# Patent

## Title
Control system and method for controlling the driving-away manoeuvre in a motor vehicle with a servo-controlled gearbox

## Abstract

What is described is a control system for controlling the driving-away maneuver in a motor vehicle provided with a gearbox comprising a primary input shaft which can be coupled to a drive shaft of a propulsion system of the vehicle by means of a servo-assisted friction clutch, wherein a control unit receives at its input signals indicating a command imparted by the driver of the motor vehicle by operating the accelerator pedal, and generates—on the basis of a mathematical reference model—reference torque request signals indicating the reference torques requested from the drive shaft and from the friction clutch during the driving-away manoeuvre, and also generates—by comparison between signals indicating the estimated angular velocities of the drive shaft and of the primary gear shaft, and detected signals indicating the actual angular velocities of the drive shaft and of the primary gear shaft—corresponding corrective contributions, in such a way as to construct command signals for controlling torque actuator devices of the propulsion system and of the friction clutch, for controlling the driving-away manoeuvre in the motor vehicle.

## Background
FIELD OF THE INVENTION
The present invention relates in a general way to the control of the propulsion of a motor vehicle, and more specifically to a control system and method for controlling the driving-away manoeuvre in a motor vehicle provided with a servo-controlled gearbox.
BACKGROUND OF THE INVENTION
In practice, a servo-controlled gearbox is a conventional mechanical gearbox operated by means of servo-controllers, comprising an actuator for disengaging and engaging the friction clutch between the drive shaft and the primary input shaft of the gearbox, an actuator for selecting the transmission ratios and an actuator for engaging the selected transmission ratio.
Servo-controlled gearboxes are well known in the prior art and are used to reproduce and optimize the driver's gear change commands.
The control strategies of a control system for a servo-controlled gearbox must adapt themselves to the operating conditions of the vehicle and must maintain the driving sensation requested by the driver by means of the commands imparted to the accelerator pedal.
A control system for a servo-controlled gearbox is known from U.S. Pat. No. 6,389,346 held by the present applicant. The system comprises an electronic control unit connected to a plurality of sensors for detecting the operating conditions of the vehicle, including a potentiometric sensor for detecting the position of the accelerator pedal, to the actuators of the gearbox, and to the actuators controlling the power delivered by the vehicle's propulsion system, in order to permit the integrated control of the propulsion system and the gearbox during a gear change operation.
The detection of the position of the accelerator pedal enables the driver's intentions to be correctly recognized.
The operation of the control unit is based on a reference model in which the actuator command signals are determined by means of a mathematical model of the driving behaviour, which is designed to adapt the behaviour of the vehicle in terms of comfort and performance, in the various stages of the gear change, according to the commands imparted by the driver by means of the accelerator pedal and a command lever or push button for selecting the transmission ratio, in other words for requesting a change to a higher or lower ratio.
The control system for the servo-controlled gearbox must be configured to control the automatic driving away (starting from stationary) of the vehicle, particularly in accordance with the performance level which is specified by the driver by means of his pressure on the accelerator pedal.
SUMMARY OF THE INVENTION
The object of the present invention is to provide a control procedure for a servo-controlled gearbox, making it possible to obtain, during a driving-away manoeuvre, the functions and performance expected by the driver in accordance with the command imparted by means of the accelerator pedal.
The definition of a servo-controlled gearbox used in the remainder of the present description refers both to a gearbox of the type defined initially and to a configuration which does not provide for the servo-assisted actuation of the selection of the transmission ratios and of the engagement of the selected ratio, which can instead be controlled manually by the driver, but only for the servo-assisted actuation of the clutch control by means of electrical or electro-hydraulic actuators.
According to the present invention, this object is achieved by means of a control system and method having the characteristics claimed in claims 1 and 12, respectively.



BRIEF DESCRIPTION OF THE DRAWINGS
Further advantages and characteristics of the invention will be made clear by the following detailed description, which refers to the attached drawings provided purely by way of example and without restrictive intent, in which:
FIG. 1 is a schematic representation of an engine and transmission assembly of a vehicle, including a servo-controlled gearbox associated with a propulsion system,
FIG. 2 is a block diagram of the system for controlling the servo-controlled gearbox proposed by the invention,
FIG. 3 is a simplified model of the motion transmission used by the control system of FIG. 2, and
FIG. 4 shows a pair of time diagrams which illustrate the variation of the variables controlled by the system.



DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
To make matters clearer, FIG. 1 shows an engine and transmission assembly 10 of a motor vehicle, comprising a propulsion system such as an internal combustion thermal engine E which can transmit the mechanical energy developed to the driving wheels of the vehicle through a gearbox G, a transmission shaft S (partially illustrated in the figure) and a differential (not shown).
The thermal engine is associated with a first electronic processing and control unit ECUE which can be interfaced with sensor devices associated with the engine and engine actuator devices, indicated in their entirety by SENSE and ACTE respectively.
The gearbox G is associated with a second electronic processing and control unit ECUG, which can be interfaced with sensor devices associated with the gearbox and actuator devices for the gearbox, indicated in their entirety by SENSG and ACTG respectively.
The two control units ECUE and ECUG are coupled to corresponding memory devices ME and MG, and are connected to a common transmission line BUS, for example a line of a communication network according to the CAN protocol.
In an alternative embodiment, the units ECUE and ECUG can be integrated into a single processing unit in order to improve the overall performance of the system.
FIG. 1 also shows the connection of a sensor SENSPACC for detecting the position of the accelerator pedal PACC at the input to the engine control unit ECUE.
FIG. 2 shows in detail the logical diagram of a control system for the servo-controlled gearbox G, indicated as a whole by 20, the system being implemented preferably in the gearbox control unit ECUG, but being distributed between the separate units ECUE and ECUG if required.
The system 20 comprises a torque reference generator module 22 arranged for calculating the variation in time of a reference torque CMRif requested from the thermal engine and of a reference torque CFRif transmittable by the friction clutch, on the basis of a command imparted by the driver by the operation of the accelerator pedal PACC to actuate a driving-away manoeuvre. The variation with time of CMRif e CFRif is calculated on the basis of a reference model as a function of intermediate parameters such as the variation in longitudinal acceleration of the vehicle (jerk), the driving-away torque CDriver and the angular velocity of the drive shaft (revolutions of the engine) on driving away ωMsp, obtained from the information on the position of the accelerator pedal.
The signals indicating the position of the accelerator pedal and the driving-away torque CDriver are communicated to the gearbox control unit ECUG by the engine control unit ECUE via the transmission line BUS of the CAN network.
The signal indicating the requested driving-away torque CDriver is calculated in the engine control unit ECUE, by means of a reference model stored in the associated memory ME, while the signals indicating the requested jerk and engine revolutions on driving away are calculated in the gearbox control unit ECUG, by means of reference models stored in the associated memory MG.
The torque reference generator module sends from its output a pair of reference torque request signals or data, indicating the reference torque CMRif requested from the thermal engine and the transmittable torque CFRif transmittable by the friction clutch.
These signals are supplied to the input of an engine speed estimator module 24, adapted to calculate the reference angular velocities of the drive shaft and of the primary gear shaft, indicated below by ωMRif and ωPRif respectively, on the basis of the information on the temporal variation of the torques CMRif and CFRif, according to a simplified transmission model which is mentioned briefly below.
The signals ωMRif and ωPRif are then supplied by feedback to the generator module 22 and to the input of a controller module 26 adapted to calculate the error between the reference angular velocities calculated by the estimator module 24 and the actual angular velocities measured by sensors installed on board the vehicle and acquired at the engine control unit and the gearbox control unit.
More specifically, the signal indicating the actual angular velocity of the drive shaft ωM is acquired at the input of the engine control unit ECUE by means of the sensor indicated as SENSE in FIG. 1, and communicated to the gearbox control unit ECUG via the line BUS, while the signal indicating the actual angular velocity of the primary gear shaft ωP is acquired directly by the unit ECUG by means of the sensor indicated by SENSG in FIG. 1.
The estimator module 24 and the controller module 26, in series, form a closed loop compensator.
On the basis of the comparison between the reference angular velocities and the actual velocities, the controller module 26 determines corrective torque contributions ΔCM and ΔCF and sends corresponding signals or data which are added to the open-loop reference torque request signals or data CFRif and CMRif originated by the module 22 in order to generate corresponding torque request signals CM and CF.
The signals CM and CF are supplied through the engine and gearbox control units to the actuators ACTE and ACTG, which are, respectively, the engine control actuator and the friction clutch operation actuator. More specifically, the signal CM is supplied by the gearbox control unit ECUG to the engine control unit ECUE via the line BUS, while the signal CF is used by the gearbox control unit ECUG for controlling the actuator ACTG which operates the friction clutch.
For the calculation of the reference torques and angular velocities and for the closed loop compensation, use is made of a linear model of the transmission in which the thermal engine and the gearbox clutch are considered to be torque actuators, and no allowance is made for resilient elements (such as flexible couplings) and frictional phenomena between the mechanical members. The model and the corresponding variables and parameters are represented in FIG. 3.
The drive shaft is indicated by 30 and an overall moment of inertia of the engine JM relates to it. ωM and CM indicate, respectively, the angular velocity of the drive shaft and the net engine torque on the shaft.
Numeral 32 indicates the coupling clutch between the drive shaft 30 and the gearbox, the latter comprising a primary input shaft 34 and a secondary shaft 36 coupled to the differential and, by means of the latter, to the driving wheels.
CF indicates the torque transmitted by the clutch, which can be modulated as a function of the degree of engagement and sliding of the clutch. ωP indicates the angular velocity of the primary shaft. This shaft, together with the secondary shaft and the devices located downstream of the gears, presents a total resistant torque CR to the clutch.
The system represented by the model of FIG. 3 is described by the following equations.
In the engaged clutch condition:




  
    
      
        
          
            
              C
              M
            
            ⁡
            
              (
              t
              )
            
          
          -
          
            
              C
              R
            
            ⁡
            
              (
              t
              )
            
          
        
        =
        
          
            (
            
              
                J
                M
              
              +
              
                J
                P
              
            
            )
          
          ·
          
            
              d
              
                ω
                M
              
            
            
              d
              t
            
          
        
      
    
    
      
        (
        1
        )
      
    
  




in the disengaged clutch condition, with modulation:





  
    
      
        
          
            
              C
              M
            
            ⁡
            
              (
              t
              )
            
          
          -
          
            
              C
              F
            
            ⁡
            
              (
              t
              )
            
          
        
        =
        
          
            J
            M
          
          ·
          
            
              d
              
                ω
                M
              
            
            
              d
              t
            
          
        
      
    
    
      
        (
        2
        )
      
    
  




on the engine side, and





  
    
      
        
          
            
              C
              F
            
            ⁡
            
              (
              t
              )
            
          
          -
          
            
              C
              R
            
            ⁡
            
              (
              t
              )
            
          
        
        =
        
          
            J
            P
          
          ·
          
            
              d
              
                ω
                P
              
            
            
              d
              t
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




on the gearbox side, where JP indicates the total moment of inertia found on the primary shaft, which depends on the moment of inertia of the driven disc of the clutch JDC, on the moment of inertia of the primary shaft of the gearbox JPS, and on the total moment of inertia of the vehicle, found at the output of the differential JV using a constant of proportionality as a function of the selected transmission ratio τ, according to the equation





  
    
      
        
          J
          P
        
        =
        
          
            J
            
              D
              ⁢
              
                
              
              ⁢
              C
            
          
          +
          
            J
            PS
          
          +
          
            
              J
              V
            
            
              τ
              2
            
          
        
      
    
    
      
        (
        4
        )
      
    
  




The total moment of inertia of the vehicle found at the output of the differential can be calculated according to the equation

JV=M ·R2+4·JW  (5)

or in other words as a function of the moment of inertia of the wheels JW and of the mass of the vehicle M and the rolling radius of the wheels R.

The variation (derivative) of longitudinal acceleration, known as the “jerk”, is particularly important in relation to driving comfort, and is defined by the equation




  
    
      
        jerk
        =
        
          
            d
            
              a
              x
            
          
          
            d
            t
          
        
      
    
    
      
        (
        6
        )
      
    
  




During the driving-away manoeuvre, the longitudinal acceleration of the vehicle is related to the acceleration of the primary gear shaft by the relation




  
    
      
        
          a
          x
        
        =
        
          
            
              
                d
                
                  ω
                  w
                
              
              
                d
                t
              
            
            ·
            R
          
          =
          
            
              
                d
                
                  ω
                  P
                
              
              
                d
                t
              
            
            ·
            
              R
              τ
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




The variation of the rotation speed of the primary gear shaft depends on the torque transmitted by the clutch according to equation (3) of the transmission model described above; in other words,




  
    
      
        
          
            d
            
              ω
              P
            
          
          
            d
            t
          
        
        =
        
          
            
              
                C
                F
              
              ⁡
              
                (
                t
                )
              
            
            -
            
              
                C
                R
              
              ⁡
              
                (
                t
                )
              
            
          
          
            J
            P
          
        
      
    
    
      
        (
        8
        )
      
    
  




The acceleration of the vehicle during driving away is therefore as follows:




  
    
      
        
          a
          x
        
        =
        
          
            
              
                d
                
                  ω
                  P
                
              
              
                d
                t
              
            
            ·
            
              R
              τ
            
          
          =
          
            
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                -
                
                  
                    C
                    R
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                J
                P
              
            
            ·
            
              R
              τ
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




and the jerk can therefore be determined as a function of the clutch torque, assuming that the resistant torque CR(t) is constant, according to the following formula:





  
    
      
        jerk
        =
        
          
            
              d
              
                a
                x
              
            
            
              d
              t
            
          
          =
          
            
              
                d
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
              
                d
                t
              
            
            ·
            
              R
              
                
                  J
                  P
                
                ·
                τ
              
            
          
        
      
    
    
      
        (
        10
        )
      
    
  




Consequently, the specification of a constant jerk value, referred to below as jerk*, which is an essential condition and fundamental to the control system proposed by the invention, produces a linear variation of the torque transmitted by the clutch CF(t), as represented in the upper graph of FIG. 4 in the period t0<t<t2.
The following equivalence will therefore be considered:




  
    
      
        
          
            d
            
              
                C
                F
              
              ⁡
              
                (
                t
                )
              
            
          
          
            d
            t
          
        
        =
        
          
            
              
                
                  C
                  F
                
                ⁡
                
                  (
                  
                    t
                    2
                  
                  )
                
              
              -
              
                
                  C
                  F
                
                ⁡
                
                  (
                  
                    t
                    0
                  
                  )
                
              
            
            
              T
              F
            
          
          =
          
            dC
            F
          
        
      
    
    
      
        (
        11
        )
      
    
  




Given relation (10) and the above equivalence, we obtain




  
    
      
        
          jerk
          *
        
        =
        
          
            
              d
              
                a
                x
              
            
            
              d
              t
            
          
          =
          
            
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      2
                    
                    )
                  
                
                -
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
              
              
                T
                F
              
            
            ·
            
              R
              
                
                  J
                  p
                
                ·
                τ
              
            
          
        
      
    
    
      
        (
        12
        )
      
    
  




from which it is possible to calculate the total duration TF of the interval required to modulate the engagement of the clutch from an initial transmitted torque CF (t0) to the final transmitted torque CF (t2):





  
    
      
        
          T
          F
        
        =
        
          
            
              (
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      2
                    
                    )
                  
                
                -
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
              
              )
            
            ·
            R
          
          
            
              jerk
              *
            
            ·
            
              J
              p
            
            ·
            τ
          
        
      
    
    
      
        (
        13
        )
      
    
  




In conclusion, the simplified model which has been adopted establishes that, in order to specify a constant jerk during a driving-away manoeuvre, it is simply necessary to control a ramp of torque transmittable by the clutch, according to the relation




  
    
      
        
          
            d
            
              
                C
                F
              
              ⁡
              
                (
                t
                )
              
            
          
          
            d
            t
          
        
        =
        
          
            
              
                J
                p
              
              ·
              τ
            
            R
          
          ·
          
            jerk
            *
          
        
      
    
    
      
        (
        14
        )
      
    
  




The variation of the torque transmittable by the clutch is therefore a function of the constant reference jerk value and of the initial value of the torque transmitted by the clutch at the instant t0, and can be summarized in the following equations:




  
    
      
        
          
            
              
                
                  C
                  F
                
                ⁡
                
                  (
                  t
                  )
                
              
              =
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
                +
                
                  
                    ∫
                    
                      t
                      0
                    
                    t
                  
                  ⁢
                  
                    
                      
                        
                          jerk
                          *
                        
                        ·
                        
                          J
                          p
                        
                        ·
                        τ
                      
                      R
                    
                    ⁢
                    
                      d
                      t
                    
                  
                
              
            
          
          
            
              
                for
                ⁢
                
                  
                
                ⁢
                
                  t
                  0
                
              
              ≤
              t
              ≤
              
                t
                2
              
            
          
        
        
          
            
              
                
                  C
                  F
                
                ⁡
                
                  (
                  t
                  )
                
              
              =
              
                
                  C
                  F
                
                ⁡
                
                  (
                  
                    t
                    2
                  
                  )
                
              
            
          
          
            
              
                for
                ⁢
                
                  
                
                ⁢
                t
              
              >
              
                
                  t
                  2
                
                .
              
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




Starting from the value of jerk desired during the driving-away manoeuvre, in order to complete the manoeuvre by reaching a desired angular velocity of the drive shaft on driving away (which can also be deduced from the information on the pressure on the accelerator pedal by the driver), it is necessary to specify the temporal variation of the torque supplied by the engine.
In the simplified model which has been adopted, the temporal variation of the engine torque is assumed to depend on the specified clutch torque (and therefore, indirectly, on the requested jerk) and on the requested angular velocity of the drive shaft on driving away, as represented in the upper graph of FIG. 4.
By integrating equation (2) between the instant t0 and the instant t2, we obtain the derivative of the reference torque command for the engine:




  
    
      
        
          
            
              
                
                  ∫
                  
                    t
                    0
                  
                  
                    t
                    2
                  
                
                ⁢
                
                  
                    
                      d
                      
                        ω
                        M
                      
                    
                    
                      d
                      t
                    
                  
                  ·
                  
                    J
                    M
                  
                  ·
                  
                    d
                    t
                  
                
              
              =
              
                
                  ∫
                  
                    t
                    0
                  
                  
                    t
                    2
                  
                
                ⁢
                
                  
                    (
                    
                      
                        
                          C
                          M
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                      -
                      
                        
                          C
                          F
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                    
                    )
                  
                  ·
                  
                    d
                    t
                  
                
              
            
          
          
            
              
                for
                ⁢
                
                  
                
                ⁢
                
                  t
                  0
                
              
              <
              t
              <
              
                t
                2
              
            
          
        
      
    
    
      
        (
        16
        )
      
    
  




Considering that

CM(t1)=CM(t2)  (17)

and resolving the integral, we obtain





  
    
      
        
          
            (
            
              
                
                  ω
                  M
                
                ⁡
                
                  (
                  
                    t
                    2
                  
                  )
                
              
              -
              
                
                  ω
                  M
                
                ⁡
                
                  (
                  
                    t
                    0
                  
                  )
                
              
            
            )
          
          ·
          
            J
            M
          
        
        =
        
          
            
              (
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      2
                    
                    )
                  
                
                -
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
              
              )
            
            ·
            
              
                T
                M
              
              2
            
          
          +
          
            
              
                C
                M
              
              ⁡
              
                (
                
                  t
                  0
                
                )
              
            
            ·
            
              T
              M
            
          
          +
          
            
              
                C
                M
              
              ⁡
              
                (
                
                  t
                  2
                
                )
              
            
            ·
            
              (
              
                
                  T
                  F
                
                -
                
                  T
                  M
                
              
              )
            
          
          -
          
            
              (
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      2
                    
                    )
                  
                
                -
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
              
              )
            
            ·
            
              
                T
                F
              
              2
            
          
          -
          
            
              
                C
                F
              
              ⁡
              
                (
                
                  t
                  0
                
                )
              
            
            ·
            
              T
              F
            
          
        
      
    
    
      
        (
        18
        )
      
    
  




We shall simplify the notation as follows:




  
    
      
        {
        
          
            
              
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      
                        t
                        0
                      
                      )
                    
                  
                  =
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                
              
            
            
              
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      
                        t
                        2
                      
                      )
                    
                  
                  =
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                
              
            
          
          ⁢
          
            {
            
              
                
                  
                    
                      
                        
                          ω
                          M
                        
                        ⁡
                        
                          (
                          
                            t
                            0
                          
                          )
                        
                      
                      =
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          ω
                          M
                        
                        ⁡
                        
                          (
                          
                            t
                            2
                          
                          )
                        
                      
                      =
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                    
                  
                
              
              ⁢
              
                {
                
                  
                    
                      
                        
                          
                            C
                            F
                          
                          ⁡
                          
                            (
                            
                              t
                              0
                            
                            )
                          
                        
                        =
                        
                          C
                          
                            F
                            ⁢
                            
                              
                            
                            ⁢
                            0
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                            C
                            F
                          
                          ⁡
                          
                            (
                            
                              t
                              2
                            
                            )
                          
                        
                        =
                        
                          C
                          
                            F
                            ⁢
                            
                              
                            
                            ⁢
                            2
                          
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        19
        )
      
    
  




so that the relation (18) becomes:





  
    
      
        
          
            (
            
              
                ω
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
              -
              
                
              
              ⁢
              
                ω
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
            
            )
          
          ·
          
            
          
          ⁢
          
            J
            M
          
        
        =
        
          
        
        ⁢
        
          
            
              -
              
                (
                
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  -
                  
                    
                  
                  ⁢
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                
                )
              
            
            ·
            
              
            
            ⁢
            
              
                T
                M
              
              2
            
          
          +
          
            
          
          ⁢
          
            
              (
              
                
                  2
                  ·
                  
                    
                  
                  ⁢
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                
                -
                
                  
                
                ⁢
                
                  C
                  
                    F
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                
                -
                
                  
                
                ⁢
                
                  C
                  
                    F
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            ·
            
              
            
            ⁢
            
              
                T
                F
              
              2
            
          
        
      
    
    
      
        (
        20
        )
      
    
  




Introducing the condition

CM(t2)=CF(t2)  (21)

into the model, equation (20) can be simplified as:





  
    
      
        
          
            (
            
              
                ω
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
              -
              
                ω
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
            
            )
          
          ·
          
            J
            M
          
        
        =
        
          
        
        ⁢
        
          
            
              -
              
                (
                
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  -
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                
                )
              
            
            ·
            
              
                T
                M
              
              2
            
          
          +
          
            
              (
              
                
                  C
                  
                    F
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                
                -
                
                  C
                  
                    F
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            ·
            
              
                T
                F
              
              2
            
          
        
      
    
    
      
        (
        22
        )
      
    
  




Specifying a linear change in the temporal variation of the engine torque, defined as




  
    
      
        
          
            d
            
              
                C
                M
              
              ⁡
              
                (
                t
                )
              
            
          
          
            d
            t
          
        
        =
        
          
            
              
                
                  C
                  M
                
                ⁡
                
                  (
                  
                    t
                    1
                  
                  )
                
              
              -
              
                
                  C
                  M
                
                ⁡
                
                  (
                  
                    t
                    0
                  
                  )
                
              
            
            
              T
              M
            
          
          =
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      2
                    
                    )
                  
                
                -
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
              
              
                T
                M
              
            
            =
            
              dC
              M
            
          
        
      
    
    
      
        (
        23
        )
      
    
  




we can obtain from relation (22) the complete relation which relates the derivative of the engine torque to the derivative of the clutch torque and to the angular velocity of the drive shaft.





  
    
      
        
          
            (
            
              
                ω
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
              -
              
                ω
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
            
            )
          
          ·
          
            J
            M
          
        
        =
        
          
            
              
                (
                
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  -
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                
                )
              
              2
            
            
              2
              ·
              
                dC
                M
              
            
          
          +
          
            
              
                (
                
                  
                    C
                    
                      F
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  -
                  
                    C
                    
                      F
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                
                )
              
              2
            
            
              2
              ·
              
                dC
                F
              
            
          
        
      
    
    
      
        (
        24
        )
      
    
  




By specifying the value of angular velocity of the drive shaft that it is desirable to reach while driving away, it is possible to calculate the derivative of the engine torque required to obtain this:




  
    
      
        
          dC
          M
        
        =
        
          
            
              (
              
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                
                -
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            2
          
          
            
              
                
                  (
                  
                    
                      C
                      
                        F
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                    
                    -
                    
                      C
                      
                        F
                        ⁢
                        
                          
                        
                        ⁢
                        0
                      
                    
                  
                  )
                
                2
              
              
                dC
                F
              
            
            -
            
              2
              ·
              
                (
                
                  
                    ω
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  -
                  
                    ω
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      0
                    
                  
                
                )
              
              ·
              
                J
                M
              
            
          
        
      
    
    
      
        (
        25
        )
      
    
  




For the particular case in which the initial and final values of the clutch and engine torque coincide with each other, we find:




  
    
      
        
          dC
          M
        
        =
        
          1
          
            (
            
              
                1
                
                  dC
                  F
                
              
              -
              
                
                  2
                  ·
                  
                    (
                    
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                      -
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                      
                    
                    )
                  
                  ·
                  
                    J
                    M
                  
                
                
                  
                    (
                    
                      
                        C
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          2
                        
                      
                      -
                      
                        C
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                      
                    
                    )
                  
                  2
                
              
            
            )
          
        
      
    
    
      
        (
        26
        )
      
    
  




In conclusion, the variation of the torque requested from the engine is therefore a function of the reference angular velocity of the drive shaft while driving away and of the variation of the torque transmitted by the clutch, and can be indicated as:




  
    
      
        
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      
                        t
                        0
                      
                      )
                    
                  
                  +
                  
                    
                      ∫
                      
                        t
                        0
                      
                      t
                    
                    ⁢
                    
                      
                        dC
                        M
                      
                      ⁢
                      
                        d
                        t
                      
                    
                  
                
              
            
            
              
                
                  for
                  ⁢
                  
                    
                  
                  ⁢
                  
                    t
                    0
                  
                
                ≤
                t
                ≤
                
                  t
                  1
                
              
            
          
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      1
                    
                    )
                  
                
              
            
            
              
                
                  for
                  ⁢
                  
                    
                  
                  ⁢
                  t
                
                >
                
                  t
                  1
                
              
            
          
        
        .
      
    
    
      
        (
        27
        )
      
    
  




When the clutch is engaged, the system changes its operating mode, moving from modulated operation with the clutch disengaged, governed by equation (3), to operation with the clutch engaged, governed by equation (1). In this instant, the inertias as seen from the engine change, and the adopted model must be capable of compensating for this variation of inertia.
It is assumed that the angular velocities of the drive shaft and of the primary shaft of the gearbox are synchronized at the instant t3 (hypothetical curve of the reference angular velocity of the primary shaft ω′PRif shown in broken lines). If the values of the engine and clutch torques are known prior to the instant t3, the rotation speeds of the drive shaft and the primary gear shaft can be synchronized according to the relation

ωP(t3)=ωM(t3)  (28)

The variation of inertia as seen from the engine generates a variation of acceleration which can be calculated considering the acceleration at the instant t3− which precedes the synchronization and at the following instant t3+.
At the instant t=t3−, the clutch is disengaged, and therefore relation (3) is still true; from this we can find the acceleration according to relation (9):




  
    
      
        
          
            a
            x
          
          ⁡
          
            (
            
              t
              
                3
                -
              
            
            )
          
        
        =
        
          
            
              
                
                  d
                  
                    ω
                    P
                  
                
                
                  d
                  t
                
              
              ·
              
                R
                τ
              
            
            ⁢
            
              |
              
                
                  r
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
                -
              
            
          
          =
          
            
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      
                        3
                        -
                      
                    
                    )
                  
                
                -
                
                  
                    C
                    R
                  
                  ⁡
                  
                    (
                    
                      t
                      
                        3
                        -
                      
                    
                    )
                  
                
              
              
                J
                P
              
            
            ·
            
              
                R
                τ
              
              .
            
          
        
      
    
    
      
        (
        29
        )
      
    
  




At the instant t=t3+, the clutch is engaged, and therefore relation (1) is true and consequently the acceleration is as follows:




  
    
      
        
          
            a
            x
          
          ⁡
          
            (
            
              t
              
                3
                +
              
            
            )
          
        
        =
        
          
            
              
                
                  d
                  
                    ω
                    M
                  
                
                
                  d
                  t
                
              
              ·
              
                R
                τ
              
            
            ⁢
            
              |
              
                
                  r
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
                +
              
            
          
          =
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      
                        3
                        +
                      
                    
                    )
                  
                
                -
                
                  
                    C
                    R
                  
                  ⁡
                  
                    (
                    
                      t
                      
                        3
                        -
                      
                    
                    )
                  
                
              
              
                
                  J
                  M
                
                +
                
                  J
                  P
                
              
            
            ·
            
              
                R
                τ
              
              .
            
          
        
      
    
    
      
        (
        30
        )
      
    
  




The variation of acceleration between the instant t3− and the instant t3+ can therefore be calculated as

Δax=ax(t3+)−ax(t3−)  (31)

and given that





  
    
      
        {
        
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      
                        3
                        -
                      
                    
                    )
                  
                
                =
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      
                        t
                        
                          3
                          +
                        
                      
                      )
                    
                  
                  =
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                
              
            
          
          
            
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      
                        3
                        -
                      
                    
                    )
                  
                
                =
                
                  
                    
                      C
                      F
                    
                    ⁡
                    
                      (
                      
                        t
                        
                          3
                          +
                        
                      
                      )
                    
                  
                  =
                  
                    C
                    
                      F
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                
              
            
          
          
            
              
                
                  
                    C
                    R
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    C
                    R
                  
                  =
                  c
                
              
            
          
        
      
    
    
      
        (
        32
        )
      
    
  




we find that





  
    
      
        
          Δ
          ⁢
          
            
          
          ⁢
          
            a
            x
          
        
        =
        
          
            [
            
              
                
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                  -
                  
                    C
                    R
                  
                
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
              
              -
              
                
                  
                    C
                    
                      F
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                  -
                  
                    C
                    R
                  
                
                
                  J
                  P
                
              
            
            ]
          
          ·
          
            R
            τ
          
        
      
    
    
      
        (
        33
        )
      
    
  
  
    
      
        
          Δ
          ⁢
          
            
          
          ⁢
          
            a
            x
          
        
        =
        
          
            [
            
              
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    3
                  
                
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
              
              -
              
                
                  C
                  
                    F
                    ⁢
                    
                      
                    
                    ⁢
                    3
                  
                
                
                  J
                  P
                
              
              +
              
                
                  C
                  R
                
                ·
                
                  (
                  
                    
                      1
                      
                        J
                        P
                      
                    
                    -
                    
                      1
                      
                        
                          J
                          M
                        
                        +
                        
                          J
                          P
                        
                      
                    
                  
                  )
                
              
            
            ]
          
          ·
          
            R
            τ
          
        
      
    
    
      
        (
        34
        )
      
    
  




Since CM3=CF3 at the instant of synchronization, and assuming for simplicity that the resistant torque is zero (CR=0), a negative variation of acceleration would be found:




  
    
      
        
          Δ
          ⁢
          
            
          
          ⁢
          
            a
            x
          
        
        =
        
          
            [
            
              
                1
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
              
              -
              
                1
                
                  J
                  P
                
              
            
            ]
          
          ·
          
            R
            τ
          
          ·
          
            C
            
              M
              ⁢
              
                
              
              ⁢
              3
            
          
        
      
    
    
      
        (
        35
        )
      
    
  
  
    
      
        
          Δ
          ⁢
          
            
          
          ⁢
          
            a
            x
          
        
        =
        
          
            -
            
              
                J
                M
              
              
                
                  (
                  
                    
                      J
                      M
                    
                    +
                    
                      J
                      P
                    
                  
                  )
                
                ·
                
                  J
                  P
                
              
            
          
          ·
          
            R
            τ
          
          ·
          
            
              C
              
                M
                ⁢
                
                  
                
                ⁢
                3
              
            
            .
          
        
      
    
    
      
        (
        36
        )
      
    
  




In order to enable the driving-away control system to compensate for the equivalent variation of inertia and the correlated discontinuities in the acceleration of the vehicle due to the engagement of the friction clutch, the reference torques as shown in the graph of FIG. 4 are considered, and both the synchronization between the angular velocities of the drive shaft and of the primary gear shaft and the cancellation of the derivative difference between ωM e ωP are imposed at the instant t4.
In mathematical terms, the aforesaid condition is expressed by the following equation:




  
    
      
        
          
            
              d
              
                ω
                M
              
            
            
              d
              t
            
          
          ⁢
          
            |
            
              /
              4
            
          
        
        =
        
          
            
              d
              
                ω
                P
              
            
            
              d
              t
            
          
          ⁢
          
            |
            
              /
              4
            
          
        
      
    
    
      
        (
        37
        )
      
    
  




According to equations (1) and (3), reproduced here for ease of reference:




  
    
      
        {
        
          
            
              
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  -
                  
                    
                      C
                      R
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                =
                
                  
                    (
                    
                      
                        J
                        M
                      
                      +
                      
                        J
                        P
                      
                    
                    )
                  
                  ·
                  
                    
                      d
                      
                        ω
                        M
                      
                    
                    
                      d
                      t
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      C
                      F
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  -
                  
                    C
                    R
                  
                
                =
                
                  
                    J
                    P
                  
                  ·
                  
                    
                      d
                      
                        ω
                        P
                      
                    
                    
                      d
                      t
                    
                  
                
              
            
          
        
      
    
    
      
        (
        38
        )
      
    
  




and with the introduction of the condition (37), we obtain:





  
    
      
        {
        
          
            
              
                
                  
                    
                      
                        C
                        M
                      
                      ⁡
                      
                        (
                        
                          t
                          4
                        
                        )
                      
                    
                    -
                    
                      
                        C
                        R
                      
                      ⁡
                      
                        (
                        
                          t
                          4
                        
                        )
                      
                    
                  
                  
                    
                      J
                      M
                    
                    +
                    
                      J
                      P
                    
                  
                
                =
                
                  
                    
                      d
                      
                        ω
                        M
                      
                    
                    
                      d
                      t
                    
                  
                  ⁢
                  
                    |
                    
                      t
                      4
                    
                  
                
              
            
          
          
            
              
                
                  
                    
                      
                        C
                        F
                      
                      ⁡
                      
                        (
                        
                          t
                          4
                        
                        )
                      
                    
                    -
                    
                      
                        C
                        R
                      
                      ⁡
                      
                        (
                        
                          t
                          4
                        
                        )
                      
                    
                  
                  
                    J
                    P
                  
                
                =
                
                  
                    
                      d
                      
                        ω
                        P
                      
                    
                    
                      d
                      t
                    
                  
                  ⁢
                  
                    |
                    
                      t
                      ⁢
                      
                        
                      
                      ⁢
                      4
                    
                  
                
              
            
          
        
      
    
    
      
        (
        39
        )
      
    
  




Assuming that the resistant torque is zero (the hypothesis that CR(t)=0, accepted for the sake of simplicity), and since the clutch torque is constant (in other words, with a zero derivative) as represented in the upper graph of FIG. 4, the following conditions are obtained:




  
    
      
        {
        
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      4
                    
                    )
                  
                
                =
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    4
                  
                
              
            
          
          
            
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      3
                    
                    )
                  
                
                =
                
                  
                    
                      C
                      F
                    
                    ⁡
                    
                      (
                      
                        t
                        4
                      
                      )
                    
                  
                  =
                  
                    
                      C
                      
                        F
                        ⁢
                        
                          
                        
                        ⁢
                        3
                      
                    
                    =
                    
                      C
                      
                        F
                        ⁢
                        
                          
                        
                        ⁢
                        4
                      
                    
                  
                
              
            
          
          
            
              
                
                  
                    C
                    R
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                0
              
            
          
        
      
    
    
      
        (
        40
        )
      
    
  




By introducing the relation (37) and substituting the conditions (40) in the relation (39), we find the constraint which provides a zero variation of acceleration:




  
    
      
        
          
            C
            
              M
              ⁢
              
                
              
              ⁢
              4
            
          
          
            
              J
              M
            
            +
            
              J
              P
            
          
        
        =
        
          
            C
            
              F
              ⁢
              
                
              
              ⁢
              3
            
          
          
            J
            P
          
        
      
    
    
      
        (
        41
        )
      
    
  




or alternatively





  
    
      
        
          C
          
            M
            ⁢
            
              
            
            ⁢
            4
          
        
        =
        
          
            C
            
              F
              ⁢
              
                
              
              ⁢
              3
            
          
          ⁢
          
            
              
                J
                M
              
              +
              
                J
                P
              
            
            
              J
              P
            
          
        
      
    
    
      
        (
        
          41
          ⁢
          bis
        
        )
      
    
  




By contrast with the assumptions made in relation (28), it is advantageous to specify the synchronization of the angular velocities of the drive shaft and of the primary gear shaft at the instant t4, i.e.:

ωP(t4)=ωM(t4)  (42)

To check that the synchronization condition has been attained at the instant t4, equations (2) and (3) are integrated between the instants t3 and t4:




  
    
      
        {
        
          
            
              
                
                  
                    ∫
                    
                      t
                      3
                    
                    
                      t
                      4
                    
                  
                  ⁢
                  
                    
                      
                        d
                        
                          ω
                          M
                        
                      
                      
                        d
                        t
                      
                    
                    ·
                    
                      J
                      M
                    
                    ·
                    
                      d
                      t
                    
                  
                
                =
                
                  
                    ∫
                    
                      t
                      3
                    
                    
                      t
                      4
                    
                  
                  ⁢
                  
                    
                      (
                      
                        
                          
                            C
                            M
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                        -
                        
                          
                            C
                            F
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                      
                      )
                    
                    ·
                    
                      d
                      t
                    
                  
                
              
            
          
          
            
              
                
                  
                    ∫
                    
                      t
                      3
                    
                    
                      t
                      4
                    
                  
                  ⁢
                  
                    
                      
                        d
                        
                          ω
                          P
                        
                      
                      
                        d
                        t
                      
                    
                    ·
                    
                      J
                      P
                    
                    ·
                    
                      d
                      t
                    
                  
                
                =
                
                  
                    ∫
                    
                      t
                      3
                    
                    
                      t
                      4
                    
                  
                  ⁢
                  
                    
                      (
                      
                        
                          
                            C
                            F
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                        -
                        
                          C
                          R
                        
                      
                      )
                    
                    ·
                    
                      d
                      t
                    
                  
                
              
            
          
        
      
    
    
      
        (
        43
        )
      
    
  




Resolving the integral and assuming, as in conditions (40), that CF3=CF4, we obtain




  
    
      
        {
        
          
            
              
                
                  
                    (
                    
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          4
                        
                      
                      -
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          3
                        
                      
                    
                    )
                  
                  ·
                  
                    J
                    M
                  
                
                =
                
                  
                    
                      
                        
                          C
                          
                            M
                            ⁢
                            
                              
                            
                            ⁢
                            4
                          
                        
                        -
                        
                          C
                          
                            M
                            ⁢
                            
                              
                            
                            ⁢
                            3
                          
                        
                      
                      2
                    
                    ·
                    
                      T
                      CI
                    
                  
                  +
                  
                    
                      C
                      
                        M
                        ⁢
                        
                          
                        
                        ⁢
                        3
                      
                    
                    ·
                    
                      T
                      CI
                    
                  
                  -
                  
                    
                      C
                      
                        F
                        ⁢
                        
                          
                        
                        ⁢
                        3
                      
                    
                    ·
                    
                      T
                      CI
                    
                  
                
              
            
          
          
            
              
                
                  
                    (
                    
                      
                        ω
                        
                          P
                          ⁢
                          
                            
                          
                          ⁢
                          4
                        
                      
                      -
                      
                        ω
                        
                          P
                          ⁢
                          
                            
                          
                          ⁢
                          3
                        
                      
                    
                    )
                  
                  ·
                  
                    J
                    P
                  
                
                =
                
                  
                    
                      C
                      F3
                    
                    ·
                    
                      T
                      CI
                    
                  
                  -
                  
                    
                      C
                      R
                    
                    ·
                    
                      T
                      CI
                    
                  
                
              
            
          
        
         
      
    
    
      
        (
        44
        )
      
    
  




Assuming, for simplicity, that the resistant torque is zero, we find:




  
    
      
        {
        
          
            
              
                
                  
                    ω
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      4
                    
                  
                  -
                  
                    ω
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                
                =
                
                  
                    
                      
                        
                          C
                          
                            M
                            ⁢
                            
                              
                            
                            ⁢
                            4
                          
                        
                        +
                        
                          C
                          
                            M
                            ⁢
                            
                              
                            
                            ⁢
                            3
                          
                        
                      
                      
                        J
                        M
                      
                    
                    ·
                    
                      
                        T
                        CI
                      
                      2
                    
                  
                  -
                  
                    
                      
                        C
                        
                          F
                          ⁢
                          
                            
                          
                          ⁢
                          3
                        
                      
                      
                        J
                        M
                      
                    
                    ·
                    
                      T
                      CI
                    
                  
                
              
            
          
          
            
              
                
                  
                    ω
                    
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      4
                    
                  
                  -
                  
                    ω
                    
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                
                =
                
                  
                    
                      C
                      
                        F
                        ⁢
                        
                          
                        
                        ⁢
                        3
                      
                    
                    
                      J
                      P
                    
                  
                  ·
                  
                    T
                    CI
                  
                
              
            
          
        
      
    
    
      
        (
        45
        )
      
    
  




and by imposing the synchronization defined by relation (42) we obtain:





  
    
      
        
          
            ω
            
              M
              ⁢
              
                
              
              ⁢
              3
            
          
          -
          
            ω
            
              P
              ⁢
              
                
              
              ⁢
              3
            
          
        
        =
        
          
            
              -
              
                
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      4
                    
                  
                  +
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      3
                    
                  
                
                2
              
            
            ·
            
              
                T
                CI
              
              2
            
          
          +
          
            
              C
              
                F
                ⁢
                
                  
                
                ⁢
                3
              
            
            ·
            
              (
              
                
                  1
                  
                    J
                    M
                  
                
                +
                
                  1
                  
                    J
                    P
                  
                
              
              )
            
            ·
            
              T
              CI
            
          
        
      
    
    
      
        (
        46
        )
      
    
  




By specifying the constraint of zero variation of the acceleration (relation (41)) and specifying that ωM3−ωP3=Δω, we obtain:




  
    
      
        
          Δω
          =
          
            
              
                -
                
                  
                    
                      C
                      
                        M
                        ⁢
                        
                          
                        
                        ⁢
                        4
                      
                    
                    +
                    
                      C
                      
                        M
                        ⁢
                        
                          
                        
                        ⁢
                        3
                      
                    
                  
                  
                    J
                    M
                  
                
              
              ·
              
                
                  T
                  CI
                
                2
              
            
            +
            
              
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    4
                  
                
                
                  J
                  M
                
              
              ⁢
              
                T
                CI
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          and
          ⁢
          
            
          
          ⁢
          therefore
        
      
    
    
      
        (
        47
        )
      
    
  
  
    
      
        Δω
        =
        
          
            
              
                C
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
              
              -
              
                C
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
              
            
            
              2
              ·
              
                J
                M
              
            
          
          ·
          
            T
            CI
          
        
      
    
    
      
        (
        48
        )
      
    
  




Given the constraint at the instant t3 

CM3=CF3  (49)

and the constraint of zero variation of acceleration specified by relation (41), relation (48) can be written as





  
    
      
        
          Δω
          =
          
            
              
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    4
                  
                
                -
                
                  
                    
                      J
                      P
                    
                    
                      
                        J
                        M
                      
                      +
                      
                        J
                        P
                      
                    
                  
                  ·
                  
                    C
                    
                      M
                      ⁢
                      
                        
                      
                      ⁢
                      4
                    
                  
                
              
              
                2
                ·
                
                  J
                  M
                
              
            
            ·
            
              T
              CI
            
          
        
        ⁢
        
          

        
        ⁢
        
          and
          ⁢
          
            
          
          ⁢
          therefore
        
      
    
    
      
        (
        50
        )
      
    
  
  
    
      
        Δω
        =
        
          
            
              C
              
                M
                ⁢
                
                  
                
                ⁢
                4
              
            
            
              2
              ·
              
                (
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
                )
              
            
          
          ·
          
            T
            CI
          
        
      
    
    
      
        (
        51
        )
      
    
  




The time TCI required for synchronization with inertia compensation from a predetermined value of Δω can therefore be calculated:




  
    
      
        
          T
          CI
        
        =
        
          
            2
            ·
            
              (
              
                
                  J
                  M
                
                +
                
                  J
                  P
                
              
              )
            
            ·
            Δω
          
          
            C
            
              M
              ⁢
              
                
              
              ⁢
              4
            
          
        
      
    
    
      
        (
        52
        )
      
    
  




The model therefore requires that, in order to obtain inertia compensation, the engine should be operated at the instant t3 with a constant torque derivative for a period equal to the inertia compensation time TCI.
Given that




  
    
      
        
          
            d
            
              
                C
                M
              
              ⁡
              
                (
                t
                )
              
            
          
          
            d
            t
          
        
        =
        
          
            
              
                
                  C
                  M
                
                ⁡
                
                  (
                  
                    t
                    4
                  
                  )
                
              
              -
              
                
                  C
                  M
                
                ⁡
                
                  (
                  
                    t
                    3
                  
                  )
                
              
            
            
              T
              CI
            
          
          =
          
            
              
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    4
                  
                
                -
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    3
                  
                
              
              
                T
                CI
              
            
            =
            
              dC
              MCI
            
          
        
      
    
    
      
        (
        53
        )
      
    
  




and substituting the value of TCI calculated in (52), we obtain:





  
    
      
        
          dC
          MCI
        
        =
        
          
            
              
                C
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  4
                
              
              -
              
                C
                
                  M
                  ⁢
                  
                    
                  
                  ⁢
                  3
                
              
            
            
              2
              ·
              
                (
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
                )
              
              ·
              Δω
            
          
          ·
          
            C
            
              M
              ⁢
              
                
              
              ⁢
              4
            
          
        
      
    
    
      
        (
        54
        )
      
    
  




To summarize, the driving-away control system with inertia compensation proposed by the invention, derived from the model described above, generates engine and clutch reference torques as indicated in FIG. 4 and as represented by the following equations:




  
    
      
        
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      
                        t
                        0
                      
                      )
                    
                  
                  +
                  
                    
                      ∫
                      
                        t
                        0
                      
                      t
                    
                    ⁢
                    
                      
                        dC
                        M
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        t
                      
                    
                  
                
              
            
            
              
                
                  for
                  ⁢
                  
                    
                  
                  ⁢
                  
                    t
                    0
                  
                
                ≤
                t
                ≤
                
                  t
                  1
                
              
            
          
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    
                      t
                      1
                    
                    )
                  
                
              
            
            
              
                
                  for
                  ⁢
                  
                    
                  
                  ⁢
                  
                    t
                    1
                  
                
                <
                t
                ≤
                
                  t
                  3
                
              
            
          
          
            
              
                
                  
                    C
                    M
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    
                      C
                      M
                    
                    ⁡
                    
                      (
                      
                        t
                        3
                      
                      )
                    
                  
                  +
                  
                    
                      ∫
                      
                        t
                        3
                      
                      t
                    
                    ⁢
                    
                      
                        dC
                        MCI
                      
                      ⁢
                      
                        
                      
                      ⁢
                      
                        d
                        t
                      
                    
                  
                
              
            
            
              
                
                  for
                  ⁢
                  
                    
                  
                  ⁢
                  
                    t
                    3
                  
                
                <
                t
                ≤
                
                  t
                  4
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        and
      
    
    
      
        (
        55
        )
      
    
  
  
    
      
        
          
            
              
                
                  C
                  F
                
                ⁡
                
                  (
                  t
                  )
                
              
              =
              
                
                  
                    C
                    F
                  
                  ⁡
                  
                    (
                    
                      t
                      0
                    
                    )
                  
                
                +
                
                  
                    ∫
                    
                      t
                      0
                    
                    t
                  
                  ⁢
                  
                    
                      dC
                      F
                    
                    ⁢
                    
                      d
                      t
                    
                  
                
              
            
          
          
            
              
                for
                ⁢
                
                  
                
                ⁢
                
                  t
                  0
                
              
              ≤
              t
              ≤
              
                t
                2
              
            
          
        
        
          
            
              
                
                  C
                  F
                
                ⁡
                
                  (
                  t
                  )
                
              
              =
              
                
                  C
                  F
                
                ⁡
                
                  (
                  
                    t
                    2
                  
                  )
                
              
            
          
          
            
              
                for
                ⁢
                
                  
                
                ⁢
                
                  t
                  2
                
              
              <
              t
              ≤
              
                t
                3
              
            
          
        
      
    
    
      
        (
        56
        )
      
    
  




The operation of the control system 20 is described below on the basis of the model described above and with reference to the diagram of FIG. 2.
The system 20 acquires signals indicating the driving-away command imparted by the driver through the accelerator pedal, and in particular a first signal indicating the reference value, jerk*, of the derivative of the longitudinal acceleration

jerk*=fjerk(Pacc)  (57)

a second signal indicating the angular velocity of the drive shaft (number of revolutions of the engine)ωMsp 

ωMsp=fωMsp(Pacc)+ωMsp min  (58)

and a third signal indicating the value of the driving-away torque CDriver 

CDriver=fcdriver(Pacc)  (59)

The driving-away torque CDriver is determined by comparison with predetermined relation maps stored in the memory device ME by the engine control unit ECUE.
The parameters jerk* and ωMsp can also be determined in the engine control unit ECUE, on the basis of relation models stored in the memory ME, or, in the currently preferred embodiment, can be determined directly in the gearbox control unit ECUG by a sub-module 22a connected upstream of a calculation sub-module 22b on the basis of predetermined relation models mapped in the memory MG.
With reference to FIG. 4, the value of the steady torque requested by the driver, CDriver, is interpreted as the reference steady torque for the engine and the clutch at the end of the driving-away manoeuvre. In order to apply the temporal variation model shown in the figure to the control of the inertia variation compensation, the driving-away control system specifies an intermediate steady torque for the engine and for the clutch, defined as follows:

CMSteady=KMSteady·CDriver  (60)

in which





  
    
      
        
          K
          MSteady
        
        =
        
          
            J
            P
          
          
            
              J
              M
            
            +
            
              J
              P
            
          
        
      
    
    
      
        (
        61
        )
      
    
  




according to relation (41) above.

The following definitions are also made:

CFSteady=CMsteady for CDriver>0  (62)

CFSteady=0 for CDriver≦0  (63)

According to relation (14) of the model, the system specifies the derivative of the torque CF to be transmitted by the clutch as a function of the determined value of jerk*:




  
    
      
        
          
            dC
            F
          
          ⁢
          
            
              K
              Jerk
            
            ·
            
              
                jerk
                *
              
              ⁡
              
                [
                
                  Nm
                  /
                  sec
                
                ]
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          in
          ⁢
          
            
          
          ⁢
          which
        
      
    
    
      
        (
        64
        )
      
    
  
  
    
      
        
          K
          Jerk
        
        =
        
          
            
              J
              P
            
            ·
            τ
          
          R
        
      
    
    
      
        (
        65
        )
      
    
  




The signal indicating the temporal variation of the reference torque CFRif transmittable by the clutch, output from the generator module 22, will be defined as

CFRif(t)=CF0+dCF·t for t0≦t≦t2 

CFRif(t)=CFSteady for t2<t≦t4  (66)

where CF0 is the initial value of the torque, i.e.

CF0=CF(t0)  (67)

The module 22 also generates a signal indicating the variation in time of the requested engine torque, by calculating the value of the derivative of the reference engine torque as a function of the derivative of the clutch torque, and of the signal indicating the angular velocity of the drive shaft during driving away according to relation (25) of the model described above:




  
    
      
        
          dC
          M
        
        =
        
          1
          
            (
            
              
                1
                
                  dC
                  F
                
              
              -
              
                
                  2
                  ·
                  
                    (
                    
                      
                        ω
                        Msp
                      
                      -
                      
                        ω
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                      
                    
                    )
                  
                  ·
                  
                    J
                    M
                  
                
                
                  
                    (
                    
                      
                        C
                        MSteady
                      
                      -
                      
                        C
                        
                          M
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                      
                    
                    )
                  
                  2
                
              
            
            )
          
        
      
    
    
      
        (
        68
        )
      
    
  




in which CM0 is the initial value of the engine torque, i.e.

CM0=CM(t0)  (69)

and ωM0 is the initial value of the rotation speed of the engine, i.e.

ωM0=ωM(t0)  (70)

The derivative of the engine torque is always greater than the derivative of the clutch torque, i.e.

dCM>dCF(71)

Clearly, the value of dCM must be limited to the maximum value that can be handled by the engine.
In particular, two different conditions are identified, one for the traction condition (accelerator pedal pressed down) and one for the condition of release of the accelerator pedal, indicated by the following relations:

dCM=min(dCM max—trz,dCM) for CDriver≧0  (72)

dCM=dCM max—ril for CDriver<0  (73)

In the temporal variation of the engine and clutch torques, at the end of the principal ramps at the instant t2 it is necessary to wait for the instant t3, in other words to wait for the attainment of the condition in which the difference between ωM and ωP is less than the predetermined threshold ΔωCI.
Thus the inertia compensation is controlled by calculating the derivative of the engine torque:




  
    
      
        
          dC
          MCI
        
        =
        
          
            
              
                C
                Driver
              
              -
              
                C
                MSteady
              
            
            
              2
              ·
              
                (
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
                )
              
              ·
              
                Δω
                CI
              
            
          
          ·
          
            C
            Driver
          
        
      
    
    
      
        (
        74
        )
      
    
  




according to relation (54) of the described model, and obtaining a signal indicating the variation of the reference engine torque, thus:

CMRif(t)=CM0+dCM·t for t0≦t≦t1 

CMRif(t)=CMSteady for t1<t≦t3  (75)

CMRif(t)=CMSteady+dCMCI·t for t3<t≦t4 

The estimator module 24 assumes two different operating conditions, namely a first operating condition with the clutch disengaged in modulation and a second operating condition with the clutch engaged, in other words with the angular velocities of the drive shaft and of the primary gear shaft synchronized.
In the first operating condition, it determines the signals




  
    
      
        
          
            ω
            MRif
          
          =
          
            ∫
            
              
                
                  
                    
                      C
                      MRif
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  -
                  
                    
                      C
                      FRif
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  J
                  M
                
              
              ⁢
              
                d
                t
              
            
          
        
        ⁢
        
          

        
        ⁢
        and
      
    
    
      
        (
        76
        )
      
    
  
  
    
      
        
          ω
          PRif
        
        =
        
          ∫
          
            
              
                
                  C
                  FRif
                
                ⁡
                
                  (
                  t
                  )
                
              
              
                J
                P
              
            
            ⁢
            
              d
              t
            
          
        
      
    
    
      
        (
        77
        )
      
    
  




In the second operating condition, it determines the signals




  
    
      
        
          
            ω
            MRif
          
          =
          
            ∫
            
              
                
                  
                    C
                    MRif
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                
                  
                    J
                    M
                  
                  +
                  
                    J
                    P
                  
                
              
              ⁢
              
                d
                t
              
            
          
        
        ⁢
        
          

        
        ⁢
        and
      
    
    
      
        (
        78
        )
      
    
  
  
    
      
        
          ω
          PRif
        
        =
        
          
            ω
            MRif
          
          =
          
            ∫
            
              
                
                  
                    C
                    MRif
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                
                  
                    
                      J
                      M
                    
                    +
                    
                      J
                      P
                    
                  
                  ⁢
                  
                    
                  
                
              
              ⁢
              
                d
                t
              
            
          
        
      
    
    
      
        (
        79
        )
      
    
  




The calculated signals ωMRif and ωPRif are then supplied by feedback to the generator module 22 to permit the recognition of the condition of synchronization between ωMRif and ωPRif which identifies the change from the operating condition with modulation of the clutch to the engaged clutch condition.
The signals CMRif and CFRif are corrected in real time, by summing the respective corrective contributions ΔCM and ΔCF calculated by the controller module 26, by comparison with the actual angular velocities of the drive shaft and of the primary gear shaft measured by the on-board sensors.
Clearly, provided that the principle of the invention is retained, the forms of application and the details of construction can be varied widely from what has been described and illustrated purely by way of example and without restrictive intent, without departure from the scope of protection of the present invention as defined by the attached claims.

## Claims

1. Control system for controlling a driving-away manoeuvre in a motor vehicle provided with a gearbox comprising a primary input shaft adapted to be coupled to a drive shaft of a propulsion system of the vehicle by means of a servo-assisted friction clutch,
comprising:
an electronic processing assembly adapted to receive at their inputs signals or data indicating a command imparted by the driver of the motor vehicle by the operation of the accelerator pedal, and arranged for generating command signals or data designed to control torque actuator devices of the propulsion system and of the friction clutch, for the control of the driving-away manoeuvre in the motor vehicle; and
memory devices, associated with the said processing assembly and storing data and/or instructions representing a mathematical reference model for the calculation of the aforesaid command signals,
the processing assembly including:
a reference torque generator module arranged for generating, on the basis of the signals or data indicating the command imparted by the driver by the operation of the accelerator pedal and of the reference model, reference torque request signals or data indicating a reference torque requested from the drive shaft and a reference torque requested from the friction clutch in the course of the driving-away manoeuvre;
an estimator module, arranged for calculating, on the basis of the reference torque request signals or data and on the basis of the reference model, signals or data indicating the angular velocities of the drive shaft and of the gearbox primary input shaft in the course of the driving-away manoeuvre; and
a controller module, arranged for calculating, on the basis of the signals or data indicating the angular velocities of the drive shaft and of the primary input shaft calculated by the estimator module, and on the basis of detected signals or data indicating the actual angular velocities of the drive shaft and of the primary input shaft, corrective contributions to the said reference torque request signals or data,
whereby the said torque request signals or data, as modified by the corresponding corrective contributions, form the command signals or data for the torque actuator devices.

2. System according to claim 1, in which the said signals or data indicating the command imparted by the driver by the operation of the accelerator pedal include a signal or datum indicating the position of the accelerator pedal.

3. System according to claim 2, in which the said signals or data indicating the command imparted by the driver by the operation of the accelerator pedal include a signal or datum indicating the requested variation of longitudinal acceleration of the vehicle, determined as a function of the signal or datum indicating the position of the accelerator pedal on the basis of a predetermined first relation model.

4. System according to claim 3, in which the said signals or data indicating the command imparted by the driver by the operation of the accelerator pedal include a signal or datum indicating the requested driving-away torque, determined as a function of the signal or datum indicating the position of the accelerator pedal on the basis of a predetermined second relation model.

5. System according to claim 4, in which the said signals or data indicating the command imparted by the driver by the operation of the accelerator pedal include a signal or datum indicating the angular velocity of the drive shaft requested during driving away, determined as a function of the signal or datum indicating the position of the accelerator pedal on the basis of a predetermined third relation model.

6. System according to claim 5, in which the said first relation model associates the signal or datum indicating the position of the accelerator pedal with a signal or datum indicating the variation of longitudinal acceleration of the vehicle which is constant over time at least during a first stage of the driving-away manoeuvre, and the said reference torque request signal indicating the reference torque requested from the friction clutch has a linear temporal variation in the form of a ramp in a first stage of the driving-away manoeuvre, the gradient of which is proportional to the value of the said signal or datum indicating the variation of the longitudinal acceleration.

7. System according to claim 6, in which the said reference torque request signal indicating the reference torque requested from the drive shaft has a linear temporal variation in the form of a ramp in a first stage of the driving-away manoeuvre, the gradient of which is a function of the angular velocity of the drive shaft requested on driving away and of the gradient of the temporal variation ramp of the signal indicating the reference torque requested from the friction clutch, and is greater than the gradient of the temporal variation ramp of the signal indicating the reference torque requested from the friction clutch.

8. System according to claim 7, in which the said reference torque request signals indicating the reference torque requested from the drive shaft and the reference torque requested from the friction clutch have a constant value over time in an intermediate stage of the driving-away manoeuvre, and the said reference torque request signal driving-away manoeuvre indicating the reference torque requested from the driver shaft has a linear temporal variation in the form of a slope in a final stage of the driving-away manoeuvre, from the instant at which the difference between the angular velocities of the drive shaft and of the gearbox primary input shaft calculated by the estimator module is less than a predetermined threshold value.

9. System according to claim 8, in which the reference torque request signal indicating the reference torque requested from the friction clutch has the following temporal variation:


CFRif(t)=CF0+dCf·t for t0≦t≦t2 



CFrif(t)=CFsteady for t2<t≦t4 


where
CF0 is the initial value of the torque, at time t0 


CF0=CF(t0);


dCF is the gradient of the temporal variation ramp, calculated as




  
    
      dC
      F
    
    =
    
      
        K
        Jerk
      
      ·
      
        
          jerk
          *
        
        ⁡
        
          [
          
            Nm
            /
            sec
          
          ]
        
      
    
  




  
    in
    ⁢
    
      
    
    ⁢
    which
  




  
    
      K
      Jerk
    
    =
    
      
        
          J
          P
        
        ·
        τ
      
      R
    
  


where JP is the total moment of inertia transferred to the primary shaft, τ is the selected transmission ratio and R is the rolling radius of the wheels; and
CFSteady is a value of intermediate steady torque, defined as




  
    
      C
      FSteady
    
    =
    
      
        K
        MSteady
      
      ·
      
        C
        Driver
      
    
  




  
    in
    ⁢
    
      
    
    ⁢
    which
  




  
    
      K
      MSteady
    
    =
    
      
        J
        P
      
      
        
          J
          M
        
        +
        
          J
          P
        
      
    
  


where JM is the total moment of inertia of the engine and CDriver is the reference steady torque for the clutch at the end of the driving-away manoeuvre;
and
the reference torque request signal indicating the reference torque requested from the drive shaft has the following temporal variation:


CMRif(t)=CM0+dCM·t for t0≦t≦t1 



CMRif(t)=CMsteady for t1<t≦t3 



CMrif(t)=CMsteady+dCMC1·t for t3<t≦t4 



where:
CM0 is the initial value of the torque, at time t0 


CM0=CM(t0);


dCM is the gradient of the temporal variation ramp, calculated as





  
    dC
    M
  
  =
  
    1
    
      (
      
        
          1
          
            dC
            F
          
        
        -
        
          
            2
            ·
            
              (
              
                
                  ω
                  Msp
                
                -
                
                  ω
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            ·
            
              J
              M
            
          
          
            
              (
              
                
                  C
                  MSteady
                
                -
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            2
          
        
      
      )
    
  



in which ωM0 is the initial value of the rotation speed of the engine, at time t0 


ωM0=ωM(t0), and


CMSteady is a value of intermediate steady torque, defined as




  
    
      C
      MSteady
    
    =
    
      
        K
        MSteady
      
      ·
      
        C
        Driver
      
    
  




  where




  
    
      K
      MSteady
    
    =
    
      
        J
        P
      
      
        
          J
          M
        
        +
        
          J
          P
        
      
    
  


and CDriver is the reference steady torque for the engine at the end of the driving-away manoeuvre; and
dCMCI is the gradient of the temporal variation ramp in a terminal stage for inertia compensation, defined as:





  
    dC
    
      MC
      ⁢
      
        
      
      ⁢
      1
    
  
  =
  
    
      
        
          C
          Driver
        
        -
        
          C
          MSteady
        
      
      
        2
        ·
        
          (
          
            
              J
              M
            
            +
            
              J
              P
            
          
          )
        
        ·
        
          Δω
          
            C
            ⁢
            
              
            
            ⁢
            1
          
        
      
    
    ·
    
      C
      Driver
    
  



in which ΔωCI is a threshold value of difference between the angular velocities of the drive shaft and of the gearbox primary input shaft calculated by the estimator module,
the said inertia compensation stage being adapted to ensure the synchronization of the angular velocities of the drive shaft and of the primary input shaft in such a way as to avoid discontinuities in the acceleration of the vehicle due to the variations of the equivalent moment of inertia of the system following the engagement of the friction clutch.

10. System according to any one of the preceding claims, in which the said processing assembly comprises separate control units for the engine and for the gearbox, coupled to corresponding memory devices and connected to a common transmission line, and adapted to be interfaced with corresponding torque actuators of the propulsion system and of the friction clutch, the engine control unit controlling the torque actuator devices of the propulsion system as a function of the torque request signal generated by the gearbox control unit.

11. System according to any one of claims 1 to 9, in which the said processing assembly comprises a single integrated electronic control unit, coupled to a memory device, and adapted to be interfaced with torque actuator devices of the propulsion system and of the friction clutch.

12. Control method for controlling a driving-away manoeuvre in a motor vehicle provided with a gearbox comprising a primary input shaft which can be coupled to a drive shaft of a propulsion system of the vehicle by means of a servo-assisted friction clutch,
comprising the following operations:
a) generating, on the basis of signals or data indicating a command imparted by the driver by the operation of the accelerator pedal and on the basis of a mathematical reference model, reference torque request signals or data indicating a reference torque requested from the drive shaft and a reference torque requested from the friction clutch in the course of the driving-away manoeuvre;
b) estimating, on the basis of the reference torque request signals or data and on the basis of the reference model, signals or data indicating the angular velocities of the drive shaft and of the gearbox primary input shaft in the course of the driving-away manoeuvre; and
c) determining, on the basis of the signals or data indicating the estimated angular velocities of the drive shaft and of the primary input shaft, and on the basis of detected signals or data indicating the actual angular velocities of the drive shaft and of the primary input shaft, corrective contributions to the said reference torque request signals or data,
the said torque request signals or data, as modified by the corresponding corrective contributions, forming command signals or data for the control of torque actuator devices of the propulsion system and of the friction clutch, for the control of the driving-away manoeuvre in the motor vehicle.

13. Method according to claim 12, comprising the detection of a signal or datum indicating the position of the accelerator pedal following the command imparted by the driver by the operation of the accelerator pedal.

14. Method according to claim 13, comprising the determination of a signal or datum indicating the variation of longitudinal acceleration of the vehicle requested by means of the command imparted by the driver, as a function of the signal or datum indicating the position of the accelerator pedal, on the basis of a predetermined first relation model.

15. Method according to claim 14, comprising the determination of a signal or datum indicating the driving-away torque requested by means of the command imparted by the driver, as a function of the signal or datum indicating the position of the accelerator pedal, on the basis of a predetermined second relation model.

16. Method according to claim 15, comprising the determination of a signal or datum indicating the angular velocity of the drive shaft torque requested on driving away, as a function of the signal or datum indicating the position of the accelerator pedal, on the basis of a predetermined third relation model.

17. Method according to claim 16, in which the said first relation model associates the signal or datum indicating the position of the accelerator pedal with a signal or datum element indicating the variation of longitudinal acceleration of the vehicle which is constant over time at least during a first stage of the driving-away manoeuvre, and the reference torque request signal indicating the reference torque requested from the friction clutch has a linear temporal variation in the form of a ramp in a first stage of the driving-away manoeuvre, the gradient of which is proportional to the value of the said signal or datum indicating the variation of the longitudinal acceleration.

18. Method according to claim 17, in which the said reference torque request signal indicating the reference torque requested from the drive shaft has a linear temporal variation in the form of a ramp in a first stage of the driving-away manoeuvre, the gradient of which is a function of the angular velocity of the drive shaft requested on driving away and of the gradient of the temporal variation ramp of the signal indicating the reference torque requested from the friction clutch, and is greater than the gradient of the tern oral variation ram of the signal indicating the reference torque requested from the friction clutch.

19. Method according to claim 18, in which the said reference torque request signals indicating the reference torque requested from the drive shaft and the reference torque requested from the friction clutch have a constant value over time in an intermediate stage of the driving-away manoeuvre, and the said reference torque request signal indicating the reference torque requested from the drive shaft has a linear temporal variation in the form of a ramp in a terminal stage of the driving-away manoeuvre, from the instant at which the difference between the angular velocities of the drive shaft and of the gearbox primary input shaft calculated by the estimator module is less than a predetermined threshold value.

20. Method according to claim 19, in which the reference torque request signal indicating the reference torque requested from the friction clutch has the following temporal variation:


CFrif(t)=CF0+dCF·t for t0≦t≦t2 



CFRif(t)=CFsteady for t2<t≦t4 


where:
CF0 is the initial value of the torque, at time t0 


CF0=CF(t0);


dCF is the gradient of the temporal variation ramp, calculated as




  
    
      dC
      F
    
    =
    
      
        K
        Jerk
      
      ·
      
        
          jerk
          *
        
        ⁡
        
          [
          
            Nm
            /
            sec
          
          ]
        
      
    
  




  
    in
    ⁢
    
      
    
    ⁢
    which
  




  
    
      K
      Jerk
    
    =
    
      
        
          J
          P
        
        ·
        τ
      
      R
    
  


where JP is the total moment of inertia transferred to the primary shaft, τ is the selected transmission ratio and R is the rolling radius of the wheels; and
CFSteady is a value of intermediate steady torque, defined as




  
    
      C
      FSteady
    
    =
    
      
        K
        MSteady
      
      ·
      
        C
        Driver
      
    
  




  
    in
    ⁢
    
      
    
    ⁢
    which
  




  
    
      K
      MSteady
    
    =
    
      
        J
        P
      
      
        
          J
          M
        
        +
        
          J
          P
        
      
    
  


where JM is the total moment of inertia of the engine and CDriver is the reference steady torque for the clutch at the end of the driving-away manoeuvre;
and
the reference torque request signal indicating the reference torque requested from the drive shaft has the following temporal variation:


CMRif(t)=CM0+dCM·t for t0≦t≦t1 



CMRif(t)=CMsteady for t1<t≦t3 



CMRif(t)=CMsteady+dCMC1·t for t3<t≦t4 



where:
CM0 is the initial value of the torque, at time t0 


CM0=CM(t0);


dCM is the gradient of the temporal variation ramp, calculated as





  
    dC
    M
  
  =
  
    1
    
      (
      
        
          1
          
            dC
            F
          
        
        -
        
          
            2
            ·
            
              (
              
                
                  ω
                  Msp
                
                -
                
                  ω
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            ·
            
              J
              M
            
          
          
            
              (
              
                
                  C
                  MSteady
                
                -
                
                  C
                  
                    M
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                
              
              )
            
            2
          
        
      
      )
    
  



in which ωM0 is the initial value of the rotation speed of the engine, at time t0 


ωM0=ωM(t0), and


CMSteady is a value of intermediate steady torque, defined as




  
    
      C
      MSteady
    
    =
    
      
        K
        MSteady
      
      ·
      
        C
        Driver
      
    
  




  where




  
    
      K
      MSteady
    
    =
    
      
        J
        P
      
      
        
          J
          M
        
        +
        
          J
          P
        
      
    
  


and CDriver is the reference steady torque for the engine at the end of the driving-away manoeuvre; and
dCMCI is the gradient of the temporal variation ramp in a terminal stage for inertia compensation, defined as:





  
    dC
    
      MC
      ⁢
      
        
      
      ⁢
      1
    
  
  =
  
    
      
        
          C
          Driver
        
        -
        
          C
          MSteady
        
      
      
        
          2
          ·
          
            (
            
              
                J
                M
              
              +
              
                J
                P
              
            
            )
          
          ·
          Δ
        
        ⁢
        
          
        
        ⁢
        
          ω
          
            C
            ⁢
            
              
            
            ⁢
            1
          
        
      
    
    ·
    
      C
      Driver
    
  



in which ΔωCI is a threshold value of difference between the angular velocities of the drive shaft and of the gearbox primary input shaft calculated by the estimator module,
the said inertia compensation stage being adapted to ensure the synchronization of the angular velocities of the drive shaft and of the primary input shaft in such a way as to avoid discontinuities in the acceleration of the vehicle due to the variations of the equivalent moment of inertia of the system following the engagement of the friction clutch.