Patent Publication Number: US-9416799-B2

Title: Methods and systems for flow sharing in a hydraulic transformer system with multiple pumps

Description:
RELATED APPLICATIONS 
     This application claims the benefit of U.S. Patent Application Ser. No. 61/791,895 filed on Mar. 15, 2013, and U.S. Patent Application Ser. No. 61/798,649 filed on Mar. 15, 2013. The entireties of these applications are hereby incorporated by reference. 
    
    
     INTRODUCTION 
     Mobile pieces of heavy machinery (e.g., excavators, backhoe loaders, wheel loaders, etc.) often include hydraulic systems having hydraulically powered linear and rotary actuators used in conjunction with hydraulic transformers to power various active machine components (e.g., swing, boom, dipper, bucket, linkages, tracks, rotating joints, etc.). By accessing a user interface of a machine control system, a machine operator controls the machinery to perform work (e.g., earth-moving). 
     In hybrid systems, hydraulic transformers are sometimes coupled to external loads (e.g., via a shaft) which require precise speed control. Throughout the work cycle, hydraulic transformers may provide a motoring function or a pumping function where torque is transferred either to or from a shaft, an external load, and/or energy storage devices (e.g., accumulator). Since pump motors have finite displacement capabilities, a hydraulic system cannot always realize a high flow demand at a specific rotational speed, such as, for example, when a system is utilized to lift or move a work element (e.g., a boom) against a force of gravity. In such hybrid work circuits, there is often a need to optimally achieve flow demand to one or more hydraulic actuators when the flow is supplied by a hydraulic transformer and one or more pump motors. In addition, such flow demand should be accomplished smoothly so as to be transparent to an operator of the machinery to enable maximum fuel efficiency and productivity. 
     SUMMARY 
     Aspects of the present disclosure relate to systems and methods for effectively flow sharing in a hydraulic system between a hydraulic transformer and one or more hydraulic pumps to achieve flow demands for high flow services. 
     One aspect is a hydraulic system including a tank, at least one system pump, a first directional flow control valve, an accumulator, a hydraulic transformer, a second load, and a controller. The at least one system pump is powered by at least one prime mover and coupled to the tank. The first directional flow control valve is coupled to the at least one system pump. The hydraulic transformer is in selective fluid communication with the at least one system pump and includes first and second displacement pump units connected to a shaft. The shaft is connected to a first load. The first displacement pump unit includes a first side that selectively fluidly connects to at least one of the at least one system pump and a second side that fluidly connects to the tank. The second displacement pump unit includes a first side that fluidly connects to the accumulator and a second side that fluidly connects with the tank. The second load is driven by an actuator in selective fluid communication with the at least one system pump and the hydraulic transformer. The controller is arranged and configured to reduce dynamic responses in the hydraulic system by causing flow sharing between the hydraulic transformer and the first directional flow control valve. 
     The controller has a memory with a set of instructions. The controller is arranged and configured to execute the set of instructions to implement a method for flow sharing. The method may include: receiving and reading operator inputs; computing a load value indicative of the second load based on the pressure measurements; computing a desired flow based on the load value; determining whether the hydraulic transformer is sufficient to independently supply the desired flow; if the hydraulic transformer is not sufficient to independently supply the desired flow: computing a flow deficit; computing and sending a command to the first directional flow control valve indicative of the flow deficit; and if the hydraulic transformer is sufficient to independently supply the desired flow: computing a desired displacement for the hydraulic transformer; and computing and sending a second transformer command to the hydraulic transformer to realize the desired displacement. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of a first hydraulic system in accordance with the principles of the present disclosure; 
         FIG. 2  is a schematic diagram of a second hydraulic system in accordance with the principles of the present disclosure; 
         FIG. 3  shows a mobile piece of excavation equipment that is an example of one type of machine on which hydraulic systems in accordance with the principles of the present disclosure can be used; 
         FIG. 4  shows an alternate view of the mobile piece of excavation equipment shown in  FIG. 3 ; 
         FIG. 5  is an example logic flow chart for operating example control systems that may be used to control certain hydraulic systems in accordance with the principles of the present disclosure; and 
         FIG. 6  is another example logic flow chart for operating example control systems that may be used to control certain hydraulic systems in accordance with the principles of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to aspects of the present disclosure that are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like structure. 
     In general, the systems and methods below describe hybrid hydraulic systems for increased fuel efficiency while maintaining operator transparency during operation of machinery utilizing such hybrid hydraulic systems. In particular, operator transparency may be achieved by reduction of undesirable dynamic responses due to inadequate and/or inefficient scheduling of flow sources. In some embodiments, this is accomplished by flow sharing between multiple sources, each capable of contributing different amounts of flow. 
       FIG. 1  shows a hydraulic system  10  in accordance with the principles of the present disclosure. In general the hydraulic hybrid system  10  includes multiple variable displacement pumps  14 ,  16 , directional control valves  24 ,  26 , and a hydraulic transformer  30 . Systems and methods described herein are implemented within the hydraulic system  10 ; however, it is understood that principles of the present disclosure are applicable to any hydraulic system where flow from multiple sources is combined to realize a desired flow rate. 
     The system  10  includes the variable displacement pumps  14 ,  16 , driven by a prime mover  18 . In some examples, two prime movers can be used to drive the variable displacement pumps  14 ,  16 , respectively. Examples of the prime mover  18  include a diesel engine, a spark ignition engine, an electric motor or other power source. It is understood that in some embodiments, only one prime mover is needed to power both the variable displacement pumps  14 ,  16 . 
     Each of the variable displacement pumps  14 ,  16  include inlets that draw low pressure hydraulic fluid from a tank  22  (i.e., a low pressure reservoir). The variable displacement pumps  14 ,  16  can include swash plates  15 ,  17  for controlling the pump displacement volume per shaft rotation. The variable displacement pumps  14 ,  16  draw the hydraulic fluid from the tank  22  and output pressurized hydraulic fluid for powering a first load, which is controlled by a first hydraulic actuator  28  (e.g., boom cylinder), a second load in the form of the hydraulic transformer  30  having a shaft  40  coupled to an external load  42 , and a third load, which is controlled by other actuators  29 . The variable displacement pumps  14 ,  16  include outlets through which the high pressure hydraulic fluid is output. The outlets are preferably fluidly coupled (directly or indirectly) to the plurality of different working load circuits, such as the first load, the second load, and the third load. In the present embodiment, the directional control valves  24 ,  26  control fluid flow between the load circuits (e.g., actuators or loads), the variable displacement pumps  14 ,  16 , and the tank  22 . It is understood that in other embodiments of the hydraulic system  10 , more or less load circuits may exist in the system. 
     In some examples where the system  10  is used to operate an excavator, the first load includes a boom, which is actuated by the first actuator  28 . The second load (the external load  42 ) includes a swing, which is operated by the transformer  30 . The third load includes an arm, a bucket and a track motor, which are actuated by the other actuators  29 . 
     The second load circuit includes the hydraulic transformer  30  including a first port  32 , a second port  34 , and a third port  35 . The first port  32  of the hydraulic transformer  30  is indirectly connected to the outlet of the variable displacement pumps  14 ,  16  via the outlet of the directional control valves  24 ,  26 . The first port  32  is also fluidly connected to the first actuator  28 . The second port  34  is fluidly connected to the tank  22 . The third port  35  is fluidly connected to a hydraulic accumulator  36 . 
     The hydraulic transformer  30  further includes an output/input shaft  38  that couples to the external rotational load  42 . In some examples, a clutch  40  can be used to selectively engage the output/input shaft  38  with the external load  42  and disengage the output/input shaft  38  from the external load  42 . When the clutch  40  engages the output/input shaft  38  with the external load  42 , torque is transferred between the output/input shaft  38  and the external load  42 . In contrast, when the clutch  40  disengages the output/input shaft  38  from the external load  42 , no torque is transferred between the output/input shaft  38  and the external load  42 . In some embodiments, gear reductions may be provided between the clutch  40  and the external load  42 . It is understood that in some embodiments of the hydraulic transformer  30 , a clutch is not present. 
     In some embodiments, the other actuators  29  are fluidly connected between the variable displacement pumps  14 ,  16  and the directional control valves  24 ,  26 . As the other actuators  29  run, the other actuators  29  change the pressures at the outlet of the variable displacement pumps  14 ,  16 . In this configuration, by detecting the pressures changed by the other actuators  29 , which are, for example, monitored by pressure sensors (P_pump 1 )  31  and (P_pump 2 )  33  ( FIG. 2 ), the stream of the working fluid can be controlled to ensure a flow continuity, as described below in further detail. 
     The system  10  further includes an electronic controller  44  that interfaces with the variable displacement pumps  14 ,  16 , the directional control valves  24 ,  26 , and the hydraulic transformer  30 . It will be appreciated that the electronic controller  44  can also interface with various other sensors and other data sources provided throughout the system  10 . For example, the electronic controller  44  can interface with pressure sensors incorporated into the system  10  for measuring the hydraulic pressure in the accumulator  36 , the hydraulic pressure provided by the variable displacement pumps  14 ,  16  to the plurality of actuators or loads in the system  10 , the pressures at the pump and tank sides of the hydraulic transformer  30  and other pressures. Moreover, the controller  44  can interface with a rotational speed sensor that senses a speed of rotation of the output/input shaft  38  and the rotational speed of the transformer shaft. In some examples, the electronic controller  44  operates to control the variable displacement pumps  14 ,  16  by, for example, controlling the position of the swash plates  15 ,  17 . In other examples, the electronic controller  44  can be used to monitor a load on the prime mover  18  and can control the hydraulic fluid flow rate across the variable displacement pumps  14 ,  16  at a given rotational speed of a drive shaft, for example, the drive shafts  19 , powered by the prime mover  18 . Thus, in some embodiments, the prime mover  18  is connected to the drive shafts  19 . In one embodiment, the hydraulic fluid displacement across the variable displacement pumps  14 ,  16  per shaft rotation can be altered by changing positions of the swash plates  15 ,  17  of the variable displacement pumps  14 ,  16 , respectively. The controller  44  can also interface with the clutch  40  for allowing an operator to selectively engage and disengage the output/input shaft  38  of the hydraulic transformer  30  with respect to the external load  42 . 
     The electronic controller  44  includes a user interface  48  and a memory  46 . A controller of the hydraulic system  10  may interact with the user interface  48  to control movement of the various machine components connected to the system, such as, the loads or actuators. In some embodiments, the user interface  48  may be arranged and configured to accept controller commands which determine the overall operation of the machine components. The user interface  48  may be any electronic or mechanical device capable of receiving commands from an operator, such as, for example, a computer, a joystick, and/or the like. The memory  46  can include various algorithms and control logic that is utilized by the electronic controller  44  in controlling the operation of the system  10 . The memory  46  can also include one or more look-up tables that help in the computation of certain measurements, such as, for example, the desired flow of a system. 
     In some embodiments, the electronic controller  44  can control operation of the hydraulic transformer  30  so as to provide a load leveling function that permits the prime mover  18  to be run at consistent operating conditions (i.e., a steady operating condition) thereby assisting in enhancing an overall efficiency of the prime mover  18 . The load leveling function can be provided by efficiently storing energy in the accumulator  36  during periods of low loading on one or more of the prime mover  18 , and efficiently releasing the stored energy during periods of high loading on one or more of the prime mover  18 . This allows the prime mover  18  to be sized for an average power requirement rather than a peak power requirement. 
       FIG. 2  depicts an alternate embodiment of the system  10  of  FIG. 1 , equipped with a hydraulic transformer  30   a  having a plurality of pump/motor units connected by a common shaft. For example, the hydraulic transformer  30   a  includes first and second variable volume positive displacement pump/motor units  100 ,  102  connected by a shaft  104 . The shaft  104  includes a first portion  106  that connects the first pump/motor unit  100  to the second pump/motor unit  102 , and a second portion  108  that forms the output/input shaft  38 . The first pump/motor unit  100  includes a first side  100   a  that is fluidly (and indirectly) connected to the variable displacement pumps  14 ,  16  and a second side  100   b  fluidly connected to the tank  22 . The second pump/motor unit  102  includes a first side  102   a  fluidly connected to the accumulator  36  and a second side  102   b  fluidly connected to the tank  22 . 
     In one embodiment, each of the first and second pump/motor units  100 ,  102  includes a rotating group (e.g., cylinder block and pistons) that rotates with the shaft  104 , and a swash plate  110  that can be positioned at different angles relative to the shaft  104  to alter the amount of pump displacement per each shaft rotation. The volume of hydraulic fluid displaced across a given one of the pump/motor units  100 ,  102  per rotation of the shaft  104  can be changed by varying the angle of the swash plate  110  corresponding to the given pump/motor unit. Varying the angle of the swash plate  110  also changes the torque transferred between the shaft  104  and the rotating group of a given pump/motor unit. When the swash plates  110  are aligned perpendicular to the shaft  104 , no hydraulic fluid flow is directed through the pump/motor units  100 ,  102 . The swash plates  110  can be over-center swash plates that allow for bi-directional rotation of the shaft  104 . The angular positions of the swash plates  110  are individually controlled by the electronic controller  44  based on the operating condition of the system  10 . Thus, by controlling the positions of the swash plates  110 , the controller  44  can operate the system  10  in several operating modes. 
     By controlling the displacement rates and displacement directions of the pump/motor units  100 ,  102 , fluid power (pressure times flow) at a particular level can be converted to an alternate level, or supplied as shaft power used to drive the external load  42 . When a deceleration of the external load  42  is desired, the hydraulic transformer  30   a  can act as a pump taking low pressure fluid from the tank  22  and directing it either to the accumulator  36  for storage, to the first actuator  28  connected indirectly to the variable displacement pumps  14 ,  16  via the directional control valves  24 ,  26 , or a combination of the two. In some examples, similarly to the clutch  40  in  FIG. 1 , a clutch can be used to selectively disengage the output/input shaft  38  from the external load  42 . In this configuration, the hydraulic transformer  30   a  can function as a stand-alone hydraulic transformer (e.g., a hydraulic transformer) when no shaft work is required to be applied to the external load  42 . This is achieved by taking energy from the system  10  at whatever pressure is dictated by the other associated system loads (e.g., the first actuator  28 ) and storing the energy, without throttling, at the current accumulator pressure. In the same way, un-throttled energy can also be taken from the accumulator  36  at its current pressure and supplied to the system  10  at the desired operating pressure. Proportioning of power flow by the hydraulic transformer  30   a  can be controlled by controlling the positions of the swash plates  110  on the pump/motor units  100 ,  102 . In certain embodiments, as depicted in  FIG. 2 , aspects of the present disclosure can be used in systems without a clutch for disengaging a connection between the output/input shaft  38  and the external load  42 . 
     In some examples, the system  10  includes a rod-to-tank valve  116 , which is fluidly connected between the rod side of the first actuator  28  and the tank  22 . When power is drawn from the accumulator  36  to operate the second pump/motor unit  102  as a motor, the swash plate  110  rotates and the first pump/motor unit  100  operates to pump the working fluid from the tank  22  to the system loads (e.g., the first actuator  28 ). In particular, when the directional control valves  24 ,  26  are closed, the working fluid is supplied to the first actuator  28 , which is operated to actuate a load, such as a boom. In this case, the working fluid contained in the top cavity of the first actuator  28  is drawn back from the rod side of the actuator  28  to the tank  22  through the rod-to-tank valve  116  as the actuator  28  works to actuate the load. 
       FIGS. 3 and 4  depict an example embodiment of mobile excavation equipment which incorporates hydraulic circuit configurations of the type described above with reference to  FIGS. 1 and 2 . In particular,  FIGS. 3 and 4  show an example excavator  200  including an upper structure  212  supported on an undercarriage  210 . The undercarriage  210  includes a propulsion structure for carrying the excavator  200  across the ground. For example, the undercarriage  210  can include left and right tracks. The upper structure  212  is pivotally movable relative to the undercarriage  210  about a pivot axis  208  (i.e., a swing axis). In certain embodiments, transformer input/output shafts of the type described above can be used for pivoting the upper structure  212  about the swing axis  208  relative to the undercarriage  210 . 
     The upper structure  212  can support and carry the prime mover (e.g., prime mover  18 ) of the machine and can also include a cab  225  which may include an operator interface, such as, for example, the user interface  48 . A boom  202  is carried by the upper structure  212  and is pivotally moved between raised and lowered positions by a boom cylinder  202   c.  An arm  204  is pivotally connected to a distal end of the boom  202 . An arm cylinder  204   c  is used to pivot the arm  204  relative to the boom  202 . The excavator  200  also includes a bucket  206  pivotally connected to a distal end of the arm  204 . A bucket cylinder  206   c  is used to pivot the bucket  206  relative to the arm  204 . In some embodiments, the boom cylinder  202   c,  the arm cylinder  204   c,  and the bucket cylinder  206   c  may be part of system load circuits of the type described above. In some embodiments, the first load  28  can function as the boom cylinder  402   c.    
     In some instances, hybrid hydraulic systems, such as the ones shown in  FIGS. 1 and 2 , require extra functionality to achieve increased fuel efficiency. It is desirable for this extra functionality to be transparent to an operator of the system, such as the operator of the excavation equipment shown in  FIGS. 3 and 4 . In other words, transitions between operating modes of the system should be smooth instead of sporadic and jerky so that the operator is unaware of mode transitions. A primary cause of undesirable dynamic responses that create such problems during mode transitions is the scheduling of flow sources. For example, as the system is recovering energy from an overrunning load (e.g., when actuators allow the load to free fall when the directional valve that controls the actuator shifts to lower the load), flow may need to move through the hydraulic transformer  30   a  to enable energy recover and storage. However, if the swing is rotating at a set speed, the hydraulic transformer may not be sufficient to supply all of the flow necessary to maintain the desired boom speed. In this instance, it is beneficial for at least some of the flow to be sent through the alternate sources, such as, for example, the directional control valves  24 ,  26 . 
     Now referring to  FIGS. 5 and 6 , example logic flow charts depicting method  300  and  400  for operating a hydraulic system with flow sharing are shown. It is understood that a control system, such as the electronic controller  44  is arranged and configured to control the hydraulic system, such as the hydraulic system  10 . The methods  300  and  400  are example methods of operation of the control system. A primary goal of the control logic/architecture is to improve operator transparency during operation of the hybrid hydraulic system or machinery that implements the hybrid hydraulic system. In particular, the methods  300  and  400  are example methods of reducing dynamic responses due to inadequate and/or inefficient scheduling of flow sources by causing flow sharing between multiple sources. The methods  300  and  400  will be described with reference to the hybrid hydraulic system  10  described in  FIG. 2 ; however, the methods  300  and  400  may be implemented in any hydraulic system. 
     It is further understood that the controller  44  may be any device suitable to process digital and/or analog instructions, such as, for example, a computing device, and implement the methods  300  and  400 . In some embodiments, the controller  44  includes at least some form of computer-readable media. Computer readable media includes any available media that can be accessed by the controller  44 . By way of example, computer-readable media include computer readable storage media and computer readable communication media. 
     Computer readable storage media includes volatile and nonvolatile, removable and non-removable media implemented in any device configured to store information such as computer readable instructions, data structures, program modules or other data. Computer readable storage media includes, but is not limited to, random access memory, read only memory, electrically erasable programmable read only memory, flash memory or other memory technology, compact disc read only memory, digital versatile disks or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and that can be accessed by the controller  44 , such as, for example, the memory  46  which may include a plurality of instructions for operating the system  10 , control algorithms, stored measurements, and the like. 
     Computer readable communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” refers to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, computer readable communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, radio frequency, infrared, and other wireless media. Combinations of any of the above are also included within the scope of computer readable media. 
     Now referring to  FIG. 5 , the method  300  begins at operation  302  when the controller  44  receives, reads, and processes operator inputs and measurements. In particular, the operator may request actions via the user interface  48 . In addition, an operator input may be, for example, the pilot pressure delta generated by a hydraulic joystick acting on each directional control valve  24 ,  26  or other pressure changes generated by movement of the joystick by the operator. The controller  44  may also read measurements, such as the head-side pressure, and/or temperature, at the actuator to compute the load. In some embodiments, a head-side pressure transducer  112  can be used to measure the head-side pressure at the actuator, and a head-side temperature transducer  114  can be used to measure the head-side temperature at the actuator. In other embodiments, a rod-side pressure transducer may be read for precise load estimation. 
     After completing the operation  302 , the method  300  moves to operation  304  at which the controller  44  computes the desired flow based on the operator&#39;s inputs, measurements, and load estimation. For example, based on the operator&#39;s joystick commands and the estimation of the actuator load, the controller  44  retrieves and utilizes a look-up table. Based on the information retrieved from the look-up table, the controller  44  computes the desired flow. 
     The method  300  then moves to operation  306  at which the controller  44  determines whether the hydraulic transformer  30   a  is sufficient to independently supply the desired flow computed at the operation  304 . To properly make the determination, the controller  44  takes one or more measurements to determine the maximum flow that could pass through the hydraulic transformer  30   a  without negative dynamic responses. At the operation  306 , the controller  44  compares the desired flow with the maximum flow to determine whether the maximum flow is sufficient to meet the desired flow. 
     If the maximum flow is not sufficient to meet the desired flow, the method  300  moves to operation  308 . At the operation  308 , the transformer is set to its maximum flow and the controller  44  computes a flow deficit that needs to be supplemented by alternate sources. The flow deficit is the amount of flow that is needed beyond the maximum flow of the hydraulic transformer  30   a  and is the amount that will be mitigated by flow from other sources, such as, for example, the directional control valves  24 ,  26 . 
     At operations  310  and  312 , the flow deficit is converted into a command that is sent from the controller  44  to the directional control valves  24 ,  26 . The amount of flow requested from each of the directional control valves  24 ,  26 , can be either the same or different amounts. The command is received at the directional control valves  24 ,  26  and the requested amount of flow is supplied to the system. 
     If, however, the maximum flow of the hydraulic transformer  30   a  is sufficient to supply the computed desired flow, the method  300  moves to operation  314  instead of the operation  308 . At the operation  314 , the controller  44  computes the displacement required to achieve the desired flow and converts this desired flow into a command. At the operation  316 , this command is sent to the hydraulic transformer  30   a  which realizes the requested displacement and supplying the desired flow for the action. 
     Upon completing either the operation  312  or the operation  316 , the method  300  ends at operation  318 . In some embodiments of the method  300 , the controller  44  may continuously operate in accordance with the method  300  within a predetermined or arbitrary amount of time. In yet other embodiments, the controller  44  may begin the operation  300  again only after receiving new inputs from the operator via the user interface  48 . 
     Now referring to  FIG. 6 , the method  400  begins at operation  402  at which the controller  44  reads operator commands. As stated above with reference to the operation  302  in the method  300 , the controller  44  receives, reads, and processes operator inputs such as the ones described herein. 
     At operation  404 , the controller  44  reads pressure measurements at the actuator. Such pressure measurements include the head-side pressure at the actuator, and can be read utilizing a head-side pressure transducer, a rod-side pressure transducer, or the like. 
     In some examples, at operation  405 , the controller  44  also reads temperature measurements at the actuator. Such temperature measurements can include the head-side temperature at the actuator, and can be read utilizing a head-side temperature transducer  114 , a rod-side temperature transducer, or the like. 
     The method  400  then moves to operation  406  at which the controller  44  computes the load based on the pressure and/or temperature measurements read at the operation  404 . 
     At operation  408 , the controller retrieves and utilizes a lookup table for the purpose of computing a desired flow. The lookup table may be an operation map that correlates certain measurements, such as, load estimations to flow. The controller  44  may, based on the operator commands read at the operation  402 , the measurements read at the operation  404 , and/or the computed load estimation at the operation  406 , utilize the lookup table to correlate one or more of these inputs with a flow. In some embodiments, this flow is the desired flow. 
     At operations  410 ,  412 , and  414 , the controller  44  reads speed sensors at the transformer shaft  38 , reads one or more position sensors connected to the lower pump-motor swash plate, and calculates a maximum flow that could pass through the lower pump-motor of the hydraulic transformer  30   a  based on the speed and displacement position measurements taken in the operations  410  and  412 . In some embodiments, at the operation  414 , the controller  44  calculates the maximum flow by multiplying the speed read from the speed sensor by a maximum possible displacement of the hydraulic transformer  30   a.    
     At operation  416 , the controller  44  determines whether the maximum flow calculated in the operation  414  is sufficient to meet the desired flow calculated in the operation  408 . If the maximum flow is not sufficient to meet the desired flow, the method  400  moves to operation  418 . At the operation  418 , in some embodiments, the controller  44  computes a flow deficit by subtracting an actual flow at the current speed and swash angle from the desired flow. This is the flow deficit that must be mitigated by flow across the directional control valves  24 ,  26 . 
     At the operation  420 , the flow deficit is converted into a command that is sent to the directional control valves  24 ,  26 , which in turn, supply the flow deficit to the system  10 . The command sent to the directional control valves  24 ,  26  may differ based on the status and/or configuration of the system  10  and/or valves  24 ,  26 . For example, in some embodiments, one of the directional control valves  24 ,  26  is coupled to the tank  22  and the other is blocked for at least one of a number of reasons. In the case of flow recovery, a pilot pressure command can be computed utilizing an orifice equation as shown in Equation  1  below. In particular, using the orifice equation, the controller  44  computes a desired orifice area needed to achieve the desired flow based on head-side pressure and tank pressure measurements taken from sensors.
 
 A _DESIRED= Q _DEFICIT/( Cd* SQRT ([ P _HEAD− P _TANK]*(2 /RHO ))),  (1)
 
where A_DESIRED is a desired orifice area, Q_DEFICIT is the flow deficit, Cd is the discharge coefficient, P_HEAD is the head-side actuator pressure, P_TANK is tank pressure, and RHO is fluid density.
 
     A lookup table, which correlates orifice area to pilot pressure delta, is then used to determine the pilot pressure delta for the orifice connected head-side to the tank  22 . In some embodiments, the lookup table is a computerized function which can be utilized to tabulate the pilot pressure delta that is required for a given orifice area, such as, in this case, the orifice connecting head-side to tank). An example of such a function is shown in Equation 2 below.
 
 X _ DCV=F _ PP  ( A _DESIRED),  (2)
 
where X_DCV is the pilot pressure delta, F_PP (A) is the lookup table, which in this case, accepts the desired orifice area calculated via Equation 1 as an input. This desired pilot pressure delta across the boom directional flow control valve is achieved using electronically controlled pressure control valves.
 
     In an alternate configuration, both of the directional control valves  24 ,  26  have orifices connecting their respective pumps  14 ,  16  to the head-side of the actuator. The controller  44  may utilize an optimization-based algorithm to compute the optimum pilot pressure command to send to both of the control valves  24 ,  26 . In this example, the command is based on pressure sensor measurements at the head-side of the actuator, the outlet of the pump  14 , the outlet of the pump  16 . In particular, Equations  3 ,  4 , and  5 , in conjunction with lookup tables created using test data prior to system commissioning, may be utilized to determine the optimum pilot pressure in a flow supply case as described above.
 
 X _ DCV−ARGMIN _ X {A 1( X )+ A 2( X )* SQRT  ( DP 2)/ SQRT  ( DP 1)− Q _DEFICIT/( Cd* SQRT  ( DP 1*2 /RHO ))},  (3)
 
 DP 1= P _PUMP1− P _HEAD,  (4)
 
 DP 2= P _PUMP2 −P _HEAD,  (5)
 
where ARGMIN_X is the function that retrieves the value of X that minimizes the function, A 1 (X) is the area-versus-pilot pressure delta map for the orifice on the DCV connecting pump  14  to head-side, and A 2 (X) is the area-versus-pilot pressure delta map for the orifice on the other DCV connecting pump  16  to head-side. The X_DCV command is realized at the directional control valves  24 ,  26  pilot ports via pressure control, for example, using electro-proportional pressure relief valves in closed loop control. The computed command, in either scenario, is sent to the actuators, and the algorithm concludes at the end operation  426 .
 
     If, however, the maximum flow is sufficient to meet the desired flow, the method  400  moves to the operations  422  and  424 . The operations  422  and  424  of the method  400  are the same or substantially the same as the operations  314  and  316  of the method  300 . Upon completing either the operation  420  or the operation  424 , the method  400  ends at operation  426 . In some embodiments of the method  400 , the controller  44  may continuously operate in accordance with the method  400  and repeat the method at sample times. In yet other embodiments, the controller  44  may begin the operation  400  again only after receiving new inputs from the operator via the user interface  48 .