Abstract:
A control device of a piston pump unit comprising at least two piston-cylinder units that operate in a phase-shifted manner for the purpose of liquid chromatography and to a piston pump unit is described. The control device corrects fluctuations of the system pressure while switching from one piston cylinder unit to the respective other piston cylinder unit. The fluctuations can occur as a result of the cooling of the liquid medium that is heated in an adiabatic manner during a pre-compression phase in the working piston. The control unit controls the piston speed of at least one piston-cylinder unit during the transition phase depending on at least one characteristic, which is ascertained from chronologically previously detected pressure values, such that variations of the system pressure as a result of the cooling of the adiabatically heated medium are at least partially compensated for.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a United States National Stage Application, under 35 U.S.C. §371, of International Application PCT/DE2012/100193, filed Jul. 2, 2012, entitled “Device for controlling a piston pump unit for liquid chromatography,” which claims the priority benefit to German Patent Application No. 10 2011 052 848.2, filed Aug. 19, 2011, entitled “Device for controlling a piston pump unit for liquid chromatography,” which applications are hereby incorporated herein by reference in their entireties. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The invention relates to a device for controlling a piston pump unit for liquid chromatography, in particular for high-performance liquid chromatography (HPLC). Furthermore, the invention relates to a piston pump unit having such a control device. 
       BACKGROUND 
       [0003]    Pumps for HPLC are to deliver the lowest possible pulsation or even completely pulsation-free flow under high pressure. For this purpose, pumps are used which operate according to the displacement principle using cyclically acting pistons. To bridge the period of time of the intake, pumps are used having a first and second head or a first and second piston-cylinder unit. Both piston-cylinder units can be arranged in parallel from a fluidic aspect, wherein the drives for the pistons are activated such that one piston always delivers while the other piston suctions. Such an arrangement is described, for example, in U.S. Pat. No. 4,752,385 A. 
         [0004]    Instead, the two piston-cylinder units can also be arranged in series in a fluidic aspect, wherein the drives for the pistons are activated in this case such that during an intake phase of the first piston, the second piston delivers and during the intake phase of the second piston, the first piston delivers and simultaneously the cylinder volume of the second piston-cylinder unit fills. Such a pump unit is described, for example, in U.S. Pat. No. 4,681,513 A. 
         [0005]    In both variants of double-piston pumps, the problem exists that, during the changeover from one piston-cylinder unit to the respective other piston-cylinder unit, for various physical and technical reasons, a drop can occur in the profile of the system pressure measurable at the outlet of the pump unit (and therefore also of the flow) or deviations can occur of the actual profile of the system pressure or the flow from a desired (idealized) constant system pressure or flow. One cause of this can be heating of the liquid medium to be delivered during a substantially adiabatic compression. This problem will be explained hereafter on the basis of the example of a serial double-piston pump according to  FIG. 1 . 
         [0006]      FIG. 1  shows the components essential for the understanding of a serial double-piston pump  1  unit in a schematic view. The double-piston pump unit  1  consists of a first piston-cylinder unit  3  having a cylinder or working head  10 , in which a working piston  11  is arranged so it is displaceable. The seal to the outside is produced by a seal  17 . The working head  10  has an inlet valve  15  and an outlet valve  16 , which are connected such that liquid can be suctioned in via an inlet connection  14  and relayed via a connecting line or capillary  24 . A pressure sensor  13  can be arranged in or on the working head  10  to detect the pressure in the cylinder volume of the working head  10 . The free volume  12  of the working head can be decreased by a displacement of the working piston  11  forward, i.e., to the right in  FIG. 1 , or enlarged by a movement in reverse, i.e., to the left in  FIG. 1 . The drive device necessary for this purpose is not shown in  FIG. 1  for the sake of clarity. Furthermore, the double-piston pump unit  1  comprises a second piston-cylinder unit  5  having a cylinder or equalizing head  20 , an equalizing piston  21 , a seal  27 , a free volume  22 , and a pressure sensor  23 . The equalizing head is connected without valves directly to the connecting capillary  24  and an outlet capillary  30 , which forms an outlet port, and which provides the delivered liquid for the HPLC system. Since the connecting capillary  24 , the equalizing head  20 , and the outlet capillary  30  are directly connected to one another in a fluidic aspect, the same pressure prevails in each of these parts, which is designated hereafter as the system pressure. 
         [0007]    The double-piston pump unit  1  shown in  FIG. 1  typically operates cyclically, to produce a continuous flow at the outlet. In a first phase of the pump cycle, which is designated as the intake phase, the working piston  11  moves in reverse and suctions liquid out of a solvent reservoir, while the equalizing piston  21  moves forward and therefore maintains the flow at the outlet port of the pump unit or the system pressure. During the intake phase, the inlet valve  15  is open and the outlet valve  16  is closed. The intake phase ends shortly before the equalizing piston  21  has reached the forward end point of its working path and therefore cannot deliver any further liquid. 
         [0008]    In a second phase following the intake phase, which is designated as the pre-compression phase, the working piston  11  moves forward to bring the previously suctioned-in liquid to the same high system pressure which prevails at the outlet port  30  of the pump unit  1  and in the free volume  22  of the equalizing head  20 . The inlet valve  15  closes. The outlet valve  16  initially also remains closed. This procedure is designated as pre-compression, since the liquid must be considered to be compressible at the high pressures typical in HPLC. During the pre-compression, the equalizing piston  21  furthermore maintains the flow or system pressure. The pre-compression phase ends when the pressure in the working head  10  has reached the system pressure, so that the outlet valve  16  opens and both free volumes  12  and  22  are connected to the outlet capillary  30  (it is to be noted here that the valves  15 ,  16  are implemented as check valves). During the pre-compression phase, the working piston  11  covers a pre-compression path, which is dependent on the compressibility of the liquid and on the pressure in the equalizing head  20  (i.e., the system pressure). 
         [0009]    In a subsequent third phase, the outlet valve  16  is open, so that both the movement of the equalizing piston  21  and also of the working piston  11  contribute to the total flow provided at the outlet port  30  of the pump unit  1 . To avoid an undesired increase of the total flow, the piston speeds must therefore be adapted such that the desired total flow again results in sum at the pump outlet. The way this is precisely performed is dependent on the precise technical implementation of the pump. In any case, the equalizing piston  21  must be retracted in a timely manner before beginning the next pump cycle or the next intake phase to fill the equalizing head  20  again. This is performed in pumps according to the prior art either in the third phase or an additional fourth phase. For the understanding of the invention, it is only decisive that the flow provided at the pump outlet in the third phase and optionally fourth phase is dependent on the sum (having the correct sign) of the two piston speeds. The phases following the pre-compression phase are generally designated hereafter in summary as the delivery phase independently of the precise technical implementation. 
         [0010]    It is problematic in such cyclically operating double-piston pump units, independently of whether they are parallel or serial pump units, that during the pre-compression, compression work is carried out on the liquid, which is located in the free volume  12  of the working head  10 , which can result in heating of this liquid if the pre-compression occurs so rapidly that sufficient heat dissipation cannot occur during the pre-compression phase. This compression work is greater the higher the pressure and the compressibility of the liquid are. Therefore, the pre-compressed liquid in the working head  10  is warmer after the pre-compression than the working head  10  and the working piston  11 . 
         [0011]    After the pre-compression, no further compression work is supplied, since the pressure in the free volume  12  of the working head  10  remains substantially constant after the opening of the outlet valve  16 . The previously heated liquid cools down especially at the beginning of the delivery phase by the contact with the surrounding components of the pump, so that its volume decreases. 
         [0012]    This volume contraction decreases the flow provided in this time, which results in a temporary drop of the provided flow or the system pressure. This repeats with each pump cycle and is noticeable overall as an undesired periodic flow pulsation or pressure pulsation at the outlet port of the pump unit. In the case of high-pressure gradient pumps, in which different solvents are mixed by multiple individual pumps, such pulsations are additionally noticeable as variations of the solvent composition. All of these effects result in worsening of the chromatographic reproducibility, which represents an important criterion for the quality of a chromatography system. 
         [0013]    Heretofore, various possibilities have been proposed to reduce the pulsation produced by heating of the liquid medium to be delivered during the pre-compression phase and subsequent cooling during the delivery phase. A method is described in GB 2 446 321 A, in which the problem is avoided in that the cooling procedure is displaced to a point in time at which no interfering effects are still to be expected. For this purpose, a sufficiently long waiting time is incorporated in the pre-compression phase after approximately 90-95% of the pre-compression to permit the liquid to cool again. Since the outlet valve is still closed at this point in time, the volume contraction does not have an effect on the flow or pressure provided at the pump outlet. After the cooling, the remainder of the pre-compression is executed and the liquid is pumped into the system with thermal equilibrium. 
         [0014]    This solution has the disadvantage that a specific minimum waiting time is necessary, since the duration of the cooling is primarily determined by the heat conduction of the material of the piston chamber and the liquid. These must be dimensioned such that the liquid also cools down sufficiently strongly under unfavorable circumstances to avoid the problem. This waiting time lengthens the pre-compression phase and therefore the cycle time of the pump. This decreases the maximum flow rate of a pump. 
         [0015]    Furthermore, this solution necessarily requires a measurement of the pressure in the working head, which means additional expenditure. In addition, this solution can only be applied if the drives for working piston and equalizing piston are independent, which also results in additional expenditure. 
         [0016]    US 2010/0275678 A1 describes a method using a pressure controller, which is to equalize the pressure drop by appropriately superimposed piston movements. For this purpose, the time profile of the system pressure at the pump outlet is already recorded before the expected pressure drop, i.e., for example, in the intake phase and/or pre-compression phase, and an expected pressure profile in a time window at the beginning of the delivery phase is calculated therefrom. At the beginning of the delivery phase, a pressure controller is then activated, which controls the piston speeds in a certain time interval such that the actual pressure profile corresponds to that expected. 
         [0017]    This solution has the disadvantage that the pressure controller reacts sensitively with respect to interference from the outside, i.e., with respect to externally induced deviations from the expected pressure profile. These can be caused by the other pumps in the case of a high-pressure gradient pump assembly, for example. This must be avoided by a synchronization of the individual pumps, so that the method cannot be applied to conventional high-pressure gradient pumps having camshaft drive. 
         [0018]    The equalizing of pulsations after the pre-compression by a pressure controller is also described in GB 2 433 792 B. This patent corresponds to the basic concept of above-discussed US 2010/0275678 A1. In addition, however, it is proposed here that a flow resistance be incorporated between working head and equalizing head to decouple the pressure in the working head from the pressure in the equalizing head. 
         [0019]    This solution also has the above-described disadvantages. The use of an additional flow resister additionally causes the disadvantage that its effect is strongly dependent on the respectively set pump flow. 
       SUMMARY 
       [0020]    Proceeding from the above-mentioned prior art, the invention is based on the object of providing a device for controlling a piston pump unit for liquid chromatography, in particular for high-performance liquid chromatography, which avoids or strongly reduces flow pulsations or pressure pulsations or variations of the solvent composition, which are caused by thermal effects arising during the compression phase and during the subsequent part of the delivery phase, in a simple manner. Furthermore, the invention is based on the object of providing a multiple-piston pump unit having such a control device. 
         [0021]    The invention proceeds from the finding that the action of the thermal effects, which result in the undesired flow pulsation or pressure pulsation, can be ascertained beforehand and then compensated for by appropriately corrected piston speeds. The piston speeds are corrected by a previously calculated correction amplitude, so that the undesired flow pulsation or pressure pulsation is substantially avoided. The control unit is implemented to detect the pressure of the medium in at least one of the piston-cylinder units during the pre-compression phase and/or to detect the system pressure during the part of the delivery phase in which the cooling of the adiabatically heated medium can result in influence of the flow. The pressure detection can be used by means of typical pressure sensors, which have a fluidic connection to the relevant piston-cylinder unit. The control unit controls the piston speed of at least one piston-cylinder unit during the transition phase, in which a pressure drop would result without a correction, depending on at least one characteristic, which is ascertained from chronologically previously detected pressure values, such that variations of the system pressure as a result of the cooling of the adiabatically heated medium are at least partially compensated for. 
         [0022]    Since suitable pressure sensors are provided in practically all already known multiple-piston pumps and these pumps also have program-controlled control units, the invention can also be implemented in existing pumps in the form of a software update or firmware update. A hardware modification of the pumps is typically not necessary for this purpose. 
         [0023]    The control according to the invention does not require a complex control mechanism, which can additionally also be accompanied by the risk that instabilities of the control loop will occur upon the occurrence of external interfering influences. 
         [0024]    In addition, the invention can be implemented in a simple manner such that interfering pulsations are reduced or completely avoided automatically and independently of the physical properties of the liquid used. 
         [0025]    According to one embodiment of the invention, the control unit, while using the at least one characteristic, can ascertain a correction guideline for the control of the piston speed of at least one of the piston-cylinder units during the transition phase, which determines the flow during the transition phase, wherein the correction guideline is preferably superimposed by addition on an activation guideline for the relevant piston, which does not consider compensation of the cooling of the adiabatically heated medium. The thermal influence to be reduced can therefore be integrated in a simple manner in an existing guideline for activating the drive device for the piston. 
         [0026]    The correction guideline can comprise a decreasing exponential function of the type v k =c·exp [(t−t 2 )/τ] or of the type v k =c·exp [(x−x II )/ε], wherein t 2  designates the chronological beginning of the transition phase of the delivery phase, c designates the amplitude of this correction function at the point in time t=t 2 , τ designates the time constant of the correction function, x designates the position of the piston, and x II  designates the starting position for the transition phase of the delivery phase. 
         [0027]    The correction guideline can also comprise a substantially ramped or stepped function, which has a sudden or ramped increase, a middle region having a substantially constant value of a determined maximum amplitude, and a sudden or ramped decrease. It has surprisingly been shown that in particular while using such a sudden or ramped function in addition to a decreasing exponential function, the drop of the pressure or flow may be corrected by means of a simple controller without closed control loop. 
         [0028]    The front flank of the ramped or stepped function can be permanently associated with a predefined piston position. This can be determined by means of simulation or also empirically. This is also true for the width of the ramped or stepped function. 
         [0029]    According to one embodiment of the invention, the control unit detects the pressure of the medium in the cylinder volume of the compressing piston-cylinder unit in an initial phase of the compression phase, in which substantially no heating of the medium by the adiabatic compression has yet occurred, and extrapolates the pressure profile as a function of the time or the position of the relevant piston. Subsequently, the control unit calculates the point in time t 1  or the position of the piston x I , at which this extrapolated curve, which represents an isothermal profile, reaches a value for the system pressure which would result in the case of an idealized isothermal compression at the end of the compression phase. The control unit can then ascertain the point in time t 2  or the position x II  of the relevant piston at which the pre-compression phase is ended, and can use, as a characteristic for determining the at least one parameter of the correction guideline, the difference of the calculated time t 1  and the detected time t 2  or the difference of the calculated position x I  and the detected position x II . 
         [0030]    In this case, the control unit, for determining the point in time t 1  or the position of the piston x I , at which the extrapolated curve reaches the value for the system pressure, which would result in the event of an idealized thermal compression at the end of the compression phase, can detect the system pressure of the medium prevailing at the outlet of the pump unit in a range before the beginning of the delivery phase depending on the time or on the position of the piston, and extrapolate it, preferably linearly, and determine the intersection point of this extrapolated curve for the system pressure with the calculated curve, which represents the isothermal profile, for the pressure in the relevant volume of the compressing piston-cylinder unit. 
         [0031]    According to another variant, the control unit, to determine the point in time t 1  or the position of the piston x I , at which the extrapolated curve reaches the value for the system pressure, which would result in the case of an idealized, thermal compression at the end of the compression phase, can also use a constant value for the system pressure, which is supplied to the control unit or which the control unit detects during the compression phase, preferably shortly before the end of the compression phase. 
         [0032]    According to a further embodiment of the invention, the control unit, to determine the point in time t 2  or the position x II  of the relevant piston, can detect the pressure during the pre-compression phase depending on the time or on the position of the piston in a range in which the influence of the heating is displayed, preferably until a point shortly before the end of the compression phase, and can extrapolate this pressure profile. The control unit can detect the system pressure of the medium, which prevails at the outlet of the pump unit, in a range before the beginning of the delivery phase depending on the time or the position of the piston and extrapolate it, preferably linearly, and determine the point in time t 2  or the position x II  of the relevant piston from the relevant intersection point of the two extrapolated curves for the system pressure and the pressure in the volume of the relevant piston-cylinder unit. The control unit preferably ascertains the correction guideline before the end of the pre-compression phase and uses this to control the drive device during the directly following delivery phase. 
         [0033]    The above-mentioned variants for determining the parameters for the correction guideline have the advantage that all parameters can be determined already immediately before a coming pressure drop, so that the immediately following pressure drop can already be corrected by control. 
         [0034]    According to another alternative, the control unit can detect the system pressure of the medium during the transition phase, in which the cooling of the medium heated during the compression phase occurs, and can use the deviation of the system pressure, which is detected during the transition phase, from an idealized system pressure as the characteristic for determining the at least one parameter of the correction guideline. 
         [0035]    The control unit can determine the idealized system pressure during the transition phase according to one of the following alternatives: 
         [0036]    the control unit uses a constant value for the system pressure, which is supplied to the control unit or which the control unit detects during the compression phase, preferably shortly before the end of the compression phase; 
         [0037]    the control unit detects the system pressure of the medium, which prevails at the outlet of the pump unit, in a range before the beginning of the delivery phase depending on the time or the position of the piston and extrapolates the pressure profile thus detected, preferably linearly. 
         [0038]    According to one embodiment of the invention, the control unit can determine the maximum deviation of the detected system pressure from the idealized system pressure and can determine at least one parameter of the correction guideline depending on the maximum deviation. 
         [0039]    In the case of these variants, the control unit can use the correction guideline thus ascertained in the control of the drive device during at least one delivery phase, which follows the delivery phase, the transition phase of which is used to determine the at least one parameter of the correction guideline. 
         [0040]    The control unit can preferably determine the value of the at least one parameter iteratively in such a manner that in transition phases of successive cycles, preferably directly successive cycles, respectively one value for the relevant parameter is determined and combined by computer, preferably added with the correct sign. 
         [0041]    If an exponential function is used to correct the pressure drop, as described above, the control unit can determine the amplitude c of the exponential function depending on the at least one characteristic. If a ramped or stepped (i.e., a rectangular) function is additionally used, the control unit can thus determine the maximum amplitude of the ramped or stepped function proportionally to the amplitude c of the exponential function. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0042]    The invention will be explained in greater detail hereafter on the basis of exemplary embodiments shown in the drawing. In the drawing. 
           [0043]      FIG. 1  shows a schematic illustration of the essential components of a serial double-piston pump according to the prior art; 
           [0044]      FIG. 2  shows a schematic illustration of the essential components of a serial double-piston pump having a control unit according to the invention; 
           [0045]      FIG. 3  shows a diagram of the pressure in the volume of the working cylinder and in the volume of the equalizing cylinder as a function of time to explain a first alternative of the invention; 
           [0046]      FIG. 4  shows a diagram of the piston speeds (added with the correct sign) as a function of the time for the correction guideline of the variant according to  FIG. 3 ; 
           [0047]      FIG. 5  shows diagrams for the pressure p, the correction amplitude c, and the difference Δc of the correction amplitudes of respectively two successive pump cycles for a second alternative of the invention. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0048]    The serial double-piston pump unit shown in  FIG. 2  substantially corresponds with respect to hardware to the known serial double-piston pump  1  shown in  FIG. 1 . Therefore, identical reference signs are used for identical components and parts. The refinement according to the invention is located in particular in a control unit  32  shown in  FIG. 2 , which can comprise a processor-controlled controller unit having suitable software or firmware in a conventional manner. Since known pump units also typically have such flexibly configurable control units, and the control according to the invention is implementable by software or firmware, the invention can also be integrated in existing pump units and also retrofitted if necessary. 
         [0049]    The signals of the pressure sensors  13  of the first piston-cylinder unit  3  and of the second piston-cylinder unit  5  are supplied to the control unit  32  of the pump unit  1  in  FIG. 2 . The control unit  32  can analyze these sensor signals in the manner described hereafter and, depending thereon, can activate a drive device  34 , which is mechanically coupled to the pistons to be driven, i.e., the working piston  11  and the equalizing piston  21 , such that the pistons  11 ,  21  are moved forward or in reverse at a predetermined speed. 
         [0050]    To solve the problem described at the beginning, of avoiding a pressure drop as a result of cooling of the liquid medium, which is heated in the pre-compression phase and is to be delivered by the pump unit, the control unit detects the pressure or pressure profile (depending on the time or the position of the relevant piston) and ascertains parameters of a correction guideline therefrom, which is used to control the piston speed during the phase in which the pressure drop would occur without correction. 
         [0051]    Two specific solution variants according to the invention are to be described in more detail hereafter, which originate from this general solution: 
         [0052]    The first solution variant will be explained on the basis of  FIG. 3 , which illustrates the profile of the pressure in the volume of the first or second piston-cylinder unit  3 ,  5 , respectively. It is suitable for pumps which respectively have a separate pressure sensor for the pressure  42  in the working head and for the system pressure  40  at the outlet port of the pump unit. The system pressure can of course be detected at arbitrary locations which are fluidically connected to the outlet port without a relevant fluidic resistance having to be considered. In  FIG. 3 , these are the sensors  13  and  23 . 
         [0053]    This variant proceeds from the finding that during a rapid compression of a liquid to high pressure, as occurs in the pre-compression phase, a substantially adiabatic state change occurs, since the resulting compression heat is only dissipated in a very small part in the short time. In contrast, if one observes only a slight compression, the temperature of the liquid hardly changes, so that the state change can be considered to be nearly isothermal, even if the compression occurs rapidly. 
         [0054]    As a result, during the pre-compression phase, as a result of the rapid compression, the pressure increase in the lower pressure range runs approximately isothermally, and the adiabatic state change is only noticeable at higher pressures. The difference between isothermal and adiabatic state change is ascertained according to the invention by analysis of the actual pressure profile as a function of the performed compression. This is explained hereafter as an example on the basis of  FIG. 3 . 
         [0055]      FIG. 3  shows, as a function of time, several pressure profiles in the working and equalizing heads  10 ,  20  during the pre-compression phase and also shortly before and after. In this example, it is presumed that the pre-compression occurs linearly, i.e., at constant piston speed. 
         [0056]    Until the point in time t 0 , the pump unit  1  is in the intake phase. During this, the pressure in the working head  10  corresponds to the ambient pressure or zero and is therefore coincident with the time axis. The system pressure p sys  is assumed to be constant in this example during the intake phase and pre-compression phase. This is indicated by the line  40 . 
         [0057]    The pre-compression phase begins at the point in time t 0 . At this point in time, a well-defined liquid quantity is located in the volume  12  of the working head, and both valves  15  and  16  are closed. Proceeding from this point, the liquid is compressed in the working head. 
         [0058]    In a hypothetical, isothermal case, i.e., without consideration of heating, the pressure would rise linearly corresponding to curve  43 , presuming a linear pre-compression, i.e., a movement of the working piston at constant speed. In this case, the pressure in the working head at a point in time t 1  would reach the system pressure p sys . At this point in time, the outlet valve would open and the delivery phase begins, as described above. 
         [0059]    In the real case, an adiabatic state change occurs during the pre-compression, since the liquid in the volume  12  of the working head  10  heats up due to the pre-compression. Because the volume in the working head  10  is determined by the piston position at every point in time between t 0  and t 1 , the temperature increase as a result of the lack of a possibility for volume expansion results in an additional pressure increase, so that the pressure profile in the working head follows the profile  42  in  FIG. 3 . The pressure rises more strongly than would be expected in the case of isothermal observation. Therefore, the pressure in the equalizing head is already reached at an earlier point in time t 2 . At the point in time t 2 , the valve  16  opens and the delivery phase begins, as described above. The heated liquid is transferred via a connecting line  24  from the working head  10  into the equalizing head  20 . Since no further compression work is supplied to the liquid, it now cools again due to contact with the surrounding, cooler components of the pump unit  1 . A volume contraction occurs during this, which reduces the total flow provided at the pump outlet port  30  and, without further measures, would result in a pressure drop according to the curve part  45  in  FIG. 3  at the beginning of the delivery phase. 
         [0060]    To avoid such a pressure drop, the difference between the points in time t 1  and t 2  is determined in this first variant. The point in time t 2  can be ascertained in a simple manner by extrapolation of the real pressure profile, since at this point in time the curve  42  (i.e., the detected pressure profile during the compression phase) reaches the system pressure p sys . This is known per se and has already been used for some time. The point in time t 1  results from the hypothetical, isothermal case, and can also be ascertained from the real pressure profile according to curve  43 . This is possible, since in the lower pressure range, no noteworthy heating has yet occurred and therefore, in this range, the curve  42  and the curve  43  run nearly identically. Thus, a measuring interval t 3  to t 4  can be established, in which the pressure is between a lower pressure p 3  and an upper pressure p 4 , wherein, even at the selected pressure p 4 , no relevant temperature increase can yet have occurred as a result of the provided compression work. In principle, the pressure p 3  can be selected to be equal to the ambient pressure. In this case, t 3 =t 0  would then be the case. 
         [0061]    Expediently, however, the pressure p 3  is selected to be at least somewhat greater than the ambient pressure, since in this way the influence of interfering effects such as air bubbles or mechanical play of the drive, for example, can be reduced. The pressure p 4  is selected to be significantly greater than p 3 , however, as mentioned above, at most sufficiently large that adiabatic heating effects are still negligible. Reasonable values for p 3  are in the range from 2 MPa to 10 MPa, in particular between 7 MPa and 10 MPa. Reasonable values for p 4  are between 10 MPa and 20 MPa, in particular between 12 MPa and 15 MPa. Of course, these values are also dependent to a certain extent on the type of the liquid. 
         [0062]    The pressure profile in the measuring interval t 3  to t 4  is linearly extrapolated to obtain the curve  43 , which corresponds to an isothermal state change. The extrapolation line can be calculated using the conventional mathematical methods (for example, linear approximation) from the pressure profile in the measuring interval. In the simplest case, only the measurement points at the beginning and at the end of the measurement interval are considered for this purpose. The intersection point of the extrapolation line or curve  43  with the system pressure p sys  corresponds to the point in time t 1  to be determined. 
         [0063]    The time difference Δt=t 1 −t 2  is a measure of the heating of the liquid during the pre-compression and therefore a measure of the pressure drop to be expected as a result of the cooling and can therefore be used to calculate a correction amplitude c of the piston speed. This correction amplitude is subsequently used to increase the flow, which is provided by both pistons together, in a time interval following t 2  during the delivery phase and thus to avoid the flow drop or pressure drop  45 . 
         [0064]    The performance of the correction will be explained on the basis of  FIG. 4 . Since both pistons  11 ,  21  participate in the flow production during the delivery phase, the correction can optionally be executed using the working piston, the equalizing pistons, or both pistons. Therefore, v stands here for the sum of the two piston speeds (added with the correct sign) of working and equalizing pistons, wherein positive speeds stand for a forward movement of the piston. The movement of the two pistons produces the desired target flow. 
         [0065]    The speed v 0  according to the line  70  in  FIG. 4  is the piston speed which is necessary to produce the set flow. In the observed example, a constant flow rate is presumed, therefore this speed is constant. 
         [0066]    For the correction of the piston speed, this (uncorrected) speed or the relevant (uncorrected) speed profile (as a function of the time or the piston position) is superimposed with a correction component  71  according to  FIG. 4 . This follows a decreasing exponential function having the amplitude  76 , which is given by the correction amplitude c as a pre-exponential factor and a time constant r. The time constant r can be calculated, for example, from a polynomial function of flow and duration of the pre-compression phase or the pre-compression path. The dimension of the correction amplitude is typically between 0% and 10% of the set target flow and is reasonably between 0% and 6%. The time constant is typically in a range from 12000 ms to 200 ms, reasonably between 5000 ms and 500 ms. 
         [0067]    The exponential profile reflects the cooling procedure, which theoretically also follows a decreasing exponential function. By way of the superposition of the correction component  71 , which is determined in a suitable manner, the pressure drop  45  is equalized, so that the system pressure follows the profile  41  beyond the point in time t 2 . 
         [0068]    Experiments have shown that from a specific location position of the working piston, which is reached here at the point in time  72 , an additional improvement can be achieved by a further correction component  74 . This is a stepped or rectangular function, which is active in a specific range in the time interval  72  to  73  and has a constant value here. Since the point in time  72  corresponds to a fixed piston position, this is later the lower the set target flow. The height of the step can preferably be selected to be proportional to the above-mentioned correction amplitude c of the exponential profile of the correction component and/or additionally proportional to the system pressure p sys . It has proven to be advantageous to use, as the amplitude of the step per 100 MPa, approximately 0.9 times the previously calculated correction amplitude c. The time length of the correction component  74  preferably extends until the end of the delivery phase (point in time  73 ) or until the beginning of the following intake phase. Of course, it can however also be adapted by simulation or empirically to the respective conditions (in particular the mechanical and thermal properties of the pump unit  1 ). 
         [0069]    Instead of a solely stepped component, another shape can also be selected, which can be found by simulation or empirically. For example, a ramped function is also conceivable having a ramped increase and a similar decrease. 
         [0070]    The sum of the correction components  71  and  74  causes the pressure drop  45  to be practically completely equalized during the delivery phase. By way of the addition of the two corrections  71  and  74 , the curve  75  results for the total speed of the two pistons  11  and  21 , as shown in  FIG. 4 . 
         [0071]    This method stabilizes flow or pressure of the pump. In the case of high-pressure gradient pumps, the mixing ratio of the solvent is also maintained more stably. The chromatographic reproducibility therefore improves. 
         [0072]    Furthermore, the method does not require any additional sensors and can thus be implemented without a hardware change, solely as a firmware solution. In this way, even existing pumps can be retrofitted. A further advantage is that the method automatically functions for all conventional liquids, without specifications about material constants of the liquid being necessary. In relation to known solutions, no heat exchanger or additional flow resistance is necessary. Since a pure controller in the strict sense is used (i.e., a closed control loop is intentionally omitted), complex control technology which is susceptible to malfunction is not necessary. 
         [0073]    The second variant, which is described hereafter, for correction of the piston speed during the delivery phase, in particular in the starting phase thereof, is also suitable for those pumps in which no sensor  13  is provided for measuring the pressure in the working head. In this case, an analysis of the pressure profile  42  in the working head, as in the case of the above-described alternative, is not possible. As explained hereafter, the correction value can be ascertained on the basis of the pressure profile at the pump outlet port  30 , however (by means of the sensor  23 ). 
         [0074]    The upper curve in  FIG. 5  shows an exemplary pressure profile  50  at the pump outlet, which rises continuously here. Such pressure changes can result, for example, in that as a result of the typical gradient operation in HPLC, the viscosity of the solvent which passes the column changes and therefore the column pressure is not constant. Such an increasing curve can, depending on the conditions, also result, of course, for the above-described first alternative of the correction of the piston speed(s) in the delivery phase. Instead of a constant value for the pressure p for determining the times t 1  and t 2 , the method described hereafter of the extrapolation of the pressure profile (which is now no longer constant) for the system pressure p sys  at the outlet port  30  can then be used. 
         [0075]    In the second alternative for the correction of the piston speed according to  FIG. 5 , in each case shortly before the end of the first pre-compression phase, the profile of the pressure  50  at the pump outlet is measured via the sensor  23 , linearly approximated, and extrapolated. This respectively results for the beginning of the following delivery phase of an expected, extrapolated pressure profile  541 . At the beginning of the delivery phase, a difference  531  of detected or measured pressure  511  and the extrapolated pressure profile  541  is calculated, which results from the pressure drop  561 . This difference  531  can be positive or negative, since instead of a pressure drop, a pressure overelevation can also occur (in particular in the event of an overcorrection). 
         [0076]    The pressure difference  531  is, similarly to the procedure in the case of the above-described first alternative, used as a measure for the determination or calculation of a correction amplitude c (see the curve  55  for the correction amplitude c in  FIG. 5 ) or for the determination of a change c (see the curve  52  for the change c in  FIG. 5 ) of a correction amplitude c already ascertained depending on the preceding pump cycle. In the case shown in  FIG. 5 , the pressure drop  561  is the first pressure drop occurring in the pressure profile  50 , which is considered for the correction method. Accordingly, the values for the correction amplitude c and the change thereof are still equal to zero before the point in time at which the pressure difference  531  is detected. This pressure drop  561  therefore still penetrates completely without a correction, since a correction can always first occur according to this alternative for the pressure drop which follows the pressure drop which is analyzed to determine the relevant correction guideline. The correction amplitude c or  521  is therefore still equal to zero before the pressure drop  561 . 
         [0077]    The amplitude change c, which is determined based on the pressure drop  561  or the detected pressure difference  531 , is added to the current value of the total amplitude c to determine the total amplitude c (or optionally used to calculate the amplitude value c according to another mathematical guideline). This results in the value  521  shown in  FIG. 5  for the change c of the correction amplitude. The value  551  for the correction amplitude c is still also equal to the value  521  for c at this point in time, since c was previously still equal to zero. The value  521  for c is used to correct the pressure drop to be expected in the next pump cycle. The correction guideline, which preferably consists of the combination of the exponentially decreasing component with the stepped component, is also determined using the value for c, as in the case of the above-described first alternative. As a result of the correction, the next pressure drop  562  shown in  FIG. 5  already results as substantially less. 
         [0078]    The above-described method is now again applied. The extrapolated pressure profile  542  is compared to the measured pressure profile  512  of the next pressure drop  562 . A correction amplitude change c, which is designated with  522  in  FIG. 5 , is again determined from the pressure difference  532 . This is added to the value  551  for the correction amplitude c (or used to calculate a total value for the correction amplitude c according to the other mathematical guideline). The new, higher value  552  for the correction amplitude c is in turn used to correct the next pressure drop  563  to be expected. 
         [0079]    This is also performed for the next pressure drop  563 . The extrapolated pressure profile  543  is compared to the measured pressure profile  513  of the pressure drop  563 . A correction amplitude change c, which is designated in  FIG. 5  with  523 , is determined from the pressure difference  533 . This is added to the value  552  for the correction amplitude c (or used to calculate a total value for the correction amplitude c according to the other mathematical guideline). The new, higher value  553  for the correction amplitude c is in turn used to correct the next pressure drop to be expected. 
         [0080]    This procedure is repeated with each cycle, wherein an iterative determination of the correction amplitude c is performed. 
         [0081]    In the simplest case, the calculation of the change c of the correction amplitude c can be performed by a proportional relationship between c and the measured pressure drop  531 ,  532 ,  533 . The factor between the measured pressure drop and the change of the correction amplitude c is then dependent on the construction of the pump, for example, the piston diameter, and on the selected units for speed and pressure. Therefore, generally valid specifications for the factor are not possible. However, the most favorable factor can be empirically ascertained and it can thus be established that an occurring pressure drop will be equalized in particular as far as possible as early as in the next cycle. 
         [0082]    During the start of the pump, it can begin, as shown in  FIG. 5 , for example with a correction amplitude c=0 (no correction). The correction amplitude is iteratively automatically optimized until the pulsation disappears by way of the changes added thereto with each cycle. If further pressure differences form, changes are again added. The time constant of the correction movement is ascertained as in the above-described first variant. The application of the correction amplitude and time constant is also performed in the same manner. 
         [0083]    Since high-pressure gradient pumps consist of two or more double-piston pumps connected in parallel, mutual influence of the individual pumps can occur here. Since high-pressure gradient pumps typically have a pressure sensor in the working head in any case, however, the above-described first alternative is preferable for them. 
         [0084]    The embodiments presented up to this point relate to an individual serial double-piston pump, as shown in  FIG. 1 . The present invention can also be applied accordingly to further embodiments of pumps known per se. 
         [0085]    The present invention may be applied not only to serial double-piston pumps, but rather also to parallel double-piston pumps, for example, as are known from the patent specification U.S. Pat. No. 4,753,581. Parallel double-piston pumps do not operate with one working piston and one equalizing piston, but rather both pistons alternately provide the flow. For this purpose, the valves  15  and  16  must be provided twice, i.e., respectively for both pump heads. The two individually produced flows of the pistons  11  and  21  are guided together after the two outlet valves  16  via a T-piece adapter, the third connection of which represents the pump outlet  30 . Parallel double-piston pumps also require a pre-compression before the relevant outlet valve  16  opens and discharges liquid to the remaining system. During and after the pre-compression, the same procedures play out as in the case of a serial double-piston pump. The correction amplitude can therefore be ascertained in the same manner as described above. 
         [0086]    The application of the calculated correction can also be performed in the same manner as described above, by correspondingly correcting the speeds of one piston or both pistons. 
         [0087]    Furthermore, the invention may advantageously be applied to multiple individual pumps connected in parallel. Each of these individual pumps can in turn optionally be implemented as a serial or parallel double-piston pump. Such a parallel connection of two or more individual pumps is used, for example, to produce and mix multiple different solvent flows (for example, high-pressure gradient pumps). The invention may then be applied to each of the participating individual pumps in the above-described manner. 
         [0088]    Both in the case of serial and also parallel double-piston pumps, both pistons can be actuated by a shared drive (for example, camshaft) or by independent drives (for example, spindle drives). In both cases, the effects of the adiabatic pre-compression are evaluated according to the invention on the basis of the pressure signals and the piston position and/or the time, as described above. In the case of pumps having a shared drive for both pistons, the correction is carried out according to the invention by changing the drive speed, whereby both piston speeds can change. In the case of pumps having independent drives, the correction can optionally be carried out with one of the two pistons or also with both pistons, in contrast. 
         [0089]    Furthermore, the invention is applicable to pumps having variable amplitude of the cyclic piston stroke. Such pumps change the stroke of the piston cycle as a function of internal control parameters, for example, the set flow rate. Piston positions are driven in a defined manner and pressures are recorded. The fundamental problem of the invention also occurs in the case of these pumps during or after the pre-compression and can similarly be solved in the same manner as described above. 
         [0090]    The pressure sensors do not necessarily have to be arranged in the pump heads for the application of the invention. Thus, for example, the pressure sensor  23  for measuring the pressure in the system does not have to be arranged directly in the equalizing head, but rather must only have a fluidic connection thereto. As a result, in the case of multiple pumps connected in parallel, a single, shared sensor is sufficient for measuring the system pressure. 
         [0091]    Instead of pressure sensors, the pressures can also be determined indirectly. For example, forces or deformations of components can be detected for this purpose and a corresponding pressure can be concluded depending on the directly detected physical variables. 
         [0092]    It is not necessary for the pre-compression to occur linearly, i.e., at constant piston speed, for the application of the invention. In the case of nonlinear embodiment of the pre-compression, deviations from a linear profile can either be taken into consideration by computer, or calculations are performed using piston positions instead of times. This is possible because for all mentioned effects, the relationship between time and pressure is less relevant than the relationship between piston position and pressure. 
         [0093]    In the practical application, this means that, for example, in  FIG. 2  on the X-axis, instead of time, the piston position is plotted, instead of the times t 0  to t 4 , calculations are then accordingly performed with piston positions x 0  to x 4 . Otherwise, nothing changes in the remaining procedure. 
         [0094]    One variant of the invention may be implemented if the pump has a fluidic connection to a further external system having piston, for example, a high-pressure injection system. In this case, the actual pump can communicate the dimension of the expected pressure drop and the point in time thereof to the external system. The pump itself does not change the piston speed. For this purpose, the external piston executes a change of its position to equalize the flow error, which would be displayed as a pressure pulsation  45  or  56 , respectively, and uses the values of the correction amplitude and time constant for this purpose for the control of the movement of this external piston. In the meaning of the present description, this external piston should be associated with the pump unit, wherein the function of a “correction piston” is transferred to the external piston (in addition to other functions possibly assigned to this piston). Thus, for example, a double-piston pump having this associated external piston (which is optionally arranged in the separate system) can be understood as a triple-piston pump or as a double-piston pump having “correction piston”, respectively. The control unit can also be distributed in this case to a control unit associated with the actual double-piston pump or multiple-piston pump and to a further control unit, which is associated with the separate system. 
         [0095]    Therefore, the present invention provides a control unit, which implements a method, using which correction parameters for influencing the piston speed(s) of a multiple-piston pump can be automatically determined from the pressure signals of the pump in a simple manner. By applying these correction parameters by means of a simple control, pulsations of the pump can be avoided or greatly reduced, without complicated pressure control loops or additional sensors or other components being necessary for this purpose. The solution according to the invention can be provided easily by firmware and can therefore also be provided for existing devices.
     1  double-piston pump unit     3  first piston-cylinder unit     5  second piston-cylinder unit     10  cylinder/working head     11  working piston     12  free volume     13  pressure sensor     14  inlet connection     15  inlet valve     16  outlet valve     17  seal     20  cylinder/equalizing head     21  equalizing piston     22  free volume     23  pressure sensor     24  connecting line or capillary     27  seal     30  outlet capillary/outlet port     32  control unit     34  drive device     40  constant pressure profile during the pre-compression phase at the outlet port     42  real pressure profile in the working head during the compression phase     43  hypothetic pressure profile in the working head with isothermal pre-compression     45  pressure drop at the beginning of the delivery phase by volume contraction as a result of cooling of the liquid   p sys  system pressure   t 0  beginning of pre-compression phase   t 1  beginning of the delivery phase with isothermal compression   t 2  beginning of the delivery phase with (at least partially adiabatic) compression   t 3  lower pressure value of the range on curve  42  for the linear extrapolation   t 4  upper pressure value of the range on curve  42  for the linear extrapolation