# Patent

## Title
Method and device for controlling a powertrain test stand

## Abstract

Disclosed are a method and a control device for controlling a powertrain test stand comprising a driving machine and a driven machine. According to the invention, a torque supplied by the driving machine is controlled, a reference variable (Mx) for controlling the torque of the driving machine in order to dampen vibrations between the driving machine and the driven machine being modified depending on a current speed (nist) of the driving machine in relation to a predefined value (Mist), the reference variable (Mx) being determined from a model of a virtual tire.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
The present application is a U.S. National Phase of International Patent Application Serial No. PCT/AT2015/050007, entitled “METHOD AND DEVICE FOR CONTROLLING A POWERTRAIN TEST STAND,” filed on Jan. 8, 2015, which claims priority to Austrian Patent Application No. A50011/2014, entitled “METHOD AND DEVICE FOR CONTROLLING A POWERTRAIN TEST STAND,” filed on Jan. 9, 2014, the entire contents of each of which are hereby incorporated by reference for all purposes.
TECHNICAL FIELD
The invention relates to a method for controlling as well as a control device of a powertrain test stand comprising a driving machine and a driven machine, wherein a torque supplied by the driving machine is controlled by an inner control loop, and comprising an outer control loop for controlling the reference variable of the inner control loop depending on a current speed of the driving machine, so that a reference variable for controlling the torque of the driving machine to dampen vibrations between the driving machine and the driven machine being modified in accordance with a current speed of the driving machine in relation to a predefined value.
BACKGROUND AND SUMMARY
In a powertrain test stand, the component to be tested (hereinafter also called test specimen), in most cases, is not necessarily connected to the environment, as is the case at its future site. For example, a powertrain on the test stand is connected to a driving machine and one or several load machines or—general—driven machines via relatively rigid shafts instead of being in contact with the road via tires. On the test stand, this mostly results in weakly damped (and thus pronounced) resonance frequencies, which the test specimen will not encounter at its actual site. If these resonance frequencies are excited by one of the machines, the resulting vibrations may heavily influence the test result or even result in destroying the test specimen and/or the test stand. Therefore, measures for damping these resonance frequencies on the test stand are necessary. The known methods will be listed below.
Above all, the use of softer, more damped connecting shafts may reduce the resonance frequencies and additionally also dampen them to a higher extent. If in normal operation the resonance frequencies are no longer excited, the problem will be solved. The low-pass effect of the soft connecting shaft turns out to be disadvantageous. In addition, quite a significant amount of power can be transformed in the shaft by friction (the shaft gets hot and might get destroyed).
Apart from such passive damping, methods for the active damping have been known, in which an additional torque corresponding to a shaft damping is applied on the driven machine. For example the differential angular velocity of the shaft, i. e. the difference between the measured speeds on the driven machine and the driving machine can be used for this (cf. e. g. DE 38 08 524 C2). The disadvantage of using the two current speeds on the driven side and the driving side is that these speeds are possibly available only in a noise-infested and considerably delayed way, e. g. due to the bus transmission time and/or filtering of the signal. In the worst case, applying such a distorted damping torque may cause the powertrain test stand to become particularly instable.
The need for high accuracy and dynamics when applying the two speeds was already recognized in EP 1 333 268 A2. It is proposed to estimate the differential angular velocity with the help of the measured shaft torque: The measured shaft torque is differentiated, weighted with a correction factor and supplied to the torque target value of the driven machine as correction value. The differentiation of a measured quantity, however, has the disadvantage that the constantly present measurement noise is intensified considerably. Indeed, the differentiated torque might be filtered by a low-pass filter, however, this method will get instable in the case of higher resonance frequencies, thus highly limiting the practical use. Furthermore, in the case of large test stands including a play and many distributed masses (e. g. in the case of powertrains with matching gears) only the first shaft close to the machine will be damped; the other shafts will remain undamped.
In addition, WO 2013/126940 A1 shows a method in which the measured shaft torque is not differentiated but as such is applied to the torque target value of the driven machine either directly or after a low-pas filtering. This measure, which initially comes as a surprise, results in very good damping in particular in the case of high resonance frequencies. However, if large masses are present on the test stand or the natural frequency to be damped is small, the attainable damping effect will be small.
Other, comparatively more complicated methods for the active damping show alternative options of using a measured torque (e. g. DE 102 47 347 A and U.S. Pat. No. 4,468,958 A) or try to predict the resonance behavior of the test stand (e. g. AT 010 301 U2 and U.S. Pat. No. 8,006,548 B2).
In connection with a highly realistic simulation or imitation of the behavior of a vehicle on a roadway, it has also been known to control the load machines of a powertrain test stand, i. e. the driven machines, by using a tire model. Either the speed (cf. AT 508 031 B1) or the torque (cf. EP 1 037 030 B1) of the driven machines may be controlled accordingly. It is the object of both methods to load the output of the powertrain more realistically and not to dampen the vibrations and, in particular, any natural frequencies of the test specimen on the test stand. Such a realistic load will obviously be achieved if the tire model is used for controlling the output (but not the input).
The US 2012/0166154 A1 relates to a slip simulation on the driven machines of a powertrain, whereby by using a tire model the test specimen on the test stand is to be subjected to a load correctly, i. e. realistically. Here, too, the reason for using a tire model on the test stand is to replace a real tire. The damping of natural frequencies, which is desired for a correct simulation, is accomplished by suitably setting a proportional and differential proportion in the speed controller.
The DE 10 2010 049 689 A1 also relates to a more realistic load of the test specimen if a real tire is replaced by a tire model. Its purpose is to simulate the tire by a better tire model on the test stand, whereby in particular by a detailed tire model, for instance, the flexing resistance, the influence of the tire temperature and the tire pressure, the proportion of roadway unevenness and dynamic tire loads etc. may be examined. Obviously, this makes only sense if instead of a real tire the tire model is used. In addition, the DE 10 2010 049 689 A1 indicates to determine individual controller parameters such as e. g. the P, I or D proportion of a PID controller on the basis of a tire model, a specific procedure not being disclosed here.
In the prior art, a tire model is used always expediently and with the sole purpose of replacing a real tire.
It is the object of the present invention to provide a method of the above given type or a device for carrying out this method, which avoids the above described vibrational problems in a simple and efficient manner or at least reduces them to an admissible degree. Problems in connection with time-delayed and time-shifted measured values are to be avoided and damping of relatively low-frequency vibrations is to succeed as well. In addition, the control is to be immune to measurement noise and achieve the desired damping also in transient examinations—in particular in the first examination of a test specimen.
To solve the object posed, the invention provides a method of the above given type, which is characterized in that the reference variable for the control of the torque of the driving machine is determined from a tire model of a virtual tire. In the control device indicated above, the invention accordingly provides that the outer control loop for controlling the reference variable of the inner control loop comprises a tire model of a virtual tire depending on a current speed of the driving machine. The invention is based on an unconventional and initially surprising use of the tire model in a place where normally (in a real setting) there are no tires. Therefore, the tire model is not used to replace a real tire (because such a tire does not exist in this place), but exclusively for its damping effect. The tire model used for controlling the driving, i. e. the driving machine of the powertrain test stand, does not result in a more realistic loading of the powertrain; only the damping effect of such a control is advantageously (also) used on the driving side. In this connection, the current speed of the driving machine (on which the virtual tire is positioned)—or an equivalent measured quantity—is inherently included in the tire model, however, it is not necessary to measure several speeds on the powertrain, so that problems resulting from the relative chronological behavior of several measured values may be avoided.
It is particularly favorable if the tire model establishes a preferably static correlation between the reference variable and a slip of the virtual tire or has such a correlation. The slip of the tire, which constitutes a prerequisite of an energy transmission, and a corresponding slip model are especially suited for the present method. In the case of a static correlation between the slip and the reference variable, i. e. the (modified) torque target value, influences of other—dynamic—measured quantities can be avoided completely.
In a particularly simple and thus preferred tire model, the reference variable is essentially calculated according to the formula MX=Fz·rdyn·D·sin(C·arctan(B·s)) and/or the outer control loop for determining the reference variable is essentially adapted according to this formula, with Fz being a contact force, rdyn a rolling radius, B, C and D constant tire-parameters and s a slip of the virtual tire. In this model, the reference variable shows a linear behavior only in a small area and the amount of abrupt changes is limited.
If a virtual roadway speed, which is included in the tire model, in particular in the slip of the virtual tire, is determined from an inverse tire model or if the outer control loop is adapted to determine a virtual roadway speed from an inverse tire model, the control of the driving machine (still) may be performed advantageously by predefining a desired torque. The inverse tire model can be chosen independently of the tire model. In particular, the inverse tire model does not have to correspond to the mathematical inverse of the tire model at all, but can be derived, for example, from a simplified tire model.
In this connection, it is advantageous if the virtual roadway speed is determined from the predefined value for the reference variable and a target speed of the driving machine, which target speed is preferably proportional to a target speed of the driven machine. Accordingly, the outer control loop is preferably adapted for determining the virtual roadway speed from a predefined value for the reference variable and a target speed of the driving machine. The exclusive use of predefined static quantities can prevent any feedbacks of dynamic measures quantities—besides the current speed of the driving machine—in the tire model.
Derivation of the inverse tire model is particularly simple if the inverse tire model makes or has a linear correlation between the virtual roadway speed and the target speed of the driving machine. The linear correlation can be used here, without having to incur any disadvantages with respect to the damping effect of the tire model, since the tire model (contrary to the inverse tire model) may very well have an at least partially non-linear correlation.



BRIEF DESCRIPTION OF THE FIGURES
Below, the invention will be illustrated by way of particularly preferred exemplary embodiments, however, to which it shall not be limited, and will be further explained with reference to the drawings, in which in detail:
FIG. 1 schematically shows a powertrain test stand comprising a differential without matching gears;
FIG. 2 schematically shows a powertrain test stand comprising a differential with matching gears on the driving side and the driven side;
FIG. 3 shows a driving torque curve in a load change on a test stand according to the prior art for comparison;
FIG. 4 schematically shows the principle of a control of the driving side with a virtual tire;
FIG. 5 shows a characteristic curve of friction coefficient and slip according to a typical tire model;
FIG. 6 shows a driving torque curve in a load change under the present control method for comparison; and
FIG. 7 shows a diagram of the characteristic curves of friction coefficient and slip according to three different tire models in comparison.



DETAILED DESCRIPTION
FIG. 1 and FIG. 2 each show a powertrain test stand 1 comprising a driving machine 2 and two driven machines 3, 3′, which are connected to a powertrain 4 to be tested. The powertrain 4 comprises a rear axle differential 5. In such a powertrain test stand 1, mostly only parts of a powertrain 4 are subjected to load with the help of driving machines 2 and driven machines 3, 3′ in accordance with predefined speed and torque curves. Due to the gear ratio iD of the differential 5 the following applies for the angular velocities of the machines 2, 3, 3′:




  
    
      
        
          ω
          E
        
        =
        
          
            i
            D
          
          ⁢
          
            
              
                ω
                
                  A
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              +
              
                ω
                
                  A
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
            
            2
          
        
      
    
    
      
        (
        1
        )
      
    
  




wherein ωε is the angular velocity of the driving machine 2, and ωA1 and ωA2, respectively are the angular velocities of the two driven machines 3, 3′. Furthermore, —apart from frictional losses in the differential 5—the following applies for the torques

MA1+MA2=iDME  (2)

To be able to subject the differential 5 to larger torques than can be supplied by the machines 2, 3, 3′, frequently also matching gears 6, 7, 7′, as shown in FIG. 2, are used. The matching gears 6 allocated to the driving machine 2 have a gear ratio iE and the matching gears 7, 7′ allocated to the driven machines 3, 3′ each have a gear ratio iA. The matching gears 6, 7, 7′ are used in such a way that the torques on the test specimen side, i. e. on the side of the powertrain 4 to be tested, are larger than on the machine side. Therefore, the following applies to the angular velocities ωE, ωA1, ωA2 of the machines 2, 3, 3′:

ωE=iEωGE, ωA1=iAωGA1, and ωA2=iAωGA2,  (3)

wherein ωGE is the angular velocity on the driving-side matching gears 6, and ωGA1 and/or ωGA2 are the angular velocities on the two driven-side matching gears 7, 7′. For the torques—again apart from friction losses in the matching gears—follows:

MGE=iEME, MGA1=iAMA1, and MGA2=iAMA2,  (4)

wherein—analogously to the angular velocities—MGE is the torque on the driving-side matching gears 6 and MGA1 or MGA2 are the torques on the two driven-side matching gears 7, 7′. Usually, for the purpose of testing on the test stand 1, the speeds nA1, nA2 of the driven side and the torque ME for the driving side are predefined. Accordingly, the driven machines 3, 3′ are mainly operated in a speed-controlled manner and the driving machine 2 in a torque-controlled manner. Without any further measures, the construction on the test stand 1 oscillates in particular with the first natural frequency (inertia of the driving machine 2 due to rigidity of the shaft connections versus inertia of the driven machines 3, 3′). This problem is still aggravated with matching gears 6, 7, 7′, since the test specimen 4 encounters considerably larger machine inertia due to the gear ratios iE, iA1, iA2. Furthermore, the inertias and backlashes of the matching gears 6, 7, 7′ themselves also have a negative effect on the oscillation behavior.
FIG. 3 shows an example of a possible driving torque curve in the case of a load change (good excitation of the first natural frequency as a result of the hard impact after passing through the backlash). The broken line 8 represents the predefined value ME,soll of the torque of the driving machine 2, which value changes over time t (which is indicated on the abscissa). The solid line 9 represents the time course of the actually acting torque ME. Of course, the extremely weakly damped, low-frequency oscillation of the torque ME shown here is undesired and should be reduced.
According to the present method for controlling the torque ME of the driving machine 2, a wheel with a tire is mounted virtually on the driving machine 2, which wheel is driving on a virtual roadway. The roadway velocity is chosen in such a way that the very desired torque ME results in stationary fashion together with the tire slip, i. e. according to a predefined value ME,soll (hereinafter abbreviated to Msoll). The principle of the control is schematically shown in FIG. 4. As is shown in FIG. 4, the reference variable M of the torque control for the driving machine 2, which reference variable is indicated as output value on the right-hand side, is obtained from the tire model represented by the block 10. Included in the tire model 10 are—apart from constant model parameters that are not shown here—the current speed nE,ist (abbreviated to nist) of the driving machine 2 as well as the virtual roadway speed v. The current driving-speed nist is measured on the driving machine 2. The virtual roadway speed v is obtained from the inverse tire model represented by the second block 11. In general, the inverse tire model 11 does not correspond to the inverse of the tire model 10, but for example pertains to a simplified tire model which is easier to be inverted. Included n the inverse tire model 11 are again apart from own constant model parameters a target speed nE,soll (abbreviated to nsoll) of the driving machine 2 as well as the predefined value Msoll for the torque ME of the driving machine 2.
The tire models on which the tire model 10 and the inverse tire model 11 are based may be any type of tire model, i. e. a model that is suited to approximate the transmission behavior of a wheel with a tire and/or comprises comparable damping properties. Below, a simplified tire model will be described in an exemplified manner, which is based on the so-called “magic formula” by Pacejka (cf. Pacejka. H., “Tyre and Vehicle Dynamics” 2nd ed., Butterworth-Heinemann, Oxford, 2007). However, one could also assume another tire model having similar qualitative properties, e. g. the model “TMsimple” by Hirschberg (cf. Hirschberg W., “TMsimple Application Manual”, 2007), the model “TMeasy” by Rill (cf. Rill G., “Simulation von Kraftfahrzeugen”, published by Vieweg-Verlag, Regensburg, 2007), the “Hohenheimer Reifenmodell” or the “TameTire” tire model developed by the Michelin company, wherein advantageously a version as simple as possible is used for the present method.
The starting point in the shown model is a wheel having the angular velocity ωR and the—here assumed to be constant—dynamic rolling radius rdyn as well as a roadway speed v. Alternatively, the dynamic rolling radius rdyn can be varied slightly depending on the roadway speed v (or the corresponding vehicle velocity), e. g. according to a polynomial approach, however, the possible influence of such a modification on the damping effect has turned out to be negligible. With the above quantities, a slip of the virtual tire can be given as follows




  
    
      
        s
        =
        
          
            
              
                r
                dyn
              
              ⁢
              
                ω
                R
              
            
            -
            v
          
          
            max
            ⁡
            
              (
              
                
                  v
                  low
                
                ,
                
                  
                  v
                  
                
              
              )
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




wherein the limit speed Vlow prevents a division by zero. The literature also indicates other definitions of slip; the one shown here is the variant preferred by Pacejka. (An alternative will be explained below). With this slip s, by means of the simple “magic formula” for the longitudinal movement, the friction value μ can be calculated from

μ(s)=D sin(C arctan(B·s))  (6)

with the three tire parameters B, C, and D.
FIG. 5 shows a characteristic curve 12 of friction coefficient versus slip for a typical tire. With the contact force Fz between the virtual tire and the virtual roadway now the longitudinal force acting in the tire contact surface

Fx=μFz  (7)

can be calculated, and finally the torque acting due to the slip s

Mx=Fxrdyn=FzrdynD sin(C arctan(B·s))  (8)

Normally, the rolling friction is also taken into consideration in a tire model. To simplify the present control, any modeling of the rolling friction is dispensed with here. A bodywork model might be used for the contact force Fz; for the sake of simplicity, however, a constant contact force Fz,0 is chosen. With these simplifications and if the equation (5) is used in equation (8),




  
    
      
        
          M
          x
        
        =
        
          
            F
            
              z
              ,
              0
            
          
          ·
          
            r
            dyn
          
          ·
          D
          ·
          
            sin
            ⁡
            
              (
              
                C
                ·
                
                  arctan
                  ⁡
                  
                    (
                    
                      B
                      ·
                      
                        
                          
                            
                              r
                              dyn
                            
                            ⁢
                            
                              ω
                              R
                            
                          
                          -
                          v
                        
                        
                          max
                          ⁡
                          
                            (
                            
                              
                                v
                                low
                              
                              ,
                              
                                
                                v
                                
                              
                            
                            )
                          
                        
                      
                    
                    )
                  
                
              
              )
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




helps to obtain the correlation between torque Mx, angular velocity ωR and roadway speed v in the case of a certain constant contact force Fz,0. In the control according to FIG. 4, the converted current speed nE,ist, (abbreviated to nist) of the driving machine 2 is used for the angular velocity ωR:




  
    
      
        
          ω
          R
        
        =
        
          
            π
            30
          
          ⁢
          
            n
            ist
          
        
      
    
    
      
        (
        10
        )
      
    
  




Indeed, calculating the suitable roadway speed v for a predefined value Msoll of the torque ME and a current speed nist is possible but very complex. Perhaps there are also several solutions or no solution at all due to the non-linear characteristic curve of friction coefficient and slip (cf. FIG. 5). A reasonable simplification in this context is to use instead of the non-linear characteristic curve of friction coefficient and slip a linear characteristic curve

μ(s)=k·s  (11)

having a gradient k, the gradient being best selected just like in the origin of the non-linear characteristic curve of friction coefficient and slip; then, the following will apply:

k=B·C·D  (12)

Thus, the equation (9) is simplified to read as follows:




  
    
      
        
          M
          x
        
        =
        
          
            F
            
              z
              ,
              0
            
          
          ·
          
            r
            dyn
          
          ·
          k
          ·
          
            
              
                
                  r
                  dyn
                
                ⁢
                
                  ω
                  R
                
              
              -
              v
            
            
              max
              ⁡
              
                (
                
                  
                    v
                    low
                  
                  ,
                  
                    
                    v
                    
                  
                
                )
              
            
          
        
      
    
    
      
        (
        13
        )
      
    
  




and one may eliminate for the road way speed in order to arrive at a simplified inverse tire model:




  
    
      
        v
        =
        
          {
          
            
              
                
                  
                    
                      F
                      
                        z
                        ,
                        0
                      
                    
                    ⁢
                    
                      r
                      dyn
                      2
                    
                    ⁢
                    k
                    ⁢
                    
                      
                    
                    ⁢
                    
                      ω
                      R
                    
                  
                  
                    
                      
                        F
                        
                          z
                          ,
                          0
                        
                      
                      ⁢
                      
                        r
                        dyn
                      
                      ⁢
                      k
                    
                    +
                    
                      M
                      z
                    
                  
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    v
                  
                  ⩾
                  
                    v
                    low
                  
                
              
            
            
              
                
                  
                    
                      
                        F
                        
                          z
                          ,
                          0
                        
                      
                      ⁢
                      
                        r
                        dyn
                        2
                      
                      ⁢
                      k
                      ⁢
                      
                        
                      
                      ⁢
                      
                        ω
                        R
                      
                    
                    -
                    
                      
                        M
                        x
                      
                      ⁢
                      
                        v
                        low
                      
                    
                  
                  
                    
                      F
                      
                        z
                        ,
                        0
                      
                    
                    ⁢
                    
                      r
                      dyn
                    
                    ⁢
                    k
                  
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                      v
                      
                    
                  
                  ≤
                  
                    v
                    low
                  
                
              
            
            
              
                
                  
                    
                      F
                      
                        z
                        ,
                        0
                      
                    
                    ⁢
                    
                      r
                      dyn
                      2
                    
                    ⁢
                    k
                    ⁢
                    
                      
                    
                    ⁢
                    
                      ω
                      R
                    
                  
                  
                    
                      
                        F
                        
                          z
                          ,
                          0
                        
                      
                      ⁢
                      
                        r
                        dyn
                      
                      ⁢
                      k
                    
                    -
                    
                      M
                      x
                    
                  
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    v
                  
                  ≤
                  
                    -
                    
                      v
                      low
                    
                  
                
              
            
          
        
      
    
    
      
        (
        14
        )
      
    
  




To determine the roadway speed v from the inverse tire model according to equation (14), the predefined value Msoll is used for the torque Mx and the converted target speed nE,soll of the driving machine 2 for the angular velocity ωR:




  
    
      
        
          
            M
            x
          
          =
          
            M
            soll
          
        
        ⁢
        
          

        
        ⁢
        
          
            ω
            R
          
          =
          
            
              π
              30
            
            ·
            
              n
              
                E
                ,
                soll
              
            
          
        
      
    
    
      
        (
        15
        )
      
    
  




The target speed nE,soll of the driving machine 2 is calculated from the target speeds nA1,soll and nA2,soll of the driven machines 3, 3′ in consideration of the applicable gear ratio iD, iE. In the case of the powertrain test stand 1 with matching gears 6, 7, 7′ according to FIG. 2, the following approximately follows for the target speed nE,soll of the driving machine 2




  
    
      
        
          n
          
            E
            ,
            soll
          
        
        =
        
          
            i
            E
          
          ⁢
          
            i
            D
          
          ⁢
          
            
              
                n
                
                  
                    A
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                  ,
                  soll
                
              
              +
              
                n
                
                  
                    A
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                  ,
                  soll
                
              
            
            2
          
        
      
    
    
      
        (
        16
        )
      
    
  




FIG. 6 shows the—in comparison to FIG. 3—dramatic improvement of the driving torque curve 9′ in a load change, i. e. a variation 8 of the predefined value Msoll. Here, the reference variable Mx for the torque control of the driving machine 2 was dynamically determined on the basis of the tire model according to equation (9) with the roadway velocity according to the inverse tire model according to equation (14).
Alternatively to the static relationship of the slip s to the angular velocity ωR and roadway speed v given in equation (5) the damping effect of the virtual tire can especially be improved by a detailed description, which takes into consideration the dynamics of the force build-up. For instance, the literature indicates the so-called “contact point model” (single contact point transient tyre model, cf. Pacejka, 2007), in which a contact point between the tire and the roadway is subjected to a certain deflection u from the rest position due to the differences in velocity, which deflection is described by the differential equation




  
    
      
        
          
            d
            u
          
          
            d
            t
          
        
        =
        
          
            
              -
              
                
                  
                  v
                  
                
                
                  σ
                  κ
                
              
            
            ⁢
            u
          
          -
          
            v
            sx
          
        
      
    
    
      
        (
        17
        )
      
    
  




with the slip speed

vsx=v−rRωR  (18)

and the maximum deflection σK (relaxation length). On principle, the slip s could be calculated with




  
    
      
        s
        =
        
          u
          
            σ
            κ
          
        
      
    
    
      
        (
        19
        )
      
    
  




To achieve a better damped behavior at lower speeds, too, Pacejka suggests the calculation according to




  
    
      
        s
        =
        
          
            u
            
              σ
              κ
            
          
          -
          
            
              
                k
                
                  v
                  ,
                  low
                
              
              
                c
                
                  F
                  ⁢
                  
                    
                  
                  ⁢
                  κ
                
              
            
            ⁢
            
              v
              sx
            
          
        
      
    
    
      
        (
        20
        )
      
    
  




with




  
    
      
        
          k
          
            v
            ,
            low
          
        
        =
        
          {
          
            
              
                
                  
                    1
                    2
                  
                  ⁢
                  
                    
                      k
                      
                        v
                        ,
                        
                          low
                          ⁢
                          
                            
                          
                          ⁢
                          0
                        
                      
                    
                    ⁡
                    
                      [
                      
                        1
                        +
                        
                          cos
                          ⁡
                          
                            (
                            
                              π
                              ⁢
                              
                                
                                  
                                  v
                                  
                                
                                
                                  v
                                  low
                                
                              
                            
                            )
                          
                        
                      
                      ]
                    
                  
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                      v
                      
                    
                  
                  ≤
                  
                    v
                    low
                  
                
              
            
            
              
                0
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                      v
                      
                    
                  
                  >
                  
                    v
                    low
                  
                
              
            
          
        
      
    
    
      
        (
        21
        )
      
    
  




and the slip rigidity cFx.
The present method or the present control device is by no means limited to a certain tire model. Alternatively to the model of Pacejka (the “magic formula”) given in equation (6), for example, the tire model “TMsimple” of Hirschberg having the fundamental formula




  
    
      
        
          μ
          ⁡
          
            (
            s
            )
          
        
        =
        
          K
          ⁢
          
            
          
          ⁢
          
            sin
            ⁡
            
              [
              
                
                  B
                  ⁡
                  
                    (
                    
                      1
                      -
                      
                        e
                        
                          
                            -
                            
                              
                              s
                              
                            
                          
                          A
                        
                      
                    
                    )
                  
                
                ⁢
                sign
                ⁢
                
                  
                
                ⁢
                
                  (
                  s
                  )
                
              
              ]
            
          
        
      
    
    
      
        (
        22
        )
      
    
  




wherein K, B, and A are model parameters, or the tire model “TMeasy” of Rill having the fundamental formula




  
    
      
        
          μ
          ⁡
          
            (
            s
            )
          
        
        =
        
          {
          
            
              
                
                  
                    
                      s
                      M
                    
                    ⁢
                    
                      μ
                      0
                      ′
                    
                    ⁢
                    
                      σ
                      
                        1
                        +
                        
                          σ
                          ⁡
                          
                            (
                            
                              
                                
                                  
                                    s
                                    M
                                  
                                  
                                    f
                                    M
                                  
                                
                                ⁢
                                
                                  μ
                                  0
                                  ′
                                
                              
                              -
                              z
                              +
                              σ
                            
                            )
                          
                        
                      
                    
                    ⁢
                    with
                    ⁢
                    
                      
                    
                    ⁢
                    mit
                    ⁢
                    
                      
                    
                    ⁢
                    σ
                  
                  =
                  
                    s
                    
                      s
                      M
                    
                  
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    0
                  
                  ⩽
                  s
                  ⩽
                  
                    s
                    M
                  
                
              
            
            
              
                
                  
                    μ
                    M
                  
                  -
                  
                    
                      (
                      
                        
                          μ
                          M
                        
                        -
                        
                          μ
                          G
                        
                      
                      )
                    
                    ⁢
                    
                      
                        σ
                        2
                      
                      (
                      
                        
                          3
                          -
                          
                            with
                            ⁢
                            
                              
                            
                            ⁢
                            mit
                            ⁢
                            
                              
                            
                            ⁢
                            σ
                          
                        
                        =
                        
                          
                            s
                            -
                            
                              s
                              M
                            
                          
                          
                            
                              s
                              G
                            
                            -
                            
                              s
                              M
                            
                          
                        
                      
                    
                  
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    
                      s
                      M
                    
                  
                  ⩽
                  s
                  ⩽
                  
                    s
                    G
                  
                
              
            
            
              
                
                  μ
                  G
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    
                      s
                      G
                    
                  
                  ⩽
                  s
                
              
            
          
        
      
    
    
      
        (
        23
        )
      
    
  




wherein SM, SG, fM, μo′, and μG are (partially depending) model parameters can be used.
The characteristic curves of friction coefficient and slip resulting from the indicated tire models are very similar, i. e. they have—at least in the area of interest—a very similar curve. The curves of the three given tire models are drawn in the diagram shown in FIG. 7, wherein only the first quadrant of the coordinate system is shown due to lack of space. The curve in the third quadrant is analogous in each case (cf. FIG. 5). The solid line in FIG. 7 represents the “magic formula” of Pacejka (cf. equation (6)), the broken line represents the “TMsimple” model (cf. equation (22)) and the dotted line the “TMeasy” model (cf. equation 23)).
Depending on the choice of the model and the model parameters, of course, any curves having a quantitatively larger deviation may be provided as well. FIG. 7 shows the qualitative behavior of the reference variable obtained in general by tire models, in particular, with a continuous curve of the characteristic curve of friction coefficient and slip, which increases initially approximately linearly starting from a zero point, subsequently levels off and finally monotonously drops with even more increasing slip.

## Claims

1. A method for controlling a powertrain test stand comprising with a driving machine and a driven machine, the method comprising:
controlling a torque supplied by the driving machine according to a reference variable (Mx),
determining a virtual roadway speed (v), which is included in a tire model of a virtual tire, from an inverse tire model,
determining the reference variable (Mx) for controlling the torque of the driving machine from the tire model of the virtual tire, and
modifying the reference variable (Mx) depending on a current speed (nist) of the driving machine in relation to a redefined value (Msoll) in order to dampen vibrations between the driving machine and the driven machine.

2. The method according to claim 1, wherein the virtual roadway speed (v) is included in a slip of the virtual tire in the tire model.

3. The method according to claim 1, further comprising:
with the tire model, correlating the reference variable (Mx) with a slip of the virtual tire.

4. The method according to claim 3, further comprising:
calculating the reference variable (Mx) essentially according to the formula MX=Fz·rdyn·D·sin(C·arctan(B·s)), with Fz being a contact force, rdyn a rolling radius, B, C, and D constant parameters, and s the slip of the virtual tire.

5. The method according to claim 3, wherein the correlation between the reference variable (Mx) and the slip of the virtual tire is a static correlation.

6. The method according to claim 1, further comprising:
determining the virtual roadway speed (v) from the predefined value (Msoll) for the reference variable (Mx) and a target speed (nsoll) of the driving machine.

7. The method according to claim 6, further comprising:
with the inverse tire model, establishing a linear correlation between the virtual roadway speed (v) and the target speed (nsoll) of the driving machine.

8. The method according to claim 6, wherein the target speed (nsoll) of the driving machine is proportional to a target speed of the driven machine.

9. A control device of a powertrain test stand comprising a driving machine and a driven machine, to perform the method according to claim 1, the control device comprising:
an inner control loop for controlling a torque applied by the driving machine, and
an outer control loop for controlling the reference variable (Mx) of the inner control loop as a function of the current speed (nist) of the driving machine,
wherein the outer control loop comprises the tire model of the virtual tire.

10. The control device according to claim 9, wherein the outer control loop is adapted to determine the virtual roadway speed (v), which is included in a slip of the virtual tire in the tire model, from the inverse tire model.

11. The control device according to claim 9, wherein the tire model comprises a correlation between the reference variable (Mx) and a slip of the virtual tire.

12. The control device according to claim 11, wherein the outer control loop is adapted to determine the reference variable (Mx) essentially in accordance with the formula MX=F·rdyn·D·sin(C·arctan(B·s)), with Fz being a contact force, rdyn a rolling radius, B, C, and D constant parameters, and s the slip of the virtual tire.

13. The control device according to claim 11, wherein the correlation between the reference variable (Mx) and the slip of the virtual tire is a static correlation.

14. The control device according to claim 9, wherein the outer control loop is adapted to determine the virtual roadway speed (v), which is included in the tire model from the inverse tire model.

15. The control device according to claim 14, wherein the outer control loop is adapted to determine the virtual roadway speed (v) from a predefined value (Msoll) for the reference variable (Mx) and a target speed (nsoll) of the driving machine.

16. The control device according to claim 15, wherein the inverse tire model establishes a linear correlation between the virtual roadway speed (v) and the target speed (nsoll) of the driving machine.

17. The control device according to claim 15, wherein the target speed (nsoll) is proportional to a target speed of the driven machine.