Abstract:
In a method for moving a machine element of an automation machine with separately controlled drive shafts moving in a common direction, a first controller receives a first desired control variable, which is filtered using a filter having a frequency-dependent transfer function. In one embodiment, first desired control variable represents an overall movement of a machine element. A difference is determined between the filtered first desired variable and a first actual variable, and the difference is supplied as a desired control variable to the second controller for controlling the movement of the second drive shaft. In another embodiment, the filtered first desired variable and a second desired variable are added to form a sum, and a difference between the formed sum and the first actual variable is supplied as a desired control variable to the second controller for controlling the movement of the second drive shaft.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
       [0001]    This application claims the priority of German Patent Application, Serial No. 10 2010 001 829.5 filed Feb. 11, 2010, pursuant to 35 U.S.C. 119(a)-(d), the content of which is incorporated herein by reference in its entirety as if fully set forth herein. 
       BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates to a method for moving a machine element of an automation machine and to a drive system. 
         [0003]    The following discussion of related art is provided to assist the reader in understanding the advantages of the invention, and is not to be construed as an admission that this related art is prior art to this invention. 
         [0004]    Machine tools, in particular, are often provided with so-called redundant kinematics. In this case, redundant kinematics are understood as meaning the possibility of moving a machine element, which may be in the form of a tool receiving apparatus or a tool which is clamped in the tool receiving apparatus for example, along a direction with the aid of two separate drive shafts. 
         [0005]      FIG. 1  uses a schematically illustrated machine tool  36  to illustrate the principle of redundant kinematics. A carrier  5  can be moved in a direction X with the aid of two linear motors  3  and  4 . The guidance of the movement in the X direction is ensured by two columns  1  and  2  in this case. A further column  6  which is used to guide the movement of a second linear motor  7  is fastened to the carrier  5 . The linear motor  7  likewise moves in the X direction. The direction of movement of the linear motors  3 ,  4  and  7  is indicated by depicted arrows  37 ,  12  and  13 . A machine element  8  which is in the form of a tool receiving apparatus within the scope of the exemplary embodiment is fitted to the linear motor  7 . A tool  9  is clamped in the tool receiving apparatus. 
         [0006]    It goes without saying that the machine tool  36  also has further motors which allow a movement of the machine element  8 , for example in the Y and Z directions, but are not illustrated in  FIG. 1  for the sake of clarity and since they are irrelevant to understanding the invention. 
         [0007]    In order to measure a first actual variable x c,ist  which indicates the position of the column  6  with respect to a stationary machine bed  35  of the machine, the machine  36  has a first measuring device which is not illustrated in  FIG. 1  for the sake of clarity. In order to measure a second actual variable x f,ist  which indicates the position of the machine element  8  with respect to the column  6 , the machine tool  36  has a second measuring device which is likewise not illustrated in  FIG. 1  for the sake of clarity. 
         [0008]    If the machine element  8  is intended to be moved to a particular desired position value in the direction X, the problem arises of how the movement required for this purpose is intended to be divided between the two linear motors  3  and  4  and the linear motor  7 . Since the linear motor  7  must move only small masses (machine element  8  and tool  9 ), it is able to carry out dynamic movements (for example movements with high accelerations) in the X direction, whereas the two linear motors  3  and  4  can carry out only relatively sluggish movements on account of the larger masses to be moved by them. It is therefore expedient to divide the movement of the machine element into a first movement component, which is carried out by the two linear motors  3  and  4 , and a second movement component which is carried out by the linear motor  7 . In this case, the first movement component comprises the movement processes which are not very dynamic, that is to say the low-frequency movement processes, whereas the second movement component comprises the dynamic, that is to say high-frequency, movement processes of the machine element. 
         [0009]      FIG. 2  illustrates a schematic block illustration of a drive system which is known to be commercially available for the machine tool  36 . A desired variable generating unit  15  which is generally part of a control device  14 , which may be in the form of a CNC controller for example, generates a first desired variable x soll  which is in the form of a desired position variable within the scope of the exemplary embodiment according to  FIG. 1  and indicates the desired position of the machine element  8  with respect to the machine bed  35 . The first desired variable x soll  is supplied, as a controlled desired variable for regulating the first movement component of the machine element  8 , to a first regulating means  16   a . The first actual variable x c,ist  which is measured using a first measuring device  10  and indicates the position of the column  6  with respect to the machine bed  35  within the scope of the exemplary embodiment according to  FIG. 1  is also supplied to the first regulating unit  16   a  as a controlled actual variable. The first actual variable x c,ist  indicates the first movement component of the machine element  8  by indicating the position of the column  6  with respect to the machine bed  35  within the scope of the exemplary embodiment according to  FIG. 1 . 
         [0010]    The first regulating means  16   a  drives a first power converter  17   a , which is illustrated by an arrow  18   a  in  FIG. 2 , in accordance with the first desired variable x soll  and the first actual variable x c,ist . The first desired variable x soll  is the controlled desired variable for regulating the first movement component of the machine element  8 . The first power converter  17   a  accordingly drives the two linear motors  3  and  4 , which is illustrated by an arrow  19   a , the linear motors  3  and  4  moving a load  19 . In this case, the load  19  comprises all elements which are moved by the linear motors  3  and  4  in the direction X. The first regulating means  16   a , the first power converter  17   a , the linear motors  3  and  4 , the load  19  and the measuring device  10  form a first drive shaft  20   a  which is used to carry out the first movement component of the machine element  8 . 
         [0011]    In order to regulate the second movement component of the machine element  8 , the so-called contouring error s is determined in the prior art by subtracting the first actual variable x c,ist  from the first desired variable x soll  using a subtractor  22 . The contouring error s is supplied, as a controlled desired variable for regulating the second movement component of the machine element  8 , to a second regulating means  16   b . The second actual variable x f,ist  which is measured using a second measuring device  11  and indicates the position of the machine element  8  with respect to the column  6  within the scope of the exemplary embodiment according to  FIG. 1  is also supplied to the second regulating unit  16   b  as a controlled actual variable. The second actual variable x f,ist  indicates the second movement component of the machine element  8  by indicating the position of the machine element  8  with respect to the column  6  within the scope of the exemplary embodiment according to  FIG. 1 . 
         [0012]    The second regulating means  16   b  drives a second power converter  17   b , which is illustrated by an arrow  18   b  in  FIG. 2 , in accordance with the contouring error s and the second actual variable x f,ist . The second power converter  17   b  accordingly drives the linear motor  7 , which is illustrated by an arrow  19   b , the linear motor  7  moving a load  21 . In this case, the load  21  comprises all elements which are moved by the linear motor  7  in the direction X. The second regulating means  16   b , the second power converter  17   b , the linear motor  7 , the load  21  and the measuring device  11  form a second drive shaft  20   b  which is used to carry out the second movement component of the machine element  8 . 
         [0013]    It is noted at this point that the desired variable generating unit  15  likewise generates corresponding desired values for controlling the movement of the drive shafts which are used to move the machine element in the Y and Z directions. These desired values and the drive shafts which are used to move the machine element in the Y and Z directions are not illustrated in  FIG. 2  and the subsequent figures for the sake of clarity and since they are irrelevant to understanding the invention. 
         [0014]      FIG. 3  again illustrates the drive system shown in  FIG. 2  in a simplified manner in the form of a block function diagram. In this case, the same elements are provided with the same reference symbols as in  FIG. 2 . In this case, the first drive shaft  20   a  has a transfer function G(s) and the second drive shaft  20   b  has a transfer function F(s). The overall position x ist  of the machine element  8 , that is to say its position with respect to the machine bed  35  (see  FIG. 1 ), results from adding the first actual variable x c,ist  and the second actual variable x f,ist . 
         [0015]      FIG. 4  illustrates another drive system which is known from the prior art, in which a movement is divided into a first movement component and a second movement component. The embodiment according to  FIG. 4  is identical to the embodiment according to  FIG. 2  insofar as it relates to the first drive shaft  20   a  and the second drive shaft  20   b . In  FIG. 4 , the same elements are therefore provided with the same reference symbols as in  FIG. 2 . The fundamental difference in the embodiment according to  FIG. 4  is that the control device  14 ′ has been extended by a dividing unit  23  in comparison with the control device  14  according to  FIG. 2 . The desired variable generating unit  15  generates a desired variable x′ soll , which corresponds to the first desired variable x soll  according to  FIG. 2 . The dividing unit  23  uses the desired variable x′ soll  to determine a first desired variable x c,soll , which is supplied to the regulating means  16   a  as a controlled desired variable, and a second desired variable x f,soll  which is supplied to the regulating means  16   b  as a controlled desired variable. 
         [0016]      FIG. 5  again illustrates the control device  14 ′ and, in particular, the dividing unit  23  in detail, the same elements in  FIG. 5  being provided with the same reference symbols as in  FIG. 4 . In order to divide the movement, the desired variable x′ soll  is filtered using a low-pass filter  24  and the first desired variable x c,soll  for the first drive shaft  20   a  is generated in this manner. The first desired variable x c,soll  is subtracted from the desired variable x′ soll  using a subtractor  26  and the second desired variable x f,soll  for the second drive shaft  20   b  is generated in this manner. 
         [0017]      FIG. 6  illustrates another implementation of the dividing unit, which is known from the prior art, in the form of the dividing unit  23 ′. In  FIG. 6 , the same elements are provided with the same reference symbols as in  FIG. 5 . The embodiment according to  FIG. 6  differs from the embodiment according to  FIG. 5  only in that, in order to compensate for the temporal delay in the desired variable x c,soll , as caused by the low-pass filter  24 , the desired variable x′ soll  is delayed by a particular time using a delay unit  25  before it is supplied to the subtractor  26  as an input variable. 
         [0018]      FIG. 7  again illustrates the drive system shown in  FIG. 6  in a simplified manner. In this case, the same elements are provided with the same reference symbols as in  FIG. 6 . In this case, the first drive shaft  20   a  has a transfer function G(s) and the second drive shaft  20   b  has a transfer function F(s). The overall position x ist  of the machine element  8 , that is to say its position with respect to the machine bed  35 , results from adding the first actual variable x c,ist  and the second actual variable x f,ist . 
         [0019]    With conventional methods, the overall dynamics of the machine are determined by the regulating dynamics of the sluggish first drive shaft (coarse drive shaft). The potential of the dynamic second drive shaft (fine drive shaft) is thus not fully exploited. 
         [0020]    Relatively large contour errors also generally occur in the known movement dividing methods. Overshooting when the desired variable changes rapidly and contour expansion in the case of circular contours to be traced by the machine element often occur in the known methods, for example. 
         [0021]    An egg-shaped contour thus results from a circular contour to be traced by the machine element, for example. 
         [0022]    It would therefore be desirable and advantageous to provide an improved to obviate prior art shortcomings and to move a machine element of an automation machine having redundant kinematics, during which contour errors of a contour to be traced by the machine element are reduced. 
         [0023]    The contour error is here the difference between a predefined desired contour and the actual contour actually traced by the machine element. 
         [0024]    The invention also makes it possible to increase the dynamics of the movement of the machine element. 
       SUMMARY OF THE INVENTION 
       [0025]    According to one aspect of the present invention, a method for moving a machine element of an automation machine having a first drive shaft performing a first movement component and a second drive shaft performing a second movement component, wherein the first and second movement components have a common direction and are controlled by separate first and second controllers, includes the steps of supplying to the first controller as a desired control variable a first desired value, supplying to the first controller as an actual control variable a first actual value representing the first movement component, and filtering the first desired variable using a filter having a frequency-dependent transfer function to generate a filtered first desired variable. 
         [0026]    According to one embodiment of the method, the first desired variable represents an overall movement, which is composed of the first and second movement components, and a difference is determined between the filtered first desired variable and the first actual variable, and the difference is supplied to the second controller as a desired control variable for controlling the second movement component. 
         [0027]    According to another embodiment of the method, the first desired variable represents the first movement component, and the filtered first desired variable and a second desired variable are added to form a sum, and a difference between the formed sum and the first actual variable are supplied to the second controller as a desired control variable for controlling the second movement component. 
         [0028]    According to another aspect of the invention, a drive system for moving a machine element of an automation machine includes a first drive shaft moving the machine element with a first movement component and a second drive shaft moving the machine element with a second movement component in a common direction relative to the first movement component. The drive system further includes a first controller controlling movement of the first drive shaft and a second controller controlling movement of the second drive shaft, wherein the first controller receives a first desired variable and a first actual value representing the first movement component as an actual control variable, and a filter having a frequency-dependent transfer function filtering the first desired variable and generating a filtered first desired variable. 
         [0029]    According to one embodiment of the drive system, the first desired variable represents an overall movement, which is composed of the first and second movement components, and a subtractor forms a difference between the filtered first desired variable and the first actual variable and supplies the difference to the second controller as a desired control variable for controlling the second movement component of the second drive shaft. 
         [0030]    According to another embodiment of the drive system, the first desired variable represents the first movement component, an adder adds the filtered first desired variable and a second desired variable to form a sum; and a subtractor then forms the difference between the sum and the first actual variable and supplies the difference to the second controller as a desired control variable for controlling the second movement component of the second drive shaft. 
         [0031]    Advantageously, the frequency-dependent transfer function V(s) of the filter may be for all intents and purposes 
         [0000]    
       
         
           
             
               
                 V 
                  
                 
                   ( 
                   s 
                   ) 
                 
               
               = 
               
                 1 
                 + 
                 
                   G 
                    
                   
                     ( 
                     s 
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                     G 
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                       ( 
                       s 
                       ) 
                     
                   
                   
                     F 
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             , 
           
         
       
     
         [0000]    wherein G(s) is the transfer function of the first drive shaft and F(s) is the transfer function of the second drive shaft and 
         [0000]        s=j· 2·π· f+σ,  
 
         [0000]    wherein f is the frequency and j is the imaginary unit and σ is the real part of s, since contour errors which then occur are particularly small. 
         [0032]    The automation machine may be in the form of a machine tool, which typically requires a high degree of precision in the movement of machine elements. However, the invention may also be used in other types of automation machines. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0033]    Other features and advantages of the present invention will be more readily apparent upon reading the following description of currently preferred exemplified embodiments of the invention with reference to the accompanying drawing, in which: 
           [0034]      FIG. 1  shows a schematically illustrated known machine tool, 
           [0035]      FIG. 2  shows a drive system which is known to be commercially available, 
           [0036]      FIG. 3  shows a known drive system which is illustrated in a simplified manner in the form of a block function diagram, 
           [0037]      FIG. 4  shows another drive system which is known to be commercially available, 
           [0038]      FIG. 5  shows a known control device, 
           [0039]      FIG. 6  shows another known control device, 
           [0040]      FIG. 7  shows another known drive system which is illustrated in a simplified manner, 
           [0041]      FIG. 8  shows a first embodiment of a drive system according to the invention, 
           [0042]      FIG. 9  shows a block function diagram of the first embodiment of a drive system according to the invention, 
           [0043]      FIG. 10  shows a second embodiment of a drive system according to the invention, 
           [0044]      FIG. 11  shows a block function diagram of the second embodiment of a drive system according to the invention, 
           [0045]      FIG. 12  shows a block diagram showing the regulation of the first drive shaft, and 
           [0046]      FIG. 13  shows a block diagram showing the regulation of the second drive shaft. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0047]    Throughout all the figures, same or corresponding elements may generally be indicated by same reference numerals. These depicted embodiments are to be understood as illustrative of the invention and not as limiting in any way. It should also be understood that the figures are not necessarily to scale and that the embodiments are sometimes illustrated by graphic symbols, phantom lines, diagrammatic representations and fragmentary views. In certain instances, details which are not necessary for an understanding of the present invention or which render other details difficult to perceive may have been omitted. 
         [0048]    Turning now to the drawing, and in particular to  FIG. 8 , there is shown a schematic block illustration of a first exemplary embodiment of the drive system according to the invention. In this case, the drive system according to the invention shown in  FIG. 8  corresponds to the drive system known from the prior art according to  FIG. 2 , but a filter  27  having a frequency-dependent transfer function V(s) has been inserted according to the invention. In  FIG. 8 , the same elements are provided with the same reference symbols as in  FIG. 2 . According to the invention, the first desired variable x soll  is filtered using the filter  27  and a filtered first desired variable x sollg  is determined in this manner. The difference d between the filtered first desired variable x sollg  and the first actual variable x c,ist  is then determined by subtracting the first actual variable x c,ist  from the filtered first desired variable x sollg  using the subtractor  22 . The difference d is supplied, as a controlled desired variable for regulating the movement of the second movement component of the machine element  8 , to the second regulating means  16   b.    
         [0049]      FIG. 9  illustrates the block function diagram associated with  FIG. 8 . In this case, the first drive shaft  20   a  has the transfer function G(s) and the second drive shaft  20   b  has the transfer function F(s). The filter  27  has the transfer function V(s). The reference symbols correspond to the elements illustrated in  FIG. 8 . 
         [0050]    Temporal variables are designated using lower-case letters within the scope of this application. The Laplace transforms of the temporal variables are each represented with a capital letter below, that is to say the Laplace transform X(s) accordingly results from the variable x(t) which is dependent on time t: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    where 
         [0000]        s=j· 2 ·π·f+σ   (2),
 
         [0000]    where f is the frequency and j is the imaginary unit and σ is the real part of s. 
         [0051]    The transfer function H(s) of the drive system according to the invention shown in  FIG. 9  is thus 
         [0000]    
       
         
           
             
               
                 
                   
                     H 
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         [0052]    A particularly great reduction in the contour errors can be achieved if the transfer function of the filter  27  is selected to be: 
         [0000]    
       
         
           
             
               
                 
                   
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         [0053]    When equation (4) is inserted into equation (3), the transfer function H(s) of the drive system is then 
         [0000]        H ( s )= F ( s )  (5),
 
         [0000]    that is to say the machine element  8  is moved using the dynamics of the second drive shaft  20   b  and the non-dynamic drive shaft, that is to say the sluggish drive shaft  20   a , is apparently no longer present in terms of regulation. If the transfer functions G(s) and F(s) are causal, which is practically always the case, there is always a transfer function V(s) which can be achieved. 
         [0054]      FIG. 12  illustrates a block diagram showing the regulation of the first drive shaft  20   a . Within the scope of the exemplary embodiment, the regulating means  16   a  has a position regulator  30   a  and a speed regulator  31   a  in this case. The first power converter  17   a  as well as the two linear motors  3  and  4  and the load  19  are simulated using a simulation function block  33   a . The first actual variable x c,ist  is differentiated with respect to time t using the differentiator  32   a  and a first actual speed v c,ist  is calculated in this manner. The round symbols illustrated in  FIG. 12  are each subtractors which subtract one output variable from the other and output the difference. The functions indicated in function blocks (square boxes) are the transfer functions of the function blocks. 
         [0055]    In this case, the index c denotes that it is a parameter of the first drive shaft  20   a . The index c may be superscript or subscript in this case. 
         [0056]    Within the scope of the exemplary embodiment, the following thus results for the transfer function G(s) of the first drive shaft  20   a   
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
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                                         T 
                                         ers 
                                         c 
                                       
                                        
                                       
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                                         c 
                                       
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                                         c 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         , 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
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         [0000]    where
 
Kv c  is the regulating gain of the position regulator
 
Kr c  is the regulating gain of the speed regulator
 
T c  is the integration time constant of the speed regulator
 
T ers   c  is the equivalent time constant of the current control loop
 
T m   c  is the mechanical time constant.
 
         [0057]      FIG. 13  illustrates a block diagram showing the regulation of the second drive shaft  20   b . Within the scope of the exemplary embodiment, the regulating means  16   b  has a position regulator  30   b  and a speed regulator  31   b  in this case. The second power converter  17   b  as well as the linear motor  7  and the load  19  are simulated using a simulation function block  33   b . The second actual variable x f,ist  is differentiated with respect to time t using the differentiator  32   b  and a second actual speed v f,ist  is calculated in this manner. The round symbols illustrated in  FIG. 13  are each subtractors which subtract one output variable from the other and output the difference. The functions indicated in function blocks (square boxes) are the transfer functions of the function blocks. 
         [0058]    In this case, the index f denotes that it is a parameter of the second drive shaft  20   b . The index f may be superscript or subscript in this case. 
         [0059]    Within the scope of the exemplary embodiment, the following thus results for the transfer function F(s) of the second drive shaft  20   b   
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           F 
                            
                           
                             ( 
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                                           K 
                                            
                                           
                                               
                                           
                                            
                                           
                                             v 
                                             f 
                                           
                                         
                                       
                                     
                                     + 
                                     
                                       
                                         s 
                                         2 
                                       
                                        
                                       
                                         1 
                                         
                                           K 
                                            
                                           
                                               
                                           
                                            
                                           
                                             v 
                                             f 
                                           
                                         
                                       
                                        
                                       K 
                                        
                                       
                                           
                                       
                                        
                                       
                                         r 
                                         f 
                                       
                                        
                                       
                                         τ 
                                         f 
                                       
                                     
                                     + 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         s 
                                         3 
                                       
                                        
                                       
                                         1 
                                         
                                           K 
                                            
                                           
                                               
                                           
                                            
                                           
                                             v 
                                             f 
                                           
                                         
                                       
                                        
                                       
                                         τ 
                                         f 
                                       
                                        
                                       
                                         T 
                                         m 
                                         f 
                                       
                                     
                                     + 
                                     
                                       
                                         s 
                                         4 
                                       
                                        
                                       
                                         1 
                                         
                                           K 
                                            
                                           
                                               
                                           
                                            
                                           
                                             v 
                                             f 
                                           
                                         
                                       
                                        
                                       
                                         T 
                                         ers 
                                         f 
                                       
                                        
                                       
                                         τ 
                                         f 
                                       
                                        
                                       
                                         T 
                                         m 
                                         f 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                         , 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where
 
Kv f  is the regulating gain of the position regulator
 
Kr f  is the regulating gain of the speed regulator
 
T f  is the integration time constant of the speed regulator
 
T ers   f  is the equivalent time constant of the current control loop
 
T m   f  is the mechanical time constant
 
D(s) is the Laplace transform of the difference d (see  FIG. 8  and  FIG. 9 ).
 
         [0060]    By inserting equation (6) and equation (7) into equation (4), the transfer function V(s) of the filter  27  is thus: 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                      
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               1 
                               + 
                               
                                 s 
                                  
                                 
                                   ( 
                                   
                                     
                                       1 
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           c 
                                         
                                       
                                     
                                     - 
                                     
                                       1 
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           f 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   s 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           r 
                                           c 
                                         
                                          
                                         
                                           τ 
                                           c 
                                         
                                       
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           c 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           r 
                                           f 
                                         
                                          
                                         
                                           τ 
                                           f 
                                         
                                       
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           f 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   s 
                                   3 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         
                                           τ 
                                           c 
                                         
                                          
                                         
                                           T 
                                           m 
                                           c 
                                         
                                       
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           c 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           τ 
                                           f 
                                         
                                          
                                         
                                           T 
                                           m 
                                           f 
                                         
                                       
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           f 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   s 
                                   4 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         
                                           T 
                                           erc 
                                           c 
                                         
                                          
                                         
                                           τ 
                                           c 
                                         
                                          
                                         T 
                                       
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           c 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           T 
                                           erc 
                                           f 
                                         
                                          
                                         
                                           τ 
                                           f 
                                         
                                          
                                         T 
                                       
                                       
                                         K 
                                          
                                         
                                             
                                         
                                          
                                         
                                           v 
                                           f 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       
                         1 
                         + 
                         
                           s 
                            
                           
                             1 
                             
                               K 
                                
                               
                                   
                               
                                
                               
                                 v 
                                 c 
                               
                             
                           
                         
                         + 
                         
                           
                             s 
                             2 
                           
                            
                           
                             
                               K 
                                
                               
                                   
                               
                                
                               
                                 r 
                                 c 
                               
                                
                               
                                 τ 
                                 c 
                               
                             
                             
                               K 
                                
                               
                                   
                               
                                
                               
                                 v 
                                 c 
                               
                             
                           
                         
                         + 
                         
                           
                             s 
                             3 
                           
                            
                           
                             
                               
                                 τ 
                                 c 
                               
                                
                               
                                 T 
                                 m 
                                 c 
                               
                             
                             
                               K 
                                
                               
                                   
                               
                                
                               
                                 v 
                                 c 
                               
                             
                           
                         
                         + 
                         
                           
                             s 
                             4 
                           
                            
                           
                             
                               
                                 T 
                                 erc 
                                 c 
                               
                                
                               
                                 τ 
                                 c 
                               
                                
                               
                                 T 
                                 m 
                                 c 
                               
                             
                             
                               K 
                                
                               
                                   
                               
                                
                               
                                 v 
                                 c 
                               
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0061]    The transfer function V(s) can be achieved. 
         [0062]    As seen from equation (8), it is easy to parameterize the filter. 
         [0063]    An effective or very effective filter results depending on how accurately the transfer functions G(s) and F(s), which indicate the transfer response of the respectively associated drive shaft, are set up, with the result that a considerable or very considerable reduction in contour errors is achieved by the invention. If the quadratic and higher-order terms in equation (8) are disregarded, the transfer function V(s) of the filter is 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                      
                     
                       ( 
                       s 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         1 
                         + 
                         
                           s 
                            
                           
                             ( 
                             
                               
                                 1 
                                 
                                   K 
                                    
                                   
                                       
                                   
                                    
                                   
                                     v 
                                     c 
                                   
                                 
                               
                               - 
                               
                                 1 
                                 
                                   K 
                                    
                                   
                                       
                                   
                                    
                                   
                                     v 
                                     f 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                       
                         1 
                         + 
                         
                           s 
                            
                           
                             1 
                             
                               K 
                                
                               
                                   
                               
                                
                               
                                 v 
                                 c 
                               
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0064]    It has been shown that, even if the transfer function of the filter in the simplified form according to equation (9) is selected, there is still a very considerable reduction in contour errors. 
         [0065]    The inverse Laplace transform ( 10 ) is defined as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       x 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             L 
                             
                               - 
                               1 
                             
                           
                            
                           
                             [ 
                             
                               X 
                                
                               
                                 ( 
                                 s 
                                 ) 
                               
                             
                             ] 
                           
                         
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                       := 
                       
                         
                           1 
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             j 
                           
                         
                          
                         
                           ∮ 
                           
                             
                               X 
                                
                               
                                 ( 
                                 s 
                                 ) 
                               
                             
                              
                             
                               e 
                               st 
                             
                              
                             
                                
                               s 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     t 
                     &gt; 
                     0. 
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0066]    The so-called convolution rule of the Laplace transform is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       L 
                       
                         - 
                         1 
                       
                     
                      
                     
                       [ 
                       
                         
                           X 
                            
                           
                             ( 
                             s 
                             ) 
                           
                         
                         · 
                         
                           Y 
                            
                           
                             ( 
                             s 
                             ) 
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     
                       
                         x 
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                       * 
                       
                         y 
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         ∫ 
                         0 
                         t 
                       
                        
                       
                         
                           
                             x 
                              
                             
                               ( 
                               
                                 t 
                                 - 
                                 τ 
                               
                               ) 
                             
                           
                           · 
                           
                             y 
                              
                             
                               ( 
                               τ 
                               ) 
                             
                           
                         
                          
                         
                             
                         
                          
                         
                           
                              
                             τ 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0067]    With the aid of equations (10) and (11), the filtered first desired variable x sollg  is thus 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             x 
                             
                               soll 
                                
                               
                                   
                               
                                
                               g 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   X 
                                   
                                     soll 
                                      
                                     
                                         
                                     
                                      
                                     g 
                                   
                                 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   V 
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                 · 
                                 
                                   
                                     X 
                                     soll 
                                   
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 V 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                           * 
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   X 
                                   soll 
                                 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 L 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 [ 
                                 
                                   V 
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                             * 
                             
                               
                                 x 
                                 soll 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         , 
                         
                           t 
                           &gt; 
                           0. 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0068]      FIG. 10  illustrates a schematic block illustration of a second exemplary embodiment of the drive system according to the invention. In this case, the drive system according to the invention shown in  FIG. 10  corresponds to the drive system known from the prior art according to  FIG. 4 , but a filter  27  having a frequency-dependent transfer function V(s) has been inserted according to the invention. In  FIG. 10 , the same elements are provided with the same reference symbols as in  FIG. 4 . According to the invention, the first desired variable x c,soll  is filtered using the filter  27  and a filtered first desired variable x c,sollg  is determined in this manner. 
         [0069]    The sum of the filtered first desired variable x c,sollg  and a second desired variable x f,soll  is then determined and a sum variable sg is determined in this manner. The difference d′ between the sum variable sg and the first actual variable x c,ist  is then determined by subtracting the first actual variable x c,ist  from the sum variable sg. The difference d′ is supplied, as a controlled desired variable for regulating the second movement component, to the second regulating means  16   b.    
         [0070]      FIG. 11  illustrates the block function diagram associated with  FIG. 10 . In this case, the first drive shaft  20   a  has the transfer function G(s) and the second drive shaft  20   b  has the transfer function F(s). The filter  27  has the transfer function V(s). The reference symbols correspond to the elements illustrated in  FIG. 8 . 
         [0071]    Equations (1), (2), (4) and (6) to (9) and the above relevant description relating to the first exemplary embodiment correspondingly apply to the transfer functions G(s), H(s) and to the transfer function V(s) of the filter  27  of the second exemplary embodiment, with the result that at this point reference is made to the description relating to the first exemplary embodiment, in which case x soll (s) should be replaced with x c,soll (s) in equation (6) and D(s) should be replaced with D′(s) in equation (7). D′(s) is the Laplace transform of the difference d′ (see  FIG. 10  and  FIG. 11 ). The transfer function V(s) of the filter  27  according to  FIG. 10  and  FIG. 11  (second exemplary embodiment) corresponds to the transfer function V(s) of the filter  27  according to  FIG. 8  and  FIG. 9  (first exemplary embodiment). 
         [0072]    In accordance with equations (10) and (11), the filtered first desired variable x c,sollg  in the second exemplary embodiment is thus: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             x 
                             
                               c 
                               , 
                               
                                 soll 
                                  
                                 
                                     
                                 
                                  
                                 g 
                               
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   X 
                                   
                                     c 
                                     , 
                                     
                                       soll 
                                        
                                       
                                           
                                       
                                        
                                       g 
                                     
                                   
                                 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   V 
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                 · 
                                 
                                   
                                     X 
                                     
                                       c 
                                       , 
                                       soll 
                                     
                                   
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 V 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                           * 
                           
                             
                               L 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               [ 
                               
                                 
                                   X 
                                   
                                     c 
                                     , 
                                     soll 
                                   
                                 
                                  
                                 
                                   ( 
                                   s 
                                   ) 
                                 
                               
                               ] 
                             
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 L 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 [ 
                                 
                                   V 
                                    
                                   
                                     ( 
                                     s 
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                             * 
                             
                               
                                 x 
                                 
                                   c 
                                   , 
                                   soll 
                                 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                         , 
                         
                           t 
                           &gt; 
                           0. 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0073]    It is noted at this point that the first regulating means  16   a , the second regulating means  16   b , the subtractor  22  and the adder  28  are generally in the form of executable software code which is executed by a single processor or a plurality of processors. In this case, the processors can be physically arranged in an individual component or in different components of the drive system. 
         [0074]    It is also noted at this point that the mathematical derivations cited above were set up for the very general continuous-time case. For the special case of discrete-time systems, the general continuous transfer function V(s) of the filter changes into the discrete-time transfer function V(z=e sT ), where T is the sampling time. 
         [0075]    While the invention has been illustrated and described in connection with currently preferred embodiments shown and described in detail, it is not intended to be limited to the details shown since various modifications and structural changes may be made without departing in any way from the spirit and scope of the present invention. The embodiments were chosen and described in order to explain the principles of the invention and practical application to thereby enable a person skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated.