator  13  can be equal to a first damping coefficient and the second damping law L 2 , to be applied to the adjustable force generator  13 , can be equal to a second damping coefficient. 
     In other words, the control means  20  are suitable for generating the control signal S in  wherein law L 1  coincides with a first damping coefficient or wherein law L 2  coincides with a second damping coefficient when the following relationship occurs:
         if the value of the ratio of ż({umlaut over (t)}) 2 /z({dot over (t)}) 2  is less than α 2  the controllable force generator  13  is imposed the first damping law L 1 , which can coincide with said first damping coefficient which in particular is the maximum damping coefficient c max .   if the value of the ratio of z({umlaut over (t)}) 2 /z({dot over (t)}) 2  is more than α 2  the controllable force generator  13  is imposed the second damping law L 2 , which can coincide with said second damping coefficient which in particular is the minimum damping coefficient c min .       

     It should be noted that the damping coefficients c max  or c min , imposed to the adjustable force generator  13 , as specific values of the control laws L 1  and L 2 , respectively, are selected by the manufacturer in the design step of suspension  12 , where c min  must be the lowest (if possible at the technical limits imposed by the type of suspension) and c max  must be sufficient to dampen the stresses induced by the profile of road  18  on suspension  12 . 
     In particular, such damping coefficients c max  or C min  are selected both in relation to the specific type of vehicle suspension  12  is intended for and for the target suspension  12  is designed for, that is, a driving comfort or grip target. 
     Moreover, it is worth noting that in order to implement the control method of the controllable force generator  13  in the embodiments illustrated in  FIGS. 4 and 5 , it is necessary to control the dynamics of the controllable suspension  12  at predetermined time intervals T. 
     For example, an interval T must be less than or equal to ½F, where F is the maximum frequency to be controlled. 
     The suspension control method  12  must therefore select every T if imposing a low damping coefficient or a high damping coefficient to the controllable force generator  13 . 
     In other words, the control method comprises the following steps:
         detecting the first signal S 1  representative of the acceleration ({umlaut over (z)}(t)) of the first element  14  of the suspended mass “M”;   detecting a second signal S 2  representative of the speed (ż(t)) of the first element  14  of the suspended mass “M”;   determining the ratio value between said first signal S 1  squared and said second signal S 2  squared; and   applying a damping control signal S in  to the controllable force generator  13  based on the value to be thus discriminated if the components of suspension  12  exhibit a high or low frequency dynamics.       

     In particular, the damping control signal S in  envisages that:
         if the value of the ratio between said first signal S 1  squared and said second signal S 2  squared (that is, the ratio of z({umlaut over (t)}) 2 /z({dot over (t)}) 2 ) is less than α 2  then impose the first damping law L 1 , so as to apply the maximum damping coefficient c max ;   if the value of the ratio between said first signal S 1  squared and said second signal S 2  squared (that is, the ratio of z({umlaut over (t)}) 2 /z({dot over (t)}) 2 ) is more than α 2  then the controllable force generator  13  is imposed the second damping law L 2 , so as to apply the minimum coefficient c min .       

     As described above, the control method may be implemented by detecting the speed and the acceleration of the second element  15 , that is, of the non suspended mass “m”, that is, the damping laws identified above L 1  and L 2  can be alternately applied to the first element  14  (or suspended mass “M” of the vehicle) or to the second element  15  (or non suspended mass “m” of such vehicle). 
     Advantageously, it is possible to improve the performance of the control method illustrated above, resorting to the embodiment of the control apparatus  11  illustrated in  FIG. 6 . 
     With reference now in particular to  FIG. 6 , it is noted that the control apparatus  11  further comprises detecting means  21  for detecting suitable physical quantities so as to generate a third S 3  and a fourth signal S 4  representative of said physical quantities. 
     The detection means  21  may for example detect physical quantities such as speed, acceleration and the like induced on suspension  12  when the vehicle (not shown in the annexed figures) covers the road profile  18 . 
     In particular, the third signal S 3  may represent the acceleration that said second element  15  undergoes while the vehicle covers the profile of said road  18  and the fourth signal S 4  may represent the speed of said second element  15  while the vehicle covers the profile of said road  18 . 
     In other words, signal S 3  can be identified with the second derivative of the movement z t  while signal S 4  can be identified with the first derivative of the movement z t , that is:
         signal S 3  can be identified with {umlaut over (z)} t (t), that is, the second derivative of movement z t ; and   signal S 4  can be identified with (ż t (t), that is, the first derivative of movement z t .       

     Advantageously, in the embodiment shown in  FIG. 6 , the control means  20  is suitable for receiving, besides the first signal S 1  and the second signal S 2 , also said third S 3  and fourth S 4  signal. 
     The second detection means  21  is an accelerometer  21 A operatively associated to said second element  15 , suitable for detecting the acceleration of said second element  15  and for generating said third signal S 3  (that is, the second derivative of movement z t , that is, {umlaut over (z)} t (t)) and an integration device  21 B suitable for carrying out the operation of integration of said third signal S 3  for obtaining signal S 4  (that is, the first derivative of movement z t , that is, ż t (t)) representative of the speed of said second element  15 . 
     Advantageously, the control means  20  are therefore suitable for generating the control signal S in  for controlling said controllable force generator  13 . 
     To this end, the control means  20  is suitable for generating said control signal S in  that must be applied to said controllable force generator  13  based on the following conditions:
         if the ratio value z({umlaut over (t)}) 2 /z({dot over (t)}) 2  is less than α 2 , the control signal S in  must satisfy the control law commonly known as Sky-Hook; whereas   if the ratio value z({umlaut over (t)}) 2 /z({dot over (t)}) 2  is more than α 2 , the control signal S in  must satisfy the control law commonly known as Acceleration-Driven-Damping (ADD).       

     The damping laws that control the control logic Sky-Hook and Acceleration-Driven-Damping (ADD) are shown hereinbelow: 
       Sky-Hook (2 stages): 
         S   in ( t )= c   MAX     ż ( ż−ż   t )≧0  [4] 
       ADD (2 stages): 
         S   in ( t )= c   MIN     ż ( ż−ż   t )&lt;0  [5] 
         S   in ( t )= c   MAX     {umlaut over (z)} ( ż−ż   t )≧0  [6] 
         S   in ( t )= c   MIN     {umlaut over (z)} ( ż−ż   t )&lt;0  [7] 
     where 
     {umlaut over (z)}(t) is the acceleration expressed in m/s of said first element  14  of the controllable suspension  12  measured at time t; 
     ż(t) is the speed expressed in m/s of said first element  14  of the controllable suspension  12  measured at time t; 
     ż t (t) is the vertical speed expressed in m/s of the second element  15  of the controllable suspension  12  calculated at time t; 
     S in (t) is the control signal to be imposed to the controllable force generator  13  on the basis of the occurrence of the above conditions. 
     In other words, the control means  20  are suitable for imposing the control law Sky-Hook to the controllable force generator  13  for ratio values z({umlaut over (t)}) 2 /z({dot over (t)}) 2  less than α 2  and the control law Acceleration-Driven-Damping for ratio values z({umlaut over (t)}) 2 /z({dot over (t)}) 2  more than α 2 . 
     More in particular, the control signal S in  can change the damping coefficient of the controllable force generator  13  in accordance with said first damping law L 1  or with said second damping law L 2  when the following conditions occur:
         imposing the first damping law L 1 , that is, damping coefficient c max  if the condition according to which function f(t) indicated in [1] is less than or equal to zero is satisfied and if the condition of the control logic of the SkyHook law indicated in [4], that is, {umlaut over (z)} 2 −α 2 ż 2 ≦0 and ż(ż−ż t )≧0 is satisfied,       

     or if the condition according to which function f(t) indicated in [1] is more than zero is satisfied and if the condition of the control logic of the Acceleration-Driven-Damping law indicated in [6], that is, {umlaut over (z)} 2 −α 2 ż 2 &gt;0 and {umlaut over (z)}(ż−ż t )≧0 is satisfied;
         imposing the second damping law L 2 , that is, damping coefficient c min  if the condition according to which function f(t) indicated in [1] is less than or equal to zero is satisfied and if the condition of the control logic of the SkyHook law indicated in [5], that is, {umlaut over (z)} 2 −α 2 ż 2 ≦0 and ż(ż−ż t )≦0 is satisfied,       

     or if the condition according to which function f(t) indicated in [1] is more than zero is satisfied and if the condition of the control logic of the Acceleration-Driven-Damping law indicated in [7], that is, {umlaut over (z)} 2 −α 2 ż 2 &gt;0 and {umlaut over (z)}(ż−ż t )&lt;0 is satisfied; 
     where α is constant (identifiable with the invariance frequency) expressed in rad/sec, that is, the constant that represents the frequency suitable for discriminating the set of frequencies between high and low frequencies, said constant α being equal to the value that can be calculated by the formula illustrated above, that is α=√{square root over (2k/M)} (see  FIG. 1  and  FIG. 2 ). 
     Advantageously, in order to implement the control method of the controllable force generator  13  in the embodiment illustrated in  FIG. 6 , it is necessary to control the dynamics of the controllable suspension  12  at a predetermined time interval T. 
     For example, an interval T must be less than or equal to ½F, where F is the maximum frequency to be controlled. 
     The suspension control method  12  must therefore be selected every T if imposing a low damping coefficient or a high damping coefficient to the controllable force generator  13 . 
     In other words, the control method in relation to the specific embodiment illustrated in  FIG. 6 , besides the steps described above with reference to the control method of the embodiments illustrated in  FIGS. 4 and 5 , also comprises the following further steps:
         detecting the third signal S 3  representative of the acceleration of said second element  15 , that is, S 3  is identifiable with {umlaut over (z)} t (t);   detecting the fourth signal S 4  representative of the speed of said second element ( 15 ), that is, S 4  is identifiable with ż t (t);   imposing the first damping law L 1 , that is, damping coefficient c max  if:       

     {umlaut over (z)} 2 −α 2 ż 2 ≦0 (that is, function f(t) indicated in [1]) and ż(ż−ż t )≧0 (that is, the control logic SkyHook indicated in [4]) 
     or {umlaut over (z)} 2 −α 2 ż 2 &gt;0 (that is, function f(t) indicated in [1]) and {umlaut over (z)}(ż−ż t )≧0 (that is, the control logic ADD indicated in [6]);
         imposing the first second damping L 2 , that is, damping coefficient c min  if:       

     {umlaut over (z)} 2 −α 2 ż 2 ≦0 (that is, function f(t) indicated in [1]) and ż(ż−ż t )&lt;0 (that is, the control logic SkyHook indicated in [5]) 
     or {umlaut over (z)} 2 −α 2 ż 2 &gt;0 (that is, function f(t) indicated in [1]) and {umlaut over (z)}(ż−ż t )&lt;0 (that is, the control logic ADD indicated in [7]). 
     It is worth noting that the controllable force generator  13  is a controllable shock absorber of the type described above with reference to the prior art, that is, CDC (Continuously Damping Control) shock absorbers, rheological shock absorbers. 
     Finally, it is worth noting that the control means  20  are an E.C.U. normally available on the market. 
     With reference now to  FIG. 8 , a first profile  22  is noted, depicting the result that can be obtained with the embodiment of the control apparatus illustrated in  FIGS. 4 and 5 , and a second profile  23  depicting the result that can be obtained with the embodiment of the control apparatus illustrated in  FIG. 6  and a third profile  24  depicting the theoretical optimum but not implementable from a semi-active suspension. 
     As is seen in this figure, profile  22 , obtained by the control apparatus described with reference to  FIGS. 4 and 5 , allows achieving satisfactory results even if slightly degraded compared to profile  23 . 
     Of course, a man skilled in the art may make several changes and adjustments to the configurations described above in order to meet specific and incidental needs, all falling within the scope of protection defined in the following claims.