Abstract:
A method for calibrating a valve having a valve element movable between a flow blocking position and a flow passing position includes pressurizing fluid directed to the valve, increasing a current directed to the valve for controlling a position of the valve element, and sensing a pressure of the fluid. The method for calibrating the valve also includes determining if a time-derivative of the sensed fluid pressure is greater than a predetermined threshold over a predetermined period of time, and determining a cracking point current command directed to the valve. The cracking point current command is directed to the valve when the time-derivative of the sensed fluid pressure is greater than the predetermined threshold.

Description:
TECHNICAL FIELD 
       [0001]    The present disclosure relates generally to a method for calibrating valves, and more particularly, to a method for calibrating independent metering valves. 
       BACKGROUND 
       [0002]    Machines such as, for example, dozers, loaders, excavators, motor graders, and other types of heavy machinery use one or more hydraulic actuators to accomplish a variety of tasks. These actuators are fluidly connected to a pump on the machine that provides pressurized fluid to chambers within the actuators. A valve arrangement is typically fluidly connected between the pump and at least one of the actuators to control a flow rate and direction of pressurized fluid to and from the chambers of the actuator. 
         [0003]    The valve arrangement may include independent metering valves (IMVs) that are independently actuated to allow pressurized hydraulic fluid to flow from the pump to the actuator chambers. The amount of the hydraulic flow to each actuator chamber can be controlled by changing the displacement of a valve spool in each IMV. Each valve spool has a series of metering slots which control flows of the hydraulic fluid in the valve arrangement, including a flow from the pump to the actuator and a flow from the actuator to a tank. When the actuator is a hydraulic cylinder, these flows are commonly referred to as pump-to-cylinder flow and cylinder-to-tank, respectively. 
         [0004]    The manufacture and assembly of the IMVs may affect the performance of the valve components such that each IMV may perform differently from the others. As a result, the valve components may not operate predictably and the performance of the hydraulic actuator may be degraded. 
         [0005]    One method of controlling flow through a valve arrangement fluidly connected between a pump and an actuator is described in U.S. Pat. No. 6,397,655 (“the &#39;655 patent”) issued to Stephenson. The &#39;655 patent describes a method of calibrating an inlet valve or an outlet valve connected to an actuator chamber. The inlet valve controls the amount of flow supplied to the actuator chamber, and the outlet valve controls the amount of flow exiting the actuator chamber. To calibrate the inlet valve, the outlet valve is closed while current to actuate the inlet valve increases, thereby increasing the pressure in the actuator chamber. A valve opening current level for the inlet valve is determined when a rate of increase in pressure in the actuator chamber exceeds a predetermined threshold. To calibrate the outlet valve, the inlet valve is opened so that the pressure in the actuator chamber increases. The inlet valve is then closed, and the current to actuate the outlet valve is increased. A valve opening current level for the outlet valve is determined when a magnitude of the rate of decrease in pressure in the actuator chamber exceeds a predetermined threshold. The calibration ensures that the difference between the valve opening current level for the inlet or outlet valve and an initial current level for the respective valve differs by at least a desired margin. 
         [0006]    The calibration method of the &#39;655 patent determines a predefined initial current level that is initially applied to the valve. This initial current level is a desired amount less than the current level at which the valve begins to open. The initial current level supplied to the inlet or outlet valve is adjusted only when there exists a difference between the measured valve opening current and the initial current level. The &#39;655 patent also requires pressure sensors at the respective cylinder ports, which requires a sensor at each cylinder port. This increases the number of sensors, thereby increasing the complexity of the calibration process. Furthermore, the &#39;655 patent measures the valve opening current level when the rate of pressure change reaches a predetermined threshold, but does not determine whether the rate of pressure change remains above the predetermined threshold for a predetermined period of time. Therefore, the calibration method of the &#39;655 patent may determine the valve opening current level prematurely if there is an error in measuring the rate of pressure change due to signal noise or leakage through the inlet or outlet valve. 
         [0007]    The disclosed system is directed to overcoming one or more of the problems set forth above. 
       SUMMARY OF THE INVENTION 
       [0008]    In one aspect, the present disclosure is directed to a method for calibrating a valve having a valve element movable between a flow blocking position and a flow passing position. The method includes pressurizing fluid directed to the valve, increasing a current directed to the valve for controlling a position of the valve element, and sensing a pressure of the fluid. The method for calibrating the valve also includes determining if a time-derivative of the sensed fluid pressure is greater than a predetermined threshold over a predetermined period of time, and determining a cracking point current command directed to the valve. The cracking point current command is directed to the valve when the time-derivative of the sensed fluid pressure is greater than the predetermined threshold. 
         [0009]    In another aspect, the present disclosure is directed to a system for calibrating a valve having a valve element movable between a flow blocking position and a flow passing position. The system includes a source configured to pressurize a fluid, a pressure sensor configured to sense a pressure of the fluid at an outlet of the source, and a controller connected to the pressure sensor. The controller is configured to increase a current directed to the valve for controlling a position of the valve element and receive a sensed fluid pressure from the pressure sensor. The controller is also configured to determine if the valve is at the flow passing position based on the measured fluid pressure at the outlet of the source and determine a cracking point current command directed to the valve when the valve is at the flow passing position. 
         [0010]    In another aspect, the present disclosure is directed to a method for determining an actual current command to control a valve. The valve includes a valve element movable between a flow blocking position and a flow passing position. The method includes determining a nominal current command based on a desired position of the valve element, determining a calibration offset current command based on a calibration of the valve, and determining the actual current command by summing the nominal current command and the calibration offset current command. 
     
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  is a side-view diagrammatic illustration of a machine according to an exemplary disclosed embodiment; 
           [0012]      FIG. 2  is a schematic illustration of an exemplary disclosed hydraulic system according to an exemplary disclosed embodiment; 
           [0013]      FIG. 3  is a schematic illustration of an exemplary current control system for controlling the valves of the hydraulic system of  FIG. 2 ; 
           [0014]      FIG. 4  is a graph illustrating a relationship between a displacement of a valve spool and nominal and actual current commands using the current control system of  FIG. 3 ; and 
           [0015]      FIGS. 5A and 5B  illustrate a flow chart of an exemplary disclosed method of calibrating the valves of the hydraulic system of  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION 
       [0016]      FIG. 1  illustrates an exemplary machine  10 . Machine  10  may be a fixed or mobile machine that performs some type of operation associated with an industry such as mining, construction, farming, or any other industry known in the art. For example, machine  10  may be an earth moving machine such as a dozer, a loader, a backhoe, an excavator, a motor grader, a dump truck, or any other earth moving machine. Machine  10  may also include a generator set, a pump, a marine vessel, or any other suitable operation-performing machine. Machine  10  may include a frame  12 , at least one implement  14 , and a hydraulic cylinder  16  or other fluid actuator connecting implement  14  to frame  12 . It is contemplated that hydraulic cylinder  16  may be omitted, if desired, and a hydraulic motor included. 
         [0017]    Frame  12  may include any structural unit that supports movement of machine  10 . Frame  12  may be, for example, a stationary base frame connecting a power source (not shown) to a traction device  18 , a movable frame member of a linkage system, or any other frame known in the art. 
         [0018]    Implement  14  may include any device used in the performance of a task. For example, implement  14  may include a blade, a bucket, a shovel, a ripper, a dump bed, a propelling device, or any other task-performing device known in the art. Implement  14  may be connected to frame  12  via a direct pivot  20 , via a linkage system with hydraulic cylinder  16  forming one member in the linkage system, or in any other appropriate manner. Implement  14  may be configured to pivot, rotate, slide, swing, or move relative to frame  12  in any other manner known in the art. 
         [0019]    As illustrated in  FIG. 2 , hydraulic cylinder  16  may be one of various components within a hydraulic system  22  that cooperate to move implement  14 . Hydraulic system  22  may include a source  24  of pressurized fluid, a head-end supply valve  26 , a head-end drain valve  28 , a rod-end supply valve  30 , a rod-end drain valve  32 , a tank  34 , and one or more pressure sensors  36 ,  37 ,  38 . Hydraulic system  22  may further include a controller  70  in communication with the fluid components of hydraulic system  22 . It is contemplated that hydraulic system  22  may include additional and/or different components such as, for example, a pressure sensor, a temperature sensor, a position sensor, a controller, an accumulator, and other components known in the art. Though the exemplary hydraulic system  22  includes hydraulic cylinder  16  in fluid communication with valves  26 ,  28 ,  30 ,  32  to be calibrated, the valves to be calibrated are not limited to valves controlling flow to and from a hydraulic cylinder. One or more valves, such as valves  26 ,  28 ,  30 ,  32 , may be used to control other various types of hydraulic flows, such as a flow to a motor circuit, e.g., a swing circuit on a hydraulic excavator, etc. 
         [0020]    Each of head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  may be an independent metering valve (IMV) that is independently operable to be in fluid communication with source  24 , hydraulic cylinder  16 , tank  34 , and/or any other device present in hydraulic system  22 . Each of head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  may be independently metered to control hydraulic flow in multiple hydraulic paths. Controller  70  controls each of the independently operable valves  26 ,  28 ,  30 ,  32 . 
         [0021]    Each of head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  includes a valve spool  26   a ,  28   a ,  30   a ,  32   a  and an actuator  26   b ,  28   b ,  30   b ,  32   b  to move respective valve spool  26   a ,  28   a ,  30   a ,  32   a  to a desired position to thereby control the hydraulic flow through valve  26 ,  28 ,  30 ,  32 . The displacement of each valve spool  26   a ,  28   a ,  30   a ,  32   a  changes the flow rate of the hydraulic fluid through the associated valve  26 ,  28 ,  30 ,  32 . Actuator  26   b ,  28   b ,  30   b ,  32   b  may be a solenoid actuator or any other actuator known to those skilled in the art. 
         [0022]    Hydraulic cylinder  16  may include a tube  46  and a piston assembly  48  disposed within tube  46 . One of tube  46  and piston assembly  48  may be pivotally connected to frame  12 , while the other of tube  46  and piston assembly  48  may be pivotally connected to implement  14 . It is contemplated that tube  46  and/or piston assembly  48  may alternately be fixedly connected to either frame  12  or implement  14 . Hydraulic cylinder  16  may include a first chamber  50  and a second chamber  52  separated by piston assembly  48 . In the exemplary embodiment shown in  FIG. 2 , first chamber  50  is located closer to a head end of hydraulic cylinder  16 , and second chamber  52  is located closer to a rod end of hydraulic cylinder  16 . The first and second chambers  50 ,  52  may be selectively supplied with a fluid pressurized by source  24  and fluidly connected with tank  34  to cause piston assembly  48  to displace within tube  46 , thereby changing the effective length of hydraulic cylinder  16 . The expansion and retraction of hydraulic cylinder  16  may function to assist in moving implement  14 . 
         [0023]    Piston assembly  48  may include a piston  54  axially aligned with and disposed within tube  46 , and a piston rod  56  connectable to one of frame  12  and implement  14  (referring to  FIG. 1 ). Piston  54  may include a first hydraulic surface  58  and a second hydraulic surface  59  opposite first hydraulic surface  58 . An imbalance of force caused by fluid pressure on first and second hydraulic surfaces  58 ,  59  may result in movement of piston assembly  48  within tube  46 . For example, a force on first hydraulic surface  58  being greater than a force on second hydraulic surface  59  may cause piston assembly  48  to displace to increase the effective length of hydraulic cylinder  16 . Similarly, when a force on second hydraulic surface  59  is greater than a force on first hydraulic surface  58 , piston assembly  48  will retract within tube  46  to decrease the effective length of hydraulic cylinder  16 . A sealing member (not shown), such as an o-ring, may be connected to piston  54  to restrict a flow of fluid between an internal wall of tube  46  and an outer cylindrical surface of piston  54 . 
         [0024]    Source  24  may be configured to produce a flow of pressurized fluid and may include a pump such as, for example, a variable displacement pump, a fixed displacement pump, or any other source of pressurized fluid known in the art. Source  24  may be drivably connected to a power source (not shown) of machine  10  by, for example, a countershaft (not shown), a belt (not shown), an electrical circuit (not shown), or in any other suitable manner. Source  24  may be dedicated to supplying pressurized fluid only to hydraulic system  22 , or alternately may supply pressurized fluid to additional hydraulic systems (not shown) within machine  10 . 
         [0025]    A head-end valve section  40  includes head-end supply valve  26  and head-end drain valve  28 . Head-end supply valve  26  may be disposed between source  24  and first chamber  50  and configured to regulate a flow of pressurized fluid to first chamber  50 . Head-end supply valve  26  may include a two-position spring biased valve mechanism that is actuated by solenoid  26   b  and configured to move valve spool  26   a  between a first (open) position at which fluid is allowed to flow into first chamber  50  and a second (closed) position at which fluid flow is blocked from first chamber  50 . Head-end drain valve  28  may be disposed between first chamber  50  and tank  34  and configured to regulate a flow of pressurized fluid from first chamber  50  to tank  34 . Head-end drain valve  28  may include a two-position spring biased valve mechanism that is actuated by solenoid  28   b  and configured to move valve spool  28   a  between a first (open) position at which fluid is allowed to flow from first chamber  50  and a second (closed) position at which fluid is blocked from flowing from first chamber  50 . 
         [0026]    A rod-end valve section  42  includes rod-end supply valve  30  and rod-end drain valve  32 . Rod-end supply valve  30  may be disposed between source  24  and second chamber  52  and configured to regulate a flow of pressurized fluid to second chamber  52 . Rod-end supply valve  30  may include a two-position spring biased valve mechanism that is actuated by solenoid  30   b  and configured to move valve spool  30   a  between a first (open) position at which fluid is allowed to flow into second chamber  52  and a second (closed) position at which fluid is blocked from second chamber  52 . Rod-end drain valve  32  may be disposed between second chamber  52  and tank  34  and configured to regulate a flow of pressurized fluid from second chamber  52  to tank  34 . Rod-end drain valve  32  may include a two-position spring biased valve mechanism that is actuated by solenoid  32   b  and configured to move valve spool  32   a  between a first (open) position at which fluid is allowed to flow from second chamber  52  and a second (closed) position at which fluid is blocked from flowing from second chamber  52 . 
         [0027]    One or more head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  may include additional or different valve mechanisms such as, for example, a proportional valve element or any other valve mechanism known in the art. Furthermore, one or more head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  may alternately be hydraulically actuated, mechanically actuated, pneumatically actuated, or actuated in any other suitable manner. Hydraulic system  22  may include additional components to control fluid pressures and/or flows within hydraulic system  22  such as relief valves, makeup valves, shuttle valves, check valves, hydro-mechanically actuated proportional control valves, etc. For example, a bypass valve (not shown) may be provided for adjusting the pressure of the fluid. The bypass valve may allow flow from pump  24  to bypass into tank  34 . 
         [0028]    Head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  may be fluidly interconnected. In particular, head-end and rod-end supply valves  26 ,  30  may be connected in parallel to an upstream fluid passageway  60 . Upstream common fluid passageway  60  may be connected to receive pressurized fluid from pump  24  via a supply passageway  62 . Head-end and rod-end drain valves  28 ,  32  may be connected in parallel to a drain passageway  64 . Head-end supply and return valves  26 ,  28  may be connected in parallel to a first chamber fluid passageway  61 . Rod-end supply and return valves  30 ,  32  may be connected in parallel to a second chamber fluid passageway  63 . 
         [0029]    Tank  34  may constitute a reservoir configured to hold a supply of fluid. The fluid may include, for example, a dedicated hydraulic oil, an engine lubrication oil, a transmission lubrication oil, or any other fluid known in the art. One or more hydraulic systems within machine  10  may draw fluid from and return fluid to tank  34 . It is also contemplated that hydraulic system  22  may be connected to multiple separate fluid tanks. 
         [0030]    Hydraulic system  22  also includes one or more pressure sensors  36 ,  37 ,  38 . For example, pressure sensor  36  monitoring an output pressure P of pump  24  may be provided in supply fluid passageway  62 . When the fluid passes from pump  24  to hydraulic system  22 , pressure sensor  36  in supply fluid passageway  62  monitors the output pressure P of the fluid supplied by pump  24  entering hydraulic system  22 , and transmits an output signal reflecting the measured pressure to controller  70 . The pressure sensor(s)  36 ,  37 ,  38  can be placed at any location suitable to determine a desired pressure of fluid supplied by pump  24 . The exemplary calibration method described below determines output pressure P of pump  24  using pressure sensor  36 . It is understood, however, that the calibration method may determine pressure P using pressure sensor(s) at other locations in hydraulic system  22 , such as, for example, pressure sensors  37 ,  38 . As shown in  FIG. 2 , pressure sensor  37  monitors a pressure associated with first chamber  50  of hydraulic cylinder  16  and pressure sensor  38  monitors a pressure associated with second chamber  52  of hydraulic cylinder  16 . One skilled in the art will appreciate that pressure sensor  36 ,  37 ,  38  may include any pressure sensor assembly capable of ascertaining a pressure of the fluid supplied by pump  24  and/or entering hydraulic system  22 . Furthermore, the location(s) and number of pressure sensors  36 ,  37 ,  38  are not limited to the specific arrangement illustrated in  FIG. 2 . 
         [0031]    Controller  70  may embody a single microprocessor or multiple microprocessors that include a means for controlling an operation of hydraulic system  22 . Numerous commercially available microprocessors can be configured to perform the functions of controller  70 . It should be appreciated that controller  70  could readily be embodied in a general machine microprocessor capable of controlling numerous machine functions. Controller  70  may include a memory, a secondary storage device, a processor, and any other components for running an application. Various other circuits may be associated with controller  70  such as power supply circuitry, signal conditioning circuitry, solenoid driver circuitry, and other types of circuitry. Controller  70  may be connected to at least one operator input device  68  that allows an operator to control the operation of one or more components of the hydraulic system  22  using one or more control devices known in the art, such as one or more pedals, switches, dials, paddles, joysticks, etc. 
         [0032]    Controller  70  is electrically coupled to pressure sensors  36  and actuators  26   b ,  28   b ,  30   b ,  32   b  of the head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32 . Controller  70  receives pressure readings from pressure sensor  36  and may be configured to receive input from operator input device  68 . Controller  70  sends one or more electrical command signals to actuators  26   b ,  28   b ,  30   b ,  32   b . In response to the electrical command signal(s), one or more actuators  26   b ,  28   b ,  30   b ,  32   b  apply a varying force to controllably move one or more valve spools  26   a ,  28   a ,  30   a ,  32   a  to a desired displacement to control the hydraulic flow through the hydraulic system  22 . 
         [0033]    Hydraulic cylinder  16  may be movable by fluid pressure in response to an operator input using operator input device  68 . Fluid may be pressurized by source  24  and directed to head-end and rod-end supply valves  26  and  30 . In response to an operator input to either extend or retract piston assembly  48 , one of head-end and rod-end supply valves  26  and  30  may move to the open position to direct the pressurized fluid to the appropriate one of first and second chambers  50 ,  52 . Substantially simultaneously, one of head-end and rod-end drain valves  28 ,  32  may move to the open position to direct fluid from the appropriate one of the first and second chambers  50 ,  52  to tank  34  to create a pressure differential across piston  54  that causes piston assembly  48  to move. For example, if an extension of hydraulic cylinder  16  is requested, head-end supply valve  26  may move to the open position to direct pressurized fluid from source  24  to first chamber  50 . Substantially simultaneous to the directing of pressurized fluid to first chamber  50 , rod-end drain valve  32  may move to the open position to allow fluid from second chamber  52  to drain to tank  34 . If a retraction of hydraulic cylinder  16  is requested, rod-end supply valve  30  may move to the open position to direct pressurized fluid from source  24  to second chamber  52 . Substantially simultaneous to the directing of pressurized fluid to second chamber  52 , head-end drain valve  28  may move to the open position to allow fluid from first chamber  50  to drain to tank  34 . 
         [0034]      FIG. 3  illustrates an exemplary current control system  80  of controller  70  for controlling valves  26 ,  28 ,  30 ,  32 . Current control system  80  receives a spool displacement command  82 , which reflects a desired spool displacement, for the valve  26 ,  28 ,  30 ,  32 . Spool displacement command  82  may be determined based on, for example, a desired amount of fluid to direct to or from one of the first and second chambers  50 ,  52  as described above. 
         [0035]    Current control system  80  transmits spool displacement command  82  to an actuator transform  84 . Actuator transform  84  creates a nominal (or desired) current command  72  based on spool displacement command  82 . Current control system  80  then transmits nominal current command  72  to a modifier  86  that outputs an actual current command  76  based on nominal current command  72 . In the exemplary embodiment shown in  FIG. 3 , modifier  86  determines actual current command  76  by summing nominal current command  72  and a calibration offset current command  74 . Actual current command  76  is transmitted to the actuator  26   b ,  28   b ,  30   b ,  32   b  of the respective valve  26 ,  28 ,  30 ,  32 . 
         [0036]    Calibration offset current command  74  is determined for each valve  26 ,  28 ,  30 ,  32  by a calibration method as described below. The calibration of valves  26 ,  28 ,  30 ,  32  includes determining the point at which flow begins through the valve being calibrated, and this point is commonly referred to as the cracking point. Calibration of one or more valves  26 ,  28 ,  30 ,  32  may occur once or multiple times, e.g., after assembling hydraulic system  22 , periodically at the work site, after certain events, etc. In the exemplary embodiment, calibration offset current command  74  is based on a current command from controller  70  at the cracking point that is determined during the calibration of valve  26 ,  28 ,  30 ,  32 . In the exemplary embodiment, calibration offset current command  74  equals the cracking point current command, i.e., the current command at the cracking point, determined using the calibration method described below, minus the expected (or desired) current command at the cracking point. The expected current command at the cracking point is a predetermined current command that is expected to open respective valve  26 ,  28 ,  30 ,  32 . It is understood, however, that the calibration offset current command  74  may also depend on other factors associated with valves  26 ,  28 ,  30 ,  32 , etc. 
         [0037]      FIG. 4  illustrates an exemplary relationship between a displacement of one of the valve spools  26   a ,  28   a ,  30   a ,  32   a  and a current command from controller  70  to the associated actuator  26   b ,  28   b ,  30   b ,  32   b  determined using current control system  80  shown in  FIG. 3 . A nominal control curve  90  shows the valve spool displacement versus nominal current command  72 . An actual control curve  92  shows the valve spool displacement versus actual current command  76 . As shown in  FIG. 4 , the difference between the nominal control curve  90  (corresponding to nominal current command  72 ) and the actual control curve  92  (corresponding to actual current command  76 ) is calibration offset current command  74 . 
         [0038]      FIGS. 5A and 5B  illustrate a flow chart showing an exemplary method of calibrating hydraulic system  22  by determining the cracking point current command consistent with certain disclosed embodiments. As shown in  FIG. 5A , controller  70  may determine which valve  26 ,  28 ,  30 ,  32  to calibrate (step  100 ). Valve  26 ,  28 ,  30 ,  32  may be selected automatically by controller  70  or by the operator or other entity and information indicating the selection may be transmitted to controller  70 . The following steps describe the calibration of head-end supply valve  26 . However, it is understood that similar steps are also executed when calibrating head-end drain valve  28 , rod-end supply valve  30 , or rod-end drain valve  32 . 
         [0039]    Controller  70  may close all valves  26 ,  28 ,  30 ,  32  by supplying zero or substantially zero current to all valves  26 ,  28 ,  30 ,  32  (step  102 ). Controller  70  then sends a command to pump  24  to raise its output pressure P to a predetermined level (step  104 ). In addition, controller  70  may send a command to a bypass valve (not shown) located downstream from pump  24  to raise the output pressure P from pump  24 . The fluid from pump  24  is supplied at the predetermined pressure level at least to valve section  40  (i.e., the valve section that includes the valve being calibrated). In the exemplary embodiment, pump  24  supplies fluid to both valve sections  40 ,  42 . 
         [0040]    Controller  70  then increases a current to actuator  26   b  of head-end supply valve  26  (i.e., the actuator of the valve being calibrated), and substantially simultaneously, controller  70  also directs a full current to actuator  28   b  of head-end drain valve  28  (i.e., the actuator of the opposite valve in the same valve section as the valve being calibrated) (step  106 ). As a result, the full current to actuator  28   b  fully opens head-end drain valve  28 . As controller  70  increases the current directed to actuator  26   b  of head-end supply valve  26 , the output pressure P of pump  24  is measured by pressure sensor  36 . The pressure sensor  36  transmits an output signal reflecting the measured output pressure P to controller  70  (step  108 ). 
         [0041]    Controller  70  also calculates a derivative dP/dt of the measured output pressure P of pump  24  with respect to time, i.e., a rate of pressure change. The derivative dP/dt of the measured output pressure P of pump  24  is zero as controller  70  increases the current to actuator  26   b  of head-end supply valve  26  and while head-end supply valve  26  is closed. When head-end supply valve  26  opens and allows flow to pass, the output pressure P of pump  24  decreases, and the derivative dP/dt of the output pressure P of pump  24  changes rapidly. Controller  70  monitors the derivative dP/dt and determines when the derivative dP/dt is greater than a predetermined threshold and remains above the threshold for a predetermined period of time (step  110 ). For example, controller  70  may determine when the derivative dP/dt of the measured output pressure P of pump  24  is greater than the predetermined threshold and continues to remain over the predetermined threshold for a predetermined time interval (e.g., 0.5 second, 1 second, etc.). If the derivative dP/dt is not greater than the predetermined threshold or the derivative dP/dt does not remain greater than the predetermined threshold before the predetermined time interval has elapsed (step  110 ; no), then the process returns to step  106 . Controller  70  then continues to increase the current to actuator  26   b  of head-end supply valve  26  and to compute the derivative dP/dt of the output pressure P of pump  24  until the derivative dP/dt is greater than the predetermined threshold for the predetermined period of time (steps  106 - 110 ). 
         [0042]    When controller  70  determines that the derivative dP/dt is greater than the predetermined threshold for the predetermined period of time (step  110 ; yes), then controller  70  determines and stores the current command sent to actuator  26   b  of head-end supply valve  26  when the derivative dP/dt of output pressure P of pump  24  begins to be greater than the predetermined threshold, i.e., the start of the predetermined period of time that the derivative dP/dt continued to remain above the predetermined threshold (step  112 ). As shown in  FIG. 5B , controller  70  then determines the number of current commands stored and determines if a predetermined number (e.g., three) of current commands have been stored (step  114 ). If the predetermined number of current commands have not been stored (step  114 ; no), then the process returns to step  102  so that controller  70  may determine and store another current command, and then determine whether the predetermined number of current commands have been stored (steps  102 - 114 ). 
         [0043]    After the predetermined number of current commands have been stored (step  114 ; yes), then controller  70  calculates an average of the stored current commands, and a maximum deviation from the calculated average. The maximum deviation is the largest difference between the predetermined number of stored current commands and the calculated average. Controller  70  then determines if the maximum deviation is less than a predetermined threshold (step  116 ). 
         [0044]    If the maximum deviation is less than a predetermined threshold (step  116 ; yes), then controller  70  computes the calibration offset current command  74  for head-end supply valve  26  by subtracting the calculated average of the stored current commands minus the expected cracking point current command (step  118 ). Controller  70  stores the computed calibration offset current command  74  (step  120 ), and then the calibration of head-end supply valve  26  is complete. The process shown in  FIGS. 5A and 5B  may then be repeated with controller  70  determining that head-end drain valve  28 , rod-end supply valve  30 , or rod-end drain valve  32  is the valve to be calibrated (step  100 ). 
         [0045]    If, at step  116 , the maximum deviation is not less than the predetermined threshold (step  116 ; no), then controller  70  determines if a predetermined maximum number of attempts (e.g., eight) to determine the cracking point current command has been reached (step  122 ). If the predetermined maximum number of attempts has not been reached (step  122 ; no), then the process returns to step  102  so that controller  70  may determine another cracking point current command by repeating steps  102  to  116 , removing the oldest cracking point current command and computing another maximum deviation with the newest cracking point current command. However, if the predetermined maximum number of attempts has been reached (step  122 ; yes), then the calibration of head-end supply valve  26  is incomplete, and the calibration offset current command  74  may be, e.g., zero or a previously determined calibration offset current command. The process may return to step  102  at a later time to determine the cracking point current command and compute the calibration offset current command  74 . 
       INDUSTRIAL APPLICABILITY 
       [0046]    The disclosed calibration method may be applicable to any valve arrangement, such as an arrangement of IMVs, for controlling a fluid actuator where balancing of pressures and/or flows of fluid supplied to the actuator is desired. The disclosed calibration method may provide consistent actuator performance in a low cost simple configuration and may achieve precise positioning of valves of the valve arrangement. 
         [0047]    The method of calibrating any of head-end and rod-end supply and drain valves  26 ,  28 ,  30 ,  32  includes determining the cracking point current command, i.e., the current command at which the valve being calibrated begins to allow fluid to pass. In the exemplary embodiment, calibration offset current command  74  is the cracking point current command minus the expected current command at the cracking point. Calibration offset current command  74  is added to nominal current command  72  to determine actual current command  76 . Therefore, actual valve behavior may be predicted based on the cracking point current command determined using the exemplary disclosed calibration method. Actual current command  76  is transmitted from controller  70  to actuator  26   b ,  28   b ,  30   b ,  32   b  of valve  26 ,  28 ,  30 ,  32  to control the respective valve  26 ,  28 ,  30 ,  32 , and is determined by summing nominal current command  72  and calibration offset current command  74 . 
         [0048]    Calibration offset current command  74  is used to shift nominal control curve  90  so that performance of valve  26 ,  28 ,  30 ,  32  becomes actual control curve  92 . This shift compensates for variations in the actual valve behavior compared to the nominal (or desired) valve position due to, for example, variations in an individual component&#39;s design and/or assembly. 
         [0049]    During the calibration of head-end supply valve  26 , zero current is first applied to actuators  26   b ,  28   b ,  30   b ,  32   b  of valves  26 ,  28 ,  30 ,  32  as the pump output pressure P is raised to a predetermined level. As a result, fluid begins to flow to valves  26 ,  28 ,  30 ,  32 . Current is applied to actuator  26   b  of head-end supply valve  26 , and the current applied to actuator  26   b  is ramped up from zero while a full current at a predetermined level is applied to actuator  28   b  of head-end drain valve  28 . Meanwhile, the pump output pressure P is monitored. Since the pump output pressure P is monitored during the calibration of valves  26 ,  28 ,  30 ,  32 , calibration may be performed for each of valves  26 ,  28 ,  30 ,  32  with a single pressure sensor  36  disposed near the outlet of pump  24 . Therefore, fewer pressure sensors may be required, thereby simplifying the valve calibration method and reducing any discrepancies that may occur when using multiple pressure sensors. 
         [0050]    The derivative dP/dt of the pump output pressure P is calculated and compared against a predetermined threshold. If the derivative dP/dt remains greater than the predetermined threshold over a predetermined time interval, then the current command applied to actuator  26   b  at the start of the time interval is determined and stored. By applying the condition for the derivative dP/dt to be greater than the predetermined threshold for a predetermined period of time, a more accurate assessment of when valve  26 ,  28 ,  30 ,  32  is opening may be determined. 
         [0051]    The calibration for a given valve  26 ,  28 ,  30 ,  32  may be performed multiple times, and the maximum deviation is calculated each time. When the maximum deviation is below the predetermined threshold, the calibration of the given valve  26 ,  28 ,  30 ,  32  is considered valid and corresponding calibration offset current command  74  is stored. As a result, pressure transients and pressure sensor noise, such as pressure spikes, may be prevented from causing an invalid calibration. Thus, pressure-based calibration may be more consistent and suitably accurate for field calibrations where conditions are not always strictly controlled. 
         [0052]    It will be apparent to those skilled in the art that various modifications and variations can be made to the method for calibrating IMVs. Other embodiments will be apparent to those skilled in the art from consideration of the specification and practice of the disclosed method for calibrating IMVs. It is intended that the specification and examples be considered as exemplary only, with a true scope being indicated by the following claims and their equivalents.