Patent Publication Number: US-7721686-B2

Title: Method and system for controlling a free-piston energy converter

Description:
The invention relates to a method and system for controlling a free-piston engine or energy converter. 
   A free-piston energy converter has at least one freely moving piston in at least one cylinder usually without any crankshaft or camshaft connected to the piston. This allows a highly compact and efficient engine design, but requires an exact control of the piston motion and of the actuation and motion of the valves for opening and closing inlet and outlet ports in the at least one cylinder. These motions and actuations are controlled by a control system which fulfills the function of an electronic crankshaft and an electronic camshaft. 
   The free piston energy converter is usually provided for converting combustion energy into electrical or mechanical or hydraulic energy. 
   One of the advantages of such a free piston engine is the fact that the compression ratio can be controlled at each stroke. This is not possible in a conventional combustion engine. This property opens up the possibility to achieve a homogeneous charge compression ignition (HCCI) in a free piston energy converter. A disadvantage of such an engine however is the fact, that it is difficult to provide a control system which is robust to disturbances. 
   The reliability and efficiency of such a free piston energy converter comprising for example one piston in one cylinder is very sensitive to disturbances because the two pistons are strongly coupled to each other and any event affecting one piston affects the other piston as well. 
   U.S. Pat. No. 6,181,110 discloses a method for controlling the movement of a linear electric generator which comprises a pair of internal combustion pistons disposed axially aligned and in opposition to each other, in which current absorption is controlled in such a manner that, during a reciprocating motion cycle of the generator, a resisting force acting on the generator is obtained which is substantially proportional to the movement speed of the generator at least at a central stroke area. 
   It is desirable to provide a method and system for controlling a free piston energy converter by which a robust control of the free piston energy converter is obtained even in case of disturbance events affecting the at least one piston and/or cylinder. 
   It is desirable to provide a method and system for controlling a free piston energy converter which comprises one piston in one cylinder for converting combustion energy into electrical and/or mechanical or any other kind of energy by which an efficient control of the converter is achieved, at least substantially independently of any disturbances and/or environmental conditions affecting at least one of the pistons and/or the processes in at least one of the two cylinders. 
   According to an aspect of the present invention, a method for controlling a free-piston energy converter by an electromagnetic force exerted onto a moving mass of the converter, by which method effects of disturbance events in at least one of at least two cylinders are decoupled from each other, comprises predicting forces acting on the moving mass of the converter during a stroke of the moving mass, wherein predicting forces is conducted based on at least one of certain present states and conditions within the converter, and evaluating or estimating on the basis of the predicted forces a value for generating the electromagnetic force which is exerted onto the moving mass, so that the moving mass reaches a desired reference condition or state, at a certain position along the stroke. 
   According to another aspect of the present invention, a system for controlling a free-piston energy converter for conducting a method as described above is also disclosed. 
   According to another aspect of the present invention, a free-piston energy converter comprising a system for controlling a free-piston energy converter for conducting a method as described above is also disclosed. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Further details, features and advantages of the invention result from the following description of exemplary embodiments of the invention in connection with the drawings in which schematically shows: 
       FIG. 1  a cross section through a free piston energy converter; 
       FIG. 2  a block diagram of the main components of an inventive system; 
       FIG. 3  a block diagram of a first component of the system according to  FIG. 2 ; 
       FIG. 4  the results of inventive simulation example describing the features of the first main component of the inventive system; 
       FIG. 5  a block diagram of a second component of the system according to  FIG. 2 ; 
       FIG. 6  a schematic view of a model of the piston movement; 
       FIG. 7  the results of the inventive simulation of an estimated position and velocity of a moving mass in a free piston energy converter; 
       FIG. 8  a schematic view of a structure of a first free piston energy converter; 
       FIG. 9  a schematic view of a structure of a second free piston energy converter; 
       FIG. 10  a schematic view of a structure of a third free piston energy converter; 
       FIG. 11  a schematic view of a structure of a fourth free piston energy converter; and 
       FIG. 12  a schematic view of a structure of a fifth free piston energy converter. 
   

   DETAILED DESCRIPTION 
     FIG. 1  shows a cross section through an exemplary free piston energy converter  1 . This converter  1  comprises a first piston  10  moving within a first cylinder  11  with a first combustion chamber  12  and a second piston  20  moving within a second cylinder  21  with a second combustion chamber  22 . 
   The first cylinder  11  has a first and a second intake opening  13  which is opened and closed by the first piston  10  and a first and a second inlet and/or outlet opening  14  which is opened and closed by a first and a second valve  15 , respectively. The second cylinder  21  accordingly comprises a first and a second intake opening  23  which is opened and closed by the second piston  20  and a first and a second inlet and/or outlet opening  24  which is opened and closed by a first and a second valve  25 , respectively. 
   The first piston  10  and the second piston  20  are connected with each other by a connecting shaft  30 . Furthermore, an electrical machine is positioned between the first and the second cylinder  11 ,  12 . This electrical machine substantially comprises at least one coil  40  which is fixed around the shaft  30  and at least one permanent magnet  41  which is fixed at the shaft  30 . The coil  40  and the permanent magnet  41  are dimensioned and positioned in such a way that they can interact electromagnetically with each other, so that an axial movement of the permanent magnet  41  within the coil  40  induces an electrical current within the coil  40  and conversely by applying an electrical current at the coil  40  an axial force can be exerted onto the permanent magnet  41 . Consequently the electric machine can operate both as a generator and as a motor. 
   Furthermore actuators for actuating the first and second valves  15 ,  25 , injectors for injecting fuel and/or gas etc., as well as sensors for detecting various operating conditions like temperature, pressure, positions of the pistons  10 ,  20  etc. are provided for the free piston energy converter  1  and are not shown in  FIG. 1 . 
     FIG. 2  shows a block diagram of the main components and the main structure of an exemplary system according to the invention for controlling a free piston energy converter  1 . This system substantially comprises a velocity servo controller  50 , an observer  60 , an ignition time controller  70  and an output power controller  80 . A main feature of this control system is that it decouples the effects of the combustions in the two cylinders  11 ,  21 . 
   A first input of this system is provided for applying a reference output power value P ref  of the converter  1  which is connected via a first summation device  81  with the output power controller  80 . A second input of the system is provided for applying a reference value for the ignition time t ign   ref  with respect to the top dead center (TDC) or the bottom dead center (BDC) of a piston  10 ;  20 , which is connected via a second summation device  71  with the ignition time controller  70 . 
   The preferred two main control variables for the converter  1  are the electromagnetic force F el  acting on the moving mass of the converter  1  (i.e. the pistons  10 ,  20 , the shaft  30  and the permanent magnet  41 ) and the fuel input Q comb  to the converter  1 . The preferred output values to be controlled by these variables are the ignition time with respect to the top dead center (TDC) or the bottom dead center (BDC) of a piston  10 ;  20  and the output power of the converter  1 , respectively. 
   In order to improve performance a feedforward controller can be used from the reference signals P ref  and t ign   ref  to the control commands Q comb  and F el . For the sake of clarity a feedforward controller is not indicated in  FIG. 2 . 
   Other control variables which could be used but are preferably not considered are the valve opening times, the fuel injection times and the current control of the electrical machine so that the desired electromagnetic force is obtained. Similarly, the outputs to be controlled might be for example the output power and the maximum efficiency of the converter  1  under certain environmental restrictions and conditions instead of the ignition time. The general function of the velocity servo controller  50  is to predict forces acting on the moving mass of the converter  1  during a stroke of the pistons  10 ,  20  and the shaft  30  and to evaluate and/or estimate a value representing an electromagnetic force Fei which is converted by a converting device (not shown) into an appropriate current for the coils  40  so that the moving mass reaches a desired reference condition or state, preferably a desired reference kinetic energy, at a certain position along the stroke and preferably near the end of the stroke within the related cylinder  11 ,  21  and especially at the next combustion event. By introducing such a velocity servo controller  50  the feedback-control system is made much more robust to process disturbances. 
   The general function of the observer  60  is to observe and estimate certain current (present) states and/or conditions within the free piston energy converter  1  which are used and evaluated especially by the velocity servo controller  50  for predicting the future development or future values of the above mentioned forces. 
   For this purpose inputs of the observer  60  are connected with related sensor outputs of the converter  1  and several first outputs of the observer  60  are connected with inputs of the velocity servo controller  50 . 
   A second output of the observer  60  is connected to the second summation device  71 , so that a difference between the value of the reference ignition time and the value of an estimated ignition time is input to the ignition time controller  70 , the output of which is connected with the velocity servo controller  50 . 
   Finally a third output of the observer  60  is connected to the first summation device  81 , so that a difference between the value of the reference output power and the value of an estimated output power is input to the output power controller  80  which generates at its output a value for the fuel input Q comb  to the converter  1  for controlling a related fuel injection device. 
   By means of this system the converter  1  is controlled in such a way that by inputting a reference value of an output power P ref  and a reference value of the ignition time t ign   ref , a desired output power P and a desired ignition time t ign  with respect to TDC or BDC is obtained by controlling the electromagnetic force F el  acting on the moving mass of the converter  1  and the fuel input Q comb . 
   In order to control the free piston energy converter  1  with such a system the following observations have to be considered: the converter  1  as such is an unstable system and the combustion process is nonlinear. Furthermore, the converter  1  is sensitive to process disturbances like for example to a sudden decrease in combustion energy. Finally, the converter  1  is an event triggered system and has multiple inputs and multiple outputs (MIMO). 
   As mentioned above the reason for being sensitive to disturbances is that the combustion properties of the two cylinders  11 ,  21  are strongly coupled. A disturbance in one of the cylinders  11  ( 21 ) affects the combustion event in the other cylinder  21  ( 11 ) which in turn affects the combustion in the first cylinder  11  ( 21 ) and so on. Consequently a robust event triggered system is needed which is more robust to disturbances and which is able to control a free piston energy converter  1  with multiple inputs and multiple outputs (MIMO). 
   Generally this is achieved by the method and system according to the invention by decoupling the effects of the combustions in the two cylinders  11 ,  21 . 
   In order to decouple these effects, the system design with respect to the velocity servo controller  50  and the observer  60  is provided as follows: 
   The design of the velocity servo controller  50  is based on a reference value which is for example a desired kinetic energy of the piston  10 ;  20  at a certain point of its stroke and especially near the end of the stroke (or another condition or state of the converter  1 ) (This is in contrary to the prior art in which usually a position or velocity trajectory during the whole stroke is followed). The desired reference kinetic energy of the piston is achieved by controlling the electrical machine by the velocity servo controller  50  and especially by generating a value for converting into a current for the coils  40  so that an appropriate electromagnetic force Fei is exerted onto the permanent magnets  41 . This feature increases the degree of freedom when designing the controller. 
   Furthermore, the design of the velocity servo controller  50  is based on a model. This means that the output value of the velocity servo controller  50  (the value for generating the applied electromagnetic force) for controlling the electrical machine is evaluated on the basis of a model of the moving mass of the pistons  10 ,  20  and the shaft  30  and on pressure-, position- and velocity-signals within the free piston energy converter  1  especially according to the description below. 
   For estimating the position and velocity of the moving mass of the converter  1 , the observer  60  is based on a physical model of how the moving mass is moving with respect to the applied total forces (i.e. substantially electromagnetic force and gas pressure within the cylinder). Such an observer  60  can also be used for fault detection (e.g. faults in Hall effect sensors, in pressure sensors, in the electric machine etc.). For estimating the pressure, a model based filtering of pressure signals can be introduced additionally. 
   The velocity servo controller  50  is shown in more details in the block diagram according to  FIG. 3  in which the free piston energy converter  1  and the observer  60  are indicated as well. The servo controller  50  substantially comprises a stabilizing compensator  52  and a servo compensator  53 , for example a Pi-controller. Preferably this is a standard configuration of a controller that solves the robust servo mechanism problem (see for example in Levine, W. S.: The Control Handbook, CRC Press 1996 on page 734). 
   The stabilizing compensator  52  receives input signals evaluated by the observer  60  which indicate the estimated pressure p within the cylinders and the estimated kinetic energy E k  of the moving mass at an estimated (current or present) position x. Furthermore the stabilizing compensator  52  receives the value of the desired reference kinetic energy E k   ref  near the end of the stroke of the piston (or at a certain position of the piston) which is set by the ignition time controller  70 . A value of the electromagnetic force F el  which is the output signal of the stabilizing compensator  52  and which is computed by this from the received input signals is fed to a third summation device  51 . A first input of the servo compensator  53  receives the value of the desired reference kinetic energy E k   ref  and a second input receives the value of the kinetic energy E k  estimated by the observer  60 . The output of the servo compensator  53  is connected with the third summation device  51 . By this, the sum of the output signals of the stabilizing compensator  52  and the servo compensator  53  is fed as a value of the electromagnetic force F el  to a converting device (not shown) for generating the appropriate current for the coils  40  in the converter  1  as mentioned above. 
   The model based simulation conducted by the velocity servo controller  50  and especially by the stabilizing compensator  52  shall be explained exemplarily with reference to  FIG. 4 . This Figure shows how the velocity servo controller  50  applies the value for the electromagnetic force F el  by predicting the forces that are acting on the moving mass during the stroke of the piston. The following algorithm is conducted: 
   1. Measuring or estimating the values of the kinetic energy E k  (or velocity v) of the piston and the pressure p within the related cylinder at a first position x 0 ; 
   2. Considering the desired reference kinetic energy E k   ref  near the end of the stroke or at a certain position x 3 ; 
   3. Predicting a constant electromagnetic force F el  so that the desired reference kinetic energy E k   ref  is reached at the position x 3  on the basis of the values measured or estimated under step 1 above; and 
   4. Jumping back to step 1 and repeating the procedure for a second (next) position x 1  of the piston. 
   In  FIG. 4  curve A indicates the positions x i  of the piston, curve B indicates the velocity v (kinetic energy E k ) of the piston and curve C indicates the value of the requested electromagnetic force Fei at the output of the velocity servo controller  50 , each over the time t which is indicated on the horizontal axis. In case of a perfect prediction of the electromagnetic force Fel, this force would be constant throughout the whole stroke. However as shown in  FIG. 4  this prediction is usually not exact because of disturbances and model imperfections. Consequently the electromagnetic force changes during the stroke as indicated in  FIG. 4 . 
   The electromagnetic force F el  is computed by the stabilizing compensator  52  in the following way: 
   1. Energy Balance: 
   Let x range  denote the distance where force is applied by the electrical machine. Let x 1  and x 2  denote the positions where the electromagnetic force starts and ends, i.e. (x 1 −x 2 )=x range . This same notations hold for the pressure p 1  and p 2  and the velocity v 1  and v 2 . 
   The robust servomechanism problem is stated as follows: Given an initial speed v 1  and an initial pressure p 1  and design a robust stabilizing controller such that
 
v 2 =v ref   (1)
 
   Here v ref  denotes the desired speed at x 2 . Furthermore, let the electromagnetic force F el  be constant during the stroke, i.e.
 
F el =constant for x 1 &gt;x&gt;x 2   (2)
 
   Observe that the applied work is equal to the loss of kinetic energy, i.e.
 
∫ x1   x2   F   tot ( x )( dx )=½ m ( v   2   2   −v   1   2 )  (3)
 
   Let the total force be the sum of the electromagnetic force, the force due to the pressure p(t) from the two cylinders, and by other forces F Δ  which may be due to non-modelled effects (friction, heat loss, etc.) and process disturbances, i.e.
 
 F   tot   =F   el   +pA+F   Δ   (4)
 
   Let the electromagnetic force F el  be the sum of the output from the servo compensator Felserv and the stabilizing compensator F el   stab . Hence from (2) to (4) it follows that:
 
( F   el   stab   +F   el   serv ) x   range +∫ x1   x2 ( Ap ( x )+ F   Δ ) dx= ½ m ( v   2   2   −v   1   2 )  (5)
 
   Assume that the output from the servo compensator is given by:
 
 F   el   serv   x   range +∫ x1   x2   F   Δ   dX= 0  (6)
 
   Hence from (5) and (6) it follows that the servo problem (1) is solved if:
 
 F   el   stab   =m ( v   ref   2   −v   1   2 )/2 x   range   −A/x   range ∫ x1   x2   p ( x ) dx   (7)
 
   2. Predicting the Pressure Profile: 
   Consider one side of the piston. Let x denote the distance between the cylinder head and the piston. Under adiabatic expansion (or compression) of an ideal gas it holds that:
 
 dp/p=−κdx/x   (8)
 
   Assuming that κ is constant throughout the stroke. Integrating (8) over an interval xε[x a  x b ] it follows that:
 
[ln(Φ)] p(xz)   p(xb) =κ[ln( s )] xz   xb   (9)
 
 p ( x   b )/ p ( x   a )=( x   b   /x   a ) −κ   (10)
 
Hence
 
                         A   ⁢       ∫   xa   xb     ⁢       p   ⁡     (   s   )       ⁢     ⅆ   s           =       ⁢       Ap   ⁡     (     x   a     )       /         x   a     -   κ       ⁡     [         s     1   -   κ       /   1     -   κ     ]       xz   xb                   =       ⁢         Ap   ⁡     (     x   a     )       /     (     1   -   κ     )       ⁢       x   a     -   κ       ⁡     (       x   b     1   -   κ       -     x   a     1   -   κ         )                     =       ⁢         Ap   ⁡     (     x   a     )       /     (     1   -   κ     )       ⁢     (         (       x   b     /     x   a       )       1   -   κ       -   1     )                     (   11   )               
Consider the compression phase of a free piston engine. Let XiV0 denote the position where the inlet valves (or ports) are opened and closed. Also, let pin denote the pressure in the cylinder when the inlet ports are open. The work W com  that the gas is carrying out on the piston over xε [x 1  x 2 ] then given by:
   W   com   =Ax   ivo   p   in (1−κ)(( x   2   /x   ivo ) 1-κ −1)+ Ap   in ( x   ivo   −x   1 )  (12) 
   (12) The same method of calculation can be made on the work W exp  that is applied on the piston during an expansion phase. From (7) it now follows that F el   stab  is given by:
 
 F   el   stab   =m ( v   ref   2   −v   1   2 )/2 x   range −( W   com   +W   exp )/x range   (13)
 
   3. Updating the electromagnetic force F el  during the stroke: 
   In Section  1 . and  2 . is has been assumed that the electromagnetic force F el  is constant throughout the stroke. However from equation (13) it is straightforward to update the electromagnetic force F el  during the stroke at arbitrary positions x i . Updating the force during the stroke improves robustness since the controller has a larger possibility to reach the desired reference kinetic energy E k   ref . 
   The observer  60  observes and estimates certain states and conditions of the free piston energy converter  1 .  FIG. 5  shows the main components of the observer  60  which are an ignition time estimator  61 , a piston state estimator  62  and an output power estimator  63 . Furthermore, a converter device  64  is provided for converting a value of an estimated velocity into a value of an estimated kinetic energy E kjn . 
   The observer  60  comprises three inputs A, B, C which connect sensor outputs of the free piston energy converter  1  with the piston state estimator  62 . The first input A receives switching signals of the Hall effect sensor x hall  effected by the piston. The second input B receives the current (present) value of the electromagnetic force F el  acting on the piston. The second input B is as well connected with the output power estimator  63 . The third input C receives the current (present) value of the pressure P within the cylinder. 
   As mentioned above, the position and velocity of the moving mass and especially of the pistons is estimated by the observer  60  on the basis of a physical model of how the moving mass is moving with respect to the applied forces. This is carried out by means of the piston state estimator  62  on the basis of the received three input signals A, B, C and is described in more details below. 
   The ignition time is calculated by the ignition time estimator  61  in dependence of the position, velocity and pressure, which are estimated by the piston state estimator  62  and provided to the inputs of the ignition time estimator  61 . This calculation is done on the basis of measuring the time between the peak pressure and the top dead center (TDC) or the bottom dead center (BDC) of the piston which is quite straightforward for a person skilled in the art. However some observations can be made and should be considered:
         the quality of the estimation is related to the sampling frequency of the controller  50 ; and   simulations show that the present feedback controller may suffer a problem if there is no ignition. This might be the case during start-up or if there is a misfire. For avoiding such problems, preferably an ignition observer is introduced which sets a flag indication whether an ignition has occurred or not.       

   The observer  60  comprises five outputs D, E, F, G, H. Via the first output D and the second output E the estimated position x of the piston and the estimated kinetic energy Ek, respectively, are provided to the stabilizing compensator  52 . The estimated kinetic energy Ek is provided from the second output E to the servo compensator  53  as well. 
   The estimated output power P is provided from the third output F to the first summation device  81 . The ignition time is submitted from the fourth output G of the observer  60  to the second summation device  71 . Finally the estimated pressure p is provided via the fifth output H of the observer  60  to the stabilizing compensator  52 . 
   Estimating the position and velocity of the moving mass and especially of the piston by the piston state estimator  62  is very important for the method and system of the invention. In this free piston engine or energy converter  1  the position of the moving mass is measured with Hall effect sensors (or other sensors). These sensors flag and generate a signal when for example the magnets on the moving mass pass the sensor. The problem however is to estimate the position and velocity of the moving mass at any time instant and not just when the Hall effect sensors generate a signal. 
   The basic idea is to estimate the motion of the moving mass by considering the total forces Ftotai acting on the moving mass. The most significant forces are the electromagnetic force and the forces due to the cylinder pressure. According to  FIG. 6  the piston state estimator  62  is based on the model of a double integrator which integrates the total force for obtaining the position x and velocity v of the moving mass. In the field of control engineering this kind of estimation problem is often solved by a Kalman filter. In this case the use of a Kalman filter is well motivated since the motion of the piston is a linear function of the applied forces. However other filters can be used as well. 
   A challenging problem with the using of Hall effect position sensors is the fact that they are not time triggered but event triggered. This means that the position measurements are only accurate when they are generated and that they are not updated synchronously. However for a Kalman filter time triggered signals are needed. To solve this problem a time varying Kalman filter can be used.  FIG. 7  shows a simulation example in which the filter estimates the position and velocity of the moving mass. In this figure the staircase plot A denotes the output signals of the Hall effect sensors and curve B denotes the position estimated by the Kalman filter. Curve C is the estimated velocity of the moving mass. 
   In the following the time varying Kalman filter shall be described in more details. 
   Given a discrete-time model
 
 x ( k+ 1)= Fx ( k )+ Gu ( k )+ v ( k )(14) y ( k )= C ( k ) x ( k )+ w ( k )  (15)
 
with the following covariance matrices of the process disturbances and measurement noise:
 
 E{v ( k ) v   T ( l )}= R   2 δ kl  
 
 E{w ( k ) w   T ( l )}= R   2 δ kl  
 
   the Kalman filter is given by:
 
 x ( k+ 1)= Fx ( k )+ Gu{k )+ K ( k )( y ( k )− Cx ( k ))  (16)
 
   Here the gain K(k) is given by:
 
 K ( k )= FP ( k ) C   T ( CP ( k ) C   T   +R   2 ) −1   (17)
 
where P(k) is the solution to the following Riccati equation:
 
 P ( k+ 1)= FP ( k ) F   T   −FP ( k ) C   T ( CP ( k ) C   T   +R   2 ) −1   CP ( k ) F   T   +R   1   (18)
 
   Usually the steady state solution of the Kalman filter is implemented, i.e. (18) is solved as an algebraic equation
 
 P= lim  P ( k )
 
k→∞
 
   However, note that the Kalman filter (16) is also valid for a time-varying system 
   [FCk), G(k), C(k), D(k)] 
   with time-varying covariance matrices R 1 (k) and R 2 (k). In such case there exists no steady state solution of (18). 
   In the free piston energy converter engine the dynamics of moving mass is given by
 
 x=F/m   (19)
 
   where x denotes the position, F denotes the applied forces on the moving mass m. The problem is to estimate the velocity x* based on position measurements and force estimates. The Kalman filter is a suitable observer for this application since (19) is linear. 
   Let (14) and (15) be the discrete-time representation of (19) where u is the applied force and y is the position measurements. A problem is that the position measurements are not updated at each sample. Furthermore, the positions measurements are not sampled synchronously. This problem can be solved by considering a time-varying R 2  matrix: 
   R 2 (k)={∞ when position is not updated
            when the position is updated       

   The variation of R 2 (k) can be interpreted in the following way: when R 2 =V no measurement information is available, whereas when R 2 =ε the measurement is very accurate with insignificant noise. An equivalent description of this is to let R 2 =εVk and vary the C-matrix in the following way: 
   C(k)={0 when position is not updated
         C when the position is updated       

   Solution of Riccati equation: 
   
     
       
         
           
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                   F   ⁢           ⁢   P   ⁢           ⁢     F   ′       =       ⁢         [         1       0           h       1         ]     ⁡     [           p   11           p   12               p   12           p   22           ]       ⁡     [         1       h           0       1         ]                   =       ⁢       [           p   11           p   12                 hp   11     +     p   12                 p   12     ⁢   h     +     p   22             ]     ⁡     [         1       h           0       1         ]                   =       ⁢     [           p   11             hp   11     +     p   12                   hp   11     +     p   12                 h   2     ⁢     p   11       +     2   ⁢     p   12       +     p   22             ]                 
and
 
             F   ⁢           ⁢   P   ⁢           ⁢     C   ′       =         [           p   11           p   12                 hp   11     +     p   12                 p   12     ⁢   h     +     p   22             ]     ⁡     [         0             c   12           ]       =       [           p   12                   p   12     ⁢   h     +     p   22             ]     ⁢     c   12                       F   ⁢           ⁢   P   ⁢           ⁢     C   ′     ⁢   C   ⁢           ⁢   P   ⁢           ⁢     F   ′       =         [           p   12                   p   12     ⁢   h     +     p   22             ]     ⁢       c   12     ⁡     [         p   12     ⁢           ⁢     p   12     ⁢   h     +     p   22       ]       ⁢     c   12       ⁢     
     ⁢           =       [           p   12   2             p   12     ⁡     (         p   12     ⁢   h     +     p   22       )                   p   12     ⁡     (         p   12     ⁢   h     +     p   22       )               (         p   12     ⁢   h     +     p   22       )     2           ]     ⁢     c   12   2               
and
 
               C   ⁢           ⁢   P   ⁢           ⁢     C   ′       +     R   2       =             [     0   ⁢           ⁢     c   12       ]     ⁢           [           p   11           p   12               p   12           p   22           ]     ⁢           [         0             c   12           ]     +     R   2       =         p   22     ⁢     c   12   2       +     R   2               
Hence
 
   
     
       
         
           
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   According to  FIG. 5  the pressure signals are not filtered in this embodiment of the observer  60 . However there are two reasons that implementing an intelligent and model based filtering of the pressure signals might be advantageous. One reason is that experimental data indicate that the pressure signals may be subjected to disturbances and/or measurement noise. Another reason is that simulations have shown that the control system (especially the feedback) is sensitive to disturbances of the pressure signal. One possibility for solving this problem is to combine the filtering of the pressure signals with the estimation of the position and velocity of the moving mass by means of the piston state estimator  62 . This could be done by using the equation (7) above. Hence this approach would lead to a model based filtering of the pressure signals. 
   Various alternative approaches are possible: 
   Instead of the above mentioned velocity or kinetic energy, the peak pressure within the cylinder can be used as a control variable as well. This has the advantage that it is a more simple solution, however it is less robust against disturbances. 
   Instead of Hall effect sensors other position sensors can be used for detecting the position of the moving mass. 
   Instead of using an ignition servo controller  70 , it is possible to use other suitable control variables as well. An alternative would be e.g. to replace the ignition time controller with a peak pressure controller that gives a reference value to the velocity servo. 
   The position and velocity of the moving mass can be as well estimated by analyzing the terminal values of the electrical machine and for example the phase of the voltage and/or the phase of the current at/through the coil  40 . A possible advantage is that less reliance on Hall effect sensors and less reliance on pressure sensors is necessary. 
   The above described method and system is especially designed for the free piston energy converter with two pistons and a two-stroke combustion. However the inventive methods and system can be used for controlling many different designs of free piston machines.  FIGS. 9 to 12  show some of such examples in comparison to the above described two combustion chambers  111  and two-stroke combustion design with an electrical machine  100  in-between according to  FIG. 8 . 
   According to  FIG. 9  a converter is provided with one combustion chamber  111  on one side, a gas spring  112  for guiding and dampening the free piston on the other side and an electrical machine  100  in-between both.  FIG. 10  shows an embodiment in which one combustion chamber  111   a  with two pistons is provided wherein each piston is guided by means of a gas spring  112  on both sides and controlled each by an electrical machine  100  at each of the pistons. Alternatively to  FIG. 10  instead of the gas springs combustion chambers could be provided as well on both sides. 
     FIG. 11  shows an embodiment of a pneumatic free piston engine which comprises a combustion chamber  111  on one end and a compressor  113  for compressing air, hydrogen or other media on the other side with an electrical machine  100  in-between. The main purpose for the electrical machine is in these cases to make it possible to control the free piston engine.  FIG. 12  shows an embodiment of a hydraulic free piston engine which comprises a combustion chamber  111  on one end and a hydraulic actuator  114  on the other end with an electrical machine  100  in-between. However in this case a hydraulic activator can be used instead of an electrical machine as well. The output is hydraulic energy. In these cases the control system can use the hydraulic actuator instead of the electrical machine. As an alternative it is possible to add a small electrical machine between both for control purposes besides the hydraulic actuator. 
   The inventive control system is very flexible to include a variety of fast as well as slow inputs like sensors and outputs like actuators. This makes it possible to use the control system for complete engine control. The inventive control system can be used to control different combustion processes (two or four stroke) like HCCI, Diesel, Spark ignition and different fuels like petrol, diesel, natural gas and hydrogen. 
   The inventive method and system can be used for controlling non-free piston machines or converters as well. In these cases the piston motion itself cannot be controlled as in a free piston machine. However, fuel injection timing, valve opening timing and spark (if any) ignition timing are examples of possibilities to be used for fast control. If the engine is equipped with ISG (Integrated Starter Converter) it can be included in the control system. 
   Furthermore, there are crankshaft engines with the possibility to change the compression ratio, usually very slow (several seconds). 
   The proposed control system is very flexible to include a variety of fast as well as slow inputs (sensors) and outputs (actuators). This makes it possible to use the control system for complete engine control. 
   A program for operating the system according to aspects of the present invention, or components of the system, can be downloaded to the system via a computer connected to, for example, the interne.