Abstract:
A conductivity measurement system provides one or more DC pulses to first and second electrodes submerged in an aqueous solution such as, for instance, the wash water of an industrial dishwasher. The voltage at the first electrode is measured at a sequence of at least three predetermined times after initiation of one of the DC pulse. A non-linear curve fitting function is applied to the sequence of at least three voltage measurements to calculate the voltage at the first electrode at the beginning of the DC pulse(s), commonly denoted as being at time t=0. The resulting calculated voltage at time t=0 is then used to calculate the conductivity of the solution, and/or to control operation of the a chemical dispenser, and/or to perform another predetermined system analysis or system control function. In addition, the difference between two of the measured voltages, such as the first and second measured voltages, is compared to a predetermined threshold value to determine whether the electrodes are so contaminated that polarization compensation is no longer feasible, thereby signaling that the electrodes should be cleaned or replaced.

Description:
This application is a continuation-in-part of U.S. patent application Ser. No. 09/078,400, filed May 13, 1998, now U.S. Pat. No. 6,223,129. 
    
    
     The present invention relates generally to conductivity measurement systems and the low-cost probes thereof, such as used in commercial dishwashers, and particularly to conductivity measurement systems which compensate for probe contamination. 
     BACKGROUND OF THE INVENTION 
     Industrial dishwashers use conductivity measurement systems to maintain proper detergent concentrations in the dishwashers&#39; wash water. Conductivity measurement systems are well known and typically include a probe that has first and second electrodes submerged in the wash water. A signal from a source circuit is applied to the electrodes to induce a current between the electrodes. This current, which is mirrored in the source circuit, is determined by dividing the voltage in the source circuit by the impedance of the source circuit. The conductivity of the wash water is then determined by dividing the current between the electrodes by the voltage across the electrodes. 
     Current flow in an aqueous solution, e.g., the wash water, is facilitated by the flow of ions between the electrodes. In an industrial dishwasher, the ions are provided by the detergent. Thus, increasing the detergent concentration results in a corresponding increase in the conductivity of the wash water. The relationship between wash water conductivity and detergent concentration for a particular detergent is typically stored in a look-up table, thereby allowing detergent concentration to be easily derived from wash water conductivity. 
     As current is induced between electrodes in an aqueous solution, ions begin accumulating on one of the electrodes. The ions accumulating on the electrode surface each occupy a finite space such that after a time period, t, there is no more available surface area on the electrodes on which ions may accumulate. This phenomena, known in the art as polarization, reduces current flow between the electrodes and may result in erroneous conductivity measurements which, in turn, lead to erroneous detergent concentration measurements. Conductivity measurements made during the wash cycle are used to control the adding of detergent to the wash water. Typically, detergent is added until the conductivity of the water reaches a predetermined level associated with a desired detergent concentration. When the electrodes of the dishwasher become polarized, the detergent concentration of the wash water is perceived by the dishwasher&#39;s control circuitry to be too low, thereby leading to the addition of detergent to wash water that may, in reality, already be at or above the desired detergent concentration. 
     Further, when used as described above, the electrodes undesirably accumulate non-conductive particles thereon which, in turn, reduce the effective area of the electrodes. As a result, contamination of the electrodes speeds the above-described polarization of the electrodes and, therefore, diminishes the useful life of the electrodes. 
     In theory, the effect of polarization upon conductivity measurements can be eliminated, or at least partially compensated, by calculating conductivity the instant current is induced between the electrodes, since at time t=0 ions have not yet accumulated on the electrodes. Here, the voltage between the electrodes must be measured just as the source signal that induces current in the wash water is asserted. Unfortunately, such an approach is not feasible. First, there are significant characteristic variations between ion species during the first 1 to 2 microseconds of aqueous current flow. Since the ion species of the detergent is typically unknown, measurements taken within the first 1 to 2 microseconds are unreliable. Second, it is very difficult to fabricate a circuit which can produce a source pulse and then immediately capture an analog reading produced by the source pulse. 
     U.S. Pat. No. 4,756,321 discloses an industrial dishwashing system in which a continuous AC signal is applied to first and second electrodes submerged in wash water to induce a current between the electrodes. The resulting current is measured over time, and then used to calculate the conductivity of the wash water. Conductivity is then converted into a logarithmically scaled detergent concentration. Here, the continuous current flow between the electrodes results in a continually increasing polarization of the electrodes. As a result, the electrodes must be either cleaned or replaced at regular intervals. The servicing of the electrodes is not only expensive, but also reduces operating efficiency of the dishwasher. Further, this system&#39;s inability to measure or predict electrode contamination makes it even more difficult to optimize the useful life of the electrode. 
     Another approach involves driving the electrodes with a pulsed DC signal as described, for instance, in U.S. Pat. No. 4,119,909. In that system, the pulsed DC signal induces short pulses of current between the electrodes in the wash water. Use of short current pulses reduces polarization and, thus, increases the useful life of the electrodes, as compared to the averaging technique disclosed in U.S. Pat. No. 4,756,321. However, conductivity measurements provided by this approach are nevertheless influenced by polarization. Further, this system, like that disclosed in U.S. Pat. No. 4,119,909, is unable to measure or predict electrode contamination. It is therefore difficult to accurately determine when or at what rate the measured conductivity deviates from the actual conductivity and, as a result, the accuracy with which this approach maintains the detergent concentration at a target level is compromised. It is thus also difficult to maximize the intervals at which the electrodes are cleaned or replaced and, therefore, difficult to maximize the useful life of the electrodes. 
     SUMMARY OF THE INVENTION 
     A conductivity measurement system provides one or more DC pulses to first and second electrodes submerged in an aqueous solution such as, for instance, the wash water of an industrial dishwasher. The voltage at the first electrode is measured at a sequence of at least predetermined times after initiation of one of the DC pulse. A curve fitting function is applied to the sequence of voltage measurements to calculate the voltage at the first electrode at the beginning of the DC pulse(s), commonly denoted as being at time t=0. The resulting calculated voltage at time t=0 is then used to calculate the conductivity of the solution, and/or to control operation of the a chemical dispenser, and/or to perform another predetermined system analysis or system control function. In addition, the difference between two of the measured voltages, such as the first and second measured voltages, is compared to a predetermined threshold value to determine whether the electrodes are so contaminated that polarization compensation is no longer feasible, thereby signaling that the electrodes should be cleaned or replaced. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of an industrial dishwasher in which a conductivity measurement system in accordance with the present invention is used; 
     FIG. 2 is a block diagram of a micro-controller suitable for use in the conductivity measurement system of FIG. 1, including a schematic diagram of a four-layer capacitor modeling the polarization of wash water; 
     FIG. 3 is a timing diagram showing various signals associated with the operation of one embodiment of the present invention; 
     FIG. 4 is a flow chart illustrating operation of a conductivity measurement system in a preferred embodiment of the present invention; 
     FIG. 5 is a graphical depiction of a curve fitting method of determining conductivity used in the second preferred embodiment; and 
     FIG. 6 is a flow chart illustrating operation of a conductivity measurement system in a second preferred embodiment of the present invention. 
    
    
     Like components in the Figures are similarly labeled. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Principles of the present invention are described below with reference to the industrial dishwasher 20 disclosed in U.S. Pat. No. 4,756,321, incorporated herein by reference, for simplicity only. It is to be understood that embodiments of the present invention may be used in other industrial dishwashers, or for any application in which it is desired to measure the conductivity of an aqueous solution. Accordingly, the present invention is not to be construed as limited to specific examples herein. 
     Referring to FIG. 1, an industrial dishwasher  20  of the type described in U.S. Pat. No. 4,756,321 is shown to include a conductivity measurement system  100  in accordance with the present invention. System  100  is connected to a probe  52  having first  54   a  and second  54   b  electrodes submerged in a tank  35  of wash water used to wash dishes  38 . In response to signals received from the probe  52 , the system  100  provides control signals to a rinse pump  28 , a detergent pump  32 , and a sanitation pump  31  so as to ensure proper concentrations of a rinse agent, detergent, and a sanitation agent, respectively, within the wash water. The rinse agent is dispensed by pump  28  from a rinse agent supply  58 , detergent is dispensed by pump  32  from a detergent supply  34 , and sanitation agent is dispensed by pump  31  from a sanitation agent supply  33 . For a discussion of the general operation of the dishwasher  20 , as well as the advantages realized thereby, see U.S. Pat. No. 4,756,321. 
     Referring to FIG. 2, the measurement circuit  100  includes a micro-controller  102  having an output terminal OUT coupled to the first electrode  54   a  via a resistor R 1 , where resistor R ON  models the on-resistance of the micro-controller  102 . The resistor R 1  should be of a value suitable for the conductivity range of the wash water. In one embodiment, where R ON  is 60 Ω, a value of 200 Ω is chosen for resistor R 1 , as explained in detail below. The micro-controller  102  also has an input terminal IN coupled to the first electrode  54   a  of the probe via a resistor R 2  which serves as a series protection resistor for the ADC input terminal. Although the resistor R 2  should be as large as possible in order to provide maximum protection for the ADC input terminal, the resistor R 2  must also be small with respect to the input impedance of the ADC  104  in order to preserve signal strength. In one embodiment, where the micro-controller  102  is able to operate accurately with a source impedance as high as 10 kΩ, a value of 4.7 kΩ is selected for the resistor R 2 . The second electrode  54   b  of the probe is tied to ground potential. Block  200  is an electrical representation on the wash water in the tank  35 , where capacitors C 1  and C 2  form a four-layer capacitor which models polarization of the wash water, and the impedance element Z models the impedance of the wash water. Increases in electrode contamination are modeled by reducing the size of the capacitors. 
     The micro-controller  102  includes an analog-to-digital converter (ADC)  104 , a look-up table  106 , a memory  108  (for storing executable procedures, computed values, and other information), a central processing unit  110 , and a timing circuit  112 . The micro-controller  102  is connected to a voltage supply VDC and ground potential. 
     Referring to the timing diagram of FIG. 3, the micro-controller  102  generates at its output terminal OUT a DC pulse having a duration of T and an amplitude equal to V DC . The voltage at the electrode  54   a  is measured at times t 1  and t 2 , where t 1 &lt;t 2 &lt;T, thereby giving measured voltages V 1  and V 2 , respectively, which are stored in the memory  108 . If there is no polarization within the wash water, the measured voltages V 1  and V 2  will be equal, as illustrated by case A of FIG.  3 . If, on the other hand, there is polarization, the current flow between the electrodes  54   a  and  54   b  will decrease between times t 1  and t 2  and, therefore, the voltage V 2  will be greater than the voltage V 1 , as illustrated by case B in FIG.  3 . The rate at which the voltage at the electrode  54   a  changes is assumed for the purposes of describing this embodiment to be substantially linear and, therefore, compensation techniques discussed below utilize linear algorithms. However, where greater accuracy is desired, more complex, non-linear compensation techniques are used. One embodiment of a conductivity measurement system using non-linear compensation techniques is described below with respect to FIGS. 5 and 6. 
     In calculating the conductivity of the wash water, linear regression is used to determine the voltage at electrode  54   a  at time t=0, i.e., at the beginning of the DC pulse. The voltage on the electrode  54   a  at time t=0 is given as:          V   0     =         (       V   1          t   2       )     -     (       V   2          t   1       )         (       t   2     -     t   1       )                              
     Since the voltage V 0  corresponds to time t=0, the voltage V 0  is not influenced by the effects of polarization. Thus, the conductivity of the wash water, which is calculated using Ohm&#39;s law and the known K factor of the electrodes  54   a  and  54   b , is not influenced by polarization within the wash water. In this manner, present embodiments compensate for polarization. 
     The difference between the first and second measured voltages, V diff =V 2 −V 1 , is indicative of the extent to which the electrodes are contaminated. Accordingly, if the difference value exceeds a predetermined threshold corresponding to the maximum degree of acceptable electrode contamination, the micro-controller  102  generates an alarm signal (e.g., a red light or other visual signal on the front panel of the device) alerting an operator of the system  20  that the electrodes  54   a  and  54   b  need to be cleaned or replaced. Further, in some embodiments, if the measured voltage V 0  at time t=0 is greater than a second predetermined threshold, the micro-controller  102  generates an alarm signal alerting the operator that the electrodes  54   a  and  54   b  are sufficiently contaminated so as to require servicing. In this manner, present embodiments facilitate servicing of the electrodes  54   a  and  54   b  before contamination becomes sufficient to degrade conductivity measurement accuracy. 
     In preferred embodiments, an inexpensive micro-controller such as, for instance, the 16C72, 16C73, or the 16C74, all available from Microchip Semiconductor Corp. is used for the micro-controller  102  in order to minimize cost. Since these micro-controllers are typically unable to take quick successive analog measurements, the first and second voltage measurements, V 1  and V 2 , are sampled during two separate pulses, as explained below, where V DC =5 volts, R ON =60 Ω, R 1 =200 Ω, R 2 =4.7 kΩ, t 1 =10 μs, t 2 =15 μs, T=20 μs, and K=0.4. 
     Referring also to the flow chart of FIG. 4, the micro-controller  102  generates at time t=0 a first DC pulse having an amplitude of 5 volts (step  1 ). The DC pulse induces an electric field between the first and second electrodes  54   a  and  54   b  which, in turn, results in current flow between the electrodes  54   a  and  54   b  in the wash water. At time t=10 μs, the micro-controller  102  samples the voltage at the first electrode  54   a  via resistor R 2  (step  2 ). The resultant analog voltage V 1  is provided to the micro-controller  102  via its input terminal IN and is thereafter converted to a digital voltage D 1  via the ADC  104 . The digital voltage D 1  is stored in the memory  108  (step  3 ). At time t=20 its, the micro-controller  102  terminates the first pulse, and the electrode  54   a  discharges to ground potential (step  4 ). After a predetermined period of time such as, for instance, 125 μs, the micro-controller  102  generates at its output terminal OUT a second DC pulse having an amplitude of 5 volts (step  5 ). The micro-controller  102  samples the voltage at the first electrode  54   a  at a time 15 μs after the second pulse is initiated (step  6 ). The resultant analog voltage V 2 ′ is converted to a digital voltage D 2 ′ via the ADC  104 , and stored in the memory  108  (step  7 ). 
     As mentioned above, the conductivity measuring system  100  alerts an operator of the dishwasher  20  when electrode contamination exceeds acceptable levels. Here, the CPU  110  of the micro-controller  102  calculates the difference between the first and second stored digital (binary) voltages, D diff =D 1 −D 2 ′ (step  8 ), and then compares the difference voltage D diff  to a predetermined threshold voltage D th  (step  9 ). If the difference voltage D diff  exceeds the predetermined threshold voltage D th , the micro-controller  102  activates an alarm signal (e.g., a visual signal and/or an audible signal) to alert an operator of the dishwasher  20  that the electrodes need to be serviced (step  10 ). 
     The first and second voltages, D 1  and D 2 ′, are then processed by the CPU  110  according to the above-mentioned linear regression algorithm to determine the digital voltage D 0  on the first electrode  54   a  at the beginning of the first DC pulse, i.e., at time t=0 (step  11 ). In one embodiment, the digital voltages D 1  and D 2 ′ are stored as eight-bit numbers, where the binary number 255 corresponds to the analog value 5 (volts). The computed voltage at time t=0 and Ohm&#39;s Law are then used to calculate the conductance of the wash water (step  12 ). The conductance is converted to a detergent concentration using the look-up table  106  (step  13 ). 
     For example, where the digital voltages D 1  and D 2 ′ are equal to 65 and 70, respectively, the value D 0  (at time t=0) is equal to ((65)(15)−(70)(10))/(10+15)=55. The analog voltage A 0 , which corresponds to the digital voltage D 0 , is therefore equal to (5)(55)/(255)=1.08 volts. The current flowing in the circuit, i.e., through resistor R 1 , is determined using Ohm&#39;s law (V=IR). Here, the current is equal to: 
     
       
           I=V/R= (5−1.08)/(60+200)=0.0151 amps.  
       
     
     The uncorrected resistance of the element Z, and thus the resistance of the wash water, is equal to 
     
       
           R=V/I= (1.08)/(0.0151)=71.5 Ω.  
       
     
     The corrected resistance of the wash water is determined by dividing the uncorrected resistance by K, i.e., (71.5)/(0.4)=178.75 Ω, which gives a conductance of 1/(178.75)=0.00559 mhos (or siemens)=5590 μsiemans. This measured conductance corresponds to the beginning of the DC pulse, i.e., time t=0, and is thus not influenced by polarization. In this manner, the conductivity measurement system  100  avoids the polarization-induced, erroneous detergent concentration measurements characteristic of conventional conductivity measurement systems. 
     The K factor is indicative of the electrodes&#39; sensitivity and is typically between 0.1 and 10, where electrodes having a small K factor are more suitable for measuring low conductances and, conversely, electrodes having a large K factor are more suitable for measuring large conductances. A cell formed of an electrode pair “sees” a conductance divided by the K factor, e.g., a cell having a K factor equal to 0.1 sees a conductance that is ten times larger than the actual conductance of the wash water. 
     In some embodiments, the micro-controller  102  converts the calculated voltage V 0  into Beta units, a logarithmic unit of measure especially suited for use in determining the conductance of a detergent solution in an industrial dishwasher. Each unitary increase of the wash water conductivity level measured in Beta units corresponds to approximately a five (5) percent increase in the detergent concentration level (e.g., as measured in units of detergent per gallon of wash water). Beta units are well known in the art and are thus not discussed in detail herein. For a detailed discussion of Beta units, see U.S. Pat. No. 4,756,321. 
     In the above example, the cell formed by electrodes  54   a  and  54   b  has a K factor equal to 0.4. The Beta unit range when using such a cell is 0 to 60, which will yield a voltage change, as measured by the ADC  104  (FIG.  2 ), of between approximately 50 millivolts to 80 millivolts per Beta unit, depending on the actual conductivity. A Beta unit conversion routine executed by the micro-controller  102  uses a lookup table  106  (FIG. 2) to convert the voltage to Beta Units. 
     The typical conductivity of wash water without detergent is about 600 μmhos, and the typical conductivity of wash water with a maximum detergent concentration is about 12,000 μmhos. Thus, the above cell formed by electrodes  54   a  and  54   b  actually “sees” wash water conductivities ranging from 600/0.4=1500 μmhos 0.0015 mhos to 12,000/0.4=30,000 μmhos=0.03 mhos. This conductivity range corresponds to a resistivity range of 1/(0.03 mhos)=33.3 Ω to 1/(0.0015 mhos)=666.7 Ω. Thus, the maximum Beta count, i.e., 180, corresponds to the minimum wash water conductance, i.e., R WATER =666.7 Ω. Using the voltage divider rule,          180   255     =       666.7      Ω       (       R   WATER     +     R   ON     +   R1     )                              
     where R ON +R 1 =277.8 Ω. Since as mentioned earlier R ON =60 Ω, a value of about 200 Ω is chosen for the resistor R 1 . Applicants found that a value of 200 Ω for resistor R 1  limited the current to a safe level. 
     In a preferred embodiment, the above-described pulse sequence is repeated every 250 ms so as to provide four conductivity measurements per second, although the interval between pulse sequences may be adjusted as desired for particular applications. 
     Second Embodiment with Higher Measurement Speed and Higher Accuracy 
     Referring to FIG. 5, the voltage at the measurement input probe, induced by the DC voltage pulse on the OUT node of the processor, often exhibits a nonlinear trajectory over the measurement interval. The “measurement interval” is defined here to be the period of time from the beginning of the DC pulse to the last measurement of the voltage on the input probe. As shown in FIG. 5, the slope of the voltage at the input probe will tend to decrease during the measurement interval. As a result, the linear approximation used in the first embodiment will tend to produce a calculated V 0  voltage value that is higher than the true V 0  voltage. For instance, if the input probe voltage were measured at times tB and tC shown in FIG. 5, the calculated V 0  voltage value would be B−2ΔBC, and that value would be much higher than the actual V 0  voltage. 
     A second preferred embodiment of the present invention automatically compensates for the nonlinearity in the shape of input probe voltage characteristic as a function of time. As a result, the second preferred embodiment generates substantially more accurate conductivity values, especially when the probes are severely fouled. The probes are considered to be severely fouled when less then 10% of the probe surface is clean and available for use in determining the conductivity of an aqueous solution. 
     The apparatus of the second preferred embodiment of the present invention remains as shown in FIG.  2 . However, the operation of the conductivity measurement system has been improved. In particular, the improved conductivity measurement system measures the input probe voltage at shorter intervals, closer to t=0, which improves the accuracy of the calculated V 0  voltage. In one implementation, the input probe voltage is measured at 3 μsec intervals, for instance at t=31 μsec, t=6 μsec, and t=9 μsec. In implementations in which the processor is unable to sample the input probe voltage at successive 3 μsec intervals, or if the analog to digital converter (ADC) in the processor is unable to convert analog inputs in successive 3 μsec intervals, the input probe voltage may be measured at these intervals, but with respect to different DC pulses. For instance, the input probe may be measured at t=3 μsec after a first DC pulse, at t=6 μsec after a second DC pulse, and at t=9 μsec after a third DC pulse. By using three input probe voltage measurements (or more) instead of two, the system is able to apply a nonlinear curve fitting function to the data so as to generate a more accurate estimate of the V 0  voltage. 
     The V 0  voltage is computed as follows. The input probe voltage is sampled at three intervals, producing voltage sample values A, B and C, as shown in FIG.  5 . From these three values the following values are computed: 
     
       
         Δ AB=B−A;    
       
     
     
       
         
           ABC=C−A;  
         
       
     
     
       
         Δ0 A=ΔAB+ (Δ AB−ΔBC ); // this is a computed estimate of Δ0A  
       
     
     
       
           V   0   =A−Δ 0 A=A−{ΔAB +( ΔAB−ΔBC )}.  
       
     
     If the slope of the voltage signal is perfectly linear, the above computation produces the same result as the first embodiment. However, if the voltage signal is not linear, the second embodiment computes a Δ0A value that takes into account the change in slope of the voltage signal over the measurement interval. 
     The computational methodology shown above uses a linear approximation of a nonlinear curve fitting function. In other embodiments, especially embodiments in which greater computational power is available, the curve fitting function may be based on (A) more than three samples, and/or (B) may use a nonlinear curve fitting function instead of a linear approximation of a nonlinear curve fitting function. From another viewpoint, given a limited number of input probe voltage samples (but at least three such samples), the linear approximation of the nonlinear curve fitting function is functionally equivalent to the corresponding nonlinear curve fitting function, but more computationally efficient. 
     Once the voltage value V 0  has been determined, or at least approximated using a curve fitting methodology such as the one described above, the operation of the second embodiment is the same as the first. That is, the calculated voltage value V 0  is used to generate an output signal. For example, calculated voltage value V 0  may be used to the determine the conductivity of the wash water in the system, and/or to determine the concentration of detergent in the wash water. Based on either the conductivity value or detergent concentration value, the system then generates one or more control signals for controlling the operation of the device in which the conductivity measurement system is embedded. For instance, the control signals may be used to control the dispensing of detergent into the wash water of a dishwasher. 
     Referring to flow chart in FIG. 6, the conductivity measurement and device control procedure in an exemplary implementation of the second preferred embodiment is as follows. First, a sequence of at least three samples of the input probe voltage V i  are taken and converted into digital values D i  and stored in memory. In one implementation, this is done by repeating the steps of generating a DC pulse on the probe ( 150 ) and sampling the voltage at the input probe at an appropriate delay interval after the beginning of the pulse ( 152 ). The pulse is then terminated ( 154 ) and the sampled analog voltage is converted into a digital value D i  (by the ADC internal to the micro-controller) and that value is stored in memory ( 156 ). The order of the pulse termination steps and analog to digital conversion steps  154  and  156  can be reversed. These steps  150 ,  152 ,  154  and  156  are repeated at least three times, each time using a different delay interval between activation of the DC pulse and the sample time, so as to develop a sequence of sample values representing the voltage at the input probe over a predefined measurement interval. For instance, the voltage at the input probe may be sampled at t=3 μsec after a first DC pulse, at t=6 μsec after a second DC pulse, and at t=9 μsec after a third DC pulse. In some embodiments, four, five or even more samples may be obtained so as to generate the data needed to more accurately compute the input probe voltage at time t=0. 
     Next, the difference between two of the voltage samples, or their digital values, is computed ( 160 ). The difference used here may be the difference between the second and first samples, but it also may be the difference between the third and second, or the third and first samples, depending on the implementation. The computed difference D diff  is compared with a threshold value D th  ( 162 ) and if the difference exceeds the threshold an alarm signal is generated ( 164 ). 
     If the alarm signal is not generated (or in some embodiments even if the alarm signal is generated), the procedure next computes a voltage V 0  representing a best approximation of the voltage at the input probe at time t=0 ( 170 ). The methodology for computing voltage V 0 , or a digital equivalent thereof, using three sample voltage values and a linear approximation of a nonlinear curve fitting function, is described in detail above. As explained above, the computed voltage V 0  is a function of the conductivity of the aqueous solution in which the probe is immersed, and this value is computed in a way so as to compensate for fouling of the probe. 
     Next, the controller generates an output signal as a function of the calculated voltage V 0  ( 172 ). For instance, the voltage V 0  could be directly compared with a threshold value V th  and a control signal could be turned on or off as a function of the result of the comparison. The threshold value V th  in this example would be a value computed in advance to correspond to a target conductivity level of the aqueous solution, or equivalently would correspond to a target detergent concentration level, or a target concentration of other chemicals or constituents in the aqueous solution. Thus, at least in some embodiments, the calculated voltage V 0  for time t=0 does not need to be converted into a conductivity value or detergent concentration value, and instead can be used directly to control the operation of a device. 
     In one implementation of the second preferred embodiment, the calculated voltage V 0  for time t=0 is used to compute the conductivity of the wash water in a dishwasher ( 174 ), using the methodology described above with respect to the first preferred embodiment. The conductivity value is converted to a detergent concentration value ( 176 ), which again can be accomplished using the methodology described above with respect to the first preferred embodiment. Finally, a control signal is generated based on comparison of the detergent concentration value, or the conductivity value, or the voltage value, with a target value ( 178 ). 
     After the control value(s) are generated, in a preferred embodiment the control procedure waits for a predetermined period of time to elapse ( 180 ) before the procedure is repeated. For instance, the control procedure may wait until an eighth of a second has elapsed, or alternately is may wait until an eighth of second (or some other predetermined amount of time) has elapsed since the current iteration of the control procedure began, thereby ensuring that the entire control procedure is repeated a predefined number of times per second (or per minute, hour or other time period). 
     Alternate Embodiments 
     In the second embodiment, the number of input probe voltage measurements may be more than three, and the nonlinear curve fitting method used may differ from that described above. For instance, if four or more probe voltage measurements are taken, a higher order curve fitting function may be used. 
     In the preferred embodiments, the conductivity measurement system  100  is implemented as software running on a micro-controller. Appropriate program modules may be stored on a CDROM, magnetic disk storage product, or any other computer readable data or program storage product. The software modules in the computer program product may also be distributed electronically, via the Internet or otherwise, by transmission of a computer data signal (in which the software modules are embedded) on a carrier wave. 
     While particular embodiments of the present invention have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from this invention in its broader aspects and, therefore, the appended claims are to encompass within their scope all such changes and modifications as fall within the true spirit and scope of this invention.