Patent Publication Number: US-2022214305-A1

Title: Method and device for determining an internal resistance of a sensor element

Description:
CROSS REFERENCE 
     The present application claims the benefit under 35 U.S.C. § 119 of German Patent Application No. DE 102021200004.5 filed on Jan. 4, 2021, which is expressly incorporated herein by reference in its entirety. 
     FIELD 
     The present invention relates to a method for determining an internal resistance of a sensor element, and to a computer program. 
     BACKGROUND INFORMATION 
     PCT Patent Application No. WO 2016/173814 A1 describes a method for determining an internal resistance of a sensor element ( 110 ) for acquiring a portion of a gas component from a gas mixture in a measurement gas space, which is intended to enable a determination that is as accurate as possible of the internal resistance of the sensor element ( 110 ). The sensor element ( 110 ) has at least one cell ( 114 ), the cell ( 114 ) having at least one first electrode ( 116 ), at least one second electrode ( 118 ), and at least one solid electrolyte ( 120 ) that connects the first electrode ( 116 ) and the second electrode ( 118 ), an electrical voltage ( 124 ) being present between the first electrode ( 116 ) and the second electrode ( 118 ). 
     SUMMARY 
     The present invention relates to a method for determining an internal resistance of a sensor element. In addition, the present invention relates to a computer program that is set up to carry out one of the methods. 
     In a first aspect of the present invention, a method is provided for ascertaining an internal resistance of a sensor element for acquiring a gas component from a gas mixture in a measurement gas space, the sensor element having at least one cell, the cell having at least one first electrode, at least one second electrode, connecting solid electrolytes, an electrical voltage being measurable between the first and the second electrode, the method including the following steps:
         ascertaining a reference voltage between the first electrode and the second electrode,   impressing a first current pulse with a first current using a pulse-generating unit at a first time,
 
the first current pulse bringing about a charge shift in the sensor element,
 
the occurrence of the charge shift causing an increase in the electrical voltage between the first electrode and the second electrode,
   ascertaining at least two voltage values at two different times, after an elapsing of a first specifiable settling time after the first time, between the first electrode and the second electrode,   ending the first current pulse and impressing an opposite second current pulse with a second current at a second time, the opposite second current pulse causing a depolarization between the first electrode and the second electrode, as well as a charge shift,   ending the second current pulse at a third time,   ascertaining a linear equation as a function of the at least two voltage values and times,   extrapolation of a voltage value at the first time using the linear equation,   ascertaining an internal resistance of the sensor element as a function of the extrapolated voltage value and of the reference voltage and of the first current of the first current pulse.       

     The method in accordance with the present invention has the particular advantage that the polarization-dependent portion of the voltage increase is assumed as linear. Consequently, from the time curve, assumed as linear, of the voltage applied to the cell during the charge shift the polarization-dependent portion of the increase can be extrapolated in linear fashion. The value ascertained in this way for the polarization-dependent portion of the increase of the electrical voltage in the cell can, as described above, consequently be used for the more accurate determination of the value of the internal resistance of the sensor element. 
     The value ascertained by this method for the polarization-dependent portion of the increase of the electrical voltage in the cell can, as described above, consequently be used for the more precise ascertaining of the value for the internal resistance of the sensor element. 
     The method according to the present invention is in addition advantageous because a linear extrapolation is easy to program, and is implemented in a manner that saves resources for calculation for the control device. 
     Consequently, by the more precise ascertaining of the internal resistance of the sensor element, a more precise temperature can be ascertained for the sensor element, so that a more accurate thermal management for the sensor element can be carried out. 
     A further advantage is that the first and the second current pulse can be kept short, because only two measurement values have to be carried out during the voltage curve, assumed as linear. Thus, the probe can be reused more quickly for measurement of the oxygen concentration of the exhaust gas. 
     In a second variant of the present invention, a method is proposed for ascertaining an internal resistance of a sensor element for acquiring a gas component from a gas mixture in a measurement gas space, the sensor element having at least one cell, the cell including at least one first electrode, at least one second electrode, and connecting solid electrolytes, such that an electrical voltage is measurable between the first and the second electrode, the method including the following steps:
         ascertaining a reference voltage between the first electrode and the second electrode,   impressing a first current pulse with the first current using a pulse generating unit at a first time,
 
the first current pulse bringing about a charge shift in the sensor element,
 
the occurrence of the charge shift causing an increase in the electrical voltage between the first electrode and the second electrode,
   ascertaining at least one voltage value between the first electrode and the second electrode at a time after an elapsing of a first settling time after the first time,   ending the first current pulse and impressing an opposite second current pulse with a second current at a second time, the opposite second current pulse causing a depolarization between the first electrode and the second electrode as well as a charge shift,   ascertaining at least two voltage values between the first electrode and the second electrode at two different times after an elapsing of a second specifiable settling time after the second time,   ending the second current pulse at a third time,   ascertaining a second slope of a straight line through the at least two voltage values at two different times,   ascertaining a voltage value at the first time as a function of the first and of the second current and of the ascertained second slope,   ascertaining the internal resistance of the sensor element as a function of the ascertained voltage value and of the reference voltage and of the first current of the first current pulse.       

     The value ascertained by this example method for the polarization-dependent portion of the increase of the electrical voltage in the cell can, as described above, consequently be used for the more precise ascertaining of the value for the internal resistance of the sensor element. 
     The method in accordance with the present invention is further advantageous because the calculation in the control device, through the voltage curve assumed as linear, is easy to program and can be realized in a manner that saves resources. 
     Consequently, using the more precise ascertaining of the internal resistance of the sensor element, a more precise temperature for the sensor element can be ascertained, so that a more accurate thermal management for the sensor element can be carried out. 
     Through the inclusion of the polarization portion, assumed as linear, of the voltage during the opposite current pulse, a further increase of the precision for ascertaining the internal resistance can be achieved. 
     In a third variant of the present invention, a method is provided for ascertaining an internal resistance of a sensor element for acquiring a gas component from a gas mixture in a measurement gas space, the sensor element having at least one cell, the cell including at least one first electrode, at least one second electrode, and a connecting solid electrolyte, an electrical voltage being measurable between the first and the second electrode, the method including the following steps:
         ascertaining at least two voltage values during a first time duration, starting at the time and ending at a time, preferably having a time duration of 10 ms, between the first electrode and the second electrode,   ascertaining a third slope as a function of the ascertained at least two voltage values during a first time duration,   impressing a first current pulse with a first current using a pulse-generating unit at a first time,
 
the first current pulse causing a charge shift in the sensor element,
 
the occurrence of the charge shift causing an increase in the electrical voltage between the first electrode and the second electrode,
   ascertaining at least one voltage value between the first electrode and the second electrode at a time after an elapsing of a first settling time after the first time,   ending the first current pulse and impressing an opposite second current pulse having a second current at a second time, the opposite second current pulse causing a depolarization between the first electrode and the second electrode, as well as a charge shift,   ascertaining at least two voltage values between the first electrode and the second electrode at two different times after elapsing of a second specifiable settling time after the second time,   ending the second current pulse at a third time,   ascertaining a second slope of a straight line through the at least two voltage values at two different times,   ascertaining a voltage value at the first time as a function of the first and of the second current, of the ascertained second slope, and of a corrected slope,   ascertaining the internal resistance of the sensor element as a function of the ascertained voltage value and of the reference voltage and of the first current of the first current pulse.       

     The value ascertained by this example method for the polarization-dependent portion of the increase of the electrical voltage in the cell can, as described above, consequently be used for the more precise ascertaining of the value for the internal resistance of the sensor element. 
     The method in accordance with the present invention is further advantageous because the calculation in the control device, using the voltage curve assumed as linear, is easy to program and can be realized in a resource-saving manner. 
     Consequently, using the more precise ascertaining for the internal resistance of the sensor element, a more precise temperature can be ascertained for the sensor element, so that a more accurate thermal management for the sensor element can be carried out. 
     Through the inclusion of the polarization portion, assumed as linear, of the voltage during the opposite current pulse, a further increase of the precision for ascertaining the internal resistance can be achieved. The ascertaining and use of the third slope for ascertaining the internal resistance is done under the assumption that modifications of the oxygen concentration in the exhaust gas during a measurement cause a change in the voltage. This effect can thus easily influence the ascertaining of the internal resistance. 
     In addition, the specifiable first settling time and the second specifiable second settling time can be determined as a function of component properties of a low-pass filter. 
     In addition, the sensor element that is connected via a low-pass filter can, the low-pass filter being connected to a control device, the low-pass filter having associated time constants, a first time for the ascertaining of a first value for the increase of the electrical voltage being selected such that the first time corresponds at least to three times, preferably at least five times, the time constant of the low-pass filter. 
     In further aspects, the present invention relates to a device, in particular to a control device and to a computer program, that are set up, in particular programmed, to carry out one of the methods. In a still further aspect, the present invention relates to a machine-readable storage medium on which the computer program is stored. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following, the present invention is described in more detail with reference to the figures, and on the basis of exemplary embodiments. 
         FIG. 1  shows a schematic representation of an electrical wiring of a sensor element. 
         FIG. 2  shows a schematic representation of the time curve of the electrical voltage between the first electrode and the second electrode of the sensor element. 
         FIG. 3  shows a first example of a sequence of an exemplary embodiment of the method of the present invention, via a flow diagram. 
         FIG. 4  shows a second example of a sequence of an exemplary embodiment of the method of the present invention, via a flow diagram. 
         FIG. 5  shows a third example of a sequence of an exemplary embodiment of the method of the present invention, via a flow diagram. 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
       FIG. 1  schematically shows a sensor element  110  for acquiring a portion of a gas component from a gas mixture in a measurement gas space, as well as the associated electrical wiring  112 . Sensor element  110 , shown here as an example, has a cell  114  that has a first electrode  116 , a second electrode  118 , and a solid electrolyte  120  that connects the first electrode  116  and the second electrode  118 . 
     The two electrodes are preferably made of zirconium dioxide. In a preferred embodiment, the first electrode  116  is connected with the measurement gas space via a porous protective layer, while the second electrode  116  is situated in an electrode hollow space that is preferably charged with gas from the measurement gas space via at least one diffusion barrier. As described above, a fixed voltage is applied between the first electrode and the second electrode of the cell. As soon as an oxygen concentration in the electrode hollow space is close to 0, a Nernst potential increases strongly, and partly compensates the applied voltage. In this way, a constant oxygen concentration can be set in the electrode hollow space with a good degree of precision. Sensor element  110 , shown here as an example, has a cell  114  that has a first electrode  116 , a second electrode  118 , and a solid electrode  120  connecting the first electrode  116  and the second electrode  118 . By applying a current  122  to cell  114 , an electrical voltage  124  between first electrode  116  and second electrode  118  can be determined using a suitable voltage detection device. Sensor element  110  shown here additionally has a heating element  126  that can be operated using an associated heat control unit  128  in such a way that the temperature of sensor element  110  can thereby be set. 
     Using a pulse-generating unit  132 , a current pulse  130  can be applied to sensor element  110 , or to cell  114 . The charging of sensor element  110  with current pulse  130  causes an occurrence of a charge shift in sensor element  110  that is expressed as a measurable increase in the electrical voltage  124  in cell  114  between first electrode  116  and second electrode  118 . 
       FIG. 2  shows a time curve of the electrical voltage U of cell  114 . Initially, electrical voltage U of cell  114  is at a voltage value U start , or reference voltage U start . At a first time t 1 , a pulse-generating unit  132  impresses a first current pulse I pulse  having a current I 1 , or a current strength I 1 , onto cell  114  until a second time t 2 . During this time span Δt 12 , voltage U has both an ohmic portion U pulse  and a polarization-dependent portion P pulse . The polarization-dependent voltage curve can be regarded as approximately linear after about a first settling time τ 1  after the impressing of the first current pulse I pulse , i.e. starting from the time t 1 +τ 1 . At a second time t 2 &gt;t 1 +τ 1 , first current pulse I pulse  ends, and an opposite second current pulse I counterpulse , having a current I 2 , or a current strength I 2 , is carried out by pulse-generating unit  132  until third time t 3 . Here, “opposite” means that first current pulse I pulse  has a different sign from second current pulse I counterpulse , and the current strengths I 2  and I 2  can differ in their magnitude. The opposite second current pulse I counterpulse  provides a depolarization of cell  114 , and shows an opposite symmetrical curve for voltage U. That is, here as well an ohmic portion U counterpulse  and a polarization-dependent portion P counterpulse  can be recognized. 
     The polarization-dependent voltage curve can be regarded as linear after approximately a second settling time τ 2  after the impressing of the second current pulse I counterpulse , i.e. starting from the time t 2 +τ 2 . At third time t 3 &gt;t 2 +τ 2 , opposite second current pulse I counterpulse  ends and the voltage again assumes its initial voltage U start . 
     Using, for example, a linear approximation in the time intervals [t 1 +τ 1 ; t 2 ] and [t 2 +τ 2 ; t 3 ], the two polarization-adjusted voltage values U pulse (t 1 ) U counterpulse (t 2 ) can be ascertained by extrapolation at first time t 1  and at second time t 2 . Subsequently, through simple subtraction of the polarization-adjusted voltage values U pulse (t 1 ) U counterpulse (t 2 ) and the voltage value U start  ascertained initially, the internal resistance R of cell  114  can be ascertained. 
     The internal resistance R of cell  114  results as: 
     
       
         
           
             
               R 
               = 
               
                 
                   
                     U 
                     
                       pulse 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           1 
                         
                         ) 
                       
                     
                   
                   - 
                   
                     U 
                     start 
                   
                 
                 
                   I 
                   1 
                 
               
             
             ⁢ 
             
               
 
             
             ⁢ 
             
               R 
               = 
               
                 
                   
                     U 
                     
                       counterpulse 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           2 
                         
                         ) 
                       
                     
                   
                   - 
                   
                     U 
                     start 
                   
                 
                 
                   I 
                   2 
                 
               
             
           
         
       
     
       FIG. 3  shows the exemplary sequence of the method for determining an internal resistance R of a sensor element  110 . 
     In a first step  500 , using the measurement system shown in  FIG. 1 , the current voltage U start  of sensor element  110 , in particular of cell  114 , without additional current loading is determined. The ascertained voltage value U start  of sensor element  110  is here received by control device  100  and is later stored. 
     Alternatively or in addition, a plurality of measurements can be carried out for a specifiable time duration and a subsequent averaging over the ascertained voltage values. 
     Subsequently, the method is continued in a step  510 . 
     In a step  510 , using pulse-generating unit  132  an additional current I 1  is impressed onto sensor element  110 , in particular onto cell  114 . The charging of sensor element  110  with first current pulse I pulse  brings about a charge shift in cell  114 , which causes an increase in the voltage in cell  114  between first electrode  116  and second electrode  118 . 
     The impressing of the first current pulse I pulse  takes place at a first time t 1  and ends at a second time t 2 ; that is, first current pulse I pulse  has a specifiable time duration Δt 12 =t 2  t 1 . 
     Specifiable time duration Δt 12  is preferably selected as a function of the component of the low-pass filter (ADC). This can be carried out for example in an application phase. 
     Subsequently, the method is continued in a step  520 . 
     In a step  520 , at least two voltage measurement values U 1 , U 2  are measured at different times t U1  and t U2 . The measurement of the at least two voltage measurement values U 1 , U 2  is here first carried out when a first specifiable settling time τ 1 &lt;Δt 12 , which is preferably selected as a function of the low-pass filter (ADC) that is used, has elapsed. This can be carried out for example in an application phase. The measurement is first carried out at the beginning of the first current pulse I pulse , started in step  510 , and is carried out after the elapsing of the first settling time τ 1 , i.e. after a time duration t meas =t 1 +τ 1 , so that t U1 ≥t meas , t U2 &gt;t U1 . The at least two measurement values U 1 , U 2 , the times t U1 , t U2  and the current I 1  of the first current pulse I pulse  are acquired and stored by control device  100  for this purpose. Subsequently, the method is continued in step  530 . 
     In step  530 , as a function of the at least two voltage measurement values U 1 , U 2  and the associated times t U1 , t U2 , a linear equation G 1  is ascertained, and subsequently, using linear extrapolation, the voltage value U pulse (t 1 ) at first time t 1  is ascertained and stored by control device  100 . Subsequently, the method is continued in step  540 . In an alternative specific embodiment, a plurality of measurements i=1, 2, . . . , n, with n∈ , as in step  520 , can be carried out with different current pulses. Subsequently, an averaging of the back-calculated voltage values Ū(t 1 )=Σ i=1   n U i (t 1 ) can be carried out. Subsequently, the method can be continued in step  540 , using the averaged voltage value. 
     In a step  540 , at second time t 2  pulse-generating unit  132  is used to impress a specifiable second current I counterpulse , in the direction opposite to first current pulse I pulse , onto sensor element  110 . In this way, a depolarization of sensor element  110 , or of cell  114 , takes place. The impressing of second current pulse I counterpulse  takes place at a second time t 2  and ends with a third time t 3 ; that is, second current pulse I counterpulse  has a specifiable time duration Δt 23 =t 3 −t 2 . With the ending of the second current pulse, i.e. at a third time t 3 , the method continues in step  550 . 
     In a step  550 , using control device  100  a subtraction is subsequently carried out between the voltage value U pulse (t 1 ) extrapolated in step  530  at first time t 1  and the voltage value U start  ascertained in step  500 . 
     Subsequently, from the ascertained voltage value U pulse =U pulse (t 1 )−U start  a corrected internal resistance R is ascertained for sensor element  100 , or cell  114 : 
     
       
         
           
             R 
             = 
             
               
                 U 
                 pulse 
               
               
                 I 
                 1 
               
             
           
         
       
     
     where U pulse  is the difference between the extrapolated voltage value U pulse (t 1 ), the current I 1 , and the ascertained voltage value U start . 
     Subsequently, the method can be started from the beginning, in step  500 , or can be ended. 
       FIG. 4  shows an alternative sequence for the method for determining an internal resistance of a sensor element  110 , in particular cell  114 . 
     In a first step  600 , using the measurement system shown in  FIG. 1  the current voltage U start  of sensor element  110 , in particular of cell  114 , without additional current loading is ascertained. The ascertained voltage value U start  of sensor element  110  is here received by control device  100  and is later stored. 
     Alternatively or in addition, it is also possible to carry out a plurality of measurements for a specifiable time duration and a subsequent averaging over the ascertained voltage values. 
     Subsequently, the method is continued in a step  610 . 
     In a step  610 , pulse-generating unit  132  is used to impress an additional current I 1  onto sensor element  110 , in particular onto cell  114 . The charging of sensor element  110  with the first current pulse I pulse  causes a charge shift in cell  114  that results in an increase of the voltage in cell  114  between first electrode  116  and second electrode  118 . 
     The impressing of first current pulse I pulse  takes place at a first time t 1  and ends at a second time t 2 ; i.e. first current pulse I pulse  has a specifiable time duration Δt 12 =t 2  t 1 . 
     The specifiable time duration Δt 12  is preferably selected as a function of the component of the low-pass filter (ADC). This can be carried out for example in an application phase. 
     Subsequently, the method is continued in a step  620 . 
     In a step  620 , at least one voltage measurement value U 1  is measured at time t U1 . The measurement of the at least one voltage measurement value U 1  is here first carried out when a first specifiable settling time τ 1 , which is preferably selected as a function of the low-pass filter (ADC) that is used, has elapsed. This can be carried out for example in an application phase. 
     The measurement is first carried out with the beginning of first current pulse I pulse , started in step  610 , and after the elapsing of the first settling time τ 1 &lt;Δt 12 , i.e. after the time t meas =t 1 +τ 1 , so that t U1 ≥t meas . The at least one measurement value U 1 , the at least one time t U1 , and current I 1  of the first current pulse I pulse  are acquired and stored by control device  100  for this purpose. It is assumed that the rise of voltage U starting at time t 1 +τ 1  is caused approximately solely by polarization effects. 
     Subsequently, the method is continued in step  630 . 
     In a step  630 , at second time t 2  pulse-generating unit  132  is used to impress a specifiable second current pulse I counterpulse , in the opposite direction to first current pulse I pulse , onto sensor element  110 . As a result, a depolarization of sensor element  110 , or of cell  114 , takes place. The impressing of the second current pulse I counterpulse  takes place at a second time t 2 , and ends at a third time t 3 , i.e. second current pulse I counterpulse  has a specifiable time duration Δt 23 =t 3 −t 2 . It is assumed that the rise of voltage U starting at time t 2 +τ 2  is caused approximately solely by polarization effects. Here, τ 2 &lt;Δt 23  is a specifiable second settling time. 
     The specifiable second settling time τ 2  and the specifiable time duration Δt 23 &gt;τ 2  are selected as a function of the installed low-pass filter (ADC). This can be carried out for example in an application phase. 
     Subsequently, the method is continued in step  640 . 
     In step  640 , after the elapsing of a second settling time τ 2  at least two voltage measurement values W 1 , W 2  are ascertained and stored by control device  100  at different times t W1  and t W2 . The measurement of the at least two voltage measurement values W 1 , W 2  is first carried out after the beginning of the second current pulse I counterpulse , started in step  630 , and after the elapsing of the second settling time τ 2 , i.e. at the earliest starting at a time t meas2 =t 2 +τ 2 , so that t W1 ≥t meas2 , t W2 &gt;t W1 . The at least two measurement values W 1 , W 2 , the corresponding at least two times t W1 , t W2 , and the current I 2  of second current pulse I counterpulse  are acquired and stored by control device  100  for this purpose. 
     Subsequently, the method is continued in step  650 . 
     In a step  650 , a linear equation G 2  having a second slope m counterpulse  is subsequently ascertained from the two voltage values W 1 , W 2  ascertained in step  640  and the associated times t W1 , t W2 . Here it is assumed that the curve of voltage U can be linearly approximated starting from time t 2 +τ 2 . 
     Subsequently, the method is continued in step  660 . 
     In a step  660 , as a function of the ascertained second slope m counterpulse  of the linear curve during the opposite second current pulse I counterpulse  and the ascertained currents I 1  of the first current pulse I pulse  and the [ . . . ] I 2  of the second current pulse I counterpulse , the first slope m pulse  of the polarization portion, assumed as linear, during the first current pulse I pulse  is ascertained as follows: 
     
       
         
           
             
               m 
               pulse 
             
             = 
             
               
                 m 
                 counterpulse 
               
               · 
               
                 ( 
                 
                   
                     I 
                     1 
                   
                   
                     I 
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     with m counterpulse  of the second slope of the voltage curve U, assumed as linear, or of straight lines G 2  during second current pulse I counterpulse , current I 1  during the first current pulse I pulse  and second current I 2  during second current pulse I counterpulse . 
     Subsequently, the method is continued in step  670 . 
     In a step  670 , using the first voltage value U 1  ascertained in step  620  and its time t U1 , the first slope m pulse , ascertained in step  660 , and first time t 1 , the extrapolated voltage value U pulse  (t 1 ) is ascertained. 
         U   pulse ( t   1 )= U   1 −( m   pulse *( t   U1   −t   1 ))
 
     Subsequently, the method is continued in step  680 . 
     In a step  680 , using control device  100  a subtraction is subsequently carried out between the extrapolated voltage value U pulse (t 1 ) and the voltage value U start  ascertained in step  600 . 
     Subsequently, from the ascertained voltage value U pulse =U pulse (t 1 )−U start  a corrected internal resistance R is ascertained for sensor element  110 , or for cell  114 : 
     
       
         
           
             
               R 
               = 
               
                 
                   U 
                   pulse 
                 
                 
                   I 
                   1 
                 
               
             
             , 
           
         
       
     
     with U pulse  the difference between the extrapolated voltage value U pulse (t 1 ) and the voltage value U start  ascertained in step  600 , the current I 1 , and the ascertained voltage value U start . 
     Subsequently, the method can be started from the beginning in step  600 , or can be ended. 
       FIG. 5  shows a third alternative sequence of the method for determining an internal resistance of a sensor element  110 , in particular of cell  114 . 
     In a first step  700 , using the measurement system shown in  FIG. 1  at least two specifiable voltage values U start,i  of sensor element  110 , in particular of cell  114 , without additional current loading are ascertained, with i=1, 2, . . . , n, n∈ . This takes place within a time duration Δ start  starting at a time t 0  and ending at a time t 1 . The time duration Δ start  can here be for example several milliseconds, preferably 10 ms. 
     Subsequently, as a function of the ascertained voltage values U start,i  and the associated times t start,i  a linear equation G 3  having a third slope m start  is ascertained. 
     Subsequently, the method is continued in a step  710 . 
     In a step  710 , pulse-generating unit  132  is used to impress an additional current I 1  onto sensor element  110 , in particular onto cell  114 . The charging of sensor element  110  with first current pulse I pulse  causes a charge shift in cell  114 , which causes an increase of the voltage in cell  114  between first electrode  116  and second electrode  118 . 
     The impressing of the first current pulse I pulse  takes place at a first time t 1  and ends at a second time t 2 ; i.e., the first current pulse I pulse  has a specifiable time duration Δt 12 =t 2 −t 1 . 
     The specifiable time duration Δt 12  is preferably selected as a function of the component of the low-pass filter (ADC). This can be carried out for example in an application phase. 
     Subsequently, the method is continued in a step  720 . 
     In a step  720 , at least one voltage measurement value U 1  is measured at time t U1 . The measurement of the at least one voltage measurement value U 1  is first carried out when a first specifiable settling time τ 1 &lt;Δt 12 , preferably selected as a function of the low-pass filter (ADC) that is used, has elapsed. This can be carried out for example in an application phase. 
     The measurement is first carried out with the beginning of the first current pulse I pulse , started in step  710 , and after elapsing of the first settling time τ 1 , i.e. after the time t meas =t 1 +τ 1 . The at least one measurement value U 1 , the time t U1 , where t U1 −t meas , and the current I 1  of the first current pulse I pulse  are acquired and stored by control device  100  for this purpose. It is assumed that the rise starting from time t 1 +τ 1  of the voltage U is caused approximately solely by polarization effects. 
     Subsequently, the method is continued in step  730 . 
     In a step  730 , at second time t 2  pulse-generating unit  132  is used to impress a specifiable second current pulse I counterpulse , in the direction opposite to first current pulse I pulse , onto sensor element  110 . As a result, a depolarization of sensor element  110 , or of cell  114 , takes place. The impression of the second current pulse I counterpulse  takes place at a second time t 2  and ends at a third time t 3 ; i.e., second current pulse I counterpulse  has a specifiable time duration Δt 23 =t 3 −t 2 . It is assumed that the rise of voltage U starting at time t 2 +τ 2  is caused approximately solely by polarization effects. Here τ 2 &lt;Δt 23  is a specifiable second settling time τ 2 . 
     The specifiable time duration Δt 23  and the specifiable settling time τ 2  are preferably selected as a function of the installed low-pass filter (ADC). This can be carried out for example in an application phase. 
     Subsequently, the method is continued in step  740 . 
     In step  740 , after the elapsing of a second settling time τ 2  at least two voltage measurement values W 1 ,W 2  are ascertained and stored by control device  100  at different times t W1  and τ W2 . The measurement of the at least two voltage measurement values W 1 ,W 2  is first carried out when the specifiable second settling time τ 2  has elapsed. The measurement is first carried out with the beginning of the second current pulse I counterpulse  started in step  630 , and is carried out after the elapsing of the second settling time τ 2 , i.e. not until after a time t meas2 =t 2 +τ 2 , so that t W1 ≥t meas2 , t W2 ≥t W1 . The at least two measurement values W 1 ,W 2 , the times t W1 ,t W2 , and the current I 2  of the second current pulse I counterpulse  are acquired and stored by control device  100  for this purpose. 
     Subsequently, the method is continued in step  750 . 
     In a step  750 , a linear equation G 2  having a second slope m counterpulse  is subsequently ascertained from the second voltage values W 1 ,W 2 , ascertained in step  740 , and the associated times t W1 ,t W2 . Here it is assumed that the curve of voltage U starting from time t 2 +τ 2  can be linearly approximated. 
     Subsequently, the method is continued in step  760 . 
     In a step  760 , as a function of the ascertained second slope m counterpulse  of the linear curve during the opposite second current pulse I counterpulse , the third slope m start  and the impressed first current I 1  and the impressed second current I 2  during the first current pulse I pulse  and the second current pulse I counterpulse , the corrected slope m pulse,corr  of the polarization portion, assumed as linear, during the first current pulse I pulse  is ascertained as follows: 
     
       
         
           
             
               m 
               
                 pulse 
                 , 
                 corr 
               
             
             = 
             
               
                 
                   ( 
                   
                     
                       m 
                       counterpulse 
                     
                     - 
                     
                       m 
                       start 
                     
                   
                   ) 
                 
                 · 
                 
                   ( 
                   
                     
                       I 
                       1 
                     
                     
                       I 
                       2 
                     
                   
                   ) 
                 
               
               + 
               
                 m 
                 start 
               
             
           
         
       
     
     Subsequently, the method is continued in step  770 . 
     In a step  770 , the extrapolated voltage value U pulse (t 1 ) is ascertained using the first voltage value U 1  ascertained in step  720  and its time t U1 , the ascertained corrected slope m pulse,corr  and the first time t 1  of the extrapolated voltage value U pulse (t 1 ). 
     Subsequently, the method is continued in step  780 . 
     In a step  780 , control device  100  carries out a subtraction between the extrapolated voltage value U pulse (t 1 ) and the voltage value U start  ascertained in step  700 . 
     Subsequently, from the ascertained voltage value U pulse =U pulse (t 1 )−U start  a corrected internal resistance R is ascertained for sensor element  110 , or for cell  114 : 
     
       
         
           
             R 
             = 
             
               
                 U 
                 pulse 
               
               
                 I 
                 1 
               
             
           
         
       
     
     where U pulse  is the difference between the extrapolated voltage value U pulse (t 1 ), the current I 1 , and the ascertained voltage value U start . 
     Subsequently, the method can be started from the beginning in step  700 , or can be ended.