Patent Publication Number: US-11661878-B2

Title: Control of selective catalytic reduction in heavy-duty motor vehicle engines

Description:
BACKGROUND 
     Technical Field 
     The present disclosure relates generally to control of selective catalytic reduction in heavy-duty motor vehicle engines and to modulation of performance of selective catalytic reduction systems in heavy-duty motor vehicle exhaust after-treatment systems. 
     Description of the Related Art 
     Regulated emissions from today&#39;s heavy-duty engines demand very low levels of tailpipe emissions, and standards are expected to be further reduced in the near future. To reduce tailpipe exhaust emissions, current technologies rely on aggressive engine control strategies and exhaust after-treatment catalyst systems (catalyst systems used to treat engine exhaust are referred to herein as exhaust after-treatment systems, emissions after-treatment systems, or EAS). The EAS for a typical heavy-duty diesel or other lean-burning engine may include a diesel oxidation catalyst (DOC) to oxidize unburned fuel and carbon monoxide, a diesel particulate filter (DPF) for control of particulate matter (PM), selective catalytic reduction (SCR) systems for reduction of oxides of nitrogen (NO x ), and/or an ammonia oxidation catalyst (AMOX). Performance of EAS systems, and of SCR systems in particular, is dependent upon exhaust gas temperature and other parameters. 
     SCR processes use catalysts to catalyze the NO x  reduction and a fluid referred to as DEF (diesel emission fluid), which acts as a NO x  reductant over the SCR catalyst. DEF is an aqueous solution that evaporates and decomposes to chemically release ammonia so that the ammonia is available for reaction. Efficiency of SCR operation is dependent upon temperature. For example, DEF evaporation and decomposition is dependent upon temperature, with higher temperatures (e.g., temperatures over 150, 160, 170, 180, 190, 200, 250, 300, or 350 degrees Celsius) generally improving performance. Temperature levels required to ensure compliance with emissions regulations may be highly dependent upon a wide variety of variables and are in some cases determined experimentally for specific engines, trucks, and operating conditions thereof. Thus, an EAS may include a heater to increase the temperature of the exhaust, to facilitate DEF injection, evaporation, and decomposition at rates sufficient to allow efficient performance of the SCR processes. 
     BRIEF SUMMARY 
     A method may be summarized as comprising: operating a diesel engine of a heavy-duty truck such that the diesel engine generates an exhaust gas flow that enters an exhaust after-treatment system of the heavy-duty truck, the exhaust after-treatment system including a close-coupled selective catalytic reduction system and an underbody selective catalytic reduction system downstream of the close-coupled selective catalytic reduction system with respect to the exhaust gas flow; monitoring a temperature of the exhaust gas flow at the underbody selective catalytic reduction system; and controlling a DEF injector upstream of the close-coupled selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature across a range of at least 25 degrees Celsius in the monitored temperature. 
     Controlling the DEF injector may include controlling the DEF injector to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature across a range of at least 50 degrees Celsius in the monitored temperature. Controlling the DEF injector may include controlling the DEF injector to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature across a range of at least 100 degrees Celsius in the monitored temperature. 
     The method may further comprise controlling a DEF injector downstream of the close-coupled selective catalytic reduction system and upstream of the underbody selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature. Controlling the DEF injector downstream of the close-coupled selective catalytic reduction system and upstream of the underbody selective catalytic reduction system may include operating the DEF injector downstream of the close-coupled selective catalytic reduction system and upstream of the underbody selective catalytic reduction system to reduce NO x  levels in the exhaust gas flow to ensure compliance with emissions regulations. Controlling the DEF injector upstream of the close-coupled selective catalytic reduction system and controlling the DEF injector downstream of the close-coupled selective catalytic reduction system and upstream of the underbody selective catalytic reduction system may include optimizing a division labor of reducing NO x  levels to comply with emissions regulations. 
     The DEF injector may inject DEF into the exhaust gas flow at a rate that decreases as the monitored temperature increases. The DEF injector may initially inject DEF into the exhaust gas flow at a rate sufficient for the close-coupled selective catalytic reduction system to reduce NO x  levels to comply with emissions regulations. After the DEF injector injects DEF into the exhaust gas flow at the rate sufficient for the close-coupled selective catalytic reduction system to reduce NO x  levels to comply with emissions regulations, the DEF injector may inject DEF into the exhaust gas flow at a lower rate sufficient for the close-coupled selective catalytic reduction system to reduce NO x  levels halfway to compliance with emissions regulations. 
     The method may further comprise, while the DEF injector upstream of the close-coupled selective catalytic reduction system injects DEF into the exhaust gas flow at the rate sufficient for the close-coupled selective catalytic reduction system to reduce NO x  levels halfway to compliance with emissions regulations, controlling a DEF injector downstream of the close-coupled selective catalytic reduction system and upstream of the underbody selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate sufficient for the underbody selective catalytic reduction system to reduce NO x  levels to comply with emissions regulations. After the DEF injector injects DEF into the exhaust gas flow at the lower rate sufficient for the close-coupled selective catalytic reduction system to reduce NO x  levels halfway to compliance with emissions regulations, the DEF injector may cease to inject DEF into the exhaust gas flow. The method may further comprise, once the DEF injector upstream of the close-coupled selective catalytic reduction system ceases to inject DEF into the exhaust gas flow, controlling a DEF injector downstream of the close-coupled selective catalytic reduction system and upstream of the underbody selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate sufficient for the underbody selective catalytic reduction system to reduce NO x  levels to comply with emissions regulations. 
     The method may further comprise monitoring a NO x  level upstream of the close-coupled selective catalytic reduction system. Controlling the DEF injector may include operating the DEF injector to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored NO x  level. Controlling the DEF injector may include operating the DEF injector to inject DEF into the exhaust gas flow to achieve a target ammonia-to-NO x  ratio in the close-coupled selective catalytic reduction system. 
     A method may be summarized as comprising: operating a diesel engine of a heavy-duty truck such that the diesel engine generates an exhaust gas flow that enters an exhaust after-treatment system of the heavy-duty truck, the exhaust after-treatment system including a close-coupled selective catalytic reduction system and an underbody selective catalytic reduction system downstream of the close-coupled selective catalytic reduction system with respect to the exhaust gas flow; monitoring a temperature of the exhaust gas flow at the underbody selective catalytic reduction system; and controlling a DEF injector upstream of the close-coupled selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature over a span of time of at least thirty seconds, at least one minute, or at least two minutes. 
     A heavy-duty truck may be summarized as comprising: a diesel engine; an exhaust after-treatment system having an upstream end and a downstream end opposite the upstream end, the upstream end coupled to the diesel engine, the exhaust after-treatment system including a close-coupled selective catalytic reduction system and an underbody selective catalytic reduction system downstream of the close-coupled selective catalytic reduction system; and an engine control unit configured to: operate the diesel engine such that the diesel engine generates an exhaust gas flow that enters the exhaust after-treatment system; monitor a temperature of the exhaust gas flow at the underbody selective catalytic reduction system; and control a DEF injector upstream of the close-coupled selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature across a range of at least 25 degrees Celsius in the monitored temperature. The engine control unit may be configured to control the DEF injector to inject DEF into the exhaust gas flow to achieve a target ammonia-to-NO x  ratio in the close-coupled selective catalytic reduction system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates a diagram of an exhaust after-treatment system including a DOC, a DPF, and dual SCR systems. 
         FIG.  2    illustrates results of experimental testing of a heavy-duty vehicle including a diesel engine and the exhaust after-treatment system of  FIG.  1   . 
         FIG.  3    illustrates additional results of experimental testing of a heavy-duty vehicle including a diesel engine and the exhaust after-treatment system of  FIG.  1   . 
         FIG.  4    illustrates a flow chart of a method of using the systems described herein. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, certain specific details are set forth in order to provide a thorough understanding of various disclosed embodiments. However, one skilled in the relevant art will recognize that embodiments may be practiced without one or more of these specific details, or with other methods, components, materials, etc. In other instances, well-known structures associated with the technology have not been shown or described in detail to avoid unnecessarily obscuring descriptions of the embodiments. 
     Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. Also, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. It should also be noted that the term “or” is generally employed in its sense including “and/or” unless the context clearly dictates otherwise. 
     The use of ordinals such as first, second and third does not necessarily imply a ranked sense of order, but rather may only distinguish between multiple instances of an act or structure. 
     Terms of geometric alignment may be used herein. Any components of the embodiments that are illustrated, described, or claimed herein as being aligned, arranged in the same direction, parallel, or having other similar geometric relationships with respect to one another have such relationships in the illustrated, described, or claimed embodiments. In alternative embodiments, however, such components can have any of the other similar geometric properties described herein indicating alignment with respect to one another. Any components of the embodiments that are illustrated, described, or claimed herein as being not aligned, arranged in different directions, not parallel, perpendicular, transverse, or having other similar geometric relationships with respect to one another, have such relationships in the illustrated, described, or claimed embodiments. In alternative embodiments, however, such components can have any of the other similar geometric properties described herein indicating non-alignment with respect to one another. 
     Various examples of suitable dimensions of components and other numerical values may be provided herein. In the illustrated, described, and claimed embodiments, such dimensions are accurate to within standard manufacturing tolerances unless stated otherwise. Such dimensions are examples, however, and can be modified to produce variations of the components and systems described herein. In various alternative embodiments, such dimensions and any other specific numerical values provided herein can be approximations wherein the actual numerical values can vary by up to 1, 2, 5, 10, 15 or more percent from the stated, approximate dimensions or other numerical values. 
     As described herein, experiments may be performed and measurements may be taken while an engine or a vehicle including an engine are operating at “steady state.” As used herein, the term “steady state” may mean that the engine or the vehicle including the engine are operating with all operating parameters, including engine speed, power level, etc., unchanged or substantially unchanged over a period of time of at least one, at least two, at least three, at least four, at least five, at least six, or at least ten seconds. 
     Traditionally, heavy-duty vehicles included many components of exhaust after-treatment systems “underbody,” that is, underneath the engine, cab, or another portion of the vehicle, where space is relatively freely available and these components can therefore generally be larger than would otherwise be practical. Some modern heavy-duty vehicles, however, have begun to include a “close-coupled,” “up-close,” or “light-off” SCR unit much closer to the engine and exhaust ports thereof (e.g., adjacent to a turbine outlet of a turbocharger) and upstream of the traditional underbody exhaust after-treatment system, which can provide certain advantages in that the temperature of the engine exhaust may be higher when it is closer to the engine, although locating an SCR unit nearer the engine limits the available space and thus its practical size. Thus, some modern heavy-duty vehicles have included both a “close-coupled” SCR unit upstream with respect to the flow of the exhaust, such as adjacent to a turbine outlet of a turbocharger, to take advantage of the higher exhaust temperatures, as well as an “underbody” SCR unit downstream with respect to the flow of the exhaust, such as under the engine or cab of the vehicle, to take advantage of the greater available space. 
       FIG.  1    illustrates a diagram of an exhaust after-treatment system  100  that has a first, upstream end  102  and a second, downstream end  104  opposite to the first, upstream end  102 . The exhaust after-treatment system  100  is a component of a vehicle, such as a large, heavy-duty, diesel truck, and in use carries exhaust from the diesel engine of the truck to a tailpipe of the truck. For example, the first, upstream end  102  of the exhaust after-treatment system  100  may be coupled directly to an exhaust port or an outlet port of the diesel engine, such as a turbine outlet of a turbocharger thereof, and the second, downstream end  104  may be coupled directly to an inlet port of a tailpipe or muffler of the truck. Thus, when the engine is running and generating exhaust, the exhaust travels along the length of the exhaust after-treatment system  100  from the first, upstream end  102  thereof to the second, downstream end  104  thereof. 
     As illustrated in  FIG.  1   , the exhaust after-treatment system  100  includes, at its first, upstream end  102 , or proximate or adjacent thereto, a first temperature sensor  106 , which may be a thermocouple, to measure the temperature of the exhaust gas flow as it leaves the engine and enters the exhaust after-treatment system  100 , before heat begins to be lost through the exhaust after-treatment system  100  to the environment. The exhaust after-treatment system  100  also includes, at its first, upstream end  102 , or proximate or adjacent thereto, or just downstream of the first temperature sensor  106 , a first NO x  sensor  108 , to measure the content of NO x  gases in the exhaust gas flow as it leaves the engine and enters the exhaust after-treatment system  100 . The exhaust after-treatment system  100  also includes, at its first, upstream end  102 , or proximate or adjacent thereto, or just downstream of the first NO x  sensor  108 , a first DEF injector  110 , to inject DEF into the exhaust gas flow as it leaves the engine and enters the exhaust after-treatment system  100 . 
     The exhaust after-treatment system  100  may also include, proximate or adjacent its first, upstream end  102 , or just downstream of the first DEF injector  110 , a first heater  112 , which may be an electrically-powered resistive heater or heating element, a burner, or any other suitable heater, to inject heat energy into the exhaust gas flow and the injected DEF as they flow through the exhaust after-treatment system  100 . The exhaust after-treatment system  100  also includes, just downstream of the first heater  112 , a second temperature sensor  114 , which may be a thermocouple, to measure the temperature of the exhaust gas flow as it leaves the first heater  112  and just before or just as it enters a first, close-coupled SCR system  116 , or at the inlet to the close-coupled SCR system  116 . The exhaust after-treatment system  100  also includes, just downstream of the first heater  112  and the second temperature sensor  114 , the first, close-coupled SCR system  116 , which is configured to reduce oxides of nitrogen (NO x ) in the exhaust gas flow. 
     The exhaust after-treatment system  100  also includes, just downstream of the first SCR system  116 , a third temperature sensor  136 , which may be a thermocouple, to measure the temperature of the exhaust gas flow as it leaves the first SCR system  116 . In some implementations, the second temperature sensor  114  and the third temperature sensor  136  may be collectively referred to as an SCR bed temperature sensor. For example, a temperature of a catalytic bed of the first, close-coupled SCR system  116  may be measured, calculated, estimated, or otherwise determined based on the measurements provided by the second temperature sensor  114  and the third temperature sensor  136 , such as by averaging the temperature measurements provided by the second temperature sensor  114  and the third temperature sensor  136 . 
     The exhaust after-treatment system  100  also includes, just downstream of the first SCR system  116  and/or the third temperature sensor  136 , a second NO x  sensor  118 , to measure the content of NO x  gases in the exhaust gas flow as it leaves the first SCR system  116 . In practice, the first NO x  sensor  108  and the second NO x  sensor  118  can be used together to monitor, assess, or measure the performance of the first SCR system  116 . Together, the first temperature sensor  106 , the first NO x  sensor  108 , the first DEF injector  110 , the first heater  112 , the second temperature sensor  114 , the first, close-coupled SCR system  116 , the third temperature sensor  136 , and the second NO x  sensor  118  can be referred to as a close-coupled portion of the exhaust after-treatment system  100 , as they can be collectively located at or adjacent to the engine of the vehicle. 
     The exhaust after-treatment system  100  also includes, downstream of the first SCR system  116 , the third temperature sensor  136 , and the second NO x  sensor  118 , a DOC component  120 , to oxidize unburned fuel and carbon monoxide in the exhaust gas flow. The exhaust after-treatment system  100  also includes, downstream of the DOC component  120 , a DPF  122 , to reduce or otherwise control particulate matter in the exhaust gas flow. The exhaust after-treatment system  100  also includes, downstream of the DPF  122 , a fourth temperature sensor  130 , which may be a thermocouple, to measure the temperature of the exhaust gas flow as it leaves the DPF  122 . The exhaust after-treatment system  100  also includes, downstream of the DPF  122 , or just downstream of the fourth temperature sensor  130 , a second DEF injector  124 , to inject DEF into the exhaust gas flow as it leaves the DPF  122 . 
     In some embodiments, the exhaust after-treatment system  100  may also include, just downstream of the fourth temperature sensor  130  and the second DEF injector  124 , a mixer  132  and a second heater, which may be an electrically-powered resistive heater or heating element, a burner, or any other suitable heater, to inject heat energy into the exhaust gas flow and the injected DEF as they flow through the exhaust after-treatment system  100 . The exhaust after-treatment system  100  also includes, just downstream of the mixer  132  and the second heater, a fifth temperature sensor  134 , which may be a thermocouple, to measure the temperature of the exhaust gas flow as it leaves the second heater and just before or just as it enters a second, underbody SCR system  126 , or at the inlet to the underbody SCR system  126 . The exhaust after-treatment system  100  also includes, just downstream of the mixer  132 , the second heater, and the fifth temperature sensor  134 , the second, underbody SCR system  126 , which is configured to reduce oxides of nitrogen (NO x ) in the exhaust gas flow. 
     The exhaust after-treatment system  100  also includes, just downstream of the second SCR system  126 , a sixth temperature sensor  138 , which may be a thermocouple, to measure the temperature of the exhaust gas flow as it leaves the second SCR system  126 . In some implementations, the fifth temperature sensor  134  and the sixth temperature sensor  138  may be collectively referred to as an SCR bed temperature sensor. For example, a temperature of a catalytic bed of the second, underbody SCR system  126  may be measured, calculated, estimated, or otherwise determined based on the measurements provided by the fifth temperature sensor  134  and the sixth temperature sensor  138 , such as by averaging the temperature measurements provided by the fifth temperature sensor  134  and the sixth temperature sensor  138 . 
     In some alternative embodiments, the exhaust after-treatment system  100  may not include the second heater and may include only a single heater, i.e., the first heater  112 , to reduce overall costs. Similarly, in some embodiments, the exhaust after-treatment system  100  may not include all of the temperature sensors described herein, such as the third temperature sensor  136 , fourth temperature sensor  130 , fifth temperature sensor  134 , and/or sixth temperature sensor  138 , such as to further reduce overall costs. In such implementations, such temperature sensors may be replaced by virtual temperature sensors, which may measure, calculate, estimate, simulate, or otherwise determine a temperature at the same location, such as based on equations, data, simulations, and/or models of the behavior of temperatures at such locations under the operating conditions of the systems described herein. 
     The exhaust after-treatment system  100  also includes, just downstream of the second SCR system  126  and/or the sixth temperature sensor  138 , and at its second, downstream end  104 , or proximate or adjacent thereto, a third NO x  sensor  128 , to measure the content of NO x  gases in the exhaust gas flow as it leaves the second SCR system  126 . In practice, the second NO x  sensor  118  and the third NO x  sensor  128  can be used together to monitor, assess, or measure the performance of the second SCR system  126 . Together, the DOC component  120 , the DPF  122 , the second DEF injector  124 , the fourth temperature sensor  130 , the mixer  132 , the second heater, the fifth temperature sensor  134 , the second SCR system  126 , the sixth temperature sensor  138 , and the third NO x  sensor  128  can be referred to as an underbody portion of the exhaust after-treatment system  100 , as they can be collectively located underneath the engine, cab, or another portion of the vehicle. 
     As noted previously, performance of exhaust after-treatment systems, and of SCR systems in particular, is dependent upon exhaust gas temperature. More specifically, DEF evaporation and decomposition is dependent upon temperature, with higher temperatures generally improving performance. Thus, operation of a heater to increase the temperature of the exhaust gas flow can be critical to maintaining compliance with emissions regulations. Nevertheless, operation of a heater to increase the temperature of the exhaust gas flow naturally incurs a fuel penalty and thus a reduction of overall system fuel efficiency. Thus, it is critical to ensure accurate and precise performance of such heaters, to ensure compliance with emissions standards without unduly reducing overall fuel efficiency. 
     There are additional trade-offs involved in relying on the close-coupled SCR system  116  and/or the underbody SCR system  126  to reduce NO x  levels in the exhaust gas flow. For example, as noted previously, use of the close coupled SCR system  116  may be advantageous because the exhaust gas flow is ordinarily already naturally at a higher temperature than it is at the underbody SCR system  126  (ignoring operation of the first heater  112  and/or the second heater), particularly under cold-start conditions and/or low load operation. Nevertheless, as also noted previously, the underbody SCR system  126  may be larger than the close-coupled SCR system  116 . 
     Furthermore, relative weighting of the burden of NO x  reduction between the close-coupled SCR system  116  and the underbody SCR system  126  results in different levels of various tailpipe emissions. NO x  (oxides of nitrogen) in the exhaust gas flow include both NO (nitric oxide) and NO 2  (nitrogen dioxide), but diesel engine exhaust typically includes NO x  predominantly in the form of NO rather than NO 2 . As the exhaust gas flow passes across the DOC  120 , however, NO is oxidized to NO 2 , and as such, the underbody SCR system  126  has higher levels of NO 2  than the close-coupled SCR system  116 . As such, the close-coupled SCR system  116  is more heavily governed by the standard SCR reaction and other NO-based reactions than the underbody SCR system  126 . Under cold conditions (e.g., SCR bed temperatures under 250 degrees Celsius), dosing of DEF in the presence of NO 2  can form nitrates, which subsequently form N 2 O, which is a greenhouse gas. Under conditions when the underbody SCR system  126  is cold, therefore, it can be preferable to leverage the close-coupled SCR system  116 . The control strategy therefore heavily weights operation of the close-coupled SCR system  116  relative to operation of the underbody SCR system  126  under cold-start and low-load operation conditions. 
     Additionally, the DPF  122  includes a catalyst that traps soot (e.g., black carbon) from the exhaust gas flow. The DPF  122  has a maximum capacity that, once reached, requires active regeneration of the DPF  122  to oxidize the soot to CO 2 . Active regeneration is achieved by raising the temperature of the exhaust to greater than 500 degrees Celsius, and therefore increases both fuel consumption and CO 2  emissions. Under warm conditions (e.g., exhaust temperature greater than 300 degrees Celsius), the soot in the DPF  122  can undergo passive regeneration using NO 2  generated by the DOC  120 . It is desirable to maximize passive regeneration (soot oxidation) in the DPF  122  to reduce, minimize, avoid, or optimize reliance on active regeneration. Therefore, under warm conditions, the dual SCR control strategy shifts the burden of NO x  reduction toward the underbody SCR system  126 , to increase, maximize, or optimize the amount of NO 2  delivered to the DPF  122 . 
     Finally, overall SCR conversion efficiency can suffer under high exhaust flow conditions such as at high load operation and hard acceleration conditions of the diesel engine. To improve overall system NO x  reduction efficiency under such conditions, or decrease the degree to which such efficiency suffers, the close-coupled SCR  116  and the underbody SCR  126  may both be used at or near their respective maximum capacities, under which conditions the close-coupled SCR system  116  may be considered additional volume to the underbody SCR system  126 . That is, under some conditions, irrespective of the temperature operating regime, the close-coupled SCR system  116  is leveraged to reduce the effective NO x  flow into the underbody SCR system  126 , to reduce high exhaust flow emissions. 
     Thus, at some times during operation of a diesel engine, only the close-coupled SCR system  116  may be used to reduce NO x  levels to comply with tailpipe emissions regulations, while at other times during operation of a diesel engine, only the underbody SCR system  126  may be used to reduce NO x  levels to comply with tailpipe emissions regulations, while at yet other times, the burden of reducing NO x  levels to comply with tailpipe emissions regulations may be shared by the two SCR systems  116 ,  126 , such as by any suitable ratio. 
     For example, the close coupled SCR system  116  may reduce NO x  levels by 10%, 25%, 50%, 75%, or 90% (or any other intermediate percentage) of the amount required to comply with tailpipe emissions regulations, while the underbody SCR system  126  may reduce NO x  levels by a complementary amount (e.g., 90%, 75%, 50%, 25%, or 10%, respectively) of the amount required to comply with tailpipe emissions regulations. Thus, it has been found that it is also valuable to balance the NO x  reduction burden between the two SCR systems  116  and  126  to further improve efficiency of operation, to ensure compliance with emissions standards without unduly reducing overall fuel efficiency, and to increase, maximize, or optimize NO x  reduction per unit DEF utilized. 
     First, an initial lookup table or database is built or populated under ideal or idealized conditions in accordance with standardized laboratory experiments. Such experiments may operate a heavy-duty diesel engine at steady state under a variety of operating conditions to determine properties of the exhaust gas flow generated by the engine at steady state under such conditions. For example, for each set of given operating conditions, the experiments may measure a mass flow rate ({dot over (m)} exh ) of the exhaust gas flow generated by the engine, which may be specified in units such as kg/s, determine a resulting molar specific heat at constant pressure (C p ) of the exhaust gas flow generated by the engine (which may be unique to each individual engine but may be expected to be constant over the range of operation of any given engine), and measure a resulting exhaust temperature (T 1 ) of the exhaust gas flow generated by the engine immediately adjacent to an exhaust port or outlet port of the engine itself, such as a turbine outlet of a turbocharger thereof, which may be measured by the first temperature sensor  106  and may be specified in units such as K or degrees Celsius. 
     Such experiments may also operate the diesel engine in combination with the exhaust after-treatment system  100  at steady state under a variety of operating conditions to determine how the operation of the exhaust after-treatment system  100  affects properties of the exhaust gas flow as it travels through the exhaust after-treatment system  100  at steady state under such conditions. For example, for each set of given operating conditions, the experiments may use the temperature sensors  106 ,  114 ,  130 ,  134 ,  136 , and  138  to measure the temperature of the exhaust gas flow at the locations of the temperature sensors  106 ,  114 ,  130 ,  134 ,  136 , and  138 , respectively. The resulting measured temperatures can be stored in the lookup table or database. 
     As another example, for each set of given operating conditions, the experiments may use the first NO x  sensor  108  to measure NO x  levels at the location of the first NO x  sensor  108 , may use the second NO x  sensor  118  to measure NO x  levels at the location of the second NO x  sensor  118 , and may use such measurements to calculate a percentage reduction in NO x  levels between the first and second NO x  sensors  108 ,  118 , which may be taken as a percentage efficiency of the close coupled SCR system  116 . Thus, as noted elsewhere herein, the first NO x  sensor  108  and the second NO x  sensor  118  can be used together to monitor, assess, or measure the performance of the first SCR system  116  at steady state under the various experimental conditions. Similarly, for each set of given operating conditions, the experiments may use the second NO x  sensor  118  to measure NO x  levels at the location of the second NO x  sensor  118 , may use the third NO x  sensor  128  to measure NO x  levels at the location of the third NO x  sensor  128 , and may use such measurements to calculate a percentage reduction in NO x  levels between the second and third NO x  sensors  118 ,  128 , which may be taken as a percentage efficiency of the underbody SCR system  126 . Thus, as noted elsewhere herein, the second NO x  sensor  118  and the third NO x  sensor  128  can be used together to monitor, assess, or measure the performance of the second SCR system  126  at steady state under the various experimental conditions. The resulting measured NO x  levels and calculated percentage efficiencies of the SCR systems can be stored in the lookup table or database. In some implementations, the resulting measured NO x  levels and calculated percentage efficiencies of the SCR systems can be stored in the lookup table or database as a function of or otherwise correlated with or related to the measured temperatures. 
     As another example, for each set of given operating conditions, the experiments may monitor the rate at which the first and second DEF injectors  110 ,  124  inject DEF into the exhaust gas flow, and may use such information in combination with the measurements provided by the first, second, and third NO x  sensors  108 ,  118 , and  128 , to calculate ammonia-to-NO x  ratios (ANR) at the close-coupled SCR system  116  and at the underbody SCR system  126 . The injection rates and calculated ANRs can be stored in the lookup table or database. 
     As another example, for each set of given operating conditions, the experiments may monitor the rate at which N 2 O is generated and emitted, as well as the state of the DPF  122 , the level of passive regeneration thereof that occurs, and the degree to which active regeneration thereof is or would be required. Such information can be stored in the lookup table or database. 
     Based on such measurements, calculations, and data stored in the lookup table or database, ideal, optimal, efficient, or most efficient relative divisions of the labor or burden of reducing NO x  levels to comply with tailpipe emissions regulations between the first, close-coupled SCR  116  and the second, underbody SCR  126  may be determined. For example, it may be determined that it is efficient to allocate the NO x  reduction burden between the close-coupled SCR  116  and the underbody SCR  126  based on the temperature of the catalytic bed of the underbody SCR  126 , such as based on the temperatures of the exhaust gas flow measured by the fifth temperature sensor  134  and/or the sixth temperature sensor  138  (e.g., an average thereof). 
     For example, it may be determined that it is more efficient to allocate a larger portion of the NO x  reduction burden, or even all of the NO x  reduction burden, to the close-coupled SCR  116  when the temperatures at the underbody SCR  126  are relatively cold (indicating, for example, that the diesel engine and/or the exhaust after-treatment system  100  are cold or just starting up), and to allocate a larger portion of the NO x  reduction burden, or even all of the NO x  reduction burden, to the underbody SCR  116  when such temperatures are relatively hot (indicating, for example, that the diesel engine and/or the exhaust after-treatment system  100  are hot or operating at or near steady-state). 
     In some embodiments, dividing the labor of reducing NO x  levels to comply with tailpipe emissions regulations includes controlling a rate at which the first DEF injector  110  injects DEF into the exhaust gas flow upstream of the close-coupled SCR system  116  (e.g., as a function of the NO x  levels measured by the first NO x  sensor  108 ) to control an ANR within the close-coupled SCR system  116  and/or to prevent ammonia slip from the close-coupled SCR system  116 , thereby controlling operation and SCR reduction efficiency of the close-coupled SCR system  116 , and operating the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. 
     As one specific example, it may be determined that when the temperature of the catalytic bed of the underbody SCR system  126  is 200 degrees Celsius or lower, it is most efficient from a systemic perspective to operate the first DEF injector  110  to inject DEF into the exhaust gas flow at a minimum rate sufficient to ensure that the ANR in the first, close-coupled SCR is equal to or 100% of the ANR required to reduce NO x  levels in the exhaust gas flow just downstream of the close-coupled SCR system  116  (e.g., as measured by the second NO x  sensor  118 ) to levels in compliance with emissions regulations, that is, such that the first, close coupled SCR system  116  handles the full NO x  reduction burden, and to not begin operating the second DEF injector  124 , the second heater, and the underbody SCR system  126 . It may further be determined that when the temperature of the catalytic bed of the underbody SCR system  126  is 225 degrees Celsius, it is most efficient from a systemic perspective to operate the first DEF injector  110  to inject DEF into the exhaust gas flow at a minimum rate sufficient to ensure that the ANR in the first, close-coupled SCR is 80% of the ANR required to reduce NO x  levels in the exhaust gas flow just downstream of the close-coupled SCR system  116  (e.g., as measured by the second NO x  sensor  118 ) to levels in compliance with emissions regulations, and to operate the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. 
     It may further be determined that when the temperature of the catalytic bed of the underbody SCR system  126  is 275 degrees Celsius, it is most efficient from a systemic perspective to operate the first DEF injector  110  to inject DEF into the exhaust gas flow at a minimum rate sufficient to ensure that the ANR in the first, close-coupled SCR is 60% of the ANR required to reduce NO x  levels in the exhaust gas flow just downstream of the close-coupled SCR system  116  (e.g., as measured by the second NO x  sensor  118 ) to levels in compliance with emissions regulations, and to operate the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. It may further be determined that when the temperature of the catalytic bed of the underbody SCR system  126  is 300 degrees Celsius, it is most efficient from a systemic perspective to operate the first DEF injector  110  to inject DEF into the exhaust gas flow at a minimum rate sufficient to ensure that the ANR in the first, close-coupled SCR is 25% of the ANR required to reduce NO x  levels in the exhaust gas flow just downstream of the close-coupled SCR system  116  (e.g., as measured by the second NO x  sensor  118 ) to levels in compliance with emissions regulations, and to operate the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. 
     It may further be determined that when the temperature of the catalytic bed of the underbody SCR system  126  reaches an upper threshold or boundary, it is most efficient from a systemic perspective to cease operating the first DEF injector  110 , the first heater  112 , and the close-coupled SCR system  116 , and to operate the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to handle the full NO x  reduction burden and reduce NO x  levels to ensure compliance with emissions regulations. At temperatures between those identified herein, or at temperatures between any other set of temperatures so studied or investigated in such experiments, any interpolation functions, such as a linear interpolation function, may be used to determine appropriate DEF injection rates. For example, it may further be determined by linear interpolation that when the temperature of the catalytic bed of the underbody SCR system  126  is 250 degrees Celsius, it is most efficient from a systemic perspective to operate the first DEF injector  110  to inject DEF into the exhaust gas flow at a minimum rate sufficient to ensure that the ANR in the first, close-coupled SCR is 70% of the ANR required to reduce NO x  levels in the exhaust gas flow just downstream of the close-coupled SCR system  116  (e.g., as measured by the second NO x  sensor  118 ) to levels in compliance with emissions regulations, and to operate the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. Such information can be stored in the lookup table or database. 
     Second, during operation of a vehicle, such as a motor vehicle such as a heavy-duty diesel truck, the exhaust after-treatment system  100 , including the first, close-coupled SCR system  116  and the second, underbody SCR system  126 , may be operated to ensure compliance with emissions regulations while minimizing an incurred fuel penalty resulting from operation of the components of the exhaust after-treatment system  100 , including the first heater  112  and/or the second heater, as described elsewhere herein. In particular, as the truck and its engine and its engine control unit (“ECU”) are operating, the engine control unit of the truck may continuously monitor how the operation of the exhaust after-treatment system  100  affects properties of the exhaust gas flow as it travels through the exhaust after-treatment system  100 . For example, the ECU may continuously measure or monitor temperatures of the exhaust gas flow at the locations of the temperature sensors  106 ,  114 ,  130 ,  134 ,  136 , and  138 , as well as temperatures of the catalytic beds of the first and second catalytic reduction systems  116 ,  126 . 
     As another example, the ECU may use the first NO x  sensor  108  to measure NO x  levels at the location of the first NO x  sensor  108 , may use the second NO x  sensor  118  to measure NO x  levels at the location of the second NO x  sensor  118 , and may use such measurements to calculate a percentage reduction in NO x  levels between the first and second NO x  sensors  108 ,  118 , which may be taken as a percentage efficiency of the close-coupled SCR system  116 . Similarly, the ECU may use the second NO x  sensor  118  to measure NO x  levels at the location of the second NO x  sensor  118 , may use the third NO x  sensor  128  to measure NO x  levels at the location of the third NO x  sensor  128 , and may use such measurements to calculate a percentage reduction in NO x  levels between the second and third NO x  sensors  118 ,  128 , which may be taken as a percentage efficiency of the underbody SCR system  126 . 
     As another example, the ECU may monitor the rate at which the first and second DEF injectors  110 ,  124  inject DEF into the exhaust gas flow, and may use such information in combination with the measurements provided by the first, second, and third NO x  sensors  108 ,  118 , and  128 , to calculate ammonia-to-NO x  ratios (ANR) at the close-coupled SCR system  116  and at the underbody SCR system  126 . 
     Based on such measurements and calculations, in combination with the data stored in the lookup table or database, the engine control unit of the truck may continuously assess or determine a desired, optimal, or most efficient division of the labor of reducing NO x  levels to comply with tailpipe emissions regulations between the first, close-coupled SCR  116  and the second, underbody SCR  126 . For example, the engine control unit may continuously use the bed temperature of the underbody SCR system  126  in combination with the data stored in the lookup table or database to determine a desired or optimal rate at which to inject DEF into the exhaust gas flow upstream of the close-coupled SCR system  116 . Such a determination may rely on interpolation between data points stored in the lookup table or database. 
     The engine control unit may then operate the first DEF injector  110  to inject DEF into the exhaust gas flow at that rate. The engine control unit may then operate the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. The engine control unit may furthermore continually control and/or adjust or update operation of the first DEF injector  110  to inject DEF into the exhaust gas flow at a rate that varies over time, such as over at least 15 seconds, 30 seconds, one minute, two minutes, or four minutes, and as a function of an average of the temperature measurements provided by the fifth temperature sensor  134  and the sixth temperature sensor  138 , such as across a range in such an average temperature of at least 25, 50, 75, 100, 125, or 150 degrees Celsius. As such operation of the first DEF injector  110  varies, the engine control unit may also continually control and/or adjust or update operation of the second DEF injector  124 , the second heater, and the second, underbody SCR system  126  to further reduce NO x  levels to ensure compliance with emissions regulations. 
     The systems and techniques described herein can facilitate continuous and simultaneous dosing of DEF onto the catalytic beds of two independent SCR systems, namely, the close-coupled SCR system  116  and the underbody SCR system  126 , such as by using two independent DEF injectors, each located upstream of a respective one of the SCR systems, namely, the first DEF injector  110  and the second DEF injector  124 , to increase overall systemic efficiency while maintaining compliance with NO x  emissions regulations. The systems and techniques described herein can be used to reduce NO x  tailpipe emissions to ultra-low levels, which may be referred to as “ultra-low NO x ” or “ULN” levels. Further, the systems and techniques described herein can be leveraged to reduce especially high NO x  emissions, such as on hard acceleration transients, to within regulated levels. The systems and techniques described herein may include or use a minimal number of sensors, that is, the systems and techniques described herein may include or use exactly or no more than a specified number of sensors necessary for performance as described herein. The systems and techniques described herein allow efficient operation of the close-coupled SCR system  116  and/or the underbody SCR system  126  without ammonia slip, or with minimal ammonia slip, from the SCR systems  116 ,  126 . 
       FIG.  2    illustrates results of experimental testing of a heavy-duty vehicle including a diesel engine and the exhaust after-treatment system  100 . In particular,  FIG.  2    illustrates two charts, one on top of the other. In the bottom of the two charts, the horizontal X-axis represents time and the vertical Y-axis represents the instantaneous NO x  levels, in units of parts per million, measured by the first, second, and third NO x  sensors  108 ,  118 , and  128 . In the top of the two charts, the horizontal X-axis represents time on the same scale and interval as in the bottom of the two charts, and the vertical Y-axis represents the cumulative NO x  measured by the first NO x  sensor  108  (see the line indicated by reference numeral  140 ), the second NO x  sensor  118  (see the line indicated by reference numeral  142 ), and the third NO x  sensor  128  (see the line indicated by reference numeral  144 ). 
     As illustrated in  FIG.  2   , the difference between the NO x  levels measured by the first and second NO x  sensors  108 ,  118 , and the resulting difference between the cumulative NO x  measured by the first and second NO x  sensors  108 ,  118 , rise early in the testing, reflecting the fact that it is generally more efficient to reduce NO x  levels near start-up or at cold temperatures at the close-coupled SCR  116  than at the underbody SCR  126 . As also illustrated in  FIG.  2   , the difference between the NO x  levels measured by the second and third NO x  sensors  118 ,  128 , and the resulting difference between the cumulative NO x  measured by the second and third NO x  sensors  118 ,  128  rise later in the testing, reflecting the fact that it is generally advantageous to reduce NO x  levels near steady-state operation or at hot temperatures at the underbody SCR  126  than at the close-coupled SCR  116 . 
       FIG.  3    illustrates results of experimental testing of a heavy-duty vehicle including a diesel engine and the exhaust after-treatment system  100 . In particular,  FIG.  3    illustrates two charts, one on top of the other. In the bottom of the two charts, the horizontal X-axis represents time and the vertical Y-axis represents the instantaneous rates of DEF dosing, in units of grams per hour, by the first DEF injector  110  and the second DEF injector  124 . In the top of the two charts, the horizontal X-axis represents time on the same scale and interval as in the bottom of the two charts, and the vertical Y-axis represents the cumulative ammonia-to-NO x  ratio resulting (e.g., from ammonia released by the DEF injected by the respective DEF injectors) in the close-coupled SCR system  116  (see the line indicated by reference numeral  150 ) and in the underbody SCR system  126  (see the line indicated by reference numeral  152 ). 
     As illustrated in  FIG.  3   , the DEF dosing by the first DEF injector  110  and the cumulative ammonia-to-NO x  ratio resulting in the close-coupled SCR system rise quickly early in the testing, reflecting the fact that it is generally more efficient to reduce NO x  levels near start-up or at cold temperatures at the close-coupled SCR  116  than at the underbody SCR  126 . As also illustrated in  FIG.  3   , the DEF dosing by the first DEF injector  110  and the cumulative ammonia-to-NO x  ratio resulting in the close-coupled SCR system  116  fall, and the DEF dosing by the second DEF injector  124  and the cumulative ammonia-to-NO x  ratio resulting in the underbody SCR system  126  rise quickly, later in the testing, reflecting the fact that it is generally advantageous to reduce NO x  levels near steady-state operation or at hot temperatures at the underbody SCR  126  than at the close-coupled SCR  116 . 
       FIG.  4    illustrates a flow chart  200  of a summarized version of a method in accordance with the present disclosure. As illustrated in  FIG.  4   , the method includes, at  202 , operating a diesel engine, thereby generating an exhaust gas flow. The method further includes, at  204 , monitoring a temperature of the exhaust gas flow at an underbody selective catalytic reduction system, and at  206 , controlling a DEF injector upstream of a close-coupled selective catalytic reduction system to inject DEF into the exhaust gas flow at a rate that varies as a function of the monitored temperature across a range of at least 25 degrees Celsius in the monitored temperature. 
     In other embodiments, the exhaust after-treatment system  100  may include three, four, or any other number of independent SCR systems, together with respective DEF injectors, heaters, temperature sensors, and/or NO x  sensors. Each upstream-downstream pair of the SCR systems and respective DEF injectors, heaters, temperature sensors, and/or NO x  sensors can have features corresponding to those described herein for the upstream close-coupled SCR system  116  and the downstream underbody SCR system  126  and their respective DEF injectors, heaters, temperature sensors, and/or NO x  sensors. 
     The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.