Patent Publication Number: US-10782205-B2

Title: Simple leakage detection in a hydraulic cylinder unit

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a 35 U.S.C. §§ 371 national phase conversion of PCT/EP2016/079582, filed Jan. 25, 2016, which claims priority of European Patent Application No. 16152531.6, filed Jan. 25, 2016, the contents of which are incorporated by reference herein. The PCT International Application was published in the German language. 
     TECHNICAL BACKGROUND 
     The present invention proceeds from a method for establishing a leakage coefficient of a hydraulic cylinder unit. The unit has a hydraulic cylinder, a piston that is displaceable in the hydraulic cylinder and a servo valve. The piston separates a first and a second working volume of the hydraulic cylinder unit from one another. The servo valve is connected to a hydraulic pump, a tank and the first and the second working volumes. 
     A pump pressure is applied to the servo valve via the hydraulic pump, and the tank has a tank pressure. 
     The servo valve is set to a defined valve position. 
     A piston position of the piston in the hydraulic cylinder and a first and a second working pressure, which are applied to the first and the second working volumes are captured. 
     Furthermore, the present invention proceeds from a computer program for an evaluation device, wherein the computer program comprises machine code that is immediately executable by the evaluation device, wherein the machine code being executed by the evaluation device causes the evaluation device to establish the leakage coefficient. 
     Furthermore, the present invention proceeds from an evaluation device for establishing a leakage coefficient of a hydraulic cylinder unit having a piston that is displaceable in a hydraulic cylinder and a servo valve, wherein the piston separates a first and a second working volume of the hydraulic cylinder unit from one another, and the servo valve is connected to a hydraulic pump and a tank on the input side and to the first and the second working volume on the output side. 
     Furthermore, the present invention proceeds from a hydraulic cylinder unit having a piston that is displaceable in the hydraulic cylinder and a servo valve. The piston separates a first and a second working volume of the hydraulic cylinder unit from one another. The servo valve is connected to a hydraulic pump and a tank on the input side and to the first and the second working volumes on the output side. 
     A pump pressure is applied to the servo valve via the hydraulic pump, and the tank has a tank pressure. The servo valve is set to a defined valve position by a control device. A piston position of the piston in the hydraulic cylinder and a first and a second working pressure, which are applied to the first and the second working volumes are captured by appropriate sensors. 
     DE 10 2007 051 857 B3 discloses a hydraulic cylinder unit having a piston that is displaceable in a hydraulic cylinder and a hydraulic valve, wherein the piston separates a first and a second working volume of the hydraulic cylinder unit from one another. The hydraulic valve is connected to a hydraulic pump and a tank on the input side and to the first and the second working volume on the output side. A pump pressure is applied to the hydraulic valve via the hydraulic pump. The tank has a tank pressure. The hydraulic valve is set to a defined valve setting. A first and a second working pressure, which are respectively applied to the first and the second working volumes and a piston position of the piston in the hydraulic cylinder are captured. 
     In DE 10 2007 051 857 B3, a linearization factor ensures a uniform operation of the hydraulic cylinder unit over the entire travel of the piston. This is established on the basis of captured, time-varying variables such as, for example, the first and the second working pressures and the piston position in conjunction with further, time-invariant variables such as the effective working faces of the piston. 
     In DE 10 2007 051 857 B3, the hydraulic valve is embodied as a two-way valve or as a four-way valve. No further statements can be found about the configuration of the hydraulic valve. 
     Sealing the two working volumes from one another is necessary in a hydraulic cylinder unit. As a rule, an appropriate seal is introduced into the piston for this purpose, in particular, a ring seal. Nevertheless, in practice, a low flow of hydraulic fluid occurs from the working volume with the respective higher working pressure to the working volume with the respective lower working pressure. This flow or leakage current is proportional to the difference of the two working pressures. The associated proportionality factor is the so-called leakage coefficient. 
     The seal introduced into the piston is subject to wear. Initially, the wear only reduces the dynamics of the hydraulic cylinder unit. However, with increasing wear, the seal may break and may cause an abrupt failure of the hydraulic cylinder unit. 
     In order to prevent such a failure of the hydraulic cylinder unit, the prior art has disclosed the practice of disassembling the hydraulic cylinder unit from time to time and replacing or at least checking the seal. This procedure, firstly, is connected to an operational interruption of the hydraulic cylinder unit and, secondly, is very complicated. 
     Furthermore, the prior art discloses providing the hydraulic cylinder unit with special additional measuring devices, in particular with flowmeters in the hydraulic feed lines to the working volumes of the hydraulic cylinder unit. Retrofitting is complicated and expensive. In new acquisitions, the additional measuring devices also present a significant cost factor. Therefore, this solution, possible in theory, is usually not taken up in practice. 
     SUMMARY OF THE INVENTION 
     The object of the present invention consists in developing options for monitoring the internal leakage of the hydraulic cylinder unit during running operation of the hydraulic cylinder unit, without requiring such special measuring devices for establishing the leakage or the leakage coefficient, i.e., the actually significant variable. 
     The object is achieved by an establishing method disclosed herein. 
     An establishing method of the type set forth at the outset is configured such that an evaluation device receives the piston position, the first and the second working pressures and the valve position, and the evaluation device establishes the leakage coefficient on the basis of the piston position, the first and the second working pressure, the valve position, the pump pressure and a value that is representative for the tank pressure in conjunction with time-invariant parameters of the hydraulic cylinder unit. 
     As a result of this procedure, it is possible to reliably establish the leakage coefficient in a simple and cost-effective manner. In particular, the piston position and the first and the second working pressure, as a rule, are required in any case for the normal operation of the hydraulic cylinder unit. Often, the valve position is also known. Should an additional sensor be required for capturing the valve position, that sensor is realizable in a cost-effective and simple manner. The value that is representative for the tank pressure can be the tank pressure as such. Alternatively, the representative value can be set to zero. This is admissible because the tank pressure is negligibly small in relation to the other employed pressures, i.e., the two working pressures and the pump pressure. 
     Establishing the leakage coefficient is possible in a particularly reliable manner by virtue of the evaluation device establishing the leakage coefficient recursively on the basis of a sequence, wherein the sequence comprises groups of values, associated in time, of the piston position, the valve position, the first and the second working pressure, the pump pressure and the value that is representative for the tank pressure. The phrase “associated in time” means that the respective values are valid for the same instant of the operation of the hydraulic cylinder unit. Recursively establishing means that, initially, a system of equations with substantially meaningful values is initialized for the leakage coefficient and internal values of the system of equations, new values for the leakage coefficient and the internal values of the system of equations are thereupon established by inserting the values of the first group, and this procedure thereupon is continued with the values of the respective next group, in each case proceeding from the values established previously. 
     Preferably, the evaluation device continuously establishes a difference between a nominal leakage coefficient and the established leakage coefficient during the operation of the hydraulic cylinder unit. In this case, it is possible, in particular, for the evaluation device to trigger an alarm as soon as the absolute value of the difference exceeds a limiting value. 
     Furthermore, the object is achieved by a computer program disclosed herein. 
     A computer program of the type set forth at the outset is configured such that the machine code executed by the evaluation device causes the evaluation device to operate. 
     The evaluation device receives a piston position of a piston of a hydraulic cylinder unit that is displaceable in a hydraulic cylinder of the hydraulic cylinder unit. The piston separates a first working volume of the hydraulic cylinder unit that is connected to a servo valve of the hydraulic cylinder unit and a second working volume of the hydraulic cylinder unit that is connected to the servo valve from one another. A first and a second working pressure are respectively applied to the first and the second working volumes, and there is a valve position of the servo valve. 
     To establish a leakage coefficient of the hydraulic cylinder unit on the basis of the piston position, the first and the second working pressures, the valve position, a pump pressure of a hydraulic pump connected to the servo valve and a value that is representative for the tank pressure of a tank connected to the servo valve in conjunction with time-invariant parameters of the hydraulic cylinder unit. 
     In a manner analogous to the establishing method, a specific embodiment of the computer program includes execution of the machine code by the evaluation device causing the evaluation device to establish the leakage coefficient recursively on the basis of a sequence, wherein the sequence comprises groups of values, associated in time, of the piston position, the first and the second working pressure, the valve position, the pump pressure and, preferably, the value that is representative for the tank pressure. 
     Likewise analogously to the establishing method, a further specific embodiment of the computer program includes execution of the machine code by the evaluation device causing the evaluation device to continuously establish a difference between a nominal leakage coefficient and the established leakage coefficient during the operation of the hydraulic cylinder unit and the evaluation device triggering an alarm as soon as the absolute value of the difference exceeds a limiting value. 
     Furthermore, the object is achieved by an evaluation device having the features disclosed herein. According to the invention, an evaluation device of the type set forth at the outset is programmed by a computer program according to the invention. 
     Furthermore, the object is achieved by a hydraulic cylinder unit disclosed herein. Specific embodiments of the hydraulic cylinder unit disclosed herein. 
     According to the invention, a hydraulic cylinder unit of the type set forth at the outset is configured such that an evaluation device receives the piston position and the first and the second working pressure from the sensors and receives the valve position from the control device or from a further sensor. The evaluation device establishes the leakage coefficient on the basis of the piston position, the first and the second working pressure, the valve position, the pump pressure and a value that is representative for the tank pressure in conjunction with time-invariant parameters of the hydraulic cylinder unit during operation of the hydraulic cylinder unit. 
     In a manner analogous to the establishing method, a specific embodiment of the hydraulic cylinder unit comprises the evaluation device being embodied such that it establishes the leakage coefficient recursively on the basis of a sequence, wherein the sequence comprises groups of values, associated in time, of the piston position, the valve position, the first and the second working pressure, the pump pressure and, preferably, the tank pressure. 
     Likewise analogous to the establishing method, a further specific embodiment of the hydraulic cylinder unit comprises the evaluation device being embodied in such a way that it continuously establishes a difference between a nominal leakage coefficient and the established leakage coefficient during the operation of the hydraulic cylinder unit and triggers an alarm as soon as the absolute value of the difference exceeds a limiting value. 
     The above-described properties, features and advantages of this invention and the manner in which they are achieved will become clearer and more easily understandable in conjunction with the following description of the exemplary embodiments, which are explained in more detail in conjunction with the drawings. Here, schematically in the figures: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a block diagram of a hydraulic cylinder unit including associated components and 
         FIG. 2  shows a flowchart. 
     
    
    
     According to  FIG. 1 , a hydraulic cylinder unit  1  has a hydraulic cylinder  2 , in which a piston  3  is movably mounted. The piston  3  is movable within the hydraulic cylinder  1  between a minimum position z min and a maximum position z max. Thus, it is situated at an actual position z that lies between the minimum position z min and the maximum position z max at all times. 
     The piston  3  has a first working face  4 A and a second working face  4 B, each respectively facing a corresponding working volume  5 A,  5 B. A first working pressure pA is prevalent in the working volume  5 A, and a second working pressure pB is prevalent in the second working volume  5 B. 
     The working volumes  5 A,  5 B are hydraulically connected to a hydraulic pump  8  and a hydraulic reservoir  9  or a tank  9  by a respective hydraulic path  6 A,  6 B and a servo valve  7 . The hydraulic paths  6 A,  6 B extend from the respective working volume  5 A,  5 B to the servo valve  7 . 
     A pump pressure pP is applied to the hydraulic liquid  10  by the hydraulic pump  8 . A tank pressure pT is prevalent in the hydraulic reservoir  9 . As a result, the pump pressure pP, the tank pressure pT and the two working pressures pA, pB are present at the servo valve  7  via the respective connector to the hydraulic pump  8 , to the tank  9  and to the working volumes  5 A,  5 B. The pump pressure pP and the two working pressures pA, pB often have high values. By contrast, the tank pressure pT is often negligibly small in relation to the other values. 
     In contrast to a proportioning valve or switch valve and given the pressure pP, pT, pA and pB, the functionality of the servo valve  7  consists of a valve position y of the servo valve  7  determining both qualitatively and quantitatively which volume flows flow via the hydraulic pump  8  to which of the working volumes  5 A,  5 B or which volumes flows flow from which working volume  5 A,  5 B into the tank  9 . Depending on requirements, the servo valve  7  can be embodied as a four-way valve or as a two-way valve. By means of a four-way valve, each of the two working volumes  5 A,  5 B can have the pump pressure pP or the tank pressure pT alternatively applied. In the case of a two-way valve, one of the two working volumes  5 A,  5 B has a constant pressure applied thereto, for example half the pump pressure pP. In this case, pump pressure pP or the tank pressure pT is alternatively applied to the other working volume  5 A,  5 B. 
     The piston  3  separates the two working volumes  5 A,  5 B from one another. Nevertheless, a leakage current I of hydraulic liquid  10  flows between the two working volumes  5 A,  5 B. The leakage current I is proportional to the difference between the working pressures pA, pB. Thus, the following relationship applies:
 
 I =ω·( pA−pB )  (1)
 
     Usually, the proportionality factor ω is referred to as leakage coefficient. Establishing, the leakage coefficient ω is subject matter of the present invention. This will subsequently be discussed in more detail. 
     The hydraulic cylinder unit  1  is controlled by a control device  11 . In particular, the servo valve  7  is set in a defined manner at all times by the control device  11  to the respective valve position y that is predetermined for the respective time. 
     Furthermore, an evaluation device  12  is present. The evaluation device  12  is embodied as a software-programmable device, corresponding to the illustration in  FIG. 1 . In  FIG. 1 , the evaluation device  12  is illustrated as a device that differs from the control device  11 . However, alternatively, the evaluation device  12  can form a unit with the control device  11 . 
     The evaluation device  12  is programmed by a computer program  13 . The computer program  13  may be supplied to the evaluation device  12  by a data medium  14 , for example, in which the computer program  13  is stored in non-transitory machine-readable form. In principle, any data medium may be considered as a data medium  14 . A CD-ROM  14  is illustrated (purely in an exemplary manner) in  FIG. 1 . 
     The computer program  13  comprises machine code  15  that is immediately executable by the evaluation device  12 . Executing machine code  15  by the evaluation device  12  causes the evaluation device  12  to carry out a method for establishing the leakage coefficient ω, which will be explained in more detail below. 
     Within the scope of the present invention, the piston position z of the piston  3  in the hydraulic cylinder  2  and the first and the second working pressure pA, PB are captured by appropriate sensors  16 . The captured variables z, pA, pB are supplied to the evaluation device  12 . The latter accepts the captured variables z, pA, pB. The variables z, pA, pB vary in time. Thus, they are newly captured at each clock cycle TS. The variables z, pA, pB captured at a certain time are constituents of a respective group of values associated in time. 
     The pump pressure pP and the tank pressure pT are also constituents of the respective group of values associated in time. It is possible that these variables pP, pT, too, are captured by sensors. In this case, the variables pP, pT can be variable in time, as they are newly captured with each clock cycle TS and supplied to the evaluation device  12 . However, alternatively, the pump pressure pP and the tank pressure pT likewise could be constant. In this case, the pump pressure pP and the tank pressure pT must only be disclosed once to the evaluation device  12 , for example by way of a parameterization of the evaluation device  12 . If the tank pressure pT is parameterized, the value of 0 can be set and parameterized for the tank pressure pT in many cases. 
     Furthermore, the respective valve position y is a constituent of the respective group of values associated in time. The valve position y is a variable that varies over time, which must be newly supplied to the evaluation device  12  with each clock cycle TS. It is possible that the valve position y is transmitted to the evaluation device  12  from the control device  11 . Alternatively, it is possible that the valve position y is captured by a further sensor  17  and supplied to the evaluation device  12  from there. It lies in the discretion of a person skilled in the art as to which of the two procedures is adopted. 
     The evaluation device  12  establishes the leakage coefficient co on the basis of the aforementioned values, i.e., on the basis of the piston position z, the first and the second working pressures pA, pB, the valve position y, the pump pressure pP and, preferably, the tank pressure pT. A number of further parameters of the hydraulic cylinder unit  1  are used thereby for establishing purposes in addition to the aforementioned variables. However, these further parameters do not change over time. Therefore, they need to be disclosed to the evaluation device  12  only once within the scope of a parameterization. 
     As a rule, the evaluation device  12  establishes the leakage coefficient ω recursively. Thus, proceeding from a previously valid solution to a system of equations established by the system of equations, the evaluation device  12  in each case establishes a new solution to the system of equations by inserting the values of a group of values associated in time. The leakage coefficient ω is part of the respective solution. The remaining part of the solution are internal values of the system of equations. The groups of values were explained above. Each group which is valid at the respective time, comprises the piston position z, the first and the second working pressure pA, pB, the valve position y, the pump pressure pP and the tank pressure pT. The system of equations is determined in such a way that the solution to the system of equations and, in particular, the leakage coefficient ω converge. 
     The precise procedure is explained in detail below. 
     The time profile of the working pressures pA, pB can be described with sufficient accuracy by the following differential equations: 
     
       
         
           
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A 
                   
                   = 
                   
                     
                       
                         E 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             pP 
                             - 
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               A 
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNAy 
                           ⁢ 
                           
                             
                               
                                 pP 
                                 - 
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AA 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                   = 
                   
                     
                       
                         - 
                         
                           E 
                           
                             VB 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             pB 
                             - 
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               T 
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNBy 
                           ⁢ 
                           
                             
                               
                                 pB 
                                 - 
                                 pT 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AB 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         - 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A 
                   
                   = 
                   
                     
                       
                         E 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               A 
                             
                             - 
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               T 
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNAy 
                           ⁢ 
                           
                             
                               
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   A 
                                 
                                 - 
                                 pT 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AA 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                   = 
                   
                     
                       
                         - 
                         
                           E 
                           
                             VB 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             pV 
                             - 
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               B 
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNBy 
                           ⁢ 
                           
                             
                               
                                 pV 
                                 - 
                                 pB 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AB 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     If approximately 0 is assumed for the tank pressure, the equations simplify as: 
     
       
         
           
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A 
                   
                   = 
                   
                     
                       
                         E 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             pP 
                             - 
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               A 
                             
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNAy 
                           ⁢ 
                           
                             
                               
                                 pP 
                                 - 
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AA 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                     ′ 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                   = 
                   
                     
                       
                         - 
                         
                           E 
                           
                             VB 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           pB 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNBy 
                           ⁢ 
                           
                             
                               pB 
                               pN 
                             
                           
                         
                         - 
                         
                           AB 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     3 
                     ′ 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A 
                   
                   = 
                   
                     
                       
                         E 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             A 
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNAy 
                           ⁢ 
                           
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AA 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                     ′ 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       p 
                       * 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                   = 
                   
                     
                       
                         - 
                         
                           E 
                           
                             VB 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             pV 
                             - 
                             pB 
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           QNBy 
                           ⁢ 
                           
                             
                               
                                 pV 
                                 - 
                                 pB 
                               
                               pN 
                             
                           
                         
                         - 
                         
                           AB 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             z 
                             * 
                           
                         
                         + 
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 B 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                     ′ 
                   
                   ) 
                 
               
             
           
         
       
     
     In the following description, the exact equations 2 to 5 are assumed. Analogous circumstances, however, emerge if equations 2′ to 5′ are alternatively assumed. However, the equations are slightly simplified. 
     Equations 2 and 3 apply if the valve position y is greater than 0, i.e., the first working volume  5 A is connected to the pump  8  via the servo valve  7  and the second working volume  5 B is connected to the tank  9  via the servo valve  7 . Equations 4 and 5 apply if the valve position y is less than 0, i.e., the first working volume  5 A is connected to the tank  9  via the servo valve  7  and the second working volume  5 B is connected to the pump  8  via the servo valve  7 . The case where the valve position y equals exactly zero can (as desired) be excluded or assigned to the case where the valve position y is greater than 0 or to the case where the valve position y is less than 0. 
     The following applies to the parameters used in equations 2 to 5:
         E is the spring constant of the hydraulic liquid  10 .   VA is the volume of hydraulic liquid  10  that is situated in the hydraulic path  6 A and in the first working volume  5 A. The volume VA emerges as
 
 VA=V  min  A+AA ( z−z  min)  (6)
   where VminA is the amount of hydraulic liquid  10  that is situated between the servo valve  7  and the working face  4 A of the piston  3  when the piston  3  is situated in its minimum position z min. AA is the size of the effective working face  4 A of the piston  3 .   VB is analogously the volume of hydraulic liquid  10  that is situated in the hydraulic path  6 B and in the second working volume  5 B. The volume VB emerges as
 
 VB=V  min  B+AB ( z  max− z )  (7)
   where VminB is the amount of hydraulic liquid  10  that is situated between the servo valve  7  and the working face  4 B of the piston  3  when the piston  3  is situated in its maximum position z max. AB is the size of the effective working face  4 B of the piston  3 .   pN is a nominal pressure.   QNA is a rated volume flow which flows into the first working volume  5 A in the case of the maximum valve position y if a difference between the pump pressure pP and the first working pressure pA present in the first working volume  5 A equals the nominal pressure pN.   QNB is a rated volume flow which flows into the second working volume  5 B in the case of the maximum valve position y if a difference between the pump pressure pP and the second working pressure pB present in the second working volume  5 B equals the nominal pressure pN.       

     The leakage coefficient ω is included linearly in equations 2 to 5. Therefore, linear parameter estimation algorithms, as known per se, are usable, by means of which the leakage coefficient ω can be established. 
     Establishing the leakage coefficient ω is explained below proceeding from equations 2 and 3. Thus, it is explained for the case where the valve position y is greater than 0. However, in analogous fashion, it would also be possible to proceed from equations 4 and 5. 
     For the applicability of the parameter estimation algorithms, it is necessary to bring equations 2 and 3 into the form
 
 x=θH ( t )  (8).
 
     In equation 8:
         x is a measurable path output value,   θ is a line vector of the unknown parameters and   H(t) is a so-called regressor vector the time-varying model.       

     Specifically, θ=ω applies in the present case. In particular, θ is consequently a scalar. Furthermore, x emerges as a vector with two components x 1 , x 2 , wherein the following applies for the components x 1 , x 2 : 
     
       
         
           
             
               
                 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   = 
                   
                     
                       
                         p 
                         * 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       A 
                     
                     - 
                     
                       
                         
                           E 
                           
                             V 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               A 
                               ⁡ 
                               
                                 ( 
                                 z 
                                 ) 
                               
                             
                           
                         
                         · 
                         
                           sign 
                           ⁡ 
                           
                             ( 
                             
                               pV 
                               - 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                             
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             QNAy 
                             ⁢ 
                             
                               
                                 
                                   pV 
                                   - 
                                   
                                     p 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     A 
                                   
                                 
                                 pN 
                               
                             
                           
                           - 
                           
                             AA 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               z 
                               * 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       
                         p 
                         * 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       B 
                     
                     - 
                     
                       
                         
                           E 
                           
                             VB 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                         · 
                         
                           sign 
                           ⁡ 
                           
                             ( 
                             
                               pB 
                               - 
                               pT 
                             
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             QNBy 
                             ⁢ 
                             
                               
                                 
                                   
                                     p 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     B 
                                   
                                   - 
                                   pT 
                                 
                                 pN 
                               
                             
                           
                           - 
                           
                             AB 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               z 
                               * 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     In analogous fashion, H(t) emerges as a vector with two components H 1 , H 2 , wherein the following applies for the components H 1 , H 2 : 
     
       
         
           
             
               
                 
                   
                     H 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       E 
                       
                         V 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           A 
                           ⁡ 
                           
                             ( 
                             z 
                             ) 
                           
                         
                       
                     
                     · 
                     
                       sign 
                       ⁡ 
                       
                         ( 
                         
                           pV 
                           - 
                           
                             p 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             A 
                           
                         
                         ) 
                       
                     
                     · 
                     
                       ( 
                       
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           A 
                         
                         - 
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           B 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     H 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       E 
                       
                         VB 
                         ⁡ 
                         
                           ( 
                           z 
                           ) 
                         
                       
                     
                     · 
                     
                       sign 
                       ⁡ 
                       
                         ( 
                         
                           pB 
                           - 
                           pT 
                         
                         ) 
                       
                     
                     · 
                     
                       ( 
                       
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           A 
                         
                         - 
                         
                           p 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           B 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     As a result, two linearly independent measured values x 1 , x 2  are consequently available for the parameter estimation problem. The two measured values x 1 , x 2  can be used to carry out the estimation of the parameter θ=ω. 
     The parameter estimation problem is formulated as a state observation problem, in which the following is set as a system to be observed: 
     
       
         
           
             
               
                 
                   
                     ϑ 
                     * 
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   x 
                   := 
                   
                     
                       [ 
                       
                         
                           
                             
                               x 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                         
                         
                           
                             
                               x 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   H 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   H 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                         · 
                         θ 
                       
                       = 
                       
                         
                           : 
                         
                         ⁢ 
                         
                           
                             H 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           · 
                           θ 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     This assumption  =0 can be made because the leakage coefficient ω only changes slowly, in relation to a sequence of measurements of the values explained above, and because, further, the relationship θ=ω applies. 
     In equation 14, some of the variables to be inserted are constant. By way of example, this applies to the rated pressure pN and the spring constant E of the hydraulic liquid  10 . Some further variables are time varying or can be time varying. In particular, this relates to the piston position z, the first and the second working pressures pA, pB and the valve position y. The variables z, pA, pB, y are readily capturable by means of measuring technology, for example by means of appropriate sensors  16 . In respect of the valve position y, it is even possible for the latter not having to be captured by measuring technology but being provided by the control device  11 . The pump pressure pP and the tank pressure pT are either varying in time or constant in time. In one case, the pump pressure pP and the tank pressure pT can be readily captured by means of appropriate sensors. In another case, they need only be parameterized in any case, wherein, furthermore, the tank pressure pT optionally can be set to the value of 0 within the scope of the parameterization. Therefore, all these variables can be readily established and inserted into equation 14. 
     However, the terms x 1 , x 2  of the equation 14 also contain the derivative of the working pressures pA, pB and of the piston position z with respect to time. Establishing the derivative of the piston position z with respect to time is possible without problems. However, the values for the working pressures pA, PB vary too strongly. Therefore, the derivative with respect to time cannot be established directly—with a meaningful result therefrom. Nevertheless, the system of equations according to equation 14 can be solved. This is explained below. 
     The system of equations according to equation 14 is subjected to filtering. The filter function G of the filter is chosen in such a way that it has a relative degree of at least 1. If g 1  and g 2  denote polynomial functions of the (complex) frequency parameter s and, furthermore, the filter function G emerges as 
     
       
         
           
             
               
                 
                   G 
                   = 
                   
                     
                       g 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                     
                       g 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     the polynomial g 1 ( s ) therefore has at least one zero less than the polynomial g 2 ( s ). 
     The variables arising from the filtering are distinguished from the unfiltered variables x, x 1 , x 2 , H, H 1 , H 2  below by virtue of the addition F being added to the filtered variables in each case. Thus, the filtered variables are denoted below as xF, x 1 F, x 2 F, HF, H 1 F and H 2 F. Furthermore, L denotes the Laplace transform. 
     Consequently, the following applies to the filtered variable x 1 F: 
     
       
         
           
             
               
                 
                   
                     L 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         F 
                       
                       ) 
                     
                   
                   := 
                   
                     
                       G 
                       ⁡ 
                       
                         ( 
                         s 
                         ) 
                       
                     
                     · 
                     
                       L 
                       ( 
                       
                         
                           
                             p 
                             * 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           A 
                         
                         - 
                         
                           
                             E 
                             
                               V 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 A 
                                 ⁡ 
                                 
                                   ( 
                                   z 
                                   ) 
                                 
                               
                             
                           
                           · 
                           
                             sign 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   P 
                                 
                                 - 
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               ) 
                             
                           
                           · 
                           
                             ( 
                             
                               
                                 QNAy 
                                 ⁢ 
                                 
                                   
                                     
                                       
                                         p 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         P 
                                       
                                       - 
                                       
                                         p 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         A 
                                       
                                     
                                     
                                       p 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       N 
                                     
                                   
                                 
                               
                               - 
                               
                                 AA 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   z 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     By exploiting the linearity of the Laplace transform, the following is obtained: 
     
       
         
           
             
               
                 
                   
                     L 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         F 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         G 
                         ⁡ 
                         
                           ( 
                           s 
                           ) 
                         
                       
                       · 
                       
                         L 
                         ⁡ 
                         
                           ( 
                           
                             
                               p 
                               * 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             A 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         G 
                         ⁡ 
                         
                           ( 
                           s 
                           ) 
                         
                       
                       · 
                       
                         L 
                         ( 
                         
                           
                             E 
                             
                               V 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 A 
                                 ⁡ 
                                 
                                   ( 
                                   z 
                                   ) 
                                 
                               
                             
                           
                           · 
                           
                             sign 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   P 
                                 
                                 - 
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   A 
                                 
                               
                               ) 
                             
                           
                           · 
                           
                             ( 
                             
                               
                                 QNAy 
                                 ⁢ 
                                 
                                   
                                     
                                       
                                         p 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         P 
                                       
                                       - 
                                       
                                         p 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         A 
                                       
                                     
                                     
                                       p 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       N 
                                     
                                   
                                 
                               
                               - 
                               
                                 AA 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   z 
                                   * 
                                 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     On account of the fact that the filter function G(s) has a relative degree of at least 1, the following relationship furthermore applies:
 
 G ( s ) L ( {dot over (p)}A )= G ( s )· s·L ( pA )  (18)
 
     Consequently, the following is obtained from an inverse Laplace transform: 
     
       
         
           
             
               
                 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     F 
                   
                   = 
                   
                     
                       
                         L 
                         
                           - 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             G 
                             ⁡ 
                             
                               ( 
                               s 
                               ) 
                             
                           
                           · 
                           s 
                           · 
                           
                             L 
                             ⁡ 
                             
                               ( 
                               
                                 p 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 A 
                               
                               ) 
                             
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         E 
                         
                           V 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             ⁡ 
                             
                               ( 
                               z 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             pP 
                             - 
                             
                               p 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               A 
                             
                           
                           ) 
                         
                       
                       · 
                       
                         ( 
                         
                           QNA 
                           · 
                           y 
                           · 
                           
                             
                               
                                 
                                   pP 
                                   - 
                                   
                                     p 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     A 
                                   
                                 
                                 
                                   p 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   N 
                                 
                               
                               - 
                               
                                 AA 
                                 · 
                                 
                                   z 
                                   * 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     As a result, it is therefore possible to establish the filtered variable x 1 F without requiring a derivative of the first working pressure pA with respect to time. Only the first working pressure pA itself is required. 
     Naturally, an analogous statement applies to x 2 F. Here, too, it is not the derivative of the second working pressure pB with respect to time but only the second working pressure pB itself that is required for the purposes of establishing the filtered variable x 2 F. 
     Naturally, the right-hand side of the equation 14 is also filtered, analogously to the left-hand side of the equation 14. Consequently, the following system of equations that is equivalent to equations 13 and 14 is obtained:
 
{dot over (θ)}=0  (20)
 
 xF=HF ( t )·θ  (21)
 
     In this system of equations, the vectors xF and HF, in particular, or the components x 1 F, x 2 F, H 1 F, H 2 F thereof, are variables that can only be established with significant computational outlay, but they are establishable, to be precise with good accuracy. This is in contrast to the original system of equations, of equations 13 and 14, in which the variables H 1  and H 2  are very easily establishable, but, by contrast, the variables x 1  and x 2  are not establishable or are not establishable with a sufficient accuracy. 
     Consequently, the object now lies in undertaking an asymptotic reconstruction of the sought state θ (where θ=ω applies), by using the sequence of “measurements” xF. 
     The system defined by equations 20 and 21 is a linear timevariant (LTV) system. Therefore, a Luneburg observer does not suffice to reconstruct the state θ. Instead, a Kalman filter is used to reconstruct the state θ. 
     The Kalman filter is a time-discrete system. Therefore, equations 20 and 21 are discretized. In this way, equations 22 and 23 are obtained: 
     
       
         
           
             
               
                 
                   
                     ϑ 
                     
                       k 
                       + 
                       1 
                     
                   
                   = 
                   
                     ϑ 
                     k 
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
             
               
                 
                   
                     xF 
                     k 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               
                                 H 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                                 ⁢ 
                                 
                                   F 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       TS 
                                       · 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 H 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                                 ⁢ 
                                 
                                   F 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       TS 
                                       · 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ) 
                       
                       · 
                       
                         ϑ 
                         k 
                       
                     
                     = 
                     
                       
                         : 
                       
                       ⁢ 
                       H 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           F 
                           k 
                         
                         · 
                         
                           ϑ 
                           k 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     TS is the cycle clock or the time constant, with which the “measurements” x follow one another. k is an index that represents the respective sampling time. 
     The structure and the equations of the Kalman filter are as follows:
 
 K   k   =P   k-1   HF   k   T ( HF   k   P   k-1   HF   k   T   +R ) −1   (24)
 
θ k =θ k-1   +K   k ( x   k   −HF   k θ k-1 )=θ k-1   +K   k   e   k   (25)
 
 P   k =(1− K   k   HF   k ) 2   P   k-1   +K   k   RK   k   T   (26)
 
     The variables K, P, HF T  and R, which have not yet been defined previously, occur in equations 24 to 26. They have the following meanings:
         K is a Kalman gain. In the present case, the Kalman gain is a vector with two components.   P is a scalar covariance factor.   HF T  is the transpose of the filtered regressor vector HF.   R is the variance of the measurement noise. The variance R relates to the filtered “measurement” xF.   e is, as emerges from equation 25, the deviation of the k-th filtered “measurement” xF k  from the (k−1)-th estimate HF k-1 θ.       

     If the covariance factor P k-1  has a value of 0, the Kalman gain K k  likewise becomes 0 on account of equation 24. As a result, the k-th estimate of the parameter ϑ, i.e. the value θ k , is no longer changed in equation 25. However, since long-term monitoring within the scope of error detection is sought after by means of the procedure according to the invention, the filtering must remain adaptive. Consequently, it is necessary to ensure that the covariance factor P k-1  always has a value above 0. On the other hand, the covariance factor P k-1  should not be able to assume arbitrarily large values so that numerical stability is ensured. This is achieved by virtue of equation 26 being replaced by the following equation 27:
 
 P   k =λ(1− K   k   HF   k ) 2   P   k-1   +K   k   RK   k   T   (27)
 
     K T  is the transpose of the Kalman gain. λ is a learning rate. By way of example, the following applies to the learning rate λ: 
     
       
         
           
             
               
                 
                   λ 
                   = 
                   
                     λ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                       ( 
                       
                         1 
                         - 
                         
                           
                              
                             
                               P 
                               
                                 k 
                                 - 
                                 1 
                               
                             
                              
                           
                           
                             k 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     λ 0  has the meaning of a maximum learning rate; k 0  has the meaning of a maximum covariance. 
     The system consisting of equations 24, 25, 27 and 28 represents a fully functional solution of the present invention. 
     In order to make the estimation algorithm more robust and, in particular, in order to counteract a parameter drift, equation 25 can furthermore be replaced by the following equation:
 
   k =   k-1   +K   k   DZ ( e   k )  (29)
 
     DZ is a dead zone or insensitive zone. The following applies to the dead zone DZ: 
     
       
         
           
             
               
                 
                   DZ 
                   := 
                   
                     { 
                     
                       
                         
                           
                             
                               e 
                               k 
                             
                             - 
                             d 
                           
                         
                         
                           
                             
                               for 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 e 
                                 k 
                               
                             
                             &gt; 
                             d 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             
                               for 
                               ⁢ 
                               
                                   
                               
                               - 
                               d 
                             
                             &lt; 
                             
                               e 
                               k 
                             
                             &lt; 
                             d 
                           
                         
                       
                       
                         
                           
                             
                               e 
                               k 
                             
                             + 
                             d 
                           
                         
                         
                           
                             
                               for 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 e 
                                 k 
                               
                             
                             &lt; 
                             
                               - 
                               d 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     d determines the size of the dead zone DZ. Preferably, the numerical value for d corresponds substantially to the typical noise of the deviation e. By way of example, a suitable numerical value for d can be established by observing the system, or it can be discovered through trials. 
     Consequently, by way of the procedure explained above, it is possible that the evaluation device  12 , in accordance with the presentation in  FIG. 2 , accepts the piston position z of the piston  3 , the working pressures pA, pB of the working volumes  5 A,  5 B and the valve position y of the servo valve  7  in each case in a step S 1 , possibly after a corresponding parameterization. To the extent that this is necessary, the evaluation device  12  accepts additional further values in step S 1 , such as the pump pressure pP and the tank pressure pT, for example. Thereupon, building on the values accepted in step S 1 , the evaluation device  12  establishes the leakage coefficient ω in a step S 2 . Step S 2  was explained in detail above. In a step S 3 , the evaluation device  12  establishes the difference δω between the established leakage coefficient ω and a predetermined nominal leakage coefficient ωN. In a step S 4 , the evaluation device  12  compares the established difference δω, more precisely: the magnitude or absolute value thereof, with a limiting value δω max. As soon as the magnitude or the absolute value of the difference δω exceeds the limiting value δω max, the evaluation device  12  proceeds to a step S 5 . In step S 5 , the evaluation device  12  triggers an alarm. Otherwise, it does not carry out step S 5 . In particular, the alarm can be embodied as an optical alarm, which is output by way of a viewing appliance to an operating person. Thereupon, the operating person can introduce maintenance of the hydraulic cylinder unit  1 , for example. 
     The evaluation device  12  carries out steps S 1  to S 4  and hence, in particular, the establishment of the leakage coefficient ω and the difference δω, as well as a comparison with the limiting value δω max, during the operation of the hydraulic cylinder unit  1 . Furthermore, the evaluation device  12  carries out steps S 1  to S 4  continuously. However, when the evaluation device  12  transitions from step S 4  to step S 5 , the alarm notification is maintained until it is acknowledged in a step S 6 , for example by the operating person. 
     In summary, the present invention consequently relates to the following circumstances: 
     A hydraulic cylinder unit  1  has a hydraulic cylinder  2 , a piston  3  that is displaceable in the hydraulic cylinder  2  and a servo valve  7 . The piston  3  separates a first and a second working volume  5 A,  5 B of the hydraulic cylinder unit  1  from one another. The servo valve  7  is connected to a hydraulic pump  8 , a tank  9  and the first and the second working volume  5 A,  5 B. A pump pressure pP is applied to the servo valve  7  via the hydraulic pump  8 . The tank  9  has a tank pressure pT. The servo valve  7  is set to a defined valve position y. A piston position z of the piston  3  in the hydraulic cylinder  2  and a first and a second working pressure pA, pB, which are applied to the first and the second working volume  5 A,  5 B, are captured. An evaluation device  12  establishes a leakage coefficient co of the hydraulic cylinder unit  1  on the basis of the piston position z, the first and the second working pressure pA, pB, the valve position y, the pump pressure pP and the tank pressure pT in conjunction with time-invariant parameters of the hydraulic cylinder unit  1 . 
     The present invention has many advantages. In particular, the procedure according to the invention allows the leakage coefficient ω to be robustly estimated on the basis of measured values that arise in any case during the running operation of the hydraulic cylinder unit  1 . A deviation of the established leakage coefficient ω from a nominal or expected leakage coefficient then can be used to trigger an alarm or to indicate an upcoming change of seal to the operating staff. Furthermore, the reliability and availability of the hydraulic cylinder unit  1  is increased since a complicated replacement of the internal ring seal can be planned during a regular servicing interval, without having to fear premature failing of the seal and without having to replace the seal prematurely before the end of its service life. The solution according to the invention is cost-efficient and realizable without noteworthy changes to the hardware. Complicated special hardware (in particular flowmeters) are not required. 
     Even though the invention was illustrated in more detail and described by way of the preferred exemplary embodiment, the invention is not restricted by the disclosed examples and other variations can be derived herefrom by a person skilled in the art, without departing from the scope of protection of the invention. 
     LIST OF REFERENCE SIGNS 
     
         
           1  Hydraulic cylinder unit 
           2  Hydraulic cylinder 
           3  Piston 
           4 A,  4 B Working faces 
           5 A,  5 B Working volumes 
           6 A,  6 B Hydraulic paths 
           7  Servo valve 
           8  Hydraulic pump 
           9  Hydraulic reservoir/tank 
           10  Hydraulic liquid 
           11  Control device 
           12  Evaluation device 
           13  Computer program 
           14  Data medium 
           15  Machine code 
           16  Sensors 
           17  Further sensor 
         AA, AB Size of the effective working faces 
         DZ Dead zone 
         E Spring constant of the hydraulic liquid 
         e Deviation 
         G Filter function 
         g 1 , g 2  Polynomials 
         H, HF Regressor vectors 
         H 1 , H 2 , H 1 F, H 2 F Components of the regressor vectors 
         I Leakage current 
         L Laplace transform 
         K Kalman gain 
         k Index 
         k 0  Maximum covariance 
         P Covariance factor 
         pA, pB Working pressures 
         pN Rated pressure 
         pP Pump pressure 
         pT Tank pressure 
         QNA, QNB Rated volume flows 
         R Variance of the measurement noise 
         s Frequency parameter 
         S 1  to S 6  Steps 
         TS Time constant 
         VA, VB Volumes 
         VminA, VminB Minimum volumes 
         x, xF Path output values 
         x 1 , x 2 , x 1 F, x 2 F Components of the path output values 
         y Valve position 
         z Piston position 
         z max Maximum position of the piston 
         z min Minimum position of the piston 
         δω Difference 
         δω max Limiting value 
         λ Learning rate 
         λ 0  Maximum learning rate 
         θ Unknown parameter 
         ω Leakage coefficient 
         ωN Nominal leakage coefficient