Patent Publication Number: US-7913548-B2

Title: Determination of engine rotational speed based on change in current supplied to engine starter

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based on and claims priority from Japanese Patent Application No. 2008-10386, filed on Jan. 21, 2008, the content of which is hereby incorporated by reference in its entirety into this application. 
     BACKGROUND OF THE INVENTION 
     1. Technical Field of the Invention 
     The present invention relates generally to engine rotational speed determining devices, engine starting possibility predicting devices, engine friction estimating devices, and engine automatic stop control devices. More particularly, the invention relates to an engine rotational speed determining device, an engine starting possibility predicting device, an engine friction estimating device, and an engine automatic stop control device, which perform the respective functions, for an internal combustion engine that is started by an electric motor, based on a change in current supplied to the motor. 
     2. Description of the Related Art 
     Japanese Patent First Publication No. 2007-83965 discloses a device that determines, during a starting operation of an internal combustion engine by a starter, the rotational speed of the engine based on a change in the terminal voltage of a battery that powers the starter. 
     More specifically, in the vicinities of compression top dead centers of the engine, forces counteracting the rotation of a crankshaft of the engine with the starter are increased, thus decreasing the rotational speed of the engine; further, the discharge current of the battery is increased, thus decreasing the terminal voltage of the battery. Therefore, the rotational speed of the engine can be determined based on the fact that the cycle of change in the terminal voltage of the battery corresponds to the time required for an angular change of (720°/Nc) for the crankshaft, where Nc is the number of cylinders of the engine. 
     However, the internal resistance of the battery depends largely on both the State of Charge (SOC) of the battery and the deterioration degree of the battery. More specifically, the internal resistance of the battery is increased with decrease in the SOC of the battery; it is also increased with increase in the deterioration degree of the battery. Accordingly, the change in the terminal voltage of the battery during the starting operation of the engine also depends largely on both the SOC and deterioration degree of the battery. 
     Consequently, it may be difficult for the device to accurately detect the rotational speed of the engine based on the change in the terminal voltage of the battery during the starting operation of the engine. 
     SUMMARY OF THE INVENTION 
     According to a first aspect of the present invention, there is provided an engine rotational speed determining device which includes a signal inputting means and a rotational speed determining means. The signal inputting means inputs a signal that indicates current supplied to an electric motor, which starts an internal combustion engine, during a starting operation of the engine by the motor. The rotational speed determining means determines a rotational speed of the engine in the starting operation based on a change in the current indicated by the signal input by the signal inputting means. 
     According to a further implementation of the invention, the engine rotational speed determining device further includes a relaxation process performing means and a relaxation process resetting means. The relaxation process performing means performs a relaxation process for the signal input by the inputting means to eliminate the influence of electrical noise included in the signal. The relaxation process resetting means resets the relaxation process at a timing when the current indicated by the signal has decreased, after an initial rapid increase thereof, to become not higher than a predetermined threshold. The rotational speed determining means determines the rotational speed of the engine based on the signal that has received the relaxation process which is performed by the relaxation process performing means and reset by the relaxation process resetting means. 
     According to a second aspect of the present invention, there is provided an engine starting possibility predicting device which includes a signal inputting means, a rotational speed determining means, a torque determining means, and a possibility predicting means. The signal inputting means inputs a signal that indicates current supplied to an electric motor, which starts an internal combustion engine, during each of a plurality of starting operations of the engine by the motor. The rotational speed determining means determines a rotational speed of the engine in each of the starting operations based on a change in the current indicated by the signal input by the signal inputting means. The torque determining means determines a torque of the motor in each of the starting operations based on the change in the current indicated by the signal input by the signal inputting means. The possibility predicting means predicts, based on the rotational speeds of the engine and the torques of the motor determined by the rotational speed determining means and the torque determining means, a possibility of the motor to successfully start the engine in an upcoming starting operation of the engine. 
     According to a further implementation of the invention, the engine starting possibility predicting device further includes a rotational speed predicting means. The rotational speed predicting means predicts a rotational speed of the engine in the upcoming starting operation based on the rotational speeds of the engine and the torques of the motor determined by the rotational speed determining means and the torque determining means. When the rotational speed of the engine in the upcoming starting operation predicated by the rotational speed predicting means is greater than or equal to a predetermined value, the possibility predicting means predicts that it is possible for the motor to successfully start the engine in the upcoming starting operation. 
     Furthermore, the motor is powered by a battery. The rotational speed predicting means predicts the rotational speed of the engine in the upcoming starting operation in the following way: 1) defining a two-dimensional coordinate plane, where one coordinate axis indicates rotational speed of the engine and the other coordinate axis indicates torque of the motor; 2) determining, on the two-dimensional coordinate plane, a friction curve based on the rotational speeds of the engine and the torques of the motor determined by the rotational speed determining means and the torque determining means, the friction curve representing friction of the engine; 3) determining, on the two-dimensional coordinate plane, a performance curve of the motor based on a State of Charge (SOC) of the battery, the performance curve representing the performance of the motor at the SOC of the battery; and 4) predicting the rotational speed of the engine in the upcoming starting operation as the rotational speed of the engine at an intersection point between the friction curve and the performance curve of the motor. 
     According to a third aspect of the present invention, there is provided an engine friction estimating device which includes a signal inputting means, a rotational speed determining means, a torque determining means, and an engine friction estimating means. The signal inputting means inputs a signal that indicates current supplied to an electric motor, which starts an internal combustion engine, during each of a plurality of starting operations of the engine by the motor. The rotational speed determining means determines a rotational speed of the engine in each of the starting operations based on a change in the current indicated by the signal input by the signal inputting means. The torque determining means determines a torque of the motor in each of the starting operations based on the change in the current indicated by the signal input by the signal inputting means. The engine friction estimating means estimates friction of the engine based on the rotational speeds of the engine and the torques of the motor determined by the rotational speed determining means and the torque determining means. 
     According to a further implementation of the invention, the engine friction estimating means estimates the friction of the engine in the form of an estimated value of the friction. 
     Furthermore, the engine friction estimating means determines the estimated value of the friction in the following way: 1) defining a two-dimensional coordinate plane, where one coordinate axis indicates rotational speed of the engine and the other coordinate axis indicates torque of the motor; 2) determining, on the two-dimensional coordinate plane, a friction curve based on the rotational speeds of the engine and the torques of the motor determined by the rotational speed determining means and the torque determining means, the friction curve representing the friction of the engine; and 3) determining the estimated value of the friction as the torque of the motor at the point on the friction curve where the rotational speed of the engine is equal to a predetermined value. 
     According to a fourth aspect of the present invention, there is provided an engine automatic stop control device which includes a signal inputting means, a rotational speed determining means, a torque determining means, an engine friction estimating means, and a controlling means. The signal inputting means inputs a signal that indicates current supplied to an electric motor, which starts an internal combustion engine, during each of a plurality of starting operations of the engine by the motor. The rotational speed determining means determines a rotational speed of the engine in each of the starting operations based on a change in the current indicated by the signal input by the signal inputting means. The torque determining means determines a torque of the motor in each of the starting operations based on the change in the current indicated by the signal input by the signal inputting means. The engine friction estimating means estimates friction of the engine based on the rotational speeds of the engine and the torques of the motor determined by the rotational speed determining means and the torque determining means. The controlling means controls an automatic stop of the engine based on the friction of the engine estimated by the engine friction estimating means. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be understood more fully from the detailed description given hereinafter and from the accompanying drawings of preferred embodiments of the invention, which, however, should not be taken to limit the invention to the specific embodiments but are for the purpose of explanation and understanding only. 
       In the accompanying drawings: 
         FIG. 1  is a schematic view showing the overall configuration of a power system for a motor vehicle according to the first embodiment of the invention; 
         FIG. 2A  is a time chart illustrating the change in the discharge current of a battery during a starting operation of an engine in the power system of  FIG. 1 ; 
         FIG. 2B  is a time chart illustrating the waveform of a signal output from a current sensor for sensing the discharge current of the battery; 
         FIG. 2C  is a time chart illustrating a waveform obtained by performing an annealing process for the signal output from the current sensor; 
         FIG. 3  is a time chart illustrating the effect of resetting the annealing process; 
         FIG. 4A  is a time chart illustrating the influence of the SOC of the battery on the discharge current of the battery; 
         FIG. 4B  is a time chart illustrating the influence of the SOC of the battery on the terminal voltage of the battery; 
         FIG. 5A  is a time chart giving a comparison between waveforms that are obtained by performing different annealing processes for the signal output from the current sensor; 
         FIG. 5B  is a time chart giving a comparison between waveforms that are obtained by resetting the same annealing process with different values of a threshold of the discharge current of the battery; 
         FIG. 6  is a flow chart illustrating a process of a battery ECU for determining the rotational speed of the engine in a starting operation of the engine; 
         FIG. 7  is a flow chart illustrating a process of the battery ECU for determining the possibility of successfully starting the engine in an upcoming starting operation of the engine; 
         FIG. 8  is a map used by the battery ECU to determine the torque of a starter for starting the engine; 
         FIG. 9  is a graphical representation illustrating the determination of a friction curve by the battery ECU; 
         FIG. 10  is a graphical representation illustrating the determination of an intersection point between the friction curve and a performance curve of the starter by the battery ECU; 
         FIG. 11  is a circuit diagram showing an equivalent circuit between the battery and the starter; 
         FIG. 12A  is a map used by the battery ECU to determine a parameter (Rv+Rs) in the equivalent circuit; 
         FIG. 12B  is a map used by the battery ECU to determine a parameter Rb in the equivalent circuit; 
         FIG. 13  is a map used by the battery ECU to determine the polarization voltage of the battery; 
         FIG. 14  is a flow chart illustrating a process of the battery ECU for estimating friction of the engine; 
         FIG. 15  is a flow chart illustrating a process of an engine ECU for performing an engine automatic stop control; and 
         FIG. 16  is a flow chart illustrating a process of the battery ECU for informing an increase in the friction of the engine. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     Preferred embodiments of the present invention will be described hereinafter with reference to  FIGS. 1-16 . 
     It should be noted that, for the sake of clarity and understanding, identical components having identical functions in different embodiments of the invention have been marked, where possible, with the same reference numerals in each of the figures. 
     First Embodiment 
       FIG. 1  shows the overall configuration of a power system for a motor vehicle according to the first embodiment of the invention. 
     The power system includes a port-injection gasoline engine  10  as a mechanical power generation unit. The engine  10  includes a crankshaft  12  that is mechanically connected to the driving wheels (not shown) of the vehicle. 
     The power system also includes an electric power generation unit  20  which includes an automotive alternator  22  for generating electric power and a voltage regulator  24  for regulating the output voltage of the alternator  22 . The alternator  22  includes a rotor (not shown) that is mechanically connected to the crankshaft  12  of the engine  10 , so that the alternator  22  can be driven by the engine  10 . 
     The electric power generation unit  20  includes a battery terminal TB, to which is electrically connected a battery  30 . In the present embodiment, the battery  30  is made up of a lead accumulator. 
     Electric loads  44  are connected to the battery  30  via corresponding switches  42 . Further, in parallel with the electric loads  44 , a starter  40  is electrically connected to the battery  30 . The starter  40  is an electric motor for starting the engine  10 . More specifically, the starter  40  functions to impart initial rotation to the crankshaft  12  of the engine  10 . 
     The electric power generation unit  20  also includes an ignition terminal TIG which is electrically connected, via an ignition switch  46 , to a power supply line extending between the battery terminal TB and the battery  30 . 
     There also are provided in the power system an engine ECU (Electronic Control Unit)  50  and a battery ECU  60 , both of which are configured with, for example, a microcomputer and powered by the battery  30 . 
     The battery ECU  60  monitors the state of the battery  30  based on signals output from a current sensor  52 , a temperature sensor  54 , and a voltage sensor  56 . The current sensor  52  senses the current charged into or discharged from the battery  30  and outputs the signal which indicates the sensed current. The temperature sensor  54  senses the temperature of the battery  30  and outputs the signal which indicates the sensed temperature. The voltage sensor  56  senses the terminal voltage of the battery  30  and indicates the signal which represents the sensed terminal voltage. 
     In particular, the battery ECU  60  determines the State of Charge (SOC) of the battery  30  through a cumulative computation of the charge/discharge current of the battery  30 . The SOC is a parameter representative of the discharge capability of the battery  30 . More specifically, the SOC represents the ratio of the amount of electricity currently stored in the battery  30  to the full capacity of the battery  30  for storing electricity. The SOC can be quantified by, for example, 5-hour rate capacity or 10-hour rate capacity. 
     In addition, the open-circuit voltage of the battery  30 , which represents the terminal voltage of the battery  30  when there is no external load connected to the terminals of the battery  30 , depends on the SOC of the battery  30 . More specifically, the open-circuit voltage of the battery  30  increases with the SOC of the battery  30 . For example, the open-circuit voltage of the battery  30  is 11.8 V when the SOC is 0%, but is 12.8 V when the SOC is 100%. 
     The engine ECU  50  controls operations of the engine  10  and the electric power generation unit  20 . 
     In particular, the engine ECU  50  controls, based on information about the SOC of the battery  30  output from the battery ECU  60 , the output voltage of the electric power generation unit  20  (i.e., the voltage at the battery terminal TB of the electric power generation unit  20 ). More specifically, the engine ECU  50  outputs a command value of the output voltage to a command terminal TR of the electric power generation unit  20 . Then, the voltage regulator  24  regulates the output voltage of the electric power generation unit  20  to the inputted command value. Moreover, the engine ECU  50  inputs, from a monitor terminal TF of the electric power generation unit  20 , a power generation state signal that indicates the state of power generation by the electric power generation unit  20 . Here, the state of power generation by the electric power generation unit  20  can be represented by the duty ratio of a switching element (not shown) included in the regulator  24 . The engine ECU  50  controls the output voltage of the electric power generation unit  20  so as to minimize the fuel consumption of the engine  10  due to the power generation while keeping the SOC of the battery  30  within an allowable range. 
     The engine ECU  50  also performs an engine automatic stop control (or idle reduction control) and an engine automatic start control. The engine automatic stop control is performed to automatically stop the engine  10  when the engine  10  is not being used to move the vehicle. The engine automatic start control is performed to automatically start, by means of the starter  40 , the engine  10  from a stop to move the vehicle. 
     To successfully start the engine  10 , it is necessary for the rotational speed of the crankshaft  12  to be raised by the starter  40  above a lower limit. Accordingly, the starter  40  is generally designed to be capable of generating enough torque to raise the rotational speed of the crankshaft  12  above the lower limit. However, friction of the engine  10 , which counteracts the rotation of the crankshaft  12  with the starter  40 , changes with the aging deterioration of the engine  10 . Thus, when the friction of the engine  10  has changed to exceed a value estimated in the design of the starter  40 , it may become impossible for the starter  40  to raise the rotational speed of the engine  10  above the lower limit. 
     Therefore, in the present embodiment, during each of starting operations of the engine  10 , the battery ECU  60  determines both the rotational speed of the engine  10  and the torque of the starter  40  based on the current supplied to the starter  40 . Then, based on the determined rotational speeds and torques, the battery ECU  60  estimates the friction of the engine  10 . Further, based on the estimated friction of the engine  10 , the battery ECU  60  estimates whether it is possible for the starter  40  to raise the rotational speed of the engine  10  above the lower limit in an upcoming starting operation of the engine  10 . 
     More specifically, when energization of the starter  40  has just started, the starter  40  does not rotate and thus there is no back electromotive force induced in the starter  40 . Therefore, current, the amount of which corresponds to the quotient of the terminal voltage of the battery  30  divided by the resistance between the battery  30  and the starter  40 , is supplied to the starter  40 , causing the starter  40  to rotate. Further, with the rotation of the starter  40 , there is induced in the starter  40  a back electromotive force which reduces the current flowing through the starter  40 . Therefore, the current flowing through the starter  40  depends on the rotational speed of the starter  40 . 
     Moreover, during a time period from the start of energization of the starter  40  to the start of combustion control of the engine  10 , the starter  40  rotates, together with the crankshaft  12 , at a speed that depends on both the torque generated by the starter  40  and a load torque imposed on the crankshaft  12 . Therefore, the current flowing through the starter  40  also depends on the load torque imposed on the crankshaft  12 . 
     Furthermore, the load torque imposed on the crankshaft  12  cyclically changes with the reciprocating movements of pistons in cylinders of the engine  10 ; thus, the rotational speed of the starter  40  also cyclically changes with the reciprocating movements of the pistons. The cyclic change in the rotational speed of the starter  40  causes a cyclic change in the current flowing through the starter  40 . 
     Therefore, based on the cyclic change in the current flowing through the starter  40 , it is possible to determine the rotational speed of the starter  40 . Further, the rotational speed of the crankshaft  12  can be computed by multiplying the rotational speed of the starter  40  by a gear ratio between the starter  40  and the crankshaft  12 . 
     In the present embodiment, there is provided no dedicated current sensor for sensing the current flowing through the starter  40 . Therefore, the battery ECU  60  determines the rotational speed of the starter  40  based on the discharge current of the battery  30  instead of the current flowing through the starter  40 . 
       FIG. 2A  shows the change in the discharge current of the battery  30  during a starting operation of the engine  10 . In  FIG. 2A , the positive (+) direction represents the direction of current being charged into the battery  30 , whereas the negative (−) direction represents the direction of current being discharged from the battery  30 . Therefore, the greater the current is in the negative direction, the more current is discharged from the battery  30 . 
     As shown in  FIG. 2A , the discharge current of the battery  30  once increases rapidly, and then decreases. After that, the discharge current repeats increasing and decreasing cyclically. Therefore, it is possible to compute the rotational speed of the starter  40  based on either a time interval between two adjacent local maximum values or on a time interval between two adjacent local minimum values of the discharge current of the battery  30 . 
     For example, in  FIG. 2A , there are shown three time intervals T 1 , T 2 , and T 3 , each of which is between two adjacent local maximum values of the discharge current of the battery  30 . The values of the rotational speed of the starter  40  for those time intervals can be respectively computed as (720/(Nc×T 1 )), (720/(Nc×T 2 )), and (720/(Nc×T 3 )), where Nc is the number of cylinders of the engine  10 . Further, the values of the rotational speed of the crankshaft  12  for the time intervals T 1 , T 2 , and T 3  can be respectively computed by multiplying the values of the rotational speed of the starter  40  for those time intervals by the gear ratio between the starter  40  and the crankshaft  12 . 
     However, the discharge current of the battery  30  sensed by the current sensor  52  behaves as shown in  FIG. 2B . This is because the signal output from the current sensor  52  includes electrical noise and thus cannot correctly reflect the actual change in the discharge current of the battery  30 . For example, for the first time interval T 1 , there are three pulses in the waveform of the signal output from the current sensor  52 . Accordingly, it is difficult for the battery ECU  60  to accurately determine the rotational speed of the starter  40  based directly on the waveform of the signal output from the current sensor  52 . 
     Therefore, in the present embodiment, the battery ECU  60  first performs an annealing process (or a relaxation process) for the signal output from the current sensor  52 . 
     For example, the battery ECU  60  may perform a “⅙ annealing process” for the signal output from the current sensor  52 , obtaining a waveform of the signal as shown in  FIG. 2C . Here, the ⅙ annealing process denotes a weighted average process which computes a current value of the discharge current by adding the product of multiplying a previously-sensed value of the discharge current by ⅚ to the product of multiplying a currently-sensed value of the discharge current by ⅙. It can be seen from  FIG. 2C  that after the annealing process, the influence of the electrical noise is completely eliminated and thus there is only one pulse for each time interval in the waveform. Accordingly, it is possible for the battery ECU  60  to accurately determine the rotational speed of the starter  40  based on the waveform obtained by the annealing process. 
     Moreover, if the battery ECU  60  starts the above annealing process at the same timing as the start of energization of the starter  40 , the initial rapid increase in the discharge current of the battery  30 , which occurs before the start of rotation of the starter  40 , will influence the results of the annealing process. Consequently, the timings of occurrence of the local maximum values of the discharge current which are determined based on the waveform obtained by the annealing process will deviate from the timings at which the local maximum values actually occur. As a result, the accuracy of the determination of the rotational speed of the starter  40  may be lowered. 
     Therefore, in the present embodiment, the battery ECU  60  further resets the annealing process at a timing when the once rapidly-increased discharge current of the battery  30  comes to decrease, thereby eliminating the influence of the initial rapid increase in the discharge current on the results of the annealing process. 
       FIG. 3  illustrates the effect of resetting the annealing process. In  FIG. 3 , the solid line indicates the waveform obtained by resetting the annealing process at a timing when the discharge current of the battery  30  decreases to −300 A, whereas the chain line indicates the waveform obtained without resetting the annealing process. It can be seen from  FIG. 3  that the waveform obtained without resting the annealing process lags behind the waveform obtained by resetting the annealing process due to the influence of the initial rapid increase in the discharge current. 
     Resetting the annealing process is effective especially when the rotational speed of the starter  40  is determined based on the change in the discharge current of the battery  30  as in the present embodiment. In comparison, in the case of determining the rotational speed of the starter  40  based on the change in the terminal voltage of the battery  30  as disclosed in Japanese Patent First Publication No. 2007-83965, it is difficult to reset an annealing process for the signal output from the voltage sensor  56 . 
     For example,  FIG. 4A  illustrates three waveforms of the signal output from the current sensor  52 , which are obtained with the SOC of the battery  30  being respectively equal to 100%, 80%, and 70%. It can be seen from  FIG. 4A  that the discharge current of the battery  30  depends only slightly on the SOC of the battery  30  and it is thus easy to set a common threshold of the discharge current to the three waveforms for determining the timing of resetting the annealing process. 
     On the other hand,  FIG. 4B  illustrates three waveforms of the signal output from the voltage sensor  56 , which are obtained with the SOC of the battery  30  being respectively equal to 100%, 80%, and 70%. It can be seen from  FIG. 4B  that the terminal voltage of the battery  30  depends heavily on the SOC of the battery  30  and it is thus difficult to set a common threshold of the terminal voltage to the three waveforms for determining the timing of resetting the annealing process. 
       FIG. 5A  gives a comparison between waveforms that are obtained by performing different annealing processes for the signal output from the current sensor  52 . More specifically, in  FIG. 5A , the dashed line A represents the waveform of the original signal; the one-dot chain line B represents the waveform obtained by performing a “½ annealing process” for the signal; the solid line C represents the waveform obtained by performing a “⅛ annealing process” for the signal; and the two-dot chain line D represents the waveform obtained by performing a “ 1/16 annealing process” for the signal. Here, similar to the ⅙ annealing process as described above, the ½, ⅛, and 1/16 annealing processes respectively denote ½, ⅛, and ⅙ weighted average processes. 
     As seen from  FIG. 5A , in the case of performing the ½ annealing process, the degree of relaxation for the change in the sensed discharge current is too small, and it is thus impossible to sufficiently eliminate the influence of the electrical noise. On the other hand, in the case of performing the 1/16 annealing process, the degree of relaxation for the change in the sensed discharge current is too large, and thus the resultant waveform cannot correctly reflect the actual change in the discharge current of the battery  30 . Accordingly, in the present embodiment, the ⅛ annealing process is adopted in consideration of the design specifications of the starter  40  and the engine  10 . 
       FIG. 5B  gives a comparison between waveforms that are obtained by resetting the annealing process (more specifically, the ⅛ annealing process) with different values of the threshold of the discharge current of the battery  30 . More specifically, in  FIG. 5B , the dashed line A represents the waveform obtained by resetting the annealing process with the threshold of the discharge current being equal to −200 A; the one-dot chain line B represents the waveform obtained by resetting the annealing process with the threshold being equal to −300 A; the solid line C represents the waveform obtained by resetting the annealing process with the threshold being equal to −400 A; and the two-dot chain line D represents the waveform obtained by resetting the annealing process with the threshold being equal to −500 A. It can be seen from  FIG. 5B  that changing the threshold of the discharge current in the range of −200 A to −500 A does not influence the timings of occurrence of the local maximum values and local minimum values of the discharge current. Accordingly, there is a flexibility in setting the threshold of the discharge current for determining the timing of resetting the annealing process. 
     In the present embodiment, the battery ECU  60  functions as an engine rotational speed determining device to determine the rotational speed of the engine  10 , more specifically, to determine the rotational speed of the crankshaft  12 . 
       FIG. 6  shows the process of the battery ECU  60  for determining the rotational speed of the crankshaft  12  during a starting operation of the engine  10 . This process is repeated, for example, in a predetermined cycle. 
     First, in step S 10 , the battery ECU  60  determines whether the engine  10  is being started by the starter  40 . More specifically, the battery ECU  60  determines whether a starter switch is turned on by the driver of the vehicle. 
     If the determination in step S 10  results in a “NO” answer, then the process directly goes to the end. Otherwise, if the determination in step S 10  results in a “YES” answer, then the process proceeds to step S 12 . 
     In step S 12 , the battery ECU  60  further determines whether a flag FC is in an OFF state. Here, the flag FC indicates whether the determination of the rotational speed of the crankshaft  12  has been completed. 
     If the determination in step S 12  results in a “NO” answer, in other words, if the determination of the rotational speed of the crankshaft  12  has been completed, then the process directly goes to the end. 
     Otherwise, if the determination in step S 12  results in a “YES” answer, in other words, if the determination of the rotational speed of the crankshaft  12  has not yet been completed, then the process proceeds to step S 14 . 
     In step S 14 , the battery ECU  60  inputs the signal output from the current sensor  52 , which indicates the discharge current of the battery  30 . 
     In step S 16 , the battery ECU  60  computes a current value Ic of the discharge current of battery  30  by performing the ⅛ annealing process for the signal output from the current sensor  52 . 
     In step S 18 , the battery ECU  60  determines whether a flag FR is in an ON state. Here, the flag FR indicates whether the annealing process has been reset. 
     If the determination in step S 18  results in a “NO” answer, in other words, if the annealing process has not yet been reset, then the process proceeds to step S 20 . 
     In step S 20 , the battery ECU  60  determines whether the current value Ic of the discharge current of the battery  30  is less than or equal to the threshold Ith of the discharge current. 
     If the determination in step S 20  results in a “NO” answer, in other words, if the discharge current of the battery  30  has not sufficiently decreased from the initial rapid increase, then the process directly goes to the end. 
     Otherwise, if the determination in step S 20  results in a “YES” answer, in other words, if the discharge current of the battery has sufficiently decreased from the initial rapid increase, then the process proceeds to step S 22 . 
     In step S 22 , the battery ECU  60  resets the annealing process, and then sets the flag FR to ON. 
     On the other hand, if the determination in step S 18  results in a “YES” answer, in other words, if the annealing process has been reset, then the process proceeds to step S 24 . 
     In step S 24 , the battery ECU  60  determines whether the number NL of local maximum values of the discharge current having been computed is greater than or equal to 2. 
     If the determination in step S 24  results in a “NO” answer, then the process directly goes to the end. Otherwise, if the determination in step S 24  results in a “YES” answer, then the process proceeds to step S 26 . 
     In step S 26 , the battery ECU  60  computes the rotational speed of the crankshaft  12 . 
     More specifically, when the number NL of the local maximum values of the discharge current is equal to 2, the battery ECU  60  computes the rotational speed of the starter  40  based on the time interval between the two local maximum values. Otherwise, when the number NL of the local maximum values of the discharge current is greater than 2, the battery ECU  60  first computes plural values of the rotational speed of the starter  40  based respectively on the time intervals between the local maximum values, and then computes the average of the plural values as the rotational speed of the starter  40 . After that, the battery ECU  60  further computes the rotational speed of the crankshaft  12  by multiplying the computed rotational speed of the starter  40  by the gear ratio between the starter  40  and the crankshaft  12 . 
     In step S 28 , the battery ECU  60  sets the flag FC to ON and the flag FR to OFF. Then, the process goes to the end. 
     In the present embodiment, the battery ECU  60  also functions as an engine starting possibility predicting device to predict the possibility of the starter  40  to successfully start the engine  10  in an upcoming starting operation of the engine  10 . 
       FIG. 7  shows the process of the battery ECU  60  for predicting the possibility of the starter  40  to successfully start the engine  10  in an upcoming starting operation of the engine  10 . This process is repeated, for example, in a predetermined cycle. 
     In step S 30 , the battery ECU  60  determines, based on the signal output from the current sensor  52 , both the rotational speed of the crankshaft  12  and the torque of the starter  40  during each of a plurality of starting operations of the engine  10 . 
     More specifically, during each of the starting operations of the engine  10 , the battery ECU  60  determines the rotational speed of the crankshaft  12  by performing the process shown in  FIG. 6 . Further, the battery ECU  60  determines the torque of the starter  40  using a map as shown in  FIG. 8 . The torque of the starter  40  depends on both the temperature of the starter  40  and the current flowing through the starter  40 . Therefore, the map may be prepared such that the temperature in the map represents the temperature of the starter  40  and the current in the map represents the current flowing through the starter  40 . However, in the present embodiment, there are provided the current sensor  52  for sensing the charge/discharge current of the battery  30  and the temperature sensor  54  for sensing the temperature of the battery  30 , but no dedicated current sensor for sensing the current flowing through the starter  40  and no dedicated temperature sensor for sensing the temperature of the starter  40 . Further, the current flowing through the starter  40  depends on the discharge current of the battery  30 , and the temperature of the starter  40  depends on the temperature of the battery  30 . Therefore, the map is preferably prepared such that the temperature in the map represents the temperature of the battery  30  and the current in the map represents the discharge current of the battery  30 . 
     In succeeding step S 32 , the battery ECU  60  determines whether the number NV of values of the rotational speed of the crankshaft  12  and the torque of the starter  40 , which have been determined during the foregone starting operations of the engine  10  with the then temperatures of the battery  30  falling in the same region as the current temperature of the battery  30 , is greater than or equal to a predetermined number NVP. 
     More specifically, the friction of the engine  10  can be estimated in the form of a friction curve which represents the relationship between the rotational speed of the crankshaft  12  and the torque of the starter  40 . Further, the friction of the engine  10  changes with the temperature of the engine  10 . In addition, before the start of combustion control of the engine  10 , the temperature of the engine  10  is almost equal to the temperature of the battery  30 . Therefore, to determine the friction curve for the current temperature, it is necessary for the number NV is so large as to be greater than the predetermined number NVP. 
     If the determination in step S 32  results in a “NO” answer, then the process directly goes to the end. Otherwise, if the determination in step S 32  results in a “YES” answer, then the process proceeds to step S 34 . 
     In step S 34 , the battery ECU  60  determines, based on the NV values of the rotational speed of the crankshaft  12  and the torque of the starter  40 , the friction curve through a single linear regression analysis. The determined friction curve is, for example, as shown in  FIG. 9 . In  FIG. 9 , the friction curve is drawn on a two-dimensional coordinate plane where the horizontal coordinate axis indicates rotational speed of the crankshaft  12  and the vertical coordinate axis indicates torque of the starter  40 . 
     In step S 36 , the battery ECU  60  determines, based on the SOC of the battery  30 , a performance curve of the starter  40  which represents the performance of the starter  40  at the SOC of the battery  30 . The determined performance curve is, for example, as shown in  FIG. 10 . In  FIG. 10 , the performance curve is drawn, together with the friction curve, on the two-dimensional coordinate plane whose horizontal and vertical coordinate axes respectively represent rotational speed of the crankshaft  12  and torque of the starter  40 . 
     The performance curve of the starter  40  is determined based on an equivalent circuit as shown in  FIG. 11 . In  FIG. 11 , Vo represents the open-circuit voltage of the battery  30 ; Vm represents the induced voltage of the starter  40  (i.e., the back electromotive force induced in the starter  40 ); Rb represents the internal resistance of the battery  30 ; Rs represents the internal resistance of the starter  40 ; and Rv represents the wiring resistance (i.e., the resistance of wires) between the battery  30  and the starter  40 . 
     In the equivalent circuit, there is satisfied the following relationship:
 
 Vo=I ×( Rb+Rv+Rs )+ Vm   (Equation 1)
 
where I is the current flowing through the circuit.
 
     Further, the following equation can be derived by substituting (Vm=B×L×N) into Equation 1, where B, L, and N are respectively the magnetic flux density of the magnetic field in the starter  40 , the length of wires traversing the magnetic field, and the rotational speed of the starter  40 .
 
 Vo=I ×( Rb+Rv+Rs )+ B×L×N   (Equation 2)
 
     On the other hand, the torque T of the starter  40  can be represented by the following equation:
 
 T=B×L×I   (Equation 3)
 
     By eliminating the current I in both Equations 2 and 3, the following equation can be derived.
 
 T =( Vo−B×L×N )× B×L /( Rb+Rv+Rs )  (Equation 4)
 
     In the present embodiment, the performance curve of the starter  40  is determined based on the above Equation 4. More specifically, the sum of the wiring resistance Rv and the internal resistance Rs of the starter  40 , which depends on temperature, is determined using a map as shown in  FIG. 12A . Moreover, the internal resistance Rb of the battery  30 , which depends on the SOC of the battery  30  as well as on temperature, is determined using a map as shown in  FIG. 12B . Furthermore, the open-circuit voltage V 0  of the battery  30  is determined based on the equation of (Vo=Vb−Rb×I−Vp), where Vp is the polarization voltage of the battery  30 . The polarization voltage Vp, which depends on both temperature and the SOC of the battery  30 , is determined using a map as shown in  FIG. 13 . 
     Returning to  FIG. 7 , in step S 38  of the process, the battery ECU  60  determines, on the two-dimensional coordinate plane shown in  FIG. 10 , the intersection point P between the friction curve and the performance curve of the starter  40 . Then, the battery ECU  60  predicts a value NP of the rotational speed of the crankshaft  12  as the value of the rotational speed at the intersection point P. More specifically, the battery ECU  60  predicts that the rotational speed of the crankshaft  12  will have the value NP in the upcoming starting operation of the engine  10  if the upcoming starting operation starts from the present moment. 
     In succeeding step S 40 , the battery ECU  60  determines whether the predicted value NP is greater than or equal to the lower limit Nmin of the rotational speed of the crankshaft  12 . As described previously, to successfully start the engine  10 , it is necessary for the rotational speed of the crankshaft  12  to be raised by the starter  40  above the lower limit Nmin. 
     If the determination in step S 40  results in a “YES” answer, then the process proceeds to step S 42 . 
     In step S 42 , the battery ECU  60  predicts that it is possible for the starter  40  to successfully start the engine  10  in the upcoming starting operation of the engine  10 . Then, the process goes to the end. 
     On the other hand, if the determination in step S 40  results in a “NO” answer, then the process proceeds to step S 44 . 
     In step S 44 , the battery ECU  60  predicts that it is impossible for the starter  40  to successfully start the engine  10  in the upcoming starting operation of the engine  10 . Then, the battery ECU  60  informs the driver of the vehicle, via a display  62  as shown in  FIG. 1 , of the impossibility of the starter  40  to successfully start the engine  10 . After that, the process goes to the end. 
     According to the present embodiment, the following advantages can be obtained. 
     In the present embodiment, the battery ECU  60  functions as an engine rotational speed determining device to determine the rotational speed of the crankshaft  12  for a starting operation of the engine  10 . More specifically, the battery ECU  60  inputs the signal output from the current sensor  52  during the starting operation of the engine  10 ; the signal indicates the discharge current of the battery  30 , in other words, the current supplied from the battery  30  to the starter  40 . Then, the battery ECU  60  determines the rotational speed of the crankshaft  12  in the starting operation based on the cyclic change in the discharge current of the battery  30  indicated by the signal input from the current sensor  52 . 
     Generally, the discharge current of the battery  30  depends only slightly on the SOC of the battery  30 , whereas the terminal voltage of the battery  30  depends heavily on the SOC of the battery  30 . Therefore, according to the present embodiment, the battery ECU  60  can more accurately determine the rotational speed of the crankshaft  12  in the starting operation in comparison with the case of determining the same based on the cyclic change in the terminal voltage of the battery  30 . 
     Further, in the present embodiment, the battery ECU  60  performs a relaxation process (or annealing process) for the signal input from the current sensor  52 , thereby eliminating the influence of electrical noise on the accuracy of determination of the rotational speed of the crankshaft  12 . 
     Furthermore, in the present embodiment, the battery ECU  60  resets the relaxation process at a timing when the discharge current of the battery  30  has decreased, after the initial rapid increase thereof, to become not higher than the threshold Ith of the discharge current. Consequently, it is possible for the battery ECU  60  to eliminate the influence of the initial rapid increase of the discharge current on the results of the relaxation process, thereby improving the accuracy of determination of the rotational speed of the crankshaft  12 . 
     In addition, steps S 14 , S 26 , S 16 , and S 22  of  FIG. 6  respectively correspond to the signal inputting means, rotational speed determining means, relaxation process performing means, and relaxation process resetting means of the present invention. 
     In the present embodiment, the battery ECU  60  also functions as an engine starting possibility predicting device to predict the possibility of the starter  40  to successfully start the engine  10  in an upcoming starting operation of the engine  10 . More specifically, the battery ECU  60  inputs the signal output from the current sensor  52  during each of a plurality of starting operations the engine  10 . Then, the battery ECU  60  determines both the rotational speed of the crankshaft  12  and the torque of the starter  40  in each of the starting operations based on the change in the discharge current of the battery  30  indicated by the signal input from the current sensor  52 . Thereafter, the battery ECU  60  predicts, based on those values of the rotational speed of the crankshaft  12  and the torque of the starter  40  which have been determined for the foregone starting operations with the then temperatures of the battery  30  falling in the same region as the current temperature of the battery  30 , the possibility of the starter  40  to successfully start the engine  10  in the upcoming starting operation. 
     The friction of the engine  10 , which counteracts the rotation of the crankshaft  12  with the starter  40 , can be estimated based on both the rotational speed of the crankshaft  12  and the torque of the starter  40 . Further, based on the friction of the engine, the battery ECU  60  can predict the possibility of the starter  40  to successfully start the engine  10  in the upcoming starting operation. Furthermore, since both the rotational speed of the crankshaft  12  and the torque of the starter  40  are determined based on the same parameter, i.e., the discharge current of the battery  30 , the battery ECU  60  can make the predication easily and accurately. 
     Moreover, in the present embodiment, the battery ECU  60  predicts the rotational speed Np of the crankshaft  12  in the upcoming starting operation based on those values of the rotational speed of the crankshaft  12  and the torque of the starter  40  as described above. When the predicted rotational speed Np of the crankshaft  12  is greater than or equal to the lower limit Nmin, the battery ECU  60  predicts that it is possible for the starter  40  to successfully start the engine in the upcoming starting operation. 
     With the above configuration, the battery ECU  60  can easily and accurately predict the possibility of the starter  40  to successfully start the engine  10  in the upcoming starting operation. 
     Furthermore, in the present embodiment, the battery ECU  60  determines, on the two-dimensional coordinate plane as shown in  FIG. 10 , the friction curve based on those values of the rotational speed of the crankshaft  12  and the torque of the starter  40  as described. The battery ECU  60  also determines, on the two-dimensional coordinate plane, the performance curve of the starter  40  based on the SOC of the battery  30 . Then, the battery ECU  60  predicts the rotational speed Np of the crankshaft  12  in the upcoming starting operation as the rotational speed of the crankshaft  12  at the intersection point P between the friction curve and the performance curve of the starter  40 . 
     The friction curve represents the friction of the engine  10 , whereas the performance curve represents the performance of the starter  40  at the SOC of the battery  30 . Therefore, with the above configuration, the battery ECU  60  can easily and accurately predict the rotational speed of the crankshaft  12  in the upcoming starting operation. 
     In addition, step S 30  of  FIG. 7  corresponds to the rotational speed determining means and torque determining means, steps S 32 , S 34 , S 36 , and S 38  of  FIG. 6  together correspond to the rotational speed predicting means, and steps S 40 , S 42 , and S 44  together correspond to the possibility predicting means of the present invention. 
     Second Embodiment 
     In the previous embodiment, the engine ECU  50  performs the engine automatic start control to automatically start the engine  10  from a stop by using the starter  40 . 
     In comparison, in the present embodiment, the engine ECU  50  performs an engine automatic start control to automatically start the engine  10  from a stop through combustion control of the engine  10  without using the starter  40 . In this case, it is essential to accurately control the stop position of the crankshaft  12  in the last automatic stop of the engine  10 . 
     In controlling the stop position of the crankshaft  12 , the manipulation of actuators, such as a throttle valve and a fuel injector, is limited. Moreover, the amount of electric power generated by the electric power generation unit  20  is also limited. Therefore, it is necessary to accurately adjust the amounts of manipulation of the actuators and the amount of electric power generated by the electric power generation unit  20 , so as to bring the stop position of the crankshaft  12  to a desired position. However, the adjustment of the amounts of manipulation of the actuators and the amount of electric power generated by the electric power generation unit  20  is also dependent on the friction of the engine  10  which changes with the aging deterioration of the engine  10 . Therefore, it is necessary to accurately estimate the present level of the friction of the engine  10  for ensuring the accuracy of the engine automatic stop control. 
     In the present embodiment, the battery ECU  60  also functions as an engine friction estimating device to estimate the friction of the engine  10 . 
       FIG. 14  shows the process of the battery ECU  60  for estimating the friction of the engine  10 . This process is repeated, for example, in a predetermined cycle. 
     Steps S 30 , S 32 , and S 34  of the process are respectively the same as those of the process shown in  FIG. 7 ; therefore, a repeated description thereof is omitted hereinafter. 
     In step S 50 , the battery ECU  60  determines an estimated value FE of the friction of the engine  10  as the torque of the starter  40  at the point on the friction curve where the rotational speed of the crankshaft  12  is equal to a predetermined value Nx. Then, the process goes to the end. 
     The estimated value Fe represents the present level of the friction of the engine  10 . This is because the higher the friction of the engine  10  is, the higher the torque of the starter  40  is at the same rotational speed of the crankshaft  12 . 
     Moreover, based on the estimated value FE of the friction of the engine  10 , the engine ECU  50  performs the engine automatic stop control. 
       FIG. 15  shows the process of the engine ECU  50  for performing the engine automatic stop control. This process is performed, for example, in a predetermined cycle. 
     First, in step S 60 , the engine ECU  50  determines whether conditions for automatically stopping the engine  10  are satisfied. Here, the conditions may be set to well-known conditions for performing an idle reduction control. 
     If the determination in step S 60  results in a “NO” answer, then the process directly goes to the end. Otherwise, if the determination in step S 60  results in a “YES” answer, then the process proceeds to step S 62 . 
     In step S 62 , the engine ECU  50  acquires the estimated value FE of the friction of the engine  10  from the battery ECU  60 . 
     In succeeding step S 64 , the engine ECU  50  performs the engine automatic stop control (abbreviated to EASC in  FIG. 15 ) based on the estimated value FE of the friction of the engine  10 . 
     More specifically, the engine ECU  50  sets, based on the estimated value FE of the friction of the engine  10 , the amounts of manipulation of the actuators and the amount of electric power generated by the electric power generation unit  20 . Then, the engine ECU  50  manipulates the actuators by the set amounts of manipulation and controls the electric power generation unit  20  to generate the set amount of electric power, thereby bringing the stop position of the crankshaft  12  to the desired position. With respect to more details about control of the stop position of the crankshaft  12 , a reference can be made to, for example, Japanese Patent First Publication No. 2005-315202. 
     After step S 64 , the process goes to the end. 
     According to the present embodiment, the following advantages can be further obtained. 
     In the present embodiment, the battery ECU  60  also functions as an engine friction estimating device to estimate the friction of the engine  10 . More specifically, the battery ECU  60  inputs the signal output from the current sensor  52  during each of a plurality of starting operations the engine  10 . Then, the battery ECU  60  determines both the rotational speed of the crankshaft  12  and the torque of the starter  40  in each of the starting operations based on the change in the discharge current of the battery  30  indicated by the signal input from the current sensor  52 . Thereafter, the battery ECU  60  estimates the friction of the engine  10  based on those values of the rotational speed of the crankshaft  12  and the torque of the starter  40  which have been determined for the foregone starting operations with the then temperatures of the battery  30  falling in the same region as the current temperature of the battery  30 . 
     The friction of the engine  10 , which counteracts the rotation of the crankshaft  12  with the starter  40 , can be estimated based on both the rotational speed of the crankshaft  12  and the torque of the starter  40 . In the present embodiment, since both the rotational speed of the crankshaft  12  and the torque of the starter  40  are determined based on the same parameter, i.e., the discharge current of the battery  30 , it is possible for the battery ECU  60  to easily and accurately estimate the friction of the engine  10 . 
     Further, in the present embodiment, the battery ECU  60  estimates the friction of the engine  10  in the form of the estimated value FE of the friction. More specifically, the battery ECU  60  determines, on the two-dimensional coordinate plane as shown in  FIG. 10 , the friction curve based on those values of the rotational speed of the crankshaft  12  and the torque of the starter  40  as described above. Then, the battery ECU  60  determines the estimated value FE as the torque of the starter  40  at the point on the friction curve where the rotational speed of the crankshaft  12  is equal to the predetermined value Nx. 
     With the above configuration, the battery ECU  60  can more easily and accurately estimate the friction of the engine  10 . 
     In addition, step S 50  of  FIG. 14  corresponds to the engine friction estimating means of the present invention. 
     In the present embodiment, the engine ECU  50  and the battery ECU  60  together function as an engine automatic stop control device to control an automatic stop of the engine  10 . More specifically, when the conditions for automatically stopping the engine  10  are satisfied, the engine ECU  50  acquires the estimated value FE of the friction of the engine  10  from the battery ECU  60 . Then, the engine ECU  50  controls the automatic stop of the engine  10  based on the estimated value FE of the friction of the engine  10 . 
     With the above configuration, the engine ECU  50  can suitably control the automatic stop of the engine  10  regardless of change in the friction of the engine  10 . 
     In addition, steps S 60  and S 64  of  FIG. 15  together correspond to the controlling means of the present invention. 
     Third Embodiment 
     In this embodiment, the battery ECU  60  is further configured to inform, when there is a considerable increase in the friction of the engine  10 , the driver of the vehicle of the increase in the friction. 
       FIG. 16  shows the process of the battery ECU  60  for informing an increase in the friction of the engine  10 . This process is repeated, for example, in a predetermined cycle. 
     First, in step S 70 , the battery ECU  60  determines whether the evaluated value FE of the friction of the engine  10  is greater than or equal to a threshold value Fmax. Here, the threshold value Fmax represents the upper limit of the friction above which the engine  10  cannot properly operate. 
     If the determination in step S 70  results in a “NO” answer, then the process directly goes to the end. Otherwise, if the determination in step S 70  results in a “YES” answer, then the process proceeds to step S 70 . 
     In step S 70 , the battery ECU  60  informs the driver of the vehicle, via the display  62  as shown in  FIG. 1 , of the increase in the friction above the upper limit. Then, the process goes to the end. 
     According to the present embodiment, the following advantages can be further obtained. 
     In the present embodiment, the battery ECU  60  determines whether the friction of the engine  10  has increased to exceed the upper limit by determining whether the evaluated value FE of the friction is greater than or equal to the threshold value Fmax. 
     With this configuration, the battery ECU  60  can easily and correctly make the determination of whether the friction of the engine  10  has increased to exceed the upper limit. 
     In addition, by informing the driver of the increase in the friction of the engine  10 , it is possible to allow the driver to take necessary measures, such as changing the engine oil, in a timely manner. 
     While the above particular embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various modifications, changes, and improvements may be made without departing from the spirit of the invention. 
     1) In the first embodiment, the battery ECU  60  determines the rotational speed of the crankshaft  12  based on the time interval (or time intervals) between local maximum values of the discharge current of the battery  30 . 
     However, it is also possible for the battery ECU  60  to compute the rotational speed of the crankshaft  12  based on the time interval (or time intervals) between local minimum values of the discharge current. 
     2) In the first embodiment, the battery ECU  60  performs the ⅛ annealing process for the signal output from the current sensor  52 . 
     However, the battery ECU  60  may also perform, instead of the ⅛ annealing process, any other annealing process whose weighting factors are suitably set according to the design specifications of the engine  10  and the starter  40 . 
     Further, the relaxation process for eliminating the influence of electrical noise is not limited to an annealing process. For example, the battery ECU  60  may also perform, instead of the ⅛ annealing process, a moving average process for the signal output from the current sensor  52 . 
     Furthermore, the relaxation process is not limited to a digital filtering process. For example, the battery ECU  60  may also perform the relaxation process using a RC filter. In this case, it is also preferable to reset the relaxation process to eliminate the influence of the initial rapid increase in the discharge current of battery  30  on the results of the relaxation process. 
     3) In the first embodiment, the battery ECU  60  determines the torque of the starter  40  based on both the temperature of the battery  30  and the discharge current of the battery  30 . 
     However, the battery ECU  60  may simply determine the torque of the starter  40  based only on the discharge current of the battery  30 . 
     4) In the first embodiment, the battery ECU  60  determines the open-circuit voltage V 0  of the battery  30  based on the equation of (Vo=Vb−Rb×I−Vp). 
     However, it is also possible for the battery ECU  60  to determine the open-circuit voltage V 0  of the battery  30  using a predetermined map that represents the relationship between the open-circuit voltage V 0  of the battery  30 , the SOC of the battery  30 , and the temperature of the battery  30 . 
     5) In the first embodiment, the battery ECU  60  predicts the engine starting possibility by determining whether the predicted value NP of the rotational speed of the crankshaft  12  is greater than or equal to the lower limit Nmin. 
     However, it is also possible for the battery ECU  60  to predict the engine starting possibility by determining whether the estimated value FE of the friction of the engine  10  is greater than or equal to a predetermined value. 
     6) In the second embodiment, the battery ECU  60  estimates the friction of the engine  10  in the form of the estimated value FE. 
     However, the battery ECU  60  may also estimate the friction of the engine  10  in the form of an estimated value NE which is the rotational speed of the crankshaft  12  at the point on the friction curve where the torque of the starter  40  is equal to a predetermined value. 
     Further, it is also possible for the battery ECU  60  to estimate the friction of the engine  10  using, instead of the friction curve, a predetermined map that represents the relationship between the friction of the engine  10 , the rotational speed of the crankshaft  12 , and the torque of the starter  40 . 
     7) In the previous embodiments, the battery ECU  60  determines the rotational speed of the crankshaft  12  and the torque of the starter  40  based on the discharge current of the battery  30 . 
     However, an additional current sensor may be further employed to sense current flowing through the starter  40 , so that the battery ECU  60  can determine the rotational speed of the crankshaft  12  and the torque of the starter  40  based on the current flowing through the starter  40 . 
     8) In the first embodiment, the battery ECU  60  resets the annealing process in the determination of the rotational speed of the crankshaft  12 . 
     However, the battery ECU  60  may simply determine the rotational speed of the crankshaft  12  without resetting the annealing process. 
     9) In the first embodiment, the engine  10  is started by the starter  40 . 
     However, in addition to the starter  40 , a motor-generator may be further employed to start the engine  10  in a restarting operation of the engine  10  after an automatic stop of the engine  10 . 
     10) In the first embodiment, the battery  30  is made up of a lead accumulator. 
     However, the battery  30  may be alternatively made up of, for example, a nickel metal-hydride battery pack. 
     11) In the previous embodiments, the engine  10  is a port-injection gasoline engine. 
     However, the engine  10  may be alternatively a cylinder-injection gasoline engine. Further, the engine  10  is not limited to a gasoline engine. For example, the engine  10  may be a diesel engine.