Abstract:
A method and circuit are provided for estimating the temperature in an internal combustion engine. The method includes, but is not limited to the steps of providing a sensor resistor (RTD) in the internal combustion engine, the sensor resistor (RTD) having a predetermined resistance-temperature characteristic, and estimating the temperature based on the resistance-temperature characteristic. The method also includes, but is not limited to the steps of providing to the sensor resistor (RTD) a reference current signal (I 1 ) so that a sensor voltage (V RTD ) is established across the sensor resistor (RTD), generating a reference voltage signal (V 2 ), comparing the established sensor voltage (V RTD ) with the reference voltage signal (V 2 ), modifying the reference current signal (I 1 ) and reference voltage signal (V 2 ) on the basis of the comparison outcome so as to minimize the difference between the sensor voltage (V RTD ) and the reference voltage signal (V 2 ), and calculating the resistance value of the sensor resistor (RTD) based on the reference voltage signal (V 2 ) and reference current signal (I 1 ).

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to British Patent Application No. 0815907.1, filed Sep. 2, 2008, which is incorporated herein by reference in its entirety. 
       TECHNICAL FIELD 
       [0002]    The present invention relates to the estimation of the temperature in an internal combustion engine and specifically to a method for estimating the temperature in an internal combustion engine, and a corresponding circuit. 
       BACKGROUND 
       [0003]    Linear resistive temperature sensors (“RTD”) are today utilized in automotive control to monitor the high temperature in the exhaust pipes and in the catalyst of internal combustion engines, both diesel and gasoline engines. 
         [0004]    The temperature to be monitored covers a wide range, from −40° C. to 1000° C., and the corresponding sensor resistance variation is typically from 170Ω to 850Ω, with quasi-linear temperature dependency. The resolution of the temperature measurement is therefore limited and measurement errors have a greater impact on the automotive control. 
         [0005]    A conventional conditioning circuit for RTD sensors used in automotive controllers is shown in  FIG. 1 . This circuit comprises a very accurate pull-up resistor R 1 , particularly having a value of 1 kΩ, connected to an accurate supply voltage source Vcc, for example having a value of 5V. A sensor resistor RTD, which is a linear resistive temperature sensor, is connected in series between the pull-up resistor R 1  and a voltage reference, particularly a ground conductor GND. A low pass filter  2  comprising a resistor R f  and a capacitor C f  is connected in parallel to the sensor resistor RTD, and is used to reduce the noise from the electrical environment. An analogue to digital converter ADC is connected in parallel to the filter  2  and is also connected to a reference voltage source V ADC  that tracks the supply voltage source Vcc. A microprocessor M is connected between the converter ADC and an output OUT of the circuit. Alternatively, the converter ADC is embedded in the microprocessor M. 
         [0006]    A voltage V meas  across the sensor resistor RTD is measured at a node A with respect to ground, and applying an equation as follows: 
         [0000]    
       
         
           
             
               V 
               meas 
             
             = 
             
               
                 RTD 
                 
                   
                     R 
                     1 
                   
                   + 
                   RTD 
                 
               
                
               
                 V 
                 cc 
               
             
           
         
       
     
         [0000]    The resistance value of the sensor resistor RTD is obtained. Specifically, the voltage V meas  across the sensor resistor RTD is measured in a known manner and it is supplied to the converter ADC that provides a digital value corresponding to the voltage. The digital value is supplied to the microprocessor M which calculates, according to the above cited equation, the resistance value of the sensor resistor RTD. Knowing the dependency between the resistance value of the sensor resistor RTD and the temperature, it is possible to obtain, at the output OUT of the circuit, the estimated value of the temperature. 
         [0007]    The overall accuracy of the temperature measurement is mainly affected by: sensor resistance accuracy; conditioning circuit tolerances; quantization steps of the converter ADC; conversion errors of the converter ADC; and leakage current of the converter ADC through the low pass filter  2 . 
         [0008]    The drawbacks of such architecture is that: it utilizes less than half span of the available converter input voltage range; the transfer function is non linear due to the voltage divider arrangement between the pull-up resistor R 1  and the sensor resistor RTD; the sensitivity ΔV meas /ΔTemperature is very low, for example not higher than 1.2 mV/° C. at about 600° C.; the sensitivity ΔV meas /ΔTemperature is not constant and decreases with the increase of the temperature; a very accurate and expensive pull-up resistor, particularly with 0.1% of tolerance, is required; and an analogue to digital converter, which is an expensive element, is needed. 
         [0009]    In view of the above, it is at least one object of the present invention to provide an alternative method for estimating the temperature in an internal combustion engine so as to improve the overall accuracy and sensitivity without the need to use complex circuits with expensive electronic components. In addition, it other objects, desirable features, and characteristics will become apparent from the subsequent summary and detailed description, and the appended claims, taken in conjunction with the accompanying drawings and this background. 
       SUMMARY 
       [0010]    1. A method is provided in accordance with an embodiment of the invention for estimating the temperature in an internal combustion engine. The method includes, but is not limited to the steps of providing a sensor resistor (RTD) in the internal combustion engine, the sensor resistor (RTD) having a predetermined resistance-temperature characteristic. The method also includes, but is not limited to estimating the temperature based on the resistance-temperature characteristic, providing to the sensor resistor (RTD) a reference current signal (I 1 ) so that a sensor voltage (V RTD ) is established across the sensor resistor (RTD), generating a reference voltage signal (V 2 ), comparing the established sensor voltage (V RTD ) with the reference voltage signal (V 2 ), modifying the reference current signal (I 1 ) and reference voltage signal (V 2 ) on the basis of the comparison outcome so as to minimize the difference between the sensor voltage (V RTD ) and the reference voltage signal (V 2 ), and calculating the resistance value of said sensor resistor (RTD) based on said reference voltage signal (V 2 ) and reference current signal (I 1 ). 
         [0011]    In addition to the method, a circuit is provided for estimating the temperature in an internal combustion engine. The circuit includes, but is not limited to a sensor resistor (RTD) having a predetermined resistance-temperature characteristic, a computer connected in parallel to the sensor resistor (RTD) and arranged to estimate a temperature value using the resistance-temperature characteristic of the sensor resistor (RTD), and electronic controller coupled to the sensor resistor (RTD) and arranged for providing to the sensor resistor (RTD) a reference current signal (I 1 ) so that a sensor voltage (VRTD) is established across the sensor resistor (RTD), generating a reference voltage signal (V 2 ), comparing the established sensor voltage (VRTD) with the reference voltage signal (V 2 ), modifying the reference current signal (I 1 ) and reference voltage signal (V 2 ) on the basis of the comparison outcome so as to minimize the difference between the sensor voltage (VRTD) and the reference voltage signal (V 2 ), and calculating the resistance value of the sensor resistor (RTD) based on the said reference voltage signal (V 2 ) and reference current signal (I 1 ). 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    The present invention will hereinafter be described in conjunction with the following drawing figures, wherein like numerals denote like elements, and: 
           [0013]      FIG. 1  is a schematic representation of a conditioning circuit for a temperature sensor of the prior art; and 
           [0014]      FIG. 2  is a schematic representation of a conditioning circuit for a temperature sensor according to an embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0015]    The following detailed description is merely exemplary in nature and is not intended to limit application and uses. Furthermore, there is no intention to be bound by any theory presented in the preceding background or the following detailed description. 
         [0016]    In  FIG. 2 , reference numeral  4  generally indicates an electronic control system for driving a sensor resistor RTD, which is a linear resistive temperature sensor (i.e. a resistor having a linear resistance-temperature characteristic). The sensor resistor RTD can be either of the NTC type or the PTC type. 
         [0017]    The sensor resistor RTD is connected to the output of a digitally-driven analogue current generator DAC 1 , typically a digital-analogue converter, which has its input connected to a microcontroller  8 . The generator DAC 1  provides at its output a reference current signal I 1  having an analogue value which corresponds to the digital value of a first N-bit digital control word W 1  provided at its input by the microcontroller  8 . The reference current I 1  flows through the sensor resistor RTD and a sensor voltage V RTD  is established across said sensor resistor RTD. 
         [0018]    The sensor resistor RTD is also connected to the non-inverting input of an analogue comparator  6 , which continuously compares the said sensor voltage V RTD  with an analogue reference voltage signal V 2  provided by the output of a digitally-driven analogue voltage generator DAC 2 , typically a digital-analogue converter, which has its input connected to the microcontroller  8 . The generator DAC 2  provides at its output the reference voltage signal V 2  having an analogue value which corresponds to the digital value of a second M-bit digital control word W 2  provided at its input by the microcontroller  8 . 
         [0019]    The generators DAC 1  and DAC 2  are each connected to a DC supply voltage source, such as the battery of the motor-vehicle, which provides a supply voltage V cc . 
         [0020]    The microcontroller  8  receives an output signal FDBK from the comparator  6  and performs a closed-loop control so as to minimize the difference between the analogue values of the sensor voltage signal V RTD  and the reference voltage signal V 2 . The microcontroller  8  sets values of the first N-bit digital control word W 1  and second digital word W 2  so as to get the minimization. 
         [0021]    In order to achieve the best resistance resolution ΔR, i.e. the resolution of the resistance value of the RTD sensor, two different operating modes can be implemented by the microcontroller  8 , according to the resolution of the two generators DAC 1  and DAC 2 : the resolution of the current generator DAC 1  is indicated ΔI, the resolution of the voltage generator DAC 2  is indicated ΔV. 
         [0022]    In order to distinguish between the two different cases above cited, it is firstly considered that the voltage generator DAC 2  is fixed and the current generator DAC 1  switches. In this case, the resistance value of the sensor resistor RTD is calculated according to an equation as follows: 
         [0000]    
       
         
           
             
               
                 
                   RTD 
                   = 
                   
                     
                       V 
                       
                         DAC 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     
                       I 
                       
                         DAC 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where V DAC2  is the analogue reference voltage signal V 2  and I DAC1  is the analogue reference current signal I 1 . 
         [0023]    The resistance resolution ΔR is calculated according to the following equations: 
         [0000]    
       
         
           
             
               
                 
                   
                     RTD 
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       R 
                     
                   
                   = 
                   
                     
                       V 
                       
                         DAC 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     
                       
                         I 
                         
                           DAC 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         I 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and by combining equations 1 and 2: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     R 
                   
                   = 
                   
                     
                       
                         V 
                         
                           DAC 
                            
                           
                               
                           
                            
                           2 
                         
                       
                        
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                     
                       
                         I 
                         
                           DAC 
                            
                           
                               
                           
                            
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             I 
                             
                               DAC 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           - 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             I 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0024]    Secondly, it is considered that the current generator DAC 1  is fixed and the voltage generator DAC 2  switches. In this case, the resistance resolution ΔR is calculated according to the following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     R 
                   
                   = 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       I 
                       
                         DAC 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0025]    Comparing the two equations of the resistance resolution ΔR: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             V 
                             
                               DAC 
                                
                               
                                   
                               
                                
                               2 
                             
                           
                           · 
                           Δ 
                         
                          
                         
                             
                         
                          
                         I 
                       
                       
                         
                           I 
                           
                             DAC 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               I 
                               
                                 DAC 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             - 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               I 
                             
                           
                           ) 
                         
                       
                     
                     &lt; 
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         V 
                       
                       
                         I 
                         
                           DAC 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                   
                   ⇒ 
                   
                     
                       
                         V 
                         
                           DAC 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       
                         ( 
                         
                           
                             I 
                             
                               DAC 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           - 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             I 
                           
                         
                         ) 
                       
                     
                     &lt; 
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         V 
                       
                       
                         Δ 
                          
                         
                             
                         
                          
                         I 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0026]    By combining equation 2 and 5 it is obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       RTD 
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         R 
                       
                     
                     &lt; 
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         V 
                       
                       
                         Δ 
                          
                         
                             
                         
                          
                         I 
                       
                     
                   
                   ⇒ 
                   
                     RTD 
                     &lt; 
                     
                       
                         V 
                         
                           DAC 
                            
                           
                               
                           
                            
                           2 
                         
                       
                       
                         ( 
                         
                           
                             I 
                             
                               DAC 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           - 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             I 
                           
                         
                         ) 
                       
                     
                     &lt; 
                     
                       2 
                        
                       RTD 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0027]    At this point, two hypothesis can be made; firstly, it is supposed that: 
         [0000]    
       
         
           
             
               
                 
                   
                     RTD 
                     expected 
                   
                   &gt; 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where RTD expected  is an expected resistance value of the resistor RTD, and therefore, according to equation 6: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       V 
                       
                         DAC 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     
                       ( 
                       
                         
                           I 
                           
                             DAC 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         - 
                         
                           Δ 
                            
                           
                               
                           
                            
                           I 
                         
                       
                       ) 
                     
                   
                   &gt; 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0028]    Secondly, it is supposed that: 
         [0000]    
       
         
           
             
               
                 
                   
                     2 
                      
                     
                       RTD 
                       expected 
                     
                   
                   &lt; 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and therefore, according to equation 6: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       V 
                       
                         DAC 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     
                       ( 
                       
                         
                           I 
                           
                             DAC 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         - 
                         
                           Δ 
                            
                           
                               
                           
                            
                           I 
                         
                       
                       ) 
                     
                   
                   &lt; 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0029]    From equations 7 and 9 it is obtained: 
         [0000]    
       
         
           
             
               
                 
                   
                     RTD 
                     expected 
                   
                   &gt; 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     RTD 
                     expected 
                   
                   &lt; 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       V 
                     
                     
                       2 
                        
                       Δ 
                        
                       
                           
                       
                        
                       I 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0030]    From equations 11 and 12 two conditions can be obtained, based on the expected resistance value of the resistor RTD expected  and the resolutions of the current generator DAC 1  and voltage generator DAC 2 . 
         [0031]    In the first case, the expected resistance value of the sensor resistor RTD to be measured is greater than ΔV/ΔI. 
         [0032]    The current generator DAC 1  starts to inject its maximum current, for example 10 mA. The voltage generator DAC 2  is set to its maximum voltage, for example 4V. 
         [0033]    If the output signal FDBK is “low”, i.e. the reference voltage signal V 2  is greater than the sensor voltage V RTD , the microcontroller  8  makes the voltage generator DAC 2  reduce its reference voltage signal V 2  of a predetermined quantity, for example 0.2V. This step is repeated until the output signal FDBK changes status, i.e., becomes “high”. At this point, the resistance value of the sensor resistor RTD is calculated according to equation 1. 
         [0034]    If the output signal FDBK is “high”, i.e., the reference voltage signal V 2  is lower than the sensor voltage V RTD , the microcontroller  8  makes the current generator DAC 1  reduce its reference current signal I 1  of a predetermined quantity, for example 1 mA. This step is repeated until the output signal FDBK changes status, i.e., becomes “low”, or until the current generator DAC 1  arrives to its minimum value, for example 5 mA. 
         [0035]    If the output signal FDBK becomes “low”, the microcontroller 8 makes the voltage generator DAC 2  reduce its reference voltage signal V 2  of a predetermined quantity, for example 0.2V. This step is repeated until the output signal FDBK changes status again, i.e., becomes “high”. After that, the resistance value of the sensor resistor RTD is calculated according to equation 1. 
         [0036]    If the current generator DAC 1  is equal to its minimum value and the output signal FDBK is still “high”, the microcontroller  8  turns on a switch S and connects a pull-up resistor R 1  essentially in series with the sensor resistor RTD, between the voltage supply Vcc and ground. If the output signal FDBK does not change status, an “open circuit fault condition” is detected. 
         [0037]    In the second case, the expected resistance value of the sensor resistor RTD to be measured is smaller than ΔV/2ΔI. 
         [0038]    The current generator DAC 1  starts to inject its maximum current, for example 10 mA. The voltage generator DAC 2  is set to its maximum voltage, for example 4V. 
         [0039]    If the output signal FDBK is “high”, the microcontroller  8  makes the current generator DAC 1  reduce its reference current signal I 1  of a predetermined quantity, for example 1 mA. This step is repeated until the output signal FDBK changes status, i.e., becomes “low”. At this point, the resistance value of the sensor resistor RTD is calculated according to equation 1. 
         [0040]    If the output signal FDBK is “low”, the microcontroller  8  makes the voltage generator DAC 2  reduce its reference voltage signal V 2  of a predetermined quantity, for example 0.2V. This step is repeated until the output signal FDBK changes status, i.e., becomes “high”, or until the voltage generator DAC 2  arrives to its minimum value. At this point, the microcontroller  8  makes the current generator DAC 1  reduce its reference current signal I 1  of a predetermined quantity, for example 1 mA. This step is repeated until the output signal FDBK changes status again, i.e., becomes “low”. At this point, the resistance value of the sensor resistor RTD is calculated according to equation 1. 
         [0041]    In the above identified case, if the voltage generator DAC 2  is equal to its minimum value and the output signal FDBK is still “low”, a “short circuit fault condition” is detected. 
         [0042]    If neither equation 11 nor equation 12 are satisfied, it is not possible to know whether the first case is better than the second one or vice versa. The microcontroller  8  performs therefore the steps of the first case or of the second one indifferently, or according to a default rule. 
         [0043]    The microcontroller  8  is arranged to transmit data to a microprocessor  10  through a serial peripheral interface SPI. Particularly, the microcontroller  8  transmits the calculated resistance value of the RTD sensor. Alternatively, the microcontroller  8  transmits both the reference voltage V 2  and the reference current I 1  and the microprocessor  10  calculates the resistance value of the RTD sensor. 
         [0044]    Advantageously, a multiplexer is connected between the sensor resistor RTD and the output of the current generator DAC 1  so as to allow measuring the resistance values of a plurality of sensor resistors. 
         [0045]    Alternatively, if an expected resistance value of the sensor resistor RTD is not known, the comparison between the two equations of the resistance resolution ΔR can be made by comparing the first digital word W 1  and second digital word W 2 . Particularly, in equation 5 is it possible to substitute W 1 *ΔI for I DAC1  and W 2 *ΔV for V DAC2 , thus obtaining: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         W 
                          
                         
                             
                         
                          
                         2 
                          
                         Δ 
                          
                         
                             
                         
                          
                         V 
                       
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           I 
                            
                           
                             ( 
                             
                               
                                 W 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     &lt; 
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         V 
                       
                       
                         Δ 
                          
                         
                             
                         
                          
                         I 
                       
                     
                   
                   ⇒ 
                   
                     
                       W 
                        
                       
                           
                       
                        
                       2 
                     
                     &lt; 
                     
                       
                         W 
                          
                         
                             
                         
                          
                         1 
                       
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0046]    If equation 13 is satisfied, the second case above disclosed is followed; otherwise, the steps of the first case are selected. 
         [0047]    Clearly, the principle of the invention remaining the same, the embodiments and the details of production can be varied considerably from what has been described and illustrated purely by way of non-limiting example, without departing from the scope of protection of the present invention as defined by the attached claims. Moreover, while at least one exemplary embodiment has been presented in the foregoing summary and detailed description, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration in any way. Rather, the foregoing summary and detailed description will provide those skilled in the art with a convenient road map for implementing an exemplary embodiment, it being understood that various changes may be made in the function and arrangement of elements described in an exemplary embodiment without departing from the scope as set forth in the appended claims and their legal equivalents.