Abstract:
A fuel injector control method comprises determining a required separation time between a termination of an on signal associated with a first injection event and an initiation of an on signal associated with a second injection event. The method comprises calculating an overlap time between the separation time and the time to charge the piezoelectric stack to a first level; dividing the overlap time into first and second time periods as a function of the charge and discharge currents; applying the charge current to the piezoelectric stack for a charge time; and applying the discharge current to the piezoelectric stack for a discharge time so as to discharge the stack to a second level, wherein the discharge time is calculated on the basis of the second time period of the overlap time. Thus, first and second injection events are merged in a pulse mode of operation.

Description:
FIELD OF THE INVENTION 
     This invention relates to a control method for controlling operation of a fuel injector, specifically a piezoelectric fuel injector, for use in the delivery of fuel to a combustion space of an internal combustion engine. In particular, the invention relates to a method for controlling the time separation between a termination of one injection event and an initiation of a subsequent injection event. 
     BACKGROUND OF THE INVENTION 
     Piezoelectric fuel injectors are well-known for use in automotive engines and employ a piezoelectric actuator, made of a stack of piezoelectric elements arranged mechanically in series, for opening and closing an injection valve to meter fuel injected into the engine. One type of piezoelectric fuel injector is the de-energize-to-inject injector described in EP174615. The injector stack is held in a charged state during periods of non-injection, and when it is required to inject fuel the stack is de-energized. When injection is to be terminated the stack is re-charged again. In an energize-to-inject injector, operation is reversed so that charging of the stack initiates injection and discharging of the stack terminates injection. 
     Piezoelectric actuators, and hence fuel delivery, are controlled by an engine control module (ECM). The ECM incorporates strategies that determine the required fuelling and timing of injection pulses based on the current engine operating conditions, including torque, engine speed and operating temperature. Such strategies determine the number, size and timings of the injections and tend to be large and complicated. Furthermore, such strategies are calibrated for specific applications (i.e., specific customers and specific engines). 
     Strategies of this type allow for multiple injection pulses, such as pilot and post injections. Pilot injections are generally used to reduce combustion noise, and make the engine sound less like older diesel engines. Post injections are generally used in a couple of ways: close to the main injection they are used to reduce soot (this is sometimes referred to as split main); and late post injections are used for aftertreatment systems, i.e., deNOx filters and particulate traps. 
     Although pilot injections are used in diesel engines to reduce combustion noise, they can lead to an increase in smoke production. Minimising the separation between the pilot and main pulses can improve the smoke-noise tradeoff, i.e., achieving good noise reduction with smaller increases in smoke. 
     The quantity, fuelling and timing of these injection pulses is continuously variable across the engine operating range. This allows optimization of the engine operation in terms of performance, fuel economy and emissions. 
     The ECM selects the injector to be opened and determines when the injector is to be opened, how long it is to remain open before being closed (this is known as an injection event), and for how long the injector is to remain closed before the next injection event. 
     The time separation between one injection event and another, i.e., the time period between a termination (i.e., conclusion) of an electrical on signal associated with the first injection event and an initiation of an electrical on signal associated with the second injection event, is known as the demand time, and is controlled by the ECM depending on the current operating strategy (i.e., driver demands and current engine operating conditions). 
     Being able to control the demand time accurately is key to the flexibility of the ECM. It allows optimization in terms of engine performance, noise and other unwanted emissions, for example nitrous oxides and particulates. 
     In known injectors of the de-energize to inject type, the stack is charged fully to ensure that the electrical charge across the stack returns to a known level, providing a reference for the next discharge phase. As a result, there is a limit to how short the demand time can be because it is governed by the time required to charge the stack fully, the time it takes to open the injector, and the time required for the switching means controlling the injection to switch on and off as appropriate. However, in order to increase flexibility of operation it is desirable to reduce the demand time beyond the limit imposed by known injection control strategies. 
     SUMMARY OF THE INVENTION 
     According to a first aspect of the invention there is provided a control method for a fuel injector having a piezoelectric stack that is charged by means of a charge current and discharged by means of a discharge current, the fuel injector having an injector opening time, the method comprising: determining a required separation time between a termination of an electrical on signal associated with a first injection event and an initiation of an electrical on signal associated with a subsequent (i.e., second) injection event; calculating an overlap time between the required separation time and the time required to charge the piezoelectric stack to a first reference level using the charge current; dividing the overlap time into first and second time periods as a function of the charge and discharge currents; applying the charge current to the piezoelectric stack for a charge time calculated on the basis of the first time period of the overlap time; and applying the discharge current to the piezoelectric stack for a discharge time so as to discharge the stack to a second reference level, wherein the discharge time is calculated on the basis of the second time period of the overlap time, such that the first and second injection events are merged in a merging pulse mode of operation. 
     The present invention advantageously enables the ECM to operate with demand times between a limit set by finite hardware times and the minimum demand time previously achievable in known systems. 
     Preferably, the charge time is calculated by subtracting the first time period of the overlap time from the time required to charge the stack to the first reference level such that the voltage across the stack increases from a low voltage level to a high voltage level. 
     The discharge time is preferably calculated by subtracting the second time period of the overlap time from the time required to discharge the stack to a second reference level such that the voltage across the stack decreases from a high voltage level to a low voltage level. 
     Operation in the merging pulse mode may be selected depending on the overlap time. It may also be selected depending on the required separation time and/or the injector closing time. 
     Optionally, the method may operate in an alternative mode of operation when not operating in the merging pulse mode, the alternative mode of operation method comprising: applying the charge current to the injector piezoelectric stack for the time required to charge the injector piezoelectric stack to a first reference level; and applying the discharge current to the piezoelectric stack for the time required to discharge the piezoelectric stack to the second reference level such that the voltage across the stack decreases from a high voltage level to a low voltage level. 
     Preferably, the required separation time is determined using an engine control module ECM. 
     The overlap time may be calculated by subtracting the required separation time from the closing time, which may be calculated by adding the charge time required to charge the piezoelectric stack to the first reference level, to a dwell time that depends on at least a hardware switching time. 
     Preferably, the overlap time is divided in inverse proportion to charge and discharge currents to result in the first and second time periods. 
     Optionally, the first reference level is a fully charged level for the stack, and the second reference level is a fully discharged level for the stack. 
     According to a second aspect of the invention there is provided: a controller for a fuel injector comprising a piezoelectric stack that is charged by means of a charge current and discharged by means of a discharge current, the fuel injector having an injector closing time, the controller comprising: means for determining a required separation time between a termination of an electrical on signal associated with a first injection event and an initiation of an electrical on signal associated with a second injection event; means for calculating an overlap time between the required separation time and the time required to charge the piezoelectric stack to a first reference level; means for dividing the overlap time into first and second time periods as a function of the charge and discharge currents; means for applying the charge current to the piezoelectric stack for a charge time calculated on the basis of the first time period of the overlap time; and means for applying the discharge current to the piezoelectric stack for a discharge time so as to discharge the stack to a second reference level, wherein the discharge time is calculated on the basis of the second time period of the overlap time, such that the first and second injection events are merged in a merging pulse mode of operation. 
     Accordingly, the second aspect of the invention may take any of the optional features of the first aspect of the invention. 
     According to a third aspect of the invention there is provided a computer program product comprising at least one computer program software portion that, when executed in an executing environment, is operable to implement one or more of the steps of the method of the first aspect of the invention. 
     According to a fourth aspect of the invention there is provided a data storage medium having the or each computer software portion according to the third aspect of the invention. 
     According to a fifth aspect of the invention there is provided a microcomputer provided with a data storage medium according to the fourth aspect of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1   a  (prior art) is a sectional view of a fuel injector of the type including a piezoelectric actuator, to which the method of the present invention may be applied, 
         FIG. 1   b  (prior art) is an enlarged view of an upper portion of the fuel injector in  FIG. 1 , 
         FIG. 1   c  (prior art) is an enlarged view of a middle portion of the fuel injector in  FIG. 1 , 
         FIG. 2   a  (prior art) shows an ideal graph of charge versus time for opening and closing phases of the fuel injector in  FIGS. 1   a  to  1   c;    
         FIG. 2   b  (prior art) shows a graph of voltage versus time, corresponding to  FIG. 2   a , for the opening and closing phases of a piezoelectrically actuated fuel injector, 
         FIG. 3  shows a block diagram of an engine control system, including an ECM, for controlling operation of fuel injectors of the type shown in  FIGS. 1   a  to  1   c,    
         FIG. 4  a hydraulic fuel pulse waveform and corresponding electrical signals (fuel pulse) and voltage waveforms for two injection events, including charge and discharge enable signals, 
         FIG. 5  shows an electrical fuel pulse waveform and a corresponding voltage waveform for a closing phase of one injection event and an opening phase of a second injection event occurring at three different times, resulting in three different demand times, 
         FIG. 6  shows a voltage waveform for a closing phase of one injection event and an opening phase of a second injection event where the pulses are merged, 
         FIG. 7  shows a flow chart of the steps required for the ECM to determine which operating mode, conventional or merging pulse, in which to operate, 
         FIG. 8  (prior art) shows a flow chart of the steps taken by the ECM when operating in conventional mode, 
         FIG. 9  shows a flow chart of the steps taken by the ECM when operating in merging pulse mode, 
         FIG. 10  shows non-merged pilot and main injection events, 
         FIG. 11  shows non-merged pilot and main injection events with a shorter separation time than that shown in  FIG. 10 , 
         FIG. 12  shows merged pilot and main injection events, and 
         FIG. 13  shows merged pilot and main injection events, where the period of the main injection event has been reduced. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Referring to  FIGS. 1   a  to  1   c , a fuel injector of the piezoelectrically operable type typically includes a valve needle  10  that is engageable with a seating to control fuel delivery to an associated engine cylinder. A surface associated with the valve needle  10  is exposed to fuel pressure within a control chamber  12 . The valve needle  10  is moveable between a first position, in which it is engaged with its seating, and a second position, in which the valve needle is lifted from its seating. When the valve needle  10  is in its first seated position fuel injection does not occur, and when it is moved away from its first position towards its second position injection is commenced. The injector receives fuel from a common rail source (not shown) of high-pressure fuel having a rail pressure, R p , that is measured by a suitable sensor (not shown). 
     The injector includes a hydraulic amplifier arrangement including a control piston  18  that is operable to vary the volume of the control chamber  12 . Movement of the control piston  18  is controlled by means of a piezoelectric actuator arrangement including a stack  14  of one or more elements formed from a piezoelectric material. The actuator stack  14  carries, at its lower end, an anvil member  16  that is coupled to the control piston  18  through a load-transmitting member  20 . By controlling the length of the actuator stack  14 , and hence the position of the control piston  18 , movement of the valve needle is controlled between its seated and unseated positions, with the change in displacement of the stack  14  being amplified to move the valve needle  10  through an amount determined by the characteristics of the hydraulic amplifier arrangement. A spring  22  serves to urge the valve needle  10  against its seating, and the biasing force of the spring is set by adjustment of a screw threaded rod  24  that passes through the control piston  18 . 
     As can be seen most clearly in  FIG. 1   b , the uppermost end of the actuator stack  14  is secured to an electrical connector  26  including first and second terminals  26   a ,  26   b  that extend into a radial drilling  28  in an actuator housing  30  to permit appropriate electrical connections to be made to control the piezoelectric actuator. 
     The piezoelectric actuator shown in  FIGS. 1   a  to  1   c  is operable to control movement of the valve needle of the injector between the open and closed positions as the piezoelectric stack length is varied. When a first relatively high voltage is applied across the actuator stack  14 , the piezoelectric material is energized to a first, higher energization level and the length of the stack is relatively long. In this position, the valve needle  10  occupies a position, in which the valve needle  10  is seated (i.e., a non-injecting state). When a second, relatively low voltage is applied the actuator stack  14 , the piezoelectric material is de-energized to second, lower energization level and the length of the stack  14  is reduced. The actuator is therefore displaced, with the result that the valve needle  10  is caused to lift away from its seating (i.e., an injecting state). Between the first and second energization levels the actuator stack  14  is said to have a “stack displacement” or “stroke” that is equal to the change in length of the stack  14  between the two energization levels. The voltages and/or other control signals are supplied to the actuator by means of a computer processor or engine controller as described further below. Further constructional and operational details of the injector in  FIGS. 1   a  to  1   c  are described in our co-pending patent application EP 0995901 A1 and so will not be described in further detail here. 
     As explained earlier, the stack  14  consists of a number of capacitive elements that are effectively connected in parallel. As capacitors block direct current (DC), the stack displacement is not directly controlled by applying a voltage across the stack  14 . Instead, the stack  14  is charged to various energization levels by driving an alternating current (AC), the root mean square (RMS) of which is a known constant, through the stack for a given time, in accordance with the relationship below:
 
Charge ( Q )=Current ( I )×time ( t )
 
       FIG. 2   a  shows a typical graph of charge as a function of time for an actuator that is driven from a closed non-injecting position to an open injecting position (i.e., an opening phase  40 ) and back again to the non-injecting position (i.e., a closing phase  41 ). 
     During the opening phase the charge changes from a first charge level Q charge  to a second charge level Q discharge  over a discharge time t discharge . The difference between Q charge  and Q discharge  equals a change in charge ΔQ that corresponds to the length of the stack  14  changing from a relatively long length to a relatively short length. 
       FIG. 2   b  shows a graph of voltage as a function of time corresponding to  FIG. 2   a . As shown, a change in charge results in a corresponding change in the voltage across the stack. 
     It is to be appreciated that the RMS current can be varied by the ECM under various specific operating conditions. 
     The ECM contains fuelling and timing strategies that determine the number of injection events per engine cycle and the time separation between these injection events. These strategies use various engine parameters including, but not exclusively, engine speed, torque, rail pressure and engine and fuel temperatures. These strategies can be calibrated to optimize engine performance, over the entire engine operating range, in terms of engine noise, emissions (NOx, particulates etc), engine performance and fuel economy. 
     This optimization in certain conditions requires minimization of the separations between injection events, in particular pilot to main separation or split main operation. Pilot to main separation influences noise and NOx formation, while split main operation is used to combat soot creation. 
       FIG. 3  shows a block diagram of an engine management control loop. A driver  50  controls the speed and acceleration of the engine/vehicle using the accelerator  52 . This is fed into the ECM  54 , which includes a sub-module  56  for determining fuelling and timing strategies between injection events, and injector drive circuitry  58  for controlling the operation of the injectors. An engine  60  is shown as including the injectors  62  and temperature, fuel pressure and engine speed sensors  64 . Data from these sensors is fed back to the ECM and is used to determine the required fuelling and timing strategies. The engine  62  delivers power and speed to the vehicle and a measure of this is fed back to the ECM  54  for determining the fuelling and timing strategies. 
       FIG. 4  shows a fuel delivery waveform (a hydraulic fuel pulse waveform) and corresponding electrical signals (fuel pulse) and voltage waveforms for two injection events, injection event one IE 1  and injection event two IE 2 . As shown, the demand time t demand  is the time separation between the time, at which the electrical fuel pulse goes “low 0” so as to stop fuel delivery and then subsequently goes “high 1” so as to resume fuel delivery. The demand time t demand  is calculated by the timing strategy in the ECM. 
     As described above, before each injection event the voltage across the stack  14  is held high 1 at a first voltage level V charge . The ECM provides a discharge enable signal  80  to drive the circuit. When the discharge enable signal  80  changes from logic low 0 to logic high 1 an RMS discharge current I discharge  is driven through the stack  14  such that the stack  14  begins to discharge, and the voltage across the stack  14  reduces. The discharge enable signal  80  is held high 1 for a predetermined discharge time t discharge  before returning to logic low 0. The discharge time t discharge  is calculated using look up tables stored within the ECM and depends on the rail pressure R p . The discharge time t discharge  is adjusted according to a proportion of the previous discharge time t discharge     —     previous , which is fed back in a control loop. At the conclusion of the discharge time t discharge  the voltage across the stack  14  is at a second voltage level V discharge . 
     The ECM controls the length of fuel delivery time depending on the operating strategy. A charge enable signal  82  controls when an RMS charge current must be driven through the stack in order to charge it from the second charge level Q discharge  to the first Q charge , which, in turn, results in the voltage across the stack  14  increasing from the second voltage level V discharge  to the first voltage level V charge . The time required by the injector to open is known, and so the time, at which the charge enable signal  82  must be changed from logic low 0 to logic high 1 in order to charge the stack  14 , can be determined. 
     The discharge time is used to calculate how much charge was removed from the stack  14  during the opening phase  40 . A charge time t charge  is therefore calculated such that the charge removed during the discharge/opening phase  40  is reapplied during the closing/charge phase  41 . In practice, the charge applied during the charge phase  41  may be higher than the charge removed during the discharge phase in order to account for any losses in the system. The time, for which the charge enable signal  82  is held high 1, is calculated from the known RMS charge current and the required charge using the formula: 
     
       
         
           
             
               charge 
               ⁢ 
               
                   
               
               ⁢ 
               enable 
               ⁢ 
               
                   
               
               ⁢ 
               time 
             
             = 
             
               
                 
                   
                     
                       charge 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       removed 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       during 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       discharge 
                       × 
                     
                   
                 
                 
                   
                     
                       system 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       losses 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gain 
                     
                   
                 
               
               
                 RMS 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 charge 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 current 
               
             
           
         
       
       
         
           
             
               t 
               charge 
             
             = 
             
               
                 
                   Q 
                   discharge 
                 
                 × 
                 
                   K 
                   losses 
                 
               
               
                 I 
                 charge 
               
             
           
         
       
     
     The relationship between the stack voltage and the stack displacement is non-linear, whereas the relationship between the charge and the displacement is linear. Although the voltage can be measured relatively easily, it cannot be used to accurately determine the position of the stack. This is mainly due to dynamic capacitance effects within the stack as it is extended or compressed. While it is common to control fuel injectors by targeting a voltage across the stack, it is actually the charge on the stack that provides the more accurate control measure. Using a so-called “charge control” method includes charging the stack  14  during a charging phase  41  to a target charge level. This provides a reference point, by which the subsequent discharging phase  40  can be controlled. 
     As shown in  FIG. 5 , the time required to ensure that the injector has returned to the first voltage level V charge  is given by:
 
 t   closing   =t   charge   +t   dwell  
 
     As explained above, t charge  is calculated by dividing the charge that was taken off during the discharging phase, including an additional amount to account for any losses, by the RMS charge current I charge . It is worth noting that the RMS charge and discharge currents need not be equal. Therefore, t discharge  need not equal t charge . The RMS current levels affect the velocity of the stack (i.e., the speed, at which the length of the stack changes). This in turn affects the rate of fuel injection. The RMS current levels may vary across the engine operating range to achieve desired performance in terms of rate of fuel injection. The time t dwell  is added to account for the fact that a finite time is required for the hardware to switch off the charge enable signal (i.e., signal  82  in  FIG. 4 ) before the discharge enable signal (i.e., signal  80  in  FIG. 4 ) can be switched on for a subsequent injection event. This is typically in the order of tens of microseconds. 
     In known injector systems the minimum demand time depends on the time it takes to fully charge the injector plus the dwell time, because as described above the injector can only begin to discharge once it has been fully charged. However, to improve flexibility, it is desirable to reduce the demand time further. 
     The present invention is used to control the delivery of fuel such that a demand time smaller than that of conventional systems is achievable, through adjustment of the charging phase and the subsequent discharging phase. 
     As shown by the short dashed line in  FIG. 5 , when the demand time required by the ECM is relatively large there is more than enough time for the injector, during the closing phase, to be charged to the first voltage level V charge  (P 0  to P 6 ), and for the charge circuit to be switched off (i.e., the dwell time, P 6  to P 4 ). In this case, no adjustment of the charging phase and subsequent discharge phase is required and the present invention operates in a conventional manner. This is referred to as operation in a conventional mode. 
     The long dashed line in  FIG. 5  shows a threshold condition where there is exactly enough time for the injector to be fully charged (P 0  to P 6 ), and for the dwell time to expire (at P 4 ) before the injector is discharged. As shown, fuel delivery stops at point A, during the charging phase  41 , before it begins again at point B, during the discharging phase  40 . The difference between points A and B is known as a threshold demand time t demand     —     threshold . A demand time larger than the threshold demand time t demand     —     threshold  would result in the present invention operating in the conventional manner described above. However, if a demand time shorter than the threshold demand time t demand     —     threshold  is required, for example that shown by the solid line in  FIG. 5 , the invention operates in a different manner in order to ensure that the required demand time is met. When operating in the latter manner the ECM effectively merges a charging/closing phase of a first pulse with a discharging/opening phase of a separate second pulse. This will be referred to as operation in a merging pulse mode. This threshold condition is the minimum demand time achievable in known conventional systems. As the demand time reduces, a seamless transition occurs between the two modes of operation. 
     The limit to how short the demand time can be is determined by the ECM hardware switching times. There is a minimum time, for which the charge enable must be active before it can be de-activated, and the dwell time must elapse before the subsequent discharge enable can be switched on. In total this limit is in the order of 50 μs. 
     However, the present invention advantageously enables the ECM to operate with demand times between the actual limit set by the finite times described above and the threshold condition that is the minimum demand time previously achievable in known systems. 
     ECM operation in the conventional or merging pulse mode is determined based on the time it takes to fully charge the injector, the dwell time and the required demand time. The time difference between the closing time (i.e., the summation of the charge time and dwell time), and the demand time is referred to as an overlap time: 
     
       
         
           
               
             
               
                 
                   
                     
                       t 
                       overlap 
                     
                     = 
                       
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             t 
                             charge 
                           
                           + 
                           
                             t 
                             dwell 
                           
                         
                         ) 
                       
                       - 
                       
                         t 
                         demand 
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                     ⁢ 
                     
                       
                         t 
                         closing 
                       
                       - 
                       
                         t 
                         demand 
                       
                     
                   
                 
               
             
           
         
       
     
     When the overlap time is negative, the pulses are sufficiently far enough apart, as shown by the short dashed line in  FIG. 5 , that no adjustment is required. In this case the ECM operates in the conventional mode. However, when the overlap time is positive, the ECM must operate in the merging pulse mode and is required to adjust the timing of the charging phase and subsequent discharge phase. 
     When the overlap time t overlap  is positive, it is necessary to reduce the time of the charge enable signal  82 , and hence the subsequent discharge enable signal  80 , so that the stack  14  does not fully charge/discharge. The merge overlap time is effectively the time that is not available for the stack  14  to charge fully prior to discharging. Therefore, the charging and discharging phases  41 ,  40  are adjusted by dividing the overlap time t overlap  proportionally between both the charging and discharging phases  41 ,  40 . As the RMS currents of both of these phases may be different, it is necessary to reduce the charging and discharging times t charge , t discharge  proportionally. In other words, it is necessary to remove an equal amount of charge from both the charging and discharging phases/slopes, as opposed to simply dividing the overlap time t overlap  in half. This is done to ensure that the total change in charge of the second injection event IE 2  with respect to the quiescent charge level remains the same, as it is this total charge that determines the relative change in the length of the stack  14 . 
     The proportion of the overlap time t overlap  to be taken from the closing phase  41  is used to recalculate the time, at which the charge enable signal  82  should be switched off, i.e., from logic high 1 to logic low 0. After the dwell time t dwell  has elapsed the discharge enable signal  80  is then switched from logic low 0 to logic high 1 such that the stack  14  begins discharging (i.e., discharging is initiated). 
     The solid line in  FIG. 5  shows the resulting waveform when two pulses are merged. During the charging phase  41  fuel delivery stops at point A and during the discharging phase  40  fuel delivery begins a point D. The time between A and D is the required demand time t demand , which is clearly smaller than the minimum demand time (t demand     —     threshold ) that is possible using conventional systems. As shown, the stack  14  stops charging at point P 1  and begins discharging at point P 2 . The present invention calculates the points P 1  and P 2  such that the required demand time t demand  is met. 
       FIG. 6  shows a merging pulse waveform in more detail. As shown, when the charge enable signal  82  goes high 1 at time t P0  the voltage across the stack  14  increases until the charge enable signal  82  goes low 0 at time t P1 . The voltage across the stack  14  remains substantially constant until the conclusion of the dwell time t dwell  at time t P2  when the discharge enable signal  80  goes high 1. The voltage across the stack  14  then decreases until the discharge enable signal  80  goes low 0 at time t P3 . 
     In addition,  FIG. 6  shows that the closing time t closing  (charge time t charge  plus dwell time t dwell ) begins at time t P0  and continues until time t P4  corresponding to point P 4 . P 4  is effectively the point, at which the voltage across the stack  14  would have reached the first voltage level V charge  during a non-merged injection event, i.e., the point, at which the first injection event IE 1  would have concluded if it were not merged with a second injection event IE 2 . 
     Furthermore,  FIG. 6  shows that the overlap time t overlap  (i.e., t closing  minus t demand ), concluding at t P4 , effectively begins at t P5 , corresponding to point P 5 . Point P 5  is in effect the point, at which the second injection event would begun (i.e., the point, at which discharging of the stack would have initiated in order to result in the dashed line in a non-merged second injection event L inj     —     event2 ). 
     The merge overlap time t overlap  is divided into two portions, a first portion of the merge overlap time t overplap     —     portion1  is applied to the closing phase  41 , and a second portion of the merge overlap time t overplap     —     portion2  is applied to the opening phase  40 . The time t P1 , at which the adjusted stop charging point P 1  occurs, is calculated by subtracting the first portion of the overlap time t overplap     —     portion1  from the time t P6 , at which charging should have stopped in a conventional non-merged injection event (i.e., point P 6 ). 
     The first portion of the merge overlap time t overplap     —     portion1 , which is applied to the closing phase, is calculated using the following equation: 
     
       
         
           
             
               t 
               
                 overlap_portion 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
               
             
             = 
             
               
                 ( 
                 
                   1 
                   - 
                   
                     ( 
                     
                       
                         I 
                         closing 
                       
                       
                         
                           I 
                           closing 
                         
                         + 
                         
                           I 
                           opening 
                         
                       
                     
                     ) 
                   
                 
                 ) 
               
               ⁢ 
               
                 t 
                 overlap 
               
             
           
         
       
     
     The overlap time t overlap  is divided in inverse proportion to the RMS current levels, in order to ensure that the portion removed from the closing phase  41  and the subsequent opening phase  40  correspond to the same electrical charge. 
     The time t P1  (stop charging point P 1 ) is calculated as follows:
 
 t   P1   =t   P6   −t   overplap     —     portion1  
 
The time t P2  (begin discharging point P 2 ) occurs at t P1  plus the dwell time t dwell .
 
     As stated earlier, in merged pulse mode the stack begins discharging at time t P2 . If the stack were to be discharged for a full discharge time t discharge     —     full , calculated for a non-merged pulse, the voltage across the stack could fall below the recommended voltage levels as shown by point P 7 . Therefore, it is necessary to adjust the discharge time by subtracting the second portion of the merge overlap time t overplap     —     portion2  from the calculated non-merged discharge time t discharge     —     full . 
     The second portion of the merge overlap time t overplap     —     portion2 , which is applied to the opening phase  40 , is calculated as follows:
 
 t   overlap     —     portion2   =t   overlap   −t   overlap     —     portion1  
 
     The time t P3 , at which the stack  14  should stop discharging (i.e., at point P 3 ), is calculated by subtracting the second portion of the merge overlap time t overplap     —     portion2  from the time t P7 , at which a full discharge would have stopped (i.e., at point P 7 ), where time t P7  occurs at time t P2  (i.e., point P 2 ) plus the full discharge time t discharge     —     full . Therefore, time t P3 , at which the stack should stop discharging, is calculated as follows: 
     
       
         
           
               
             
               
                 
                   
                     
                       t 
                       
                         P 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     = 
                       
                     ⁢ 
                     
                       
                         t 
                         
                           P 
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     How the ECM operates, in order to decide which operating mode applies and the calculation of the stop charging, start discharging and stop discharging times t P1 , t P2 , and t P3  discussed above, will now be described with reference to the flowcharts shown in  FIGS. 8 to 10 . 
       FIG. 7  shows a flowchart of steps, in which the ECM determines which operating mode, conventional or merging pulse, in which to operate. In a first step  101 , the ECM  54  determines the demand time t demand  required by the engine  60 . As discussed above the demand time t demand  depends on the current engine operating condition. 
     In a second step  102 , the charge time t charge     —     full  required to charge the stack  14  fully is calculated. This is effectively the time that the RMS charge current I charge  is to be driven through the stack  14 , such that the charge previously removed during the discharge phase  40 , plus a fraction more, is re-applied to the stack  14 , to increase the voltage across the stack  14  to V charge . 
     The injector closing time t closing  is then calculated in a third step  103  by adding the charge time t charge  and the dwell time t dwell  together. This time takes account of the hardware switching times and is the time it takes to guarantee that the voltage across the stack  14  has returned to V charge . 
     The closing time t closing , calculated in the third step  103 , and the demand time t demand , calculated in the first step  101 , are then used in a fourth step  104  to determine the overlap time t overlap  between the first and second pulses/injection events IE 1 , IE 2 . 
     In a fifth step  105 , the ECM determines whether the overlap time t overlap  is positive. If the overlap time t overlap  is not positive, control passes to a sixth step  106  and the ECM  54  operates in the conventional mode. 
     Alternatively, if the overlap time t overlap  is positive there is insufficient time to permit the stack  14  to fully charge during the charging phase  41  of the first pulse IE 1 , prior to the discharging phase  40  of the second pulse IE 2 , in order to achieve the demand time t demand  that the ECM  54  requires. Therefore, control passes to a seventh step  107  and the ECM  54  operates in the merging pulse mode. 
     The overlap time t overlap  is proportioned such that the first portion t overplap     —     portion1  is deducted from the charging phase  41  of the first pulse IE 1 , and the second portion t overplap     —     portion2  is deducted from the discharging phase  40  of the second pulse IE 2 . The first portion of the overlap time t overplap     —     portion1  is calculated in an eighth step  108 , and the second overlap time portion t overplap     —     portion2  is calculated in a ninth step  109  by deducting the first portion of the overlap time t overplap     —     portion1  from the overall overlap time t overlap . 
       FIG. 8  shows a flowchart for conventional mode operation, corresponding to the sixth step  106  in  FIG. 7 , and  FIG. 9  shows a flowchart for merging pulse mode operation, corresponding to the seventh step  107  in  FIG. 7 . 
     The flowchart in  FIG. 8  shows the present invention operating in the conventional mode. Hence, during an injection event the stack  14  is discharged for the required discharge time such that the injector opens and fuel is delivered. 
     In a first step  201  of the conventional mode, the discharge enable signal  80  is set to logic high 1, and the stack  14  begins to discharge. The discharge enable signal  80  is held in this state, in a second step  202 , for the required discharge time t discharge     —     full . At the conclusion of this time interval, in a third step  203 , the discharge enable signal  80  is set to logic low 0, as the stack  14  is now discharged. In a fourth step  204 , the stack is held in this state for the required injector opening time as determined by the ECM  54 . 
     At the appropriate time, as determined by the ECM fuelling and timing strategy  56 , in a fifth step  205 , the charge enable signal  82  is set to logic high 1, such that the stack  14  begins to charge. The charge enable signal  82  is held high 1 during a sixth step  206  for the required charge time t charge     —     full , which is the time needed to charge the stack  14  fully and return the voltage across the stack  14  to V charge . 
     At the conclusion of the charge time t charge , in a seventh step  207 , the charge enable signal  82  is switched to logic low 0 as the stack  14  is now fully charged. During an eighth step  208 , the stack  14  is held in this state for a time, longer than the dwell time t dwell , which is determined by the ECM fuelling and timing strategy  56 . Control of the ECM  54  then passes back to the first step in  FIG. 7 . 
     The flowchart in  FIG. 9  shows the present invention operating in the merging pulse mode. In a first step  301  of the merging pulse mode, the discharge enable signal  80  is set to logic high 1, and the stack  14  begins to discharge. In a second step  302 , the discharge enable signal  80  is held in this state for the required discharge time. At the conclusion of this time interval, in a third step  303 , the discharge enable signal  80  is set to logic low 0, as the stack  14  is now discharged. In a fourth step  304 , the stack  14  is held in this state for the required injector opening time. 
     At the appropriate time (calculated depending on how long fuel is required for), the charge enable signal  82  is set to logic high 1 in a fifth step  305 , such that the stack  14  begins to charge. During a sixth step  306 , the charge enable signal  82  is held high 1 until time t P1 , which is determined by subtracting the first portion of the overlap time t overplap     —     portion1  calculated in the eighth step  108  of  FIG. 7  from the time t charge     —     full  required to charge fully the stack  14  and return the voltage across the stack  14  to V charge . 
     In a seventh step  306 , at time t P1 , the charge enable signal  82  is switched to logic low 0. The stack  14  is not fully charged but is sufficiently charged such that the injector is closed and fuel delivery ceases. In an eighth step  308 , the stack  14  is held in this state for the dwell time t dwell , in order to allow enough time for the hardware switching devices to change state. 
     In a ninth step  309 , at the conclusion of the dwell time interval t dwell , the discharge enable signal  80  is set to logic high 1 at time t P2  such that the stack  14  begins to discharge again. In a tenth step  310 , the discharge enable signal  80  is held high 1 until time t P3 , which is determined by subtracting the second portion of the overlap time t overplap     —     portion2  (calculated in the ninth step of  FIG. 7 ) from the discharge time t discharge     —     full  that would be required for full discharge. At time t P3 , in an eleventh step  311 , the discharge enable signal  80  is set to logic low 0. 
     In a twelfth step  312 , the stack  14  is held in this state for the required injector opening time before the stack  14  is charged again and the sequence repeated. 
     In the above example, it is assumed that a full discharge occurs in the first instance prior to the charging phase  41  of the first injection event IE 1  being merged with the discharge phase  40  of a second injection event IE 2 . However, it is to be appreciated that the stack  14  need not fully discharge and in that case the discharge time is adjusted accordingly. 
     The ECM  54  operating in the merging pulse mode of the invention ensures a greater flexibility in the demand time t demand  in comparison to prior art systems operating in a conventional mode where the demand time t demand  cannot be reduced below the time it takes to charge the stack  14  fully. This is advantageous since a shorter demand time results in increased flexibility of operation, allowing for optimization of engine performance and emissions. 
     It will be appreciated that the invention provides the further flexibility of being able to switch between a conventional mode of operation, and a merging pulse mode of operation, depending upon the demand time required by the ECM in accordance with the engine operating conditions. 
       FIGS. 11 to 14  show example waveforms for different operating conditions. 
       FIG. 10  shows typical linked pilot and main injection events with sufficient separation such that there is no overlap between the pilot and main events and the ECM operates in the conventional mode. The linked pilot and main injection events shown in  FIG. 11  are similar to those shown in  FIG. 10 , with a reduced separation between both events. 
       FIG. 12  shows linked pilot and main injections, which have been merged such that the charging phase of the pilot injection and the discharging phase of the main injection have been truncated (i.e., merged pulse mode). 
     The pilot and main injection events shown in  FIG. 13  are again merged. However, in this case the period of the main injection event has also been reduced such that the stack does not discharge fully prior to the subsequent charging phase of the main injection event. It is to be appreciated that the minimum stack voltage is not necessarily equal during the two injection events. 
     It is to be appreciated that although the present invention is described above in relation to de-energize-to-inject injectors, the present invention can also be implemented using energize-to-inject injectors.