Abstract:
A dosing system for delivering reductant into an exhaust gas treatment system of an internal combustion engine using an air driven hydraulic pump, which includes a pressure pump tank and a liquid supply tank, for closed-loop controlling reductant pressure, and a three-stage PWM control method for dosing rate control. Reductant residue in the dosing system is purged by using compressed air, and when the air driven hydraulic pumps is positioned inside a reductant tank, heating means in the reductant tank can also be used for heating the air driven hydraulic pump. The closed-loop pressure control together with the three-stage PWM control allow dosing accuracy insensitive to pressure variations in compressed air, thereby a variety of compressed air sources can be used.

Description:
[0001]    This present application claims priority from U.S. provisional application No. 61/689,517 having the same title as the present invention and filed on Jun. 7, 2012. 
     
    
     TECHNICAL FIELD OF THE INVENTION 
       [0002]    The present invention relates to an apparatus and method for delivering reductant into an exhaust gas treatment system of an internal combustion engine for removing regulated species in exhaust gas, and more specifically, to an apparatus and method using an air driven hydraulic pump to deliver liquid reducing agents into an exhaust gas treatment system of an internal combustion engine. 
       BACKGROUND OF THE INVENTION 
       [0003]    Environmentally harmful species in the exhaust gas emitted from an internal combustion engine, such as hydrocarbons (HC), carbon monoxide (CO), particulate matters (PM), and nitric oxides (NOx) are regulated species that need to be removed from the exhaust gas. In lean combustion engines, due to the existence of large amount oxygen excess, passive means without extra dosing agents, such as that using a three-way catalyst, normally are not able to effectively remove the oxidative specie NOx, as that in most of spark-ignition engines. To reduce NOx in lean combustion engines, a variety of active means with reducing agents (reductants) being dosed in exhaust gas are developed. In these technologies, the reductant is metered and injected into the exhaust gas, and the result mixture flows into a SCR (Selective Catalytic Reduction) catalyst, where the reductant selectively reacts with NOx generating non-poisonous species, such as nitrogen, carbon dioxide, and water. 
         [0004]    A variety of reductants, such as ammonia (NH3), HC, and hydrogen (H2) can be used in SCR systems. Among them, ammonia SCR is used most broadly due to high conversion efficiency and wide temperature window. Ammonia can be dosed directly. However, due to safety concerns and difficulties in handling pure ammonia, normally urea solution is used in ammonia SCR systems. Urea can be decomposed to ammonia through thermolysis and hydrolysis in exhaust gas, and urea solution, therefore, is also called reductant in an ammonia SCR system. 
         [0005]    Typically, in a SCR control system, the required ammonia dosing rate is calculated in an ECU (Engine Control Unit). If a reductant other than ammonia, e.g., urea solution, is used, then according to its ammonia conversion ratio, e.g. the ammonia conversion ratio is 1:2 for urea (i.e. one urea molecule is able to generate two ammonia molecules), the required reductant flow rate is calculated and the dosing rate command is sent to a dosing system, where reductant is metered and injected into exhaust gas. Generally, similar to fueling control, there are two methods in metering reductant. One method is using a metering pump, with which the reductant flow rate is precisely controlled by controlling the motor speed of the pump. The other method is more like that used in a common rail fueling control system. In this method, a pressure is built up and maintained constant in a reductant rail or a buffer, and reductant flow rate is controlled by adjusting the open time of an injector, which is fluidly connected to the buffer, in a periodically repeating cycle. 
         [0006]    Atomization of reductant is important to SCR conversion efficiency, especially in a urea SCR system, where dosed urea needs to be decomposed to ammonia through thermolysis and hydrolysis, and the heat energy provided by exhaust gas is limited. In the first reductant metering method, though the control is simple, the reductant pressure is not controlled. Therefore, to have a good atomization, in addition to having a well-designed nozzle facilitating atomization, normally the reductant dosing needs to be mixed with an extra air supply which provides a continuous air flow. The requirements of a continuous air flow and a precisely controlled metering pump limit the application of this method. The second reductant metering method doesn&#39;t need an extra air supply to facilitate atomization, since under high pressure, injected reductant from a well-designed nozzle has good atomization. However, in this method, due to the requirement of pressure control, typically a liquid pump, such as a membrane pump driven by a motor, is needed in establishing and maintaining the rail pressure, and a motor control system is required. 
         [0007]    Additionally, to avoid being frozen under low ambient temperature, reductant residue inside the dosing system need to be purged before the dosing system is shut off. In a system using the first reductant metering method, compressed air can be used to press reductant residue into exhaust air and back to reductant tank, while in that using the second method, an extra reductant flow control is needed to drive reductant residue back. In dosing systems which have reductant residue in connection lines, line heating means are also required. Different from reductant tank heating control, line heating is a distributed heating and it is difficult to use closed-loop controls. Except using costly PTC (Positive Temperature Coefficient) materials, heating efficiency or heating power and line durability need to be carefully balanced, since locally high temperature could damage the heating line. 
         [0008]    To decrease the complexity of a reductant dosing system and at the same time achieve good performance, a primary object of the present invention is to provide a reductant dosing apparatus using air driven hydraulic pumps with simple pressure control to build up and maintain a high pressure in a rail. The air driven hydraulic pump doesn&#39;t have a motor inside and, therefore, doesn&#39;t need electrical energy and a complex motor control to drive it. Neither the air driven hydraulic pump needs a continuous air supply. 
         [0009]    A further object of the present invention is to provide a dosing rate control insensitive to variations in reductant pressure, so that accurate pressure control is not required. 
         [0010]    Another object of the present invention is to provide a control means using compressed air to drain reductant residue back to tank when dosing completes. 
         [0011]    Yet another object of the present invention is to provide a dosing apparatus with an air driven hydraulic pump positioned inside a reductant tank, thereby no extra heating means other than tank heating is required. 
       BRIEF SUMMARY OF THE INVENTION 
       [0012]    The present invention provides an apparatus and method for delivering reductant into an exhaust gas treatment system of an internal combustion engine. More specifically, this apparatus includes a reductant supply module with a pressure pump tank (PPT) and a liquid supply tank (LST), a reductant tank, a dosing control unit (DCU), and an injector. In an embodiment of the present invention, a pressure sensor is positioned in the PPT to measure the pressure of reductant supplied from the LST, which has a liquid port fluidly coupled to the reductant tank and a gas port fluidly connected to a three-way solenoid valve that further connects the gas port either to compressed air or ambient depending on its control status. When the three-way solenoid valve connects the gas port to ambient, compressed air in the liquid supply tank is released, and liquid reductant then flows from the reductant tank to the LST. Reductant in the LST is pressed into the PPT when the three-way solenoid valve connects the gas port of the LST to compressed air. The PPT has a liquid port fluidly connected to the injector, and a gas inlet port fluidly coupled to compressed air through a two-way solenoid valve for compensating air loss in the PPT. Reductant dosing rate is controlled by opening the injector for a period of time in a periodically repeating cycle, and the LST refills reductant to the PPT, i.e., the three-way solenoid valve of the LST connects its gas port to compressed air, whenever the reductant level in the PPT is detected low. The inlet of the injector is also fluidly coupled to the reductant tank through a flow control valve. After dosing finishes, the flow control valve is energized open and reductant residue is then pressed back to the reductant tank. 
         [0013]    In another embodiment of the present invention, the PPT further includes a gas outlet port, which is fluidly connected to another two-way solenoid valve for releasing air. The gas outlet port in the PPT allows pressure be controlled within a pre-determined range. To refill PPT, the upper limit of the pre-determined range should be lower than the compressed air pressure. 
         [0014]    In the dosing system of the present invention, control signals are generated in the DCU. The control of the dosing system includes five states: Off, Idle, Priming, Normal-dosing, and Purge. The Off state is a state when the engine is keyed off. After engine is keyed on, the control firstly goes into the Idle state, then upon a command, the system enters the Priming state, in which the PPT is filled with reductant to a pre-determined level. When a dosing command is received, the Normal-dosing state starts, in which both of the PPT pressure and the dosing rate are controlled, and the PPT is refilled if the reductant level in the PPT is lower than a threshold value. After dosing, when engine is keyed off or an idle command is received, the system goes into the Purge state and reductant residue in the PPT, the LST, and connecting passages is emptied therefrom. 
         [0015]    The structure of the dosing system allows the pressure sensor together with the control solenoid valves be used in detecting reductant level in the PPT, PPT pressure control, and reductant dosing rate control. In detecting reductant level, both of the change in PPT pressure and the ratio between dosing amount and the change in PPT pressure are used in calculating PPT reductant volume depending on control states. Also the changing rate of the PPT pressure is used in detecting if the PPT is empty. In PPT pressure control, in a system of the first embodiment, sensing values obtained from the pressure sensor are used to calculate the amount of trapped air in the PPT. When the calculated amount is lower than a threshold value, the two-way solenoid valve connected to the gas inlet port of the PPT is energized open to refill air into the PPT. In a system of the second embodiment, pressure sensing values are compared to the upper limit and the lower limit of the predetermined range, and control modes, which are the combination of the control status of the two-way solenoid valves, are changed according to the comparison results. 
         [0016]    In reductant dosing control, the pressure sensor is used in a three-stage PWM controller, which generates a PWM signal for driving the injector according to predetermined dosing commands. In the three-stage PWM controller, the first stage control creates a first-stage PWM signal by periodically setting control parameters to the second stage controller, which generates a second-stage PWM signal, while the control parameters of the second-stage control are used in creating a third-stage PWM signal. The values of the control parameters are calculated by the first stage controller according to the sensing values obtained from the pressure sensor positioned inside the PPT. In this way, variation in the pressure is compensated by the PWM controller, and the dosing rate accuracy, therefore, is insensitive to pressure variation in the PPT. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  is a schematic representation of an internal combustion engine with an exhaust gas treatment system; 
           [0018]      FIG. 2   a  depicts an air driven hydraulic pump system with a reductant tank, a pressure pump tank fluidly coupled to compressed air, a liquid supply tank, a DCU, an injector, and control solenoid valves; 
           [0019]      FIG. 2   b  depicts an air driven hydraulic pump system with a reductant tank, a pressure pump tank fluidly coupled to compressed air and ambient, a liquid supply tank, a DCU, an injector, and control solenoid valves; 
           [0020]      FIG. 3  is a state flow diagram of a reductant delivery control; 
           [0021]      FIG. 4   a  is a flow chart of a routine for a sub-state PR1 in a Priming state; 
           [0022]      FIG. 4   b  is a flow chart of a routine for a sub-state PR2 in a Priming state; 
           [0023]      FIG. 4   c  is a flow chart of a service routine for a timer based interrupt used in a Priming state for calculating reductant volume in a PPT; 
           [0024]      FIG. 4   d  is a flow chart of a routine for a sub-state PR3 in a Priming state; 
           [0025]      FIG. 5   a  a flow chart of a routine for a sub-state D1 in a Normal-dosing state; 
           [0026]      FIG. 5   b  is a flow chart of a service routine for a timer based interrupt used in a sub-state D1 for calculating reductant volume in a PPT; 
           [0027]      FIG. 5   c  is a flow chart of a service routine for a timer based interrupt used in a Normal-dosing state for controlling reductant pressure in a PPT; 
           [0028]      FIG. 5   d  is a flow chart of a service routine for a timer based interrupt used in a sub-state D2 for calculating reductant volume in a PPT; 
           [0029]      FIG. 5   e  shows a timing chart of parameter values in a service routine of  FIG. 5   d;    
           [0030]      FIG. 6   a  is a block diagram of a three-stage PWM controller for controlling reductant dosing rate; 
           [0031]      FIG. 6   b  is a block diagram of a PWM signal controller in a three-stage PWM controller of  FIG. 6   a;    
           [0032]      FIG. 6   c  is a flow chart of a service routine for a timer based interrupt used in a first-stage PWM signal generation for calculating values for control parameters of a second-stage PWM signal; 
           [0033]      FIG. 6   d  shows a timing chart of parameter values in a service routine of  FIG. 6   c;    
           [0034]      FIG. 6   e  is a block diagram of a circuit for generating a second-stage and a third-stage PWM signals; 
           [0035]      FIG. 6   f  is a timing chart for signals generated in the circuit of  FIG. 6   e;    
           [0036]      FIG. 7   a  a flow chart of a routine for a sub-state PU1 in a Purge state; 
           [0037]      FIG. 7   b  a flow chart of a routine for a sub-state PU2 in a Purge state; 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0038]    Referring to  FIG. 1 , in an engine aftertreatment system, exhaust gas generated by an engine  100  enters a passage  166  through a manifold  101 . On the passage  166 , a reductant injector  130  is installed. The solenoid valve of the injector  130  is controlled by a Dosing Control Unit (DCU)  140  through signal lines  145  connected to a port  136 . And reductant is provided by a redutant supply module  110  through a pressure line  131  fluidly connected to a port  133 . To avoid damages caused by high temperature exhaust gas, engine coolant is cycled from an inlet port  134  to an outlet port  135 . The reductant injected from the injector  130  mixes with exhaust gas, and through a mixer and diffuser  161 , the result gas enters a catalyst  163 , where SCR reactions reduce NOx in the exhaust gas. 
         [0039]    The reductant supply module  110  has a port  115  fluidly connected to the port  133  of the injector  130  with the line  131  for providing pressurized reductant supply to the injector. A pressure sensor (not shown in  FIG. 1 ) reports pressure value inside the reductant supply module to the DCU through signal lines  143  connected to a port  114 . The reductant supply module draws reductant from a reductant tank  120  through a port  117 , a supply line  123 , and a port  122  of the reductant tank. And compressed air enters reductant supply module through an inlet port  111  to pressurize the reductant inside, while the reductant pressure is controlled by the DCU through signal lines  146  connected to a port  116 . Compressed air is released from an outlet port  112 . 
         [0040]    A tank level sensor and a temperature sensor report, respectively, reductant level and temperature inside the reductant tank  120  to the DCU through signal lines  141  and  142 , which are connected to a port  126 . And the reductant tank is heated by engine coolant cycling through an inlet port  127  and an outlet port  128 . The engine coolant flow is controlled by a solenoid shutoff valve  127  commanded by the DCU through signal lines  147 . To avoid reductant residue inside the pressure line  131  being frozen under low temperature when engine is off, a return line  125 , and a port  121  are used as a passage for reductant to flow back to the tank in a purge process. Reductant flow inside the return line  125  is controlled by a shut-off valve  137  commanded by the DCU via signal lines  148 . Electrical heaters  132 ,  129 ,  124 , and  113  controlled by the DCU through signal lines  144  are used to thaw frozen reductant in the pressure line  131 , the return line  125 , the supply line  123 , and the reductant supply module  110  respectively, and keep the temperature above reductant freezing point. 
         [0041]    Commands of reductant dosing rate to the DCU are generated in the ECU according to catalyst inlet exhaust temperature reported by a sensor  162  through signal lines  155 , catalyst outlet temperature reported by a sensor  164  through signal lines  154 , catalyst outlet NOx rate obtained from a sensor  165  through communication lines  153 , and engine information, such as engine state, coolant and oil temperature, engine speed, fueling rate, exhaust flow rate, NOx rate, and NO2/NOx ratio, obtained from sensors in the engine  100  through signal lines  152 , or calculated from sensing values. 
         [0042]    One embodiment of the reductant supply module  110  in  FIG. 1  is an air driven pumping system depicted in  FIG. 2   a  positioned in the reductant tank  120 . In the pumping system, a Liquid Supply Tank (LST)  210  and a Pressure Pump Tank (PPT)  200  are positioned inside the reductant tank  120 , which has a cover  228  fastened on a container  220  with bolts  229  mounted on a flanged portion. On the cover  228 , a cap  236  is used for refilling reductant. Since the PPT and the LST are positioned inside the reductant tank, the reductant passage line  131  is connected to the port  115  through a port  221  on the cover  228 , and the signal lines  143  are connected to the port  114  via a port  225 . Inside the reductant tank  120 , the LST  210  is fixed by a restrainer  227  and has a liquid inlet port  211  fluidly connected to the reductant liquid in the tank  120 . A check valve  212  inside the port  211  prevents the liquid from flowing back into the tank  120 . The LST  210  also has a liquid outlet port  204  fluidly coupled to an inlet port  201  of the PPT  200  through a passage  203 . Inside the port  201 , a check valve  202  keeps liquid from flowing back to the LST  210 . On the top of the LST  210 , through a passage  214  and a port  237  on the cover  228 , a port  213  is connected to a port  241  of a chamber  240 , which is held by a restrainer  238 , and the port C of a three-way solenoid valve  232 , which is hold by a restrainer  234 . The port B of the three-way solenoid valve  232  is connected to an air muffler  233 , which is fluidly connected to the port  112 , and the port A is connected to an outlet of a Tee connector  235  through a passage  207 . The three-way solenoid valve  232  is controlled by the DCU  140  via the signal lines  146 . Determined by control signals, the port C of the three-way solenoid  232  is either connected to the port A or the port B. Next to the LST  210 , the PPT  200  is fixed by a restrainer  226 . On the top of the PPT  200 , through the liquid outlet port  115 , a tubing  209  is fluidly connected to the reductant passage line  131  extended through the port  221  on the cover  228 . A port  205  is connected to the port A of the two-way solenoid valve  230 , which is fixed on the cover  228  by a restrainer  231 , via a passage  206  passing through the port  222 . The port B of the two-way solenoid valve  230  is connected to an outlet of the Tee connector  235 , which has another outlet connected to the three-way solenoid valve  232  and its inlet connected to the port  111 . Inside the PPT  200 , a pressure sensor  250  is mounted, and the signals obtained from the pressure sensor is sent to the DCU  140  via the signal lines  143  passing through the port  114  of the PPT  200  and the port  225  on the cover  228 . In addition to the reductant supply pump tanks  200  and  210 , inside the reductant tank  120 , there are a temperature sensor  224  linked to the DCU through the signal lines  142  for detecting reductant temperature and a level sensor  223  reporting reductant level to the DCU through the signal lines  141 . A coolant heating tube  225 , which is connected to the inlet  127  and the outlet  128 , is used in heating reductant. 
         [0043]    The system of  FIG. 2   a  works under the control of the DCU  140 , and the basic control of the system includes a prime control, a dosing control, and a purge control. In the prime control, reductant fluid is loaded in the PPT  200  and trapped air is released from the injector  130  and the liquid path from the PPT to the reductant tank  120 , including the reductant lines  131 ,  209 , and  125  and the solenoid valve  137 , while in a dosing control, reductant deliver rate is accurately controlled according to a dosing command generated in the ECU  150  ( FIG. 1 ). After dosing completes, the purge control empties the PPT  200 , the liquid path from the PPT to the injector, and the injector  130 , to protect the injector and save heating efforts when operating under low temperature. 
         [0044]    In the prime control, the first step is to refill reductant fluid into the PPT  200  to a certain level. A variety of methods can be used in this step. An example of such methods includes a volume re-zero and a refilling control. In the volume re-zero control, the compressed air is filled into the PPT  200 , establishing a certain pressure therein. And then the solenoid valve  137  is energized open. Under the pressure, the reductant fluid remains inside the PPT  200  is pressed back into the reductant tank  120  through the tubing  209 , the passage  131 , the solenoid valve  137 , and the passage  125 . When the PPT  200  is empty, compressed air is pressed into the reductant tank  120 , and a sudden change of pressure is detected by the pressure sensor  250  due to the significant change of fluid density. Upon the sudden pressure change, the liquid volume in the PPT  200  is re-zeroed, and the solenoid valve  137  is de-energized closed. After the liquid volume is re-zeroed, a pressure is controlled to a level P1, which is lower than the compressed air pressure Pc, by controlling the opening time of the solenoid valve  230 . And then the solenoid valve  230  is closed and the solenoid  232  is energized, connecting its port A to port C, and the pressure in the LST  210  is then increased to the compressed air pressure Pc. Under the pressure drop between Pc and P1, reductant liquid flows from the LST  210  into the PPT  200 . By measuring the pressure change in the PPT  200 , the liquid level in the PPT can be calculated if the re-fill time is short and thereby, liquid temperature change is insignificant. When the liquid volume reaches to a value Vh, the solenoid  232  is de-energized, connecting the port B to port C, releasing pressure in the LST  210 . At the same time, the solenoid valve  137  is energized open for a period of time to release trapped air in the passage  131  and the tubing  209 , and the solenoid valve  133  is also opened shortly to release trapped air in it. Then the prime control completes. De-energizing the solenoid  232  releases compressed air in the LST  210 . When the pressure in the LST  210  is lower than P1, the check valve  202  blocks liquid from flowing back to the LST, and if the LST pressure decreases below the pressure drop across the check valve  211 , the LST is refilled with the reductant liquid in the tank  120 . 
         [0045]    In the prime control, when the solenoid valve  230  is closed after the liquid level is re-zeroed and the pressure is controlled at P1, compressed air is trapped in the PPT  200 . If temperature in the PPT  200  doesn&#39;t change, according to ideal gas law, the pressure P and liquid volume V inside the PPT then have the following relation: 
         [0000]        P ( Va−V )= P 1* Va   (1)
 
         [0046]    where Va is the volume of the trapped air after the liquid level is re-zeroed. According to equation (1), the liquid volume V then can be calculated with equation (2): 
         [0000]        V=Va *(1− P 1/ P )  (2)
 
         [0047]    After the prime control, the dosing control starts with controlling the pressure inside the PPT to a value P2 through controlling the opening time of the solenoid valve  230 . The dosing control includes a dosing rate control, a PPT refill control, and a PPT pressure control. In the dosing rate control, the liquid reductant in the PPT is released to exhaust air by opening the injector  130 , and the opening time of the injector  130  is controlled according a dosing rate command Dc in a periodically repeating cycle. The liquid volume in the PPT decreases with dosing. When the liquid volume decreases below a value Vl, the PPT needs to be refilled. In the PPT refill control, the solenoid valve  232  is energized, connecting the port A to the port C. The LST is then pressurized. When the pressure in the LST is higher than the pressure in the PPT, liquid reductant flows from the LST to the PPT. When the liquid volume in the PPT is higher than a threshold Vh, the solenoid valve  232  is de-energized, releasing the pressure in the LST. With the compressed air in the LST being released, the LST is refilled under the liquid pressure in the reductant tank  120  for the next PPT refill control. In the system of  FIG. 2   a , since the solenoid  230  can only be used for pressurizing the PPT, the trapped air in the PPT cannot be released through the solenoid  230 . As a result, in the PPT refill control, which requires a pressure difference between LST and the PPT, at the volume Vh, the PPT pressure should be lower than the LST pressure. According to equation (1), the PPT pressure at volume Vl will be even lower, and the pressure change is determined by the change in the volume V if the temperature change is insignificant. When dosing time is long, however, the amount of trapped air dissolved in the reductant liquid and brought out by dosing will be significant, and a pressure control is then required to compensate this loss. A variety of methods can be used in the pressure control. One exemplary method is calculating the mass of the trapped air in the PPT using the ideal gas equation: 
         [0000]        m=P *( Va−V )* Mw/RT   (3)
 
         [0048]    where R is the gas constant and T is the temperature of the liquid reductant measured with the temperature sensor  224 , and Mw is the molecular weight of the trapped air. When the calculated mass m is lower than a threshold, then the solenoid valve  230  is energized open to fill the compressed air into the PPT. The solenoid valve  230  is de-energized when the mass m is higher than a threshold. 
         [0049]    The change of pressure in the PPT is not desirable in dosing rate control. To decrease the pressure change, one method is decreasing the ratio of Vh to Vl and refilling the PPT more frequently. According to the ideal gas law, if temperature is constant, the pressure change is determined by the volume change of the trapped air. Therefore, decreasing the volume change lowers the pressure change. Another method of decreasing the pressure change is controlling the pressure in the PPT constant. To control the pressure in the PPT, one method is using a solenoid valve to release the trapped air in the PPT. An exemplary system based on this method is shown in  FIG. 2   b . Compared to the system of  FIG. 2   a , in the system of  FIG. 2   b , the port  205  of the PPT  200  is connected to the central port of a Tee connector  253  instead of the port A of the solenoid valve  230 . The inlet port on the left side of the Tee connector  253  is connected to the port B of a two-way solenoid valve  250  that is normally closed, through a passage  252 , while through a passage  249 , the outlet port on the right side is connected to the port A of a two-way solenoid valve  244  that is normally closed. The port A of the solenoid valve  250  is connected to the outlet on the right side of a Tee connector  251 , the central port of which is connected to the port B of a three-way solenoid valve  246 , which has its port C connected to the port A when de-energized and connected to the port B if energized. Compressed air is provided through the port  111  to the inlet port on the left side of the Tee connector  251 . The port A of the solenoid valve  246  is connected to the central port of a tee connector  248 , which has the inlet port on its left side connected to the port B of the solenoid valve  244 . The outlet port on the right side of the Tee connector  248  is coupled to the port  112  through a muffler  247 . Similar to that of the  FIG. 2   a , in  FIG. 2   b , the port  239  is connected to the port C of the solenoid  246 . 
         [0050]    In the system of  FIG. 2   b , similar to that of  FIG. 2   a , when the solenoid valve  246  is energized, its port B is connected to the port C, passing compressed air into LST  210 . If the solenoid valve  246  is de-energized, the port C is then connected to the port A, releasing compressed air in the LST  210 . The pressure in the PPT  200  can be controlled by energizing and de-energizing the solenoid valves  250  and  244 , and the controls to the two valves have four modes shown in the following table. 
         [0000]    
       
         
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Mode 
                 Status of the  
                 Status of the  
                   
               
               
                 number 
                 valve 250 
                 valve 244 
                 Actions 
               
               
                   
               
             
             
               
                 0 
                 Not energized 
                 Not energized 
                 Keeping air in PPT 
               
               
                 1 
                 Not energized 
                 Energized 
                 Releasing air from PPT 
               
               
                 2 
                 Energized 
                 Not energized 
                 Filling air to PPT 
               
               
                 3 
                 Energized 
                 Energized 
                 Releasing  
               
               
                   
                   
                   
                 compressed air 
               
               
                   
               
             
          
         
       
     
         [0051]    In Mode 0, neither of the solenoid valves  250  and  244  is energized, and compressed air is trapped in the PPT. In Mode 1, since the solenoid valve  244  is energized and the solenoid valve  250  is de-energized, compressed air is released from the PPT. Mode 2 is an air refilling mode. In this mode, the solenoid valve  244  is de-energized, disconnecting the PPT from ambient, while the solenoid valve  250  is energized, connecting the PPT to the compressed air supply. Mode 3 is a special mode and should be avoided. In this mode, when both of the solenoid valves  250  and  244  are energized, the compressed air source is connected to ambient. 
         [0052]    A simple relay control can be used in controlling the PPT pressure. In this control, when the PPT pressure increases higher than an upper threshold, the mode 1 is triggered, releasing air from the PPT and thereby decreasing the PPT pressure. If the PPT pressure decreases lower than a bottom threshold, then the mode 2 is triggered, refilling air to the PPT. If the pressure is in between these two thresholds, then the mode 0 is triggered, trapping air in the PPT. A hysteresis can be used to avoid frequent actions of the solenoid valves when the pressure is dithering around thresholds. 
         [0053]    In the systems of  FIGS. 2   a  and  2   b , since compressed air can be filled in or released from the PPT  200 , the reductant level in the PPT  200  can be calculated using the pressure change in the period of time when there is no action of the compressed air control, assuming temperature change is negligible and the ratio of the dissolved air in the reductant to the compressed air in the PPT  200  is low. According to the ideal gas equation, the relation between the pressure change and the volume change in the PPT  200  follows the equation: 
         [0000]        dP/dV=−P /( Va−V )  (4)
 
         [0054]    assuming the mass of the trapped air and the temperature are constant. With the measured pressure value of P, the reductant volume V then can be calculated with the following equation: 
         [0000]        V=Va+P*dV/dP   (5)
 
         [0055]    where dV can be calculated using the amount of dosed reductant, Dr, that causes the pressure change: 
         [0000]        dV=Dr*ρ   (6)
 
         [0056]    where ρ is the reductant density. 
         [0057]    In reductant doing rate control, to increase control accuracy, a three-stage PWM control can be used. In the three-stage PWM control, the third stage is a PWM control for driving the injector  130 . When the injector is energized, this PWM control generates a pull-in voltage to move the plunger in the injector to a latched position, and a hold-in voltage for maintaining the plunger at the latched position, by changing the duty cycle values of a PWM signal. Upon this third stage PWM signal, a second-stage PWM control and a first-stage PWM control work together to generate an activation signal for the injector to open the injector periodically according to a dosing rate command. The first-stage PWM control periodically calculates an estimated dosing amount based on pressure sensing values obtained from the pressure sensor  250 . In a PWM cycle of the first-stage PWM control, the control error, i.e., the difference between the estimated dosing amount and a target value calculated based on the dosing rate command, is used to determine the duty cycle of the second-stage PWM signal. 
         [0058]    A variety of methods can be used in the determination of the duty cycle of the second-stage PWM signal. In an exemplary method, the duty cycle is set by using the ratio between the second-stage PWM capacity to the control error. In this method, if in a PWM cycle of the second-stage PWM control, the PWM capacity, i.e., the maximum dosing amount at 100% duty cycle, is Dmax, and the difference between the estimated dosing amount and the target value is Er, then when Er is higher or equal to Dmax, a 100% duty-cycle second-stage PWM signal is generated, otherwise, a duty-cycle of Er/Dmax is set. 
         [0059]    After dosing, the system needs to be purged to remove reductant residue in the injector  130 , the reductant passage  131 , the reductant passage lines, the PPT  200 , the LST  210 , and the passage  203 , to avoid damage caused by frozen reductant and to save energy in thawing frozen reductant when operating under low temperature. The purge can be done by using the compressed air to press the reductant back to the tank  120 . In doing so, referring to  FIG. 2   a , firstly the solenoid valve  230  is de-energized and the solenoid valve  232  is energized. Then the solenoid valve  137  is energized. Under the pressure of the compressed air, reductant in the LST  210  enters the PPT  200 , and through the passages  209  and  131 , the solenoid valve  137 , and the passage  125 , the reductant flows back to the tank  120 . When the path from the PPT  200  to the passage  125  is empty, a sudden pressure drop will be detected by the pressure sensor  114 . Upon this signal, the solenoid  137  is de-energized, and the compressed air is trapped in the path and the LST  210 . To clean the injector  130 , after the solenoid  137  is de-energized, the injector  130  can be opened for a short period of time, releasing remains from the injector into the exhaust pipe. When the purge process completes, the solenoid valve  232  is de-energized. With air pressure being released, reductant is refilled in the LST  210 . However, due to the trapped compressed air, the PPT  200  and the path from the PPT  200  to the passage  125  is still empty. To avoid damage to the LST  210  during frozen expansion, the volume of the chamber  240  should be at least large enough for the frozen expansion. 
         [0060]    To avoid freezing damage to the LST  210 , another method is using a three-way solenoid valve with port A connected to port C when de-energized, and connected to port B when energized, as the solenoid valve  232 . With this solenoid valve, when the purge process completes, the solenoid valve  232  is de-energized, connecting the path from the LST  210  to the solenoid  137  (including the LST  210 , the passage  203 , the PPT  200 , the tubing  209 , the passage  131 , and the solenoid  137 ) to the compressed air source. The air pressure in the path then keeps reductant from being refilled into the path and thereby prevents freezing damage. 
         [0061]    Referring back to  FIG. 1 , the reductant delivery control can be realized with a routine run in the DCU  140 , which receives commands and system status from the ECU  150 , and operates actuators to release reductant in a rate as commanded by the ECU. In system level, a state machine can be used in the reductant delivery control. As shown in  FIG. 3 , in an exemplary reductant delivery control routine, there are five main states: an Off state  301 , an Idle state  302 , a Prime state  310 , a Normal-dosing state  320 , and a Purge state  330 . 
         [0062]    Upon a Key-on flag, the routine goes from the Off state  301  into the Idle state  302 . If a command CMD-Priming is received, then the routine enters the Prime state  310 , otherwise, if a Key-off flag is received, then the routine goes back to the Off state  301 . The Prime state further includes three sub-states: a PR1 sub-state  311 , in which the reductant volume in the PPT  200  is re-zeroed, a PR2 sub-state  312  for filling the PPT  200  with reductant, and a PR3 sub-state for releasing trapped air in the injector  130 . After the Prime state is completed, if a command CMD-Normal dosing is received, then the routine enters the Normal-dosing state  320 , otherwise, if a Key-off flag or a CMD-Idle command is obtained, then the routine goes into the Purge state  330 . The Normal-dosing state also includes three sub-states: a D1 sub-state  321  in which the LST is refilled, a D2 sub-state  322  for refilling reductant from the LST  210  to the PPT  200 , and a Dosing-rate control sub-state  323 , in which reductant delivery rate is controlled with the three-stage PWM control. In the D1 sub-state and the D2 sub-state, reductant pressure in the PPT  200  is controlled at a constant value (in a system of  FIG. 2   b ) or within a range (in a system of  FIG. 2   a ). The Dosing-rate control sub-state is independent to the D1sub-state and the D2 sub-state, i.e., in the Normal-dosing state, the Dosing-rate control sub-state runs all the time, while the D1 sub-state and D2 sub-state run alternately. Running in the Normal-dosing state, if a command CMD-Idle or a Key-off flag is received, the routine enters the Purge state. As the Normal-dosing state, the Purge state also includes three sub-states: a PU1 sub-state  331  for draining reductant in the path from the LST  210  to the passage  125 , a PU2 sub-state  332 , in which the remains in the injector is released into exhaust pipe, and a PU3 sub-state  333 , in which air is trapped in the PPT  200  or the LST  210  is fluidly connected to a compressed air source for keeping the PPT  200  or the LST  210  from being refilled. 
         [0063]    Among all the states, the Off state  301  and the Idle state  302  are simple states. In the Off state  301 , all actuators including the solenoid valves and the injector, and reductant temperature control are de-energized. In the Idle state  302 , reductant temperature control is enabled while actuators are still de-energized. 
         [0064]    In the Priming state  310 , the sub-state PR1 can be realized with a routine depicted in  FIG. 4   a . In this routine, the system is initialized at the beginning. The initialization process, which includes de-energizing the solenoid valves and the injector, is to turn off the system before the priming process starts. After the initialization, the state flag is set to PR1 and the PPT  200  is connected to compressed air to build pressure in it. When the pressure in the PPT is higher than a threshold Thd1, the PPT  200  is disconnected from compressed air, and the solenoid valve  137  is energized. Under the pressure in the PPT  200 , remains in the PPT flows back to the reductant tank  120 . When a high pressure changing rate is detected, indicating the PPT  200  and the path from the PPT to the solenoid valve  137  are empty, the solenoid valve  137  is de-energized, and the routine enters the sub-state PR2 after a variable, Vr, which is an indication of the reductant volume in the PPT  200 , is set to 0, and the pressure variable P1 is initialized with the currently measured pressure value, P. 
         [0065]    A routine for the sub-state PR2 is shown in  FIG. 4   b . The routine starts with setting the state flag to PR2. Then the LST  210  is connected to compressed air by connecting the port C of the control solenoid valve (e.g. the solenoid valve  232  in  FIG. 2   a  and the solenoid valve  246  in  FIG. 2   b ) to its port B, and the reductant volume in the PPT  200 , Vr, is compared to a threshold Thd2. If the reductant level is higher than Thd2, then the LST  210  is disconnected from compressed air by connecting the port C of the control solenoid valve to its port A, and the routine goes into the sub-state PR3. Otherwise, if a sudden pressure increase is detected, i.e., the LST  210  is empty, then the LST  210  is disconnected from compressed air for a period of time Tf for refill. The PR2 restarts after the refill. If there is no sudden pressure increase, the routine then waits until the reductant volume Vr is higher than the threshold Thd2. 
         [0066]    In the routine of  FIG. 4   b , the reductant volume Vr can be calculated in a service routine running periodically for a timer-based interrupt. As shown in  FIG. 4   c , the interrupt routine starts with checking the State value. If it doesn&#39;t equal to PR2, then the routine ends, otherwise, a timer TimerPR is incremented by the execution period value dT. If the TimerPR value is higher or equal to a time value TI, then the Vr value is calculated and the TimerPR is reset to 0. The routine ends thereafter. Since in the sub-state PR1, the reductant volume is re-zeroed, the Vr value can be calculated with the measured pressure values according to equation (2). 
         [0067]    The routine enters sub-state PR3 after PR2 is completed. An exemplary PR3 routine is depicted in  FIG. 4   d . At the beginning of this routine, the State value is set to PR3. Then the injector  130  is energized open for a short period of time Tr to release trapped air. The State value is set to Prime_completed thereafter and the routine enters sub-state D1 upon receiving a command CMD_Normal_Dosing from the ECU. 
         [0068]    Referring to  FIG. 5   a , in an exemplary routine of the sub-states D1 and D2, which belong to the Normal-dosing state  320 , a dosing initialization is executed at the beginning. During the dosing initialization, pressure control for the PPT and dosing rate control are enabled. After the dosing initialization, the State value is set to D1 and the reductant volume Vr is compared to a threshold Thd3. When the Vr value is higher than the threshold, a variable D2N, which indicates a cycle number in the sub-state D2. The State is then set to D2 and the reductant volume Vr is compared to another threshold Thd4. The routine goes back to setting State to D1 when the Vr value is higher than Thd4. 
         [0069]    In the sub-state D1, the reductant volume Vr can be measured based on the relation between the reductant volume change and PPT pressure change, according to equation (5). An interrupt service routine as shown in  FIG. 5   b  can be used for the calculation of Vr. The interrupt service routine runs periodically with a timer interrupt. Referring to  FIG. 5   b , at the beginning, the State value is checked. If it doesn&#39;t equal to D1, then the routine ends, otherwise, the pressure control status is examined. If compressed air is released from the PPT, e.g., the solenoid  244  ( FIG. 2   b ) is energized, or compressed air is filled into the PPT, e.g., the solenoid  230  ( FIG. 2   a ), or the solenoid  250  ( FIG. 2   b ) is energized, then a timer TimerD1 is reset to 0, and the routine ends, otherwise, the value of TimerD1 is examined. If it is 0, then the routine ends after a variable CmdSumD1, the value of which is the dosing amount during pressure change, is set to 0, and the value of a variable P0 is set to the current pressure sensing value P. If the value of TimerD1 is not 0, then the variable CmdSumD1 is incremented with the dosing amount calculated with the dosing rate Dc and the interrupt execution period dT, and the variable TimerD1 is incremented with dT. The pressure change, deltaP, is calculated thereafter and the value of the timer TimerD1 is compared to a pressure sampling time Td1. Upon the TimerD1 value higher than Td1, the reductant volume Vr is calculated using the following equation according to equation (5) and (6), and the routine ends after the variable TimerD1 is set to 0: 
         [0000]        Vr=Va+P*CmdSumD 1* p/deltaP   (7)
 
         [0070]    where the volume of the PPT  200  can be used as the Va value. If the TimerD1 value is not higher than the pressure sampling timeTd1, the routine ends. 
         [0071]    In the Normal-dosing state, in the system of  FIG. 2   a , reductant pressure in the PPT is not controlled to a target value or a range, and the pressure control is to compensate for the loss of compressed air caused by leaking and dissolving in reductant. The loss of compressed air is a slow process, therefore, in an exemplary algorithm, the compressed air loss can be calculated and compensated according to equation (2) in the sub-state D1 and the pressure control is disabled in the sub-state D2. The algorithm can be realized with a simple service routine running periodically with a timer-based interrupt. 
         [0072]    In the system of  FIG. 2   b , however, reductant pressure in the PPT can be controlled within a pre-determined range. The pressure control releases compressed air from the PPT when the reductant pressure is high and refills when it is low. The pressure control can also be realized with a service routine running periodically for a timer-based interrupt. Referring to  FIG. 5   c , in an example of the interrupt service routine, the value of a flag, State, is examined first. If it doesn&#39;t equal to D1 or D2, then routine ends, otherwise, the currently measured pressure value is compared to the lower end of the pre-determined range, P1. If is not higher than Pl, then the pressure control mode is set to 2 to refill compressed air into the PPT, and the routine ends, otherwise, the pressure value is compared to the upper end of the range, Ph. If it not lower than Ph, then the pressure control mode is set to 1, and the routine ends, otherwise, the pressure control keeps its previous value when two conditions are satisfied before the routine ends. One of the two conditions is that the pressure control mode is 1 and the pressure is higher than the middle value of the range, Pt, and the other one is that the pressure control mode is 2 and the pressure is lower than Pt. The pressure control mode is set to 0 before the routine ends if the two conditions are not satisfied. 
         [0073]    In the sub-state D2, the reductant volume Vr in the system of  FIG. 2   a  can be measured using a similar method used in the Priming state with the pressure control disabled, while in the system of  FIG. 2   b , since reductant pressure in the PPT is controlled within a pre-determined range by filling in or releasing compressed air from the PPT, a different algorithm needs to be used. An example of such an algorithm is realized with a service routine for a timer-based interrupt, as shown in  FIG. 5   d . The routine starts with checking the State value. If it doesn&#39;t equal to D2, then the routine ends, otherwise, the pressure control status is checked. When the pressure control is in mode 2, i.e., compressed air is being filled into the PPT, the routine ends after a flag RLFlag is reset to 0. The flag RLFlag is set to 1 if the pressure control is in mode 1, i.e., compressed air is being released from the PPT. When the pressure control is in mode 0, i.e., compressed air is being trapped in the PPT, the RLFlag value is examined. If RLFlag is not 1, the routine ends, otherwise, RLFlag is reset to 0, and the variable D2N is incremented by 1, and the reductant volume Vr is calculated before the routine ends. 
         [0074]    With the pressure control algorithm of  FIG. 5   c , the reductant volume Vr can be calculated with the D2N value and the dosing amount CmdSumD2. As illustrated in  FIG. 5   e , in the pressure control, each time when the control mode changes from 1 to 0, (i.e., the RLFlag value changes from 1 to 0) compressed air is released, and the pressure value changes from Ph to Pt. According to the ideal gas equation, when there is no temperature change, the reductant volume change in each cycle when the pressure increases from Pt to Ph is determined by the values of Pt and Ph: 
         [0000]        Vr ( Ph )= Va−[Va−Vr ( Pt )]* Ph/Pt   (8)
 
         [0075]    where Vr(Ph) is the reductant volume at pressure Ph, and Vr(Pt) is that at pressure Pt. Accordingly, when pressure releasing time is short, in the routine of  FIG. 5   d , the reductant volume Vr then can be calculated according to the equation: 
         [0000]        Vr ( D 2 N )= Va−[Va−Vr ( D 2 N− 1)]* Ph/Pt   (9)
 
         [0000]    where Vr(D2N) and Vr(D2N−1) are the reductant volume values in cycle D2N and D2N−1. In the equation (9), since Pt and Ph are pre-determined values, and Va is a constant, the only factors that determine the Vr value are the cycle number D2N and the initial Vr value, which is the value of Vr when the sub-state D2 starts. If the initial Vr value is set to a constant value, then the D2N number can be used directly in  FIG. 5   a  in deciding if the routine needs to go back to sub-state D1 (replacing Vr in comparing with Thd4). 
         [0076]    Referring back to  FIG. 3 , in the sub-state  323  (Dosing-rate control), a three-stage PWM control as shown in  FIG. 6   a  can be used in compensating the pressure variation in the PPT. In this control, the signal obtained from the pressure sensor  250  is sent to a sensor signal processing unit  602 , where the analog pressure sensing signal is filtered and converted to digital signal. The result signal is fed into a PWM control module  610  in a PWM signal controller  601  together with a dosing mass-flow rate command. The PWM control module then calculates the values for control parameters of a PWM signal generator  620  and set the values. A PWM signal is generated by the PWM signal generator and provided to a power switch circuit  603 , where the PWM signal is converted to a switching signal driving the solenoid valve of the injector  130  through signal lines  145 . 
         [0077]    The PWM signal generation in the PWM signal controller  601  includes three stages. In the first stage, the control parameters for the PWM signal generator  620  are set. In the second stage, a second stage PWM signal is created by the PWM signal generator  620 . A third-stage PWM signal, which provides the pull-in and hold-in voltage, is also generated in the PWM signal generator  620  in the third-stage signal generation. 
         [0078]    An embodiment of the PWM control module  610  is shown in  FIG. 6   b . In this module, upon receiving the dosing mass-flow rate command, in blocks  611  and  612 , the duty cycle and period of the first stage PWM signal are calculated and provided to a block  614 , where a target value is determined. The target value is then compared with a current value calculated in a block  613  with the pressure feedback value provided by the sensor signal processing unit  602 . And the result error value is used by a block  615  to calculate the on-time setting value of the second stage PWM signal, On-time2. The on-time value of the third stage PWM signal, On-time3, is generated thereafter with the On-time2 value in a block  618 , which can also be implemented in the control module  620 . In the control module  610 , the period setting value for the second stage PWM signal, Period2, is determined with the dosing mass-flow rate command in a block  616 , and that for the third stage PWM signal, Period3, is generated with the Period2 value in a block  617 . Preferably, the control module  610  is realized with a routine run in the DCU. 
         [0079]    An exemplary routine for the control module  610  is a service routine for a timer-based interrupt running periodically with a time interval of P3. The flow chart of the exemplary routine is shown in  FIG. 6   c . In this chart, t v  and Fault_Thd are constant values, and P1 is the period value of the first-stage PWM signal. Status is the PWM pulse status flag. When the on-time variable of the second-stage PWM signal, On_time2, is set to t v , the Status value is ON, otherwise, it is OFF. The variable target_value contains the target on-time value of the first-stage PWM signal, while the variable current_value saves the calculated on-time value of the first-stage PWM signal at the current moment. The value of P2 is the cycle period value of the second-stage PWM signal, and the variable Timer saves the current time in a first-stage PWM cycle. Values of the variable C1 in this chart are indicative to the PWM capacity of the second-stage PWM control. 
         [0080]    When the interrupt routine is triggered, the C1 value is calculated, and the value of Timer is compared to the period value P1 of the first-stage PWM signal. If the current cycle is finished, i.e., Timer &gt;=P1, then the on_time value of the second stage PWM signal is examined. When the on_time value is lower than t v , the total error of this PWM cycle is calculated and assigned to a variable previous_error. And after the Timer value is reset to P3, in a step  636 , the current_value is initialized, and the register P2 and the variable target_value are updated for a new cycle, which starts with calculating the error to be corrected in the current cycle by adding the current_error value to the previous_error value. If the error to be corrected is higher than t v , then the on-time of the second PWM signal, On_time2, is set to t v  and the Status flag is set to ON, otherwise, the error value is assigned to the variable On_time2, and the Status flag is reset to OFF. The routine ends thereafter. Referring back to the comparison between the Timer value and the P1 value, if current cycle ends (Timer &gt;=P1) with the On_time2 value not lower than t v , then it means the error cannot be corrected in this PWM cycle. In this case, the error in the previous cycle is calculated, and assigned to the variable previous_error. And the Status flag is set to ON after the Timer is set to P3 and the current_value is initialized. Since the error is not corrected, it is accumulated. When the accumulated error is higher than the threshold Fault_Thd, a fault is reported before the routine ends. Again referring back to the comparison between the Timer value and the P1 value, when the Timer value is greater than P1 (the routine is called again in the same first-stage PWM cycle), the Timer value is incremented by P3, and then the Status flag is examined. If the Status flag is OFF, then the variable On_time2 is cleared to 0, and the routine ends, otherwise, current_value is calculated in a step  635  and the error is updated thereafter. Before the routine ends, the error value is compared to the product of t v  and C1, t v *C1. If the error value is equal or greater than the product, then the On_time2 value is set to t v , otherwise, the value of error/C1 is set to On_time2 and the Status flag is reset to OFF. 
         [0081]    In the interrupt routine, normally the t v  value is selected greater than the error to be corrected (e.g. t v  equals P2). And the interrupt period value (P3) can be the same as that of the second-stage PWM signal (P2). With the interrupt routine of  FIG. 6   c , a signal timing chart when t v  equals P3 and P2 is shown in  FIG. 6   d . An interrupt is triggered at a moment  646 . Since the error, which is calculated by comparing the value of current_value and a target value  647 , is higher than t v , the On_time2 value is set to t v . The current_value accumulates with time. At a moment  642 , when the calculated error is lower than the product of t v  and C1, the value of error/C1 is assigned to On_time2. In the next interrupt triggered at a moment  643 , On_time2 is set to 0 and the current_value variable is locked at a value  648 . At a moment  645 , the current PWM cycle ends, and the previous_error ( FIG. 6   c ) is updated for the next cycle by including the error between the current_value value  648  and the target value  647 . 
         [0082]    In the interrupt routine of  FIG. 6   c , the target_value can be calculated with the reductant flow rate command using the following formula: 
         [0000]      target_value( i )=Massflow_rate_cmd* S   0   (F1)
 
         [0000]    where Massflow_rate_cmd is the dosing mass-flow rate command to the PWM control, and S o  is the period value of the first stage PWM signal. The formula for calculating current_value in the step  635  can be: 
         [0000]      current_value( i )= K *sqrt( Pr ( i )− Pc ))* P 3+current_value( i− 1)  (F2)
 
         [0000]    where i is the number of interrupts after Timer is reset to 0: 
         [0000]        i =Timer/ P 3  (F3)
 
         [0000]    sqrt is the square root calculation, K a pre-determined constant, Pr(i) the pressure sensing value for the calculation in the i-th interrupt cycle, and Pc the pressure in the exhaust passage  166 . The constant K can be calculated using the discharge coefficient of the injector, C D , the minimum area of the injector nozzle, A n , and the density of the reductant, ρ: 
         [0000]        K=C′   D   A′   n √{square root over (2ρ)}  (10)
 
         [0000]    and the value of current_value(0) is set to 0 in the step  636 . And the C1 value can be calculated using the following equation: 
         [0000]        C 1= K *sqrt( Pr ( i )− Pc ))* P 3 /P 2  (F4)
 
         [0083]    Referring back to  FIG. 6   a , the PWM signal generator  620  can also be realized with a routine. However, to have a high PWM frequency, especially for the third-stage PWM signal, it is preferred to have it implemented with logic circuits. The block diagram and signal flow chart of an exemplary circuit is shown in  FIG. 6   e . In this circuit, the ratios of the period and on-time values of the second signal to the period value of the third PWM signal are set to a Period Register  621  and an On-time Register  622  respectively, and the period value of the third PWM signal is set to the Period Register  621 . Upon a rising edge of an LD signal  651  generated by a Load Control Logic  632 , the values of the second-stage PWM signal in the Period Register  621  and the On-time Register  622  are further, respectively, loaded in a Period Counter  627  and an On-time Register  629 . The Period Counter  627  is a counting-down counter and its clock signal is a signal  650  generated in another Load Control Logic  625 . When the Period Counter  627  counts to 0, in the LD signal  651 , a pulse is generated. At a rising edge of the LD pulse, a signal  652 , which is ratio of the on-time value of the second-stage PWM signal to the period of the third-stage PWM signal (On-time2/Period3) loaded in the On-time Register  629 , also appears at a port DB of a Signal Control Logic  633 , which has a port DA connected to an output of a Timer  631 . The Timer  631  can be a counting-up counter and has its clock input connected to the signal  650  generated by the Load Control Logic  625 . The Timer  631  is reset by a signal generated in a Latch  630 , which can be latched by a signal  654  provided from an output of the Signal Control Logic  633 , Out1, and reset by the LD signal produced by the Load Control Logic  632 . In the Signal Control Logic  633 , if the value at the port DB is higher than that at the port DA, then a high level latch signal is generated for the Latch  630 , otherwise, a zero signal is provided. The Signal Control Logic  633  has another output Out2 connected to the Reset port of a Timer  635 , which can also be a counting-up counter, having its clock input connected to the signal  650  and its data output connected to a DB port of a Signal Control Logic  636 . The Signal Control Logic  636  has a DA port connected to the output of the Timer  631 , and an outlet port connected to a Flash Memory  634 , providing an address value. In the Signal Control Logic  633 , when its DB value is zero, then a reset signal of one is provided to the Timer  635 , otherwise a zero signal is provided, while in the Signal Control Logic  636 , a value of zero is generated to the Flash Memory  634  if its DA value is zero, and its DB value is provided otherwise. The Flash Memory  634  is used to generate an on-time value of the third-stage PWM signal for producing pull-in and hold-in voltages. It functions as a one-dimensional look-up table with a zero value saved in an address of zero, and pull-in and hold-in on-time values saved thereafter. The output of the Flash Memory  634  is connected to an On-time Counter  624 , which is a counting-down counter clamped at zero with its clock input connected to a high frequency clock signal. Upon a rising edge of the signal  650  produced by the Load Control Logic  625 , the output value of the Flash Memory  634 , On-time3, is loaded into the On-time Counter  624 , and upon a falling edge of the signal  650 , the period value of the third-stage PWM signal saved in the Period Register  621 , Period3, is loaded into a Period Counter  623 , which is also a counting down counter clocked by the high frequency clock signal. The output of the Period Counter  623  communicates to a DA port of the Load Control Logic  625 , in which, a high level signal is generated when its DA value is 0 and its clock is at high level, while the output of the On-time Counter  624  is connected to a DA port of a Signal Control Logic  626 , which is clocked by the high frequency clock signal, and a high level signal is generated when the DA value is higher than 0 at a rising edge of its clock signal. 
         [0084]    A timing chart for the signals  650 - 655  is depicted in  FIG. 6   f . In the figure, the LD signal  650  is a pulse sequence  660 . Synchronized by the LD signal  650 , the LD signal  651 , which is another pulse sequence  661 , is generated. At the rising edge in the pulse sequence  661 , at a moment  667 , the DB signal  652  is updated to a new value as shown in a curve  662 , and the latch signal  654 , which is a pulse sequence  664 , is reset to 0. At a moment  668 , a falling edge in the pulse sequence  660  increments the value of the DA signal  653 , as shown in a curve  663 , and at a moment  669 , i.e., upon the following rising edge, the DA signal  665  is updated to a new value, as shown in a curve  665 . When the DA value of the Signal Control Logic  633  equals to its DB value, at a moment  670 , the latch signal  654  is set to 1, resetting the DA signal  653  to 0. The DA signal  655  is then updated to 0 thereafter upon the following rising edge of the LD signal  650 , and stays at the 0 value until the next cycle starting at a moment  661 . 
         [0085]    Referring back to  FIG. 3 , in the Priming state  310  and the Normal-dosing state  320 , whenever a command CMD-Idle or a Key-Off signal is received, the control enters the Purge state  330 , which includes three sub-states, PU1, PU2, and PU3. The sub-state PU1 can be realized with a routine as shown in  FIG. 7   a . In this routine, the system is initialized at the beginning. In the initialization process, both of the solenoid valves and the injector are de-energized. After the initialization, the state flag is set to PU1 and the PPT  200  is connected to compressed air to build up pressure. When the pressure in the PPT is higher than a threshold Thd1, the PPT  200  is disconnected from compressed air, and the solenoid valve  137  is energized. Under the pressure in the PPT  200 , reductant residue in the PPT flows back to the reductant tank  120 . When a high pressure changing rate is detected, indicating the PPT  200  and the fluid path from the PPT to the solenoid valve  137  is empty, the solenoid valve  137  is de-energized, and the routine enters the sub-state PU2. 
         [0086]    A routine with a flow chart depicted in  FIG. 7   b  can be used for the sub-states PU2 and PU3. This routine starts with setting the State to PU2. Then the injector solenoid valve is energized open for a period of time is to purge the reductant residue in the injector to exhaust pipe. The solenoid valve is de-energized thereafter and the State is set to PU3. In the sub-state PU3, the PPT  200  is connected to compressed air to refill air into the PPT. When the PPT pressure is higher than a threshold Trap_Thd, the refill stops, and the key flag is examined. If the key flag is Key_off, then the control goes into the Off state, otherwise, the control enters the Idle state. 
         [0087]    While the present invention has been depicted and described with reference to only a limited number of particular preferred embodiments, as will be understood by those of skill in the art, changes, modifications, and equivalents in form and function may be made to the invention without departing from the essential characteristics thereof. Accordingly, the invention is intended to be only limited by the spirit and scope as defined in the appended claims, giving full cognizance to equivalents in all respect.