Abstract:
A free-piston (“FP”) engine is a type of internal combustion engine with no crankshaft, so that its piston trajectory is no longer constrained by the mechanical linkage. FP engines have a high potential in terms of energy saving given their simple structure, high modularity and high efficiency, among other attributes. One of the technical barriers that affect FP engine technology is a lack of precise piston trajectory control. For example, the presence of a transient period after a single combustion event can prevent the engine from continuous firing. The present subject matter provides a control scheme that can utilize a reference and control signal shifting technique to modify the tracking error and the control signal to reduce the transient period.

Description:
CLAIM OF PRIORITY 
       [0001]    This patent application claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 61/812,462, filed on Apr. 16, 2013, which is hereby incorporated by reference herein in its entirety. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    This invention was made with government support under Grant No. EEC-0540834, awarded by the National Science Foundation. The government has certain rights in this invention. 
     
    
     BACKGROUND 
       [0003]    A free-piston (“FP”) engine is a “crank-less” internal combustion engine in which the piston moves within an elongated chamber by a combustion within the combustion portion of the chamber. In conventional crank internal combustion (“IC”) engines, the piston is connected to a flywheel by a linear crankshaft such that the linear movement of the piston from the combustion event actuates the crankshaft to rotate the flywheel for operating a hydraulic pump or other mechanical system. In conventional IC engines, the continued rotation of the flywheel is translated to the piston via the crankshaft to cycle the piston back to the original position. In contrast, the expansion of the piston of the FP engine operates a hydraulic pump, linear alternator or other load device to store or use the kinetic energy. In certain FP engines, the exhaust gases from the combustion event are also fed through a gas turbine engine. The piston of the FP engine is compressed by using a portion of the stored energy to reverse the load device or with a rebound device, such as an opposing free-piston engine. 
         [0004]    The absence of a crankshaft and flywheel assembly in an FP engine reduces the number of moving parts thereby reducing frictional losses in the load device from the moving parts providing improved efficiency of the FP engine. Without the crankshaft and flywheel, the cycling of the FP engine is mainly dependent on the dynamic coupling of the in-cylinder gas dynamics, the load applied by the load device and the piston trajectory. However, unlike conventional IC engines where the crankshaft can be used to correct irregular movement, FP engines cannot directly mechanically control the piston movement. As a result, the operation of FP engines often varies cycle-to-cycle, especially during transient operation such as combustion events, which can make engine control difficult and cause the engine to misfire. In particular, the FP engine is subject to transient behavior when switching between operational modes such as from motoring mode to a firing mode and vice versa resulting in large tracking errors and other ill effects. 
         [0005]    The transient nature of FP engines makes achieving robust and precise engine operation control difficult. The current control methodologies for FP engines are primarily calibration methodologies that have had limited success and are primarily limited to single piston FP engines. In a calibration-based methodology, the system is set for normal operating mode based on desired operation conditions and at an effective efficiency. However, transient events can create irregular piston trajectory that cannot be efficiently regulated by current calibration-based methodology. 
       OVERVIEW 
       [0006]    This document pertains generally, but not by way of limitation, to free piston engine designs and architectures, and in particular, to control systems and methodologies for a free piston engine for active and dynamic control of piston trajectory of a FP engine through transient events, such as combustion events. The present inventors have recognized, among other things, that a problem to be solved can include irregular piston trajectory for a transient period following a transient event. The irregular piston trajectory can cause substantial tracking errors between the actual piston trajectory and a reference trajectory, which can result in the control methodology operating substantially out-of-phase with the actual piston trajectory. In an example, the present subject matter can provide a solution to this problem, such as by providing a control algorithm that includes detecting a combustion event and applying a reference shift corresponding to the transient period to the reference trajectory and the control signal to realign the control signal with the actual piston trajectory following the combustion event. The present inventors have recognized that the actual piston trajectory returns to a regular periodic trajectory following the irregular trajectory following the combustion event. Accordingly, the shifting of the reference shifting can include determining the timing of the combustion or other event causing the transient period and shifting the reference trajectory to realign the reference trajectory of the control signal with the actual piston trajectory following the transient period. Detection of transient events and reference shifting of the reference trajectory until after the transient period avoids large tracking errors and operating of the FP engine when the control signal and the actual piston trajectory are out-of-phase. The shifting of the reference trajectory and control signal provides a more robust control of FP engine during transient events and allows implantation of multi-occurrence combustion events or continuous firing operation of the FP engine with reduced risk of misfire or other negative engine behavior. 
         [0007]    In an example, a method for operating a FP engine can include reciprocating a piston in an engine cylinder to displace a force transducer, the piston traveling along an actual piston trajectory. The method can further include monitoring engine operation by comparing actual piston trajectory of an oscillating piston to a reference trajectory and locating a first local extremum for the actual piston trajectory. The first extremum can correspond to a first actual reversal point of the reciprocating piston. The method can further include recording a first time instant corresponding to the first local extremum and comparing the first time instant to a first reference time index to detect a first combustion event. The reference time index can correspond to a first reference reversal point corresponding to the first actual reversal point. The method can include applying a first reference shift to the reference trajectory upon detecting of the first combustion event. The reference shift can correspond to the difference between the first time instant and the first reference time index. The method can include operating the force transducer to influence the actual piston trajectory to approximate the shifted reference trajectory. 
         [0008]    In an example, a free-piston engine can include a controller configured to compare an actual piston trajectory of an oscillating piston to a reference trajectory. The controller can also be configured to locate a first local extremum for the actual piston trajectory, the extremum corresponding to a first actual reversal point for the oscillating piston and record a first time instant corresponding to the local extremum. The controller can also be configured to detect a first combustion event by comparing the first time instant to a first reference time index. The reference time index can correspond to a first reference reversal point corresponding to the first actual reversal point. The controller can also be configured to apply a first reference shift to the reference trajectory upon detecting the first combustion event. The first reference shift can correspond to the difference between the first time instant and the reference time index. The free-piston engine can also include an engine cylinder for slidably receiving the piston and a force transducer coupled to the piston. The controller can be coupled to the force transducer and configured to control the force transducer to influence the piston oscillation such that the actual piston trajectory approximates the reference trajectory. 
         [0009]    This overview is intended to provide an overview of subject matter of the present patent application. It is not intended to provide an exclusive or exhaustive explanation of the present subject matter. The detailed description is included to provide further information about the present patent application. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    In the drawings, which are not necessarily drawn to scale, like numerals may describe similar components in different views. Like numerals having different letter suffixes may represent different instances of similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments discussed in the present document. 
           [0011]      FIG. 1  is a schematic view of a control system, according to an example. 
           [0012]      FIG. 2  is a chart illustrating engine piston position over time with a single combustion event, according to an example. 
           [0013]      FIG. 3  is a flow chart illustrating a method of applying a reference shift to compensate for a combustion event, according to an example. 
           [0014]      FIG. 4  is a schematic view of a FP engine piston trajectory controller, according to an example. 
           [0015]      FIG. 5  is a chart illustrating engine pressure over time with a single combustion event, according to an example. 
           [0016]      FIG. 6  is a schematic illustrating updating and shifting of a control signal, according to an example. 
           [0017]      FIG. 7  is a flow chart illustrating a method of controlling a FP engine, according to an example. 
           [0018]      FIG. 8  is a schematic illustration of a single piston free piston engine according to an example. 
           [0019]      FIG. 9  is a schematic illustration of an opposed chamber architecture for a free piston engine according to an example. 
           [0020]      FIG. 10  is a schematic view of a hydraulic FP engine, according to an example. 
           [0021]      FIG. 11A  is a chart illustrating a pressure trace after a single combustion event, under control of an algorithm, according to an example. 
           [0022]      FIG. 11B  is a chart illustrating an actual piston trajectory and a reference trajectory after a single combustion event, under control of an algorithm, according to an example. 
           [0023]      FIG. 12A  is a chart illustrating a piston pressure of a dual piston FP engine after a continuous combustion event, under control of an algorithm, according to an example. 
           [0024]      FIG. 12B  is a chart illustrating an actual piston trajectory and a reference trajectory after a continuous combustion event, under control of an algorithm, according to an example. 
       
    
    
     DETAILED DESCRIPTION 
       [0025]    The present subject matter is directed to an FP engine and related control methodologies for operating the FP engine. In an example, the present subject matter is related to a “virtual” crankshaft control methodology that compares actual piston trajectory with a reference trajectory to coordinate combustion events and operation of a load device, such as a force transducer, to adjust piston trajectory in a similar manner to a mechanical crankshaft of a conventional IC engine. The “virtual” crankshaft control is described in U.S. patent application Ser. No. 13/855,363, filed Apr. 2, 2013, entitled “Methods and Systems for Free-piston Engine Control,” which claims the benefit of U.S. Provisional Patent Application No. 61/619,169, filed Apr. 2, 2012, entitled “Methods and Systems for Free-piston Engine Control”, each of which is incorporated herein by reference in their entirety. Specifically, the present subject matter relates to a “virtual” crankshaft control methodology configured to detect a transient event, such as a combustion event, and applies a corresponding reference shift to the reference trajectory for to minimize tracking errors between the actual piston trajectory and the reference trajectory and prevent out-of-phase control of the piston. 
         [0026]    As the piston trajectory in an FP engine is periodic, a control method that can be adopted is repetitive control as depicted in  FIG. 1 . The control method includes a stabilized system  102  and a repetitive controller  104 . The controller  104  operates as a “virtual” crankshaft that guides the piston trajectory via control of the load device, such as a linear alternator or a hydraulic accumulator with a hydraulic servo valve regulating the high pressure fluid in the accumulator. The control algorithm and the reference trajectory of the virtual crankshaft can be altered digitally to achieve a wide range of piston trajectory profile within a short time period, which is not achievable through mechanical crankshaft. With a mechanical crankshaft, the piston trajectory is fixed and is independent from engine speed and load limiting means for optimizing the engine efficiency. However, with the virtual crankshaft, the piston trajectory can be varied in real time by altering the reference trajectory. Optimal trajectories can be determined for the engine under various frequencies and load conditions, such that the engine would always run at its maximum efficiency. 
         [0027]    As depicted in  FIG. 2 , a transient event, such as combustion event, can disrupt the oscillating movement of the piston for a transient period. The repetitive controller  104  of the piston is based on an estimated linear model of the piston trajectory: 
         [0000]    
       
         
           
             
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                   A 
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                     ( 
                     
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                 u 
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         [0000]    where k indicates the current time, u(k) is the control signal and y(k) is the measured piston position. The control signal u(k) can be expressed as: 
         [0000]        u ( k )= q ( q   −1 )[ u ( k−N )+ R ( q   −1 )· e ( k−N )]
 
         [0000]    where Q is a low pass filter, q −1  is the one sample delay operator, N is the delay steps that equal to the reference period, and e(k−N) is the tracking error. As such, the current control signal u(k) depends on the control signal u(k−N) and the tracking error e(k−N) from the prior piston cycle. As the transient event disrupts the periodic movement of the piston, the actual piston trajectory of subsequent piston cycles following the transient event will differ substantially from the actual piston trajectory, resulting in large tracking errors and cause the control signal to be substantially out-of-phase with the actual piston trajectory. It is recognized that while the piston trajectory and control signal are out-of-phase, the piston trajectory returns to a trajectory having a similar slope to cycles prior to the combustion cycle. Accordingly, the phase shift of the actual piston trajectory resulting from the combustion event can be compensated for by applying a corresponding reference shift to the reference trajectory, tracking error and the control signal. 
         [0028]    As depicted in  FIG. 3 , a method  300  for correcting the phase shift following a combustion event includes monitoring  310 , compensating  320 , shifting  330  and updating  340 . The method can be incorporated into the repetitive controller  104  as depicted in  FIG. 4 . 
         [0029]    Method  300  at monitoring  310  includes monitoring piston trajectory for a combustion event. In an example, monitoring  310  includes monitoring the piston trajectory for a local extremum minimum, such as a local minimum or maximum, at a time instant k. The local extremum corresponds to a reversal point for the oscillating piston such as an actual top dead center (TDC) position or a bottom dead center (BDC) position. The piston position at time instant k is compared to the reference piston position at a time index j on the reference trajectory, the time index j corresponding to reference piston position at a corresponding TDC or BDC position. In an example, if the difference between the time instant k and the time index j exceeds a predetermined threshold, a combustion event or other transient event has likely occurred as the piston has reached TDC or BDC too quickly or slowly. In certain examples, if the difference between the piston position at time instant k and the reference piston position at time index j is greater than a predetermined amount than the piston trajectory has substantially deviated from the prior cycle indicating that combustion event has likely occurred. Similarly, a combustion event will cause the piston to travel faster than the average velocity of the piston or accelerate faster than the piston in a non-combustion cycle. Accordingly, if the average velocity or acceleration of the piston is greater than the historical average velocity of the piston then a combustion event has likely occurred. Accordingly, in certain examples, monitoring  310  can include monitoring for both the differences in piston position and average velocity and declaring a combustion event only when the timing of the reversal points for the piston, piston position at reversal points, average velocity measurements, piston acceleration or at least two indicia signal a combustion event. In certain examples, other indicia unrelated to piston motion can be used to detect or confirm a combustion event such as temperature changes, pressure changes, auditory signals, vibrations and other indicia of combustion events or changes in the piston trajectory. 
         [0030]    In an example, at compensating  320 , method  300  can also include evaluating combustion strength to more accurately tailor the reference shift to the particular combustion event. As combustion events and the effects therefrom are often non-repetitive, a reference shift calculated for a prior combustion event may not correct the reference trajectory and control signal for the present combustion event. In an example, the combustion strength can be correlated with the peak pressure and other factors representative of the combustion strength as illustrated in  FIG. 5 . In this configuration, the combustion strength of a present combustion event is compared to the combustion strength of a prior combustion event to generate a strength compensation term. The strength compensation term can be used to modify the reference shift. In an example, compensating  320  can also include monitoring acceleration of the piston following the time instant k. The acceleration of the piston can also be indicative of the strength and other characteristics of the particular combustion event. In an example, a correction based on the measured acceleration can be applied to the reference trajectory in addition to the reference shift to adjust the amplitude or frequency of the reference trajectory. Each combustion event can influence the characteristics of the actual piston trajectory such as the amplitude or frequency of the reference trajectory. While the changes can be relatively minor as compared to the shifting actual piston trajectory, the correction can further reduce the tracking errors between the actual piston trajectory and the reference trajectory. 
         [0031]    At shifting  330 , method  300  can include calculating the reference shift if a combustion event is detected. The reference shift is the difference between time instant k and time index j. The reference shift is applied to the reference trajectory to generally align the reference trajectory to the actual piston trajectory following the combustion event. 
         [0032]    In an example, the method  300  can include a tracking error and control signal update  340 . The error update corresponds to the time elapsed between the actual combustion event and when the combustion event is actually detected. As the control signal from j+N to k+N is dependent on the error signal from j to k, large errors from j to k are replaced by the new errors to avoid undesired control signal. The new errors are the difference between the piston position and the shifted reference trajectory from j+N to k+N. Since the reference has been shifted forward by a time period of k−j, the control signal needs to be shifted accordingly as well. In an example, the tracking error e(k) and the control signal u(k) are shifted by a corresponding reference shift as with the reference trajectory. Accordingly, as depicted in  FIG. 6 , the control signal u(k) is calculated by using u(j−N) rather than u(k−N) at time instant k. Similarly, the tracking error e(k) is determined by using e(j−N) rather than e(k−N) at time instant k. 
         [0033]    A method  400  of controlling an FP engine, according to an example, is depicted in  FIG. 7 . At  402 , the method can include reciprocating a piston in an engine cylinder to displace a force transducer. In an example, an energy storage device coupled to the force transducer to store force transducer energy and power the force transducer. In certain examples, the force transducer comprises a linear alternator and the energy storage device comprises a battery. In other examples, the force transducer comprises a hydraulic pump, and the piston is connected with a plunger of a hydraulic pump that is coupled with the energy storage device. At  404 , the method can include controlling the force transducer to influence the actual piston trajectory, wherein the controller is controlling stored energy from the force transducer in the energy storage device, and to control powering the force transducer with energy from the energy storage device. The controller can include a processor and be configured to execute instructions stored on a machine-readable medium including instructions that, when performed by a machine, cause the machine to perform any one or more of the functions of method  400 . At  406 , the method can include storing the piston trajectory over multiple piston cycles. The method can include predetermining the piston location over time to determine a reference trajectory. At  408 , the method can include controlling the force transducer in association with the reference trajectory such that the actual piston trajectory aligns with the reference trajectory. In a method, this can include a one-to-one correspondence between cycles of the reference trajectory and cycles of the engine. At  410 , the method can include detecting combustion in the engine cylinder during a combustion cycle and for a subsequent cycle to the combustion cycle. At  412 , the method can include applying a reference shift to the reference trajectory with respect to the subsequent cycle by N cycles as illustrated in  FIG. 6 . N can be an integer. This can include shifting from a first cycle of the reference trajectory to another cycle of the reference trajectory. At  414 , the force transducer is controlled according to the shifted reference trajectory to influence the actual piston trajectory of the piston to minimize tracking errors between the shifted reference trajectory and the actual piston trajectory. The force transducer can be configured to adjust movement of the piston to align the actual trajectory of the piston with the reference trajectory. 
         [0034]    A method can include, or can optionally be combined with any portion or combination of any portions of any one or more of the previous methods, comprising detecting combustion in the cylinder by monitoring at least one of intake port pressure, exhaust port pressure, and location of the piston. A method can include, or can optionally be combined with any portion or combination of any portions of any one or more of the previous methods, wherein detecting combustion includes determining whether the piston has arrived at a specific location before a time in the reference trajectory at which the piston is predetermined to reach the location. A method can include, or can optionally be combined with any portion or combination of any portions of any one or more of the previous methods, wherein detecting combustion includes predetermining cylinder pressure over time over multiple cycles of the engine, storing the predetermined pressure over multiple cycles in the reference trajectory, and determining whether the pressure at a specific time in the reference trajectory is higher than the predetermined pressure in the reference trajectory. 
         [0035]      FIG. 8  depicts a single piston configuration for a hydraulic FP engine  10 A for use with a control methodology, according to an example of the present subject matter. Engine  10 A includes a piston  14  and a cylinder  16 . The piston  14  and the cylinder  16  cooperate to define a combustion chamber  18 . The piston  14  is connected to a rod  20  to a first plunger  22 A and a second plunger  22 B positioned within a hydraulic cylinder  24  such that the oscillation of the piston  14  oscillates the first plunger  22 A and the second plunger  22 B. 
         [0036]    The hydraulic cylinder  24  includes a large diameter portion  25 A and a small diameter portion  25 B. The first plunger  22 A is sized to correspond to the inner diameter of the hydraulic cylinder  24  at the large diameter portion  25 A. The second plunger  22 B is sized to correspond to the inner diameter of the hydraulic cylinder  24  at the small diameter portion  25 B. The first plunger  22 A and the second plunger  22 B are spaced along the rod  20  within the hydraulic cylinder  24  to define three chambers within the hydraulic cylinder  24 : the left most first chamber  27 A, the center second chamber  27 B and the right most third chamber  27 C. The first chamber  27 A has a constant diameter corresponding to the inner diameter of the large diameter portion  25 A throughout the oscillation of the piston  14 . The third chamber  27 C has a constant diameter corresponding to the inner diameter of the small diameter portion  25 B throughout the oscillation of the piston  14 . The second chamber  27 B has a constant diameter corresponding to the inner diameter of the large diameter portion  25 A throughout the oscillation of the piston  14 , wherein an intermediate wall is positioned between the second chamber  27 B and the second plunger  22 B. 
         [0037]    A low pressure hydraulic fluid accumulator  26  is fluidly connected via a line  28  to the hydraulic cylinder  24  at the second chamber  27 B and the third chamber  27 C. The flow from the second chamber  27 B and third chamber  27 C to line  28  are regulated by check valves. A high pressure fluid accumulator  30  is fluidly connected via line  32  to each chamber  27 A,  27 B,  27 C of the hydraulic cylinder  24 . The flow from the second chamber  27 B and third chamber  27 C to line  32  are regulated by check valves. A valve  36  selectively connects the third chamber  27 C to the high pressure accumulator  30  and the low pressure accumulator  26  via line  34 . The valve  36  is configured to switch the connection to the third chamber  27 C between the high pressure accumulator  30  and the low pressure accumulator  26 . 
         [0038]    During expansion of combustion chamber  18 , combustion gas is introduced into the combustion chamber  18  by a valve (not shown in this figure). When the piston  14  is positioned at top dead center (TDC), the gas is ignited by auto-ignition or a spark device (not shown) including, but not limited to, a spark plug. The ignited gases push the piston  14  through the cylinder  16 , which correspondingly moves the plungers  22 A,  22 B within the hydraulic cylinder  24  compressing hydraulic fluid in the third chamber  27 C. During expansion of the combustion chamber  18  the valve  36  can be positioned to direct the fluid compressed in the third chamber  27 C to the high pressure accumulator  30 . The pressure of the compressed fluid can also overcome the check valve coupled to chamber  27 C and is directed to the high pressure accumulator via line  32 . Accordingly, the kinetic energy of the piston movement is converted into hydraulic energy that is stored in the accumulator  30 . Similarly, movement of piston  14  will also cause the effective volume of the second chamber  27 B to decrease, thus compressing the fluid within the second chamber  27 B until the pressure exceeds the pressure limit of corresponding check valve allowing the excess fluid to enter line  32 . The movement of piston  14  will also cause the volume of the first chamber  27 A to expand. In an example, the large diameter portion  25 A and the small diameter portion  25 B are sized such that the volume of fluid expelled from the second chamber  27 B approximates the amount of fluid drawn in the first chamber  27 A as the first chamber  27 A expands. 
         [0039]    During combustion chamber compression, valve  36  is positioned such that high pressure hydraulic fluid from the high pressure accumulator  30  is directed into the third chamber  27 C causing the third chamber  27 C to expand and compressing the first chamber  27 A. The compression of the hydraulic fluid in the first chamber  27 A forces the excess hydraulic fluid in the first chamber  27 A to the high pressure accumulator  30  via line  32 . Similarly, movement of the piston  14  to compress the combustion chamber causes the volume of the second chamber  27 B to increase. Hydraulic fluid is drawn from the low pressure accumulator  26  into the second chamber  27 B to accommodate the increasing volume of the second chamber  27 B. 
         [0040]    If a misfire occurs during expansion and the piston  14  fails to move or moves slowly toward bottom dead center, valve  36  can be switched to direct fluid from the third chamber  27 C to the low pressure accumulator  26  thereby reducing resistance for the movement of the piston  14 . Similarly, if the pressure in the high pressure accumulator  30  is too high causing the piston  14  to return to TDC too quickly, the valve  36  can be alternated between operably connecting the third chamber  27 C with the high pressure accumulator  30  and the low pressure accumulator  26  thereby reducing the effective fluid pressure of the hydraulic fluid within the third chamber  27 C slowing the return of the piston  14 . 
         [0041]    The operation of valve  36  can be controlled by a control device  38  operably connected by a signal line  40 . In an example, a repetitive control  42  can be operatively connected with sensors for determining at least one of piston position, combustion chamber pressure, engine or hydraulic cylinder chamber pressure, combustion chamber temperature, and engine or hydraulic chamber temperature. The repetitive control  42  can also be coupled with the control device  38  or may itself comprise the control device  38 . Either of control  42  or control device  38  can include a processor. The present subject matter is directed to the ability to control a free piston engine in both the engine motoring mode and during an engine firing mode to control piston trajectory, including stroke distance and its speed profile over such stroke, including when the piston is firing normally and recovers quickly after an engine misfire. 
         [0042]      FIG. 9  depicts a dual piston configuration for the hydraulic FP engine  10 B. In this configuration, two pistons  14  are sequentially fired within combustion chambers  18  to drive rod  20  connected to plunger  22  of the hydraulic cylinder  24  from opposing sides such that the plunger  22  reciprocates axially between the two cylinders  16 . Depending on the particular piston  14  being fired and the corresponding direction of the plunger  22 , the low pressure side of the cylinder  24  for that particular piston  14  stroke is connected to a low pressure fluid source  26  by hydraulic line  28 . Similarly, the high pressure side of the cylinder  24  for that particular piston  14  stroke is connected to a high pressure accumulator  30  by hydraulic line  32 . The hydraulic lines  28  and  32  accommodate the provision of low pressure fluid to either side of the plunger  22  and the outflow of high pressure fluid from the respective side of plunger  22 , as controlled by conventional valves. A line  34  operably connects the high pressure line  32  to the low pressure line  28  for transfer of hydraulic fluid between the high pressure side of the hydraulic cylinder  24  and the low pressure side of the hydraulic cylinder  24 . A control valve  36  regulates the flow of hydraulic fluid between the high pressure side and the low pressure side. The control valve  36  can be selectively connected to one or more of the different hydraulic chambers in real-time by providing control signals to the control valve  36 , or any number of such control valves as operatively arranged. The valve  36  can be controlled by a control device  38  for control of the high and low pressure sides of the hydraulic cylinder  24  or the particular stroke to adjust the dynamics of pistons  14 . Control device  38  can include a processor. This arrangement gives flexibility for controlling the trajectory of pistons  14  during both motoring and firing modes. 
         [0043]      FIG. 10  depicts an opposed piston and opposed cylinder (“OPOC”), two-stroke configuration for a FP engine  210 . As depicted, the FP engine  210  includes a pair of inner pistons  212 , a connection rod  214  and a pair of outer pistons  216 . The inner pistons  212  are connected by the connection rod  214  such that the inner pistons  212  move independently of the outer pistons  216 . Each inner piston  212  corresponds to one outer piston  216  to form a left piston pair  218  and a right piston pair  220 . 
         [0044]    In an example, the engine can be started, for example, from a bottom dead center (“BDC”) position in which an inner piston  212  of the left piston pair  218  is at the maximum distance from the corresponding outer piston  216  as depicted in  FIG. 10 . Upon combustion within the combustion chamber of the right piston pair  220 , the inner piston  212  of the left piston pair  218  moves towards the top dead center (“TDC”) position in which the inner piston  212  of the left piston pair  218  is at the minimum distance from the corresponding outer piston  216 . For the purposes of this discussion, the BDC positions and the TDC positions of the piston pairs  218 ,  220  are equivalent to the reversal points of an oscillating piston of a single FP engine, such as depicted in  FIG. 8 . Similarly, the outer pistons  216  are operably connected by side push rods  228  such that a combustion event in the combustion chamber of the right piston pair  220  pushes the outer piston  216  of the right piston pair  220  away from the inner piston  212  and pulls the outer piston  216  of the left piston pair  218  toward the inner piston  212  of the left piston pair  218 . As depicted in  FIG. 10 , the pistons  212 ,  216  of the left piston pair  218  are oriented in positions approximating BDC and the pistons  212 ,  216  of the right piston pair  220  are oriented in positions approximating TDC. As the inner piston  212  and the outer piston  216  of the left piston pair  218  are move toward the TDC position, the gases within the combustion chamber of the left piston pair  218  are compressed for an ignition process such as auto-ignition or spark drive ignition. The second combustion event returns the left piston pair  218  to the BDC position while pushing the right piston pair  220  to the TDC position. The two combustion chambers of the two piston pairs  218 ,  220  can be fired alternatively to keep the inner pistons  212  and outer pistons  216  moving linearly in a reciprocal fashion. 
         [0045]    As depicted in  FIG. 10 , in an example, the hydraulic block for the FP engine  210  includes a plurality of hydraulic pumps  222 ,  224 ,  226 . As shown in the figure, the right-hand chambers of pumps  222 ,  224 , and  226  are coupled together by fluid lines. In certain examples, at least two of the hydraulic pumps  222 ,  226  are each operably connected to the outer pistons  216  by side push rods  228 . Similarly, at least one hydraulic pump  224  is operably connected to the inner pistons  212  by the connection rod  214 . In an example, inner hydraulic pump  224  has a plunger area equal to the combined plunger area to the outer hydraulic pumps  222 ,  226 . 
         [0046]    As depicted in  FIG. 10 , as the outer piston  216  of the left piston pair  218  is pushed toward the TDC position, hydraulic fluid is pushed from the right chambers of outer hydraulic pumps  222 ,  226  into a high pressure source or accumulator  230 . In this configuration, the kinetic energy of the outer hydraulic pumps  222 ,  226  is converted into hydraulic energy stored in the high pressure accumulator  230 . Similarly, the movement of the inner pistons  212  also causes hydraulic fluid to be drawn into the right chamber of the inner hydraulic pump  224  from a low pressure source or accumulator  232 . Upon reversal of movement, the outer piston  216  of the left piston pair  218  move toward the BDC position, hydraulic fluid is pulled into the right chambers of outer hydraulic pumps  222 ,  226  from the low pressure accumulator  232 , wherein a valve  234 , sometimes referred to as a Lee valve, is used to control such synchronization. Similarly, a valve  236  directs fluid from the right chamber of the inner hydraulic pump  224  toward the high pressure source  230 . 
         [0047]    As depicted in  FIG. 10 , a valve  238 , such as a Moog-type valve, can be used to switch between the engine operating modes. That is, between the engine motoring mode, during which hydraulic energy, such as that stored in the high pressure accumulator  230 , can be used to influence the pistons  212 ,  216  to achieve a desired piston trajectory. When the valve  238  is at its bottom position depicted in  FIG. 10  (that is, the fluid passages are both open and crossing), high pressure fluid, as hydraulically connected such as illustrated by hydraulic lines  240 , is directed into the left chamber of the inner piston pump  224  to push the inner piston  212  of the right piston pair  220  toward TDC and compressing fluid in the right chamber of the inner hydraulic pump  234 . The movement of the inner hydraulic pump  224  also causes the outer pump  222 ,  226  to move to compress fluid in the left chambers in the outer pumps  222 ,  226 . However, when the valve  238  is at its top position depicted in  FIG. 10  (lines are open and uncrossed), the hydraulic forces change direction and moves the piston pairs  218 ,  220  in the opposite direction. The engine is switched to a pumping mode during which the fluid in the hydraulic chambers are pumped into the high pressure accumulator  230  when the valve  238  is at its middle position. The low pressure side is also illustrated with appropriate hydraulic lines  242  to provide fluid as needed on either side of each hydraulic pump  222 ,  224  and  226  for adjusting the oscillation of the pumps  222 ,  224  and  226  and correspondingly the oscillation of the left piston pair  218  and the right piston pair  220 . 
       Operation Example 
       [0048]    In an example, a control algorithm according to the present subject matter is implemented on the hydraulic free-piston engine, and the result of single-occurrence combustion on the left combustion chamber, such as depicted in  FIG. 10 , is depicted in  FIGS. 11A-11B .  FIG. 11A  depicts the pressure within the combustion chamber illustrating ignition detection while  FIG. 11B  depicts the piston position illustrating a shifted reference trajectory relative to the actual piston trajectory to avoid tracking errors from the combustion event. 
         [0049]    Multi-occurrence combustion events having varying combustion conditions validate the robustness of the control algorithm. Due to the design of certain combustion systems, the gas mixing condition of each cycle can vary, which can mean that the combustion timing and combustion strength can also vary. However, the control algorithm is able to detect the transient period following a combustion event and adjust the control signal to avoid excessive tracking errors or an outer-of-phase control signal resulting from a misalignment of the reference trajectory of the control signal from the actual piston trajectory. 
         [0050]      FIGS. 12A-12B  depicts the result of firing on both sides of the FP engine  210  such as depicted in  FIG. 10 . Four injection events were scheduled alternating between the right piston pair  220  and the left piston pair  218 . The first combustion occurs at around 3.42 s when right side reaches its TDC, then around 3.44 s when the left piston pair  218  reaches TDC, a second combustion can be observed. The third combustion occurs around 3.46 s, and the last combustion occurs around 3.48 s. The control algorithm disclosed herein detected all four combustion events and applied the reference shifting accordingly, such that the effects of shifting of the actual piston trajectory from the combustion events were minimized and thereby permitting continuous firing. 
         [0051]    Each of these non-limiting examples can stand on its own, or can be combined in any permutation or combination with any one or more of the other examples. 
         [0052]    The above detailed description includes references to the accompanying drawings, which form a part of the detailed description. The drawings show, by way of illustration, specific embodiments in which the present subject matter can be practiced. These embodiments are also referred to herein as “examples.” Such examples can include elements in addition to those shown or described. However, the present inventors also contemplate examples in which only those elements shown or described are provided. Moreover, the present inventors also contemplate examples using any combination or permutation of those elements shown or described (or one or more aspects thereof), either with respect to a particular example (or one or more aspects thereof), or with respect to other examples (or one or more aspects thereof) shown or described herein. 
         [0053]    In the event of inconsistent usages between this document and any documents so incorporated by reference, the usage in this document controls. 
         [0054]    In this document, the terms “a” or “an” are used, as is common in patent documents, to include one or more than one, independent of any other instances or usages of “at least one” or “one or more.” In this document, the term “or” is used to refer to a nonexclusive or, such that “A or B” includes “A but not B,” “B but not A,” and “A and B,” unless otherwise indicated. In this document, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Also, in the following claims, the terms “including” and “comprising” are open-ended, that is, a system, device, article, composition, formulation, or process that includes elements in addition to those listed after such a term in a claim are still deemed to fall within the scope of that claim. Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. 
         [0055]    Method examples described herein can be machine or computer-implemented at least in part. Some examples can include a computer-readable medium or machine-readable medium encoded with instructions operable to configure an electronic device to perform methods as described in the above examples. An implementation of such methods can include code, such as microcode, assembly language code, a higher-level language code, or the like. Such code can include computer readable instructions for performing various methods. The code may form portions of computer program products. Further, in an example, the code can be tangibly stored on one or more volatile, non-transitory, or non-volatile tangible computer-readable media, such as during execution or at other times. Examples of these tangible computer-readable media can include, but are not limited to, hard disks, removable magnetic disks, removable optical disks (e.g., compact disks and digital video disks), magnetic cassettes, memory cards or sticks, random access memories (RAMs), read only memories (ROMs), and the like. 
         [0056]    The above description is intended to be illustrative, and not restrictive. For example, the above-described examples (or one or more aspects thereof) may be used in combination with each other. Other embodiments can be used, such as by one of ordinary skill in the art upon reviewing the above description. The Abstract is provided, to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. Also, in the above Detailed Description, various features may be grouped together to streamline the disclosure. This should not be interpreted as intending that an unclaimed disclosed feature is essential to any claim. Rather, inventive subject matter may lie in less than all features of a particular disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description as examples or embodiments, with each claim standing on its own as a separate embodiment, and it is contemplated that such embodiments can be combined with each other in various combinations or permutations. The scope of the present subject matter should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.