Determnstc Control Strategy for a Hybrd Hydraulc System wth Intermedate Pressure Lne Dpl.-Ing. Peter Dengler Karlsruhe Insttute of Technology (KIT), Char of Moble Machnes, Karlsruhe, Germany Prof. Dr.-Ing. Marcus Gemer Karlsruhe Insttute of Technology (KIT), Char of Moble Machnes, Karlsruhe, Germany Dpl.-Ing. René von Dombrowsk FLUIDON GmbH, Aachen, Germany ABSTRACT The paper ntroduces a new hydraulc system for moble machnes based on a constant pressure system wth the am to ncrease the effcency of actuaton of hydraulc cylnders. Usng a thrd pressure level located between hgh pressure and tank pressure called ntermedate pressure the system enables addtonal pressure potentals from hgh pressure to ntermedate pressure and from ntermedate pressure to tank pressure. Ths reduces throttle losses at hydraulc cylnders when drven at low or medum loads. An accumulator connected to the ntermedate pressure lne s beng charged or dscharged n functon of whch pressure potental s currently used. Due to the dscrete pressure potentals of the system a control strategy s requred whch reduces throttle losses at the proportonal valves and allows maxmum recuperaton of potental energy. Best results can be obtaned f the future loads on the cylnders are predctable. For ths reason a Model Predctve Control (MPC) was developed for a wheel loader whch was used as a reference system. By usng ts specfc geometrc propertes the MPC allows a precse load predcton as a functon of the pston s poston. Usng the crtera of Bellman, an analytc onlne calculaton of the optmum sequence of pressure potentals and ther duratons for one complete cylnder stroke can be effectuated usng Dynamc Programmng. Ths leads to a determnstc algorthm whch s easy to handle and whch can be mplemented nto an onlne control loop of the wheel loader. The paper furthermore shows how an optmal swtchng sequence and the optmal accumulator parameters can be found offlne usng mult objectve optmzaton and closes wth smulaton results showng an ncrease of effcency of 13% compared to a LS system at the example of a typcal duty cycle of a wheel loader.
1 INTRODUCTION Constant pressure (CP) systems are one of the smplest hydraulc systems. They are not very effcent as hgh pressure losses occur when lower loads are lfted. Advanced systems are equpped wth a pressure controlled pump and a hydraulc accumulator connected to the man pressure lne. In these Advanced Constant Pressure Systems /1/ secondary controlled hydraulc rotary drves can be operated wthout system-related losses /2/. Furthermore secondary controlled four quadrant drves can be operated n pump mode whle brakng whch enables recovery of potental or brakng energy whch s stored n a hydraulc accumulator for later use. Both aspects, hgh system effcency and energy recovery, make Advanced Constant Pressure Systems to a sutable drve system for hydraulc hybrd drves for moble machnes. These systems already exst at the market /3/, even though not n moble applcatons yet. One nconvenent of a large scale applcaton of ths system s ts ncompatblty wth lnear actuators as the hgh pressure stll needed to be throttled to adapt t to the actual load pressure. One concept of an effcent ntegraton of hydraulc cylnders nto a constant pressure system s the secondary controlled lnear actuator whch allows an at least dscrete adaptaton of the pston area to the present load /4/. Another way s the so called hydraulc transformer whch conssts of a constant flow pump connected to a secondary controlled drve /5/. Both systems have n common that they need components whch are costly or whch are smply not avalable at the market. Another approach for the effcent ntegraton of lnear actuators n a CP system by the use of standard components s shown n Fgure 1. Fgure 1: Basc layout of a CPIP system In ths system multple dscrete pressure potentals are used to reduce pressure losses at the proportonal valves. These can be created f a supplementary pressure lne s used. The
pressure level of the addtonal lne s located between hgh pressure (HP) and tank pressure (TP) and s therefore called ntermedate pressure (IP) lne /6/ so the system s called Constant Pressure System wth Intermedate Pressure Lne (CPIP). A hydraulc accumulator s connected to the IP lne to enable recovery of potental energy. A second accumulator s connected to the HP lne to buffer pressure oscllatons. Two swtchng valves for each actuator can change the pressure on the nlet and the outlet port of the proportonal valve between hgh-, ntermedate- and tank pressure. Losses can be reduced by adaptng the appled pressure dfference at the pston of the hydraulc cylnder to the actual load. For very hgh loads, the swtchng valves connect the nlet port of the proportonal valve to HP and the outlet port to TP and the system acts lke a conventonal constant pressure system. For lower loads the nlet port of the proportonal valve s connected to the IP lne and the accumulator s beng dscharged. The next lower swtchng state connects the nlet port of the proportonal valve to the HP lne and the outlet port to the IP lne, the accumulator s beng charged. For very low loads both ports of the proportonal valve can be connected to the IP lne. Due to energetc reasons the IP lne can be connected to the sucton sde of the pump whch results n lower energy demand of the system when usng the pump. Ths results n sx swtchng states wth dfferent use of pump and accumulator energy. Fgure 2 llustrates the energy flows for a pston movement at constant speed and constant load when a swtchng sequence s used whch contans all possble swtchng states. 1 HP IP 2 IP IP 3 HP IP (2) 4 IP TP 5 HP TP 700 35 Sense of movement F load accumulator s beng dscharged poston [mm] 600 500 400 300 200 100 0 Throttle losses Pump energy Accumulator energy Used energy 1 2 3 4 5 6 30 25 20 15 10 5 0 Power [kw] accumulator s beng charged -100-200 -5-10 1 2 3 4 5 6 7 8 9 10 11 12 6 HP TP (2) tme [s] Fgure 2: Possble swtchng states to effectuate a pston movement
Besdes the hydraulc components the system needs a control algorthm to be operated. Ths control algorthm s programmed nto a programmable logc controller (PLC) and determnes the actual load at the cylnders by measurng the pressures n the chambers and the poston of the pston and chooses the approprate swtchng state by actuatng the swtchng valves. Once the swtchng state s set, the fne control of the pston s enabled wth the proportonal valve accordng to the needed flow gven by the operator. Furthermore, the algorthm has a swtchng strategy whch performs actuaton of the swtchng valves not only n terms of havng enough force to move the pston but also n terms of the global effcency of the system. It therefore allows swtchng states whch may cause hgh throttle losses at the moment but allow chargng or dschargng the accumulator n order to reach a more advantageous state of charge for future energy demands. These control strateges for hybrd drves are subject of ntensve research /7/ as they essentally nfluence the overall effcency of the system and represent the most mportant part of the control archtecture, also n ths system. 2 SYSTEM IMPROVEMENT WITH MULTI OBJECTIVE OPTIMIZATION To develop a swtchng strategy whch s able to fnd an optmum swtchng sequence a duty cycle wth cylnder strokes and loads s needed. For ths reason, the CPIP system was analyzed for the workng hydraulcs of a 4.7 t wheel loader. The consdered actuators of the workng hydraulcs are two hydraulc cylnders, one for lftng and one for tltng. A typcal duty cycle for ths applcaton s the so called Load & Carry cycle. In ths cycle the loader loads the bulk materal nto the bucket and carres t to a transport vehcle where t s dumped. It can be composed n fve dfferent stages as llustrated n Fgure 3: 1. The wheel loader drves from the startng poston (A) to the materal (B). The bucket s lowered and algned to the ground. 2. The machne drves nto the materal and loads the bucket. In the followng the wheel loader transports the materal to the transport vehcle at (C). 3. The machne drves to the transport vehcle and lfts the bucket when arrvng. 4. When the bucket s above the bed of the transport vehcle the tlt cylnder s actuated and the bucket s dumped. 5. The loader backs off and the operator brngs the bucket back nto the startng poston. The descrbed cycle was repeated durng tests about 90 tmes at realstc dggng condtons. For the system optmzaton one representatve duty cycle was chosen and the load pressures were transformed nto forces actng on the pstons of the cylnders. Ths allows dentfyng the needed forces and calculatng the needed energes n the dfferent stages wth the am to get an energy profle of the duty cycle as shown exemplarly n Fgure 2. To obtan an effcent system a sequence of swtchng states must be found whch allows performng the movements of the duty cycle but wth a lower energy demand than the current LS system.
600 Lftng cylnder Tltng cylnder C 500 transport pston postons [mm] 400 300 200 1 2 3 4 B 100 5 0 0 5 10 15 20 25 tme [s] A tlt cylnder lftng cylnder Stages: 1 2 3 4 Fgure 3: Load and Carry cycle of a wheel loader accordng to /8/ 2.1 Optmal swtchng sequence An optmum swtchng sequence for the gven duty cycle s the one wth the lowest use of energy delvered by the pump. As the pump drectly feeds the hgh pressure lne all swtchng states takng ol from the HP lne lke HP/IP, HP/IP (2), HP/TP and HP/TP (2) ncrease the energy demand of the system. These swtchng states have energy costs n form of the hydraulc energy E Pump generated by the pump. Consderng a swtchng sequence wth n swtchng decsons the costs for HP/TP and HP/IP at decson can be calculated (supposng 1 n). Assumng a constant pressure p HP n the HP lne the costs for HP/TP and HP/IP can be calculated accordng to the ol volume V Cyl,HP, taken from the HP lne at a cylnder stroke effectuated at. EPump, = VCyl, HP, php (1) Consderng the entre duty cycle the total energy demand of the system after n swtchng decsons can be descrbed as n = E, (2) Pump E Pump The swtchng states IP/IP and IP/TP have no energy costs accordng to the defnton gven above as they only take energy from the accumulator. When used nstead of HP/TP or HP/IP equaton (2) s mnmzed as E Pump, becomes zero. However, IP/TP and IP/IP reduce the state of charge (SOC) of the accumulator by V Cyl,IP, so the used potental energy can be calculated as IP 2 E = p ( V ) dv (3) Acc, V V IP1 IP, IP IP
V = V V (4) Cyl, IP, IP1 IP2 E Acc, s negatve f the accumulator s beng dscharged and postve f the accumulator s beng charged. Ths potental energy must be created by chargng the accumulator usng HP/IP or by lowerng hgh loads wth TP/IP (recuperaton mode) or medum loads wth HP/IP (2). The total accumulator energy after n swtchng decsons s therefore n = E, (5) Acc E Acc The swtchng states HP/IP (2) and HP/TP (2) combne pump energy and accumulator energy to reduce ther costs as the accumulator of the IP lne s connected to the sucton sde of the pump. The costs for HP/IP (2) and HP/TP (2) can be gven as IP 2 E = V p + p ( V ) dv (6) Pump, Cyl, out, HP The optmum swtchng sequence balances swtchng states wth hgh costs and hgh generaton of potental energy and swtchng states wth low or zero costs and hgh consumpton of accumulator energy n a manner that the global costs, e.g. the total energy demand E Pump for the gven duty cycle, become mnmal. Ths s an optmzaton problem whch can be solved wth a mult objectve optmzaton consderng both energy types E Pump and E Acc as equvalent. The optmal decson changes the current energy state nto a Pareto optmum as shown n Fgure 4. V V IP1 IP, IP IP E Pump swtchng alternatves for tme step +1 L/P HP/TP L/P HP/IP L L HP/TP (2) HP/IP (2) E Pump,+1 L IP/TP L/P IP/IP E Acc,+1 energes after swtchng decsons P: Pareto optmal swtchng decson L: Legal swtchng decson E Acc Fgure 4: Pareto optmal decsons To apply mult objectve optmzaton the duty cycle s dvded n n dscrete tme steps. At each tme step all legal swtchng states are dentfed. A swtchng state s legal f t generates a force whch s hgh enough to move the pston n the current load stuaton.
Furthermore swtchng states whch take ol from the accumulator can only be legal f the SOC s hgh enough to effectuate the cylnder stroke n the gven tme step. Startng from a state of total energy demand E Pump and total accumulator energy E Acc at a tme step the energes E Pump and E Acc for the next tme step +1 are calculated for all legal swtchng alternatves and added to E Pump and E Acc. The optmal swtchng decsons are those whch do not worsen one energy type wthout mprovng the other one and therefore called Pareto optmal (see Fgure 4). They are added to the already exstng sequence of Pareto optmal swtchng decsons. If there s more then one optmal swtchng alternatve the exstng sequence must be duplcated by the number of optmal alternatves. The calculated energes E Pump and E Acc are used as startng energes for the next tme step and the procedure s repeated. At the end of the duty cycle a set of ponts s found wth dfferent energes E Pump and E Acc followng a Pareto fronter whch begns wth very low values for E Pump and E Acc and endng wth very hgh values for both energy types. The searched sequence of optmal decsons s the one wth the lowest pump energy demand and s shown n Fgure 5. 600 500 400 Throttle losses Pump energy Accumulator energy Used energy Swtchng states tlt 30 25 20 pston postons [mm] 300 200 100 0 3 3 2 lft 4 3 1 2 4 3 3 potental energy 1 3 15 10 5 0 Power [kw] -100-5 -200-300 Accumulator: SOC start : 1,86 L; SOC end : 1,91 L HP: 150 bar, 93bar < IP < 115 bar, TP: 0 bar p precharge : 90 bar; V acc : 20 L -15 2 4 6 8 10 12 14 16 18 20 22 24 tme [s] -10 Fgure 5: Optmal swtchng sequence for the gven duty cycle 2.2 Optmal accumulator parameters The descrbed optmzaton method s done for a gven duty cycle and fx accumulator parameters. In order to buld up an optmzed system the parameters precharge pressure and accumulator sze can be found wth the same method. Supposng a hydro-pneumatc accumulator wth a polytropc gas behavor wth the polytropc ndex κ the relaton between gas volume and gas pressure can be gven as p κ V = Acc const. (7)
Applyng the mult objectve optmzaton on the same duty cycle by gradually changng the values for precharge pressure and gas volume of the accumulator a characterstc correlaton between those parameters and the total energy demand can be observed n Fgure 6. A valley can be dentfed showng low energy demands for all tested accumulator szes at a precharge pressure of 90 bar. Ths valley has a smooth slope and reaches the global mnmum of hydraulc energy consumpton at 20 L gas volume and 90 bar precharge pressure. An accumulator wth these parameters enables therefore the hghest effcency mprovement of the system and was chosen to be mounted on the wheel loader. Fgure 6: Results of parameter varaton reveal optmal accumulator settngs 3 MODEL PREDICTIVE CONTROL USING DYNAMIC PROGRAMMING Besdes an optmal swtchng sequence Fgure 5 shows the mechancal energy whch s needed n the hydraulc cylnders of the wheel loader. The workng stages 1 and 2 (descrbed n Fgure 3) are characterzed by load peaks whch are relatvely hgh but short so the needed energy s qute low. In these stages the swtchng valves must be fast enough to create the forces whch are needed at the pstons but due to the spontaneous character of these peaks an optmzaton of the swtchng sequence can not really take place. At stage 4 potental energy occur at the tltng cylnder when the bucket s dumped and at the lftng cylnder when the arm s lowered. Ths energy must be recuperated n order to mprove the energy demand of the system. At stage 3 t can be seen that most of the energy s needed for the lftng cylnder when the arm s lfted. Here the loads are hgh and the movement lasts long so an onlne optmzaton of the swtchng sequence can be effectuated. An
optmzaton algorthm must be found whch can take an optmal swtchng decson at any nstant of the pston movement. Ths algorthm must be flexble, fast and easy to handle to use t as an onlne control algorthm. The most promsng approach can be created wth Model Predctve Control (MPC) /9/. MPC mples a mathematcal model of the system and extrapolates the present state of charge for a defnte tme step nto the future, called predcton horzon. Usng ths model the controller can approxmate the future response of the system to nteractons of actuators at the present nstant of tme whch allows a postve nfluence on the system behavor for the predcton horzon. In general, the pston movements of a wheel loader are very quck (a couple of seconds to lft the bucket) and can furthermore be nterrupted at any nstant by the operator. At these condtons a tme extrapolaton of the present load would be qute dffcult to carry out. Dong ths, a tme related MPC would not mprove the system as the precson of predcton would be very poor. For ths reason a poston related MPC was created whch predcts precsely the development of loads on the lftng cylnder accordng to the present poston of the pston. 3.1 Modelng of loads and of the accumulator Due to the geometrc propertes of the wheel loader the load at the lftng cylnder s a lnear functon of the pston s poston. Once the arm s lfted and the present load and poston are known the future evoluton of loads s determned no matter whch velocty wll be chosen or whether the movement wll be nterrupted or not. Usng ths nformaton the optmzaton problem s lmted to the queston at whch postons the system needs to change from one swtchng state nto another. Another mportant aspect s the modelng of the accumulator. Accordng to equaton (7) t has a nonlnear behavour whch s dffcult to handle. For ths reason the accumulator behavour needs to be lnearzed. One of the results of the mult objectve optmzaton (shown n Fgure 5) s that the accumulator s never charged wth more than 5 L so a lnear model represents a good approxmaton f compared to the real measured behavour shown n Fgure 7. F Load [kn] 100 80 60 40 20 Modelng of pston loads Real load behavour (measured wth m=1t) Lnear behavour due to smple knematcs of wheel loader: m F Load Pressure p IP [bar] 140 130 120 110 100 V IP, p IP Modelng of accumulator Real accumulator behavour (measured at T=40 C) 0 0 100 200 300 400 500 600 700 Cylnder poston h [mm] Load model: F Load = F ( 0 m) + b h 90 0 1 2 3 4 5 6 State of charge V IP [L] Accumulator model: p IP = 0 p + V IP c Fgure 7: Modelng of loads and accumulator usng measurng data
3.2 Onlne optmzaton algorthm wth Dynamc Programmng Due to the lnear correlaton between load and pston poston the loads on the lftng cylnder can be precsely predcted. The predcton horzon s therefore the cylnder stroke from the present poston (whch s measured) untl ts end poston (whch s estmated). A smplfcaton of the optmzaton problem can be acheved f the varety of possbltes s lmted by sortng the swtchng states n ascendng order of maxmal reachable force as shown n Fgure 8. The swtchng sequence therefore conssts of n=6 perods wth dfferent swtchng states for each perod. The sequence begns wth perod =1 and IP/IP as the swtchng state wth the lowest force and fnshes wth =6 and HP/TP as the one wth the hghest force. For the gven predcton horzon the duraton of each perod can be descrbed wth the length s representng the cylnder stroke drven wth the respectve swtchng state. The predcton horzon s therefore the sum of all lengths s 1 s 6. As almost all swtchng states nfluence the SOC of the accumulator, the choce of the length s at the perod s called polcy as t nfluences all swtchng decsons n the succeedng perods and therefore the effcency of the whole movement. When drvng the pston at HP/IP for example, the accumulator s beng charged and therefore the maxmum possble force s contnuously lowered due to the ncreasng pressure n the accumulator (whch s consdered as a lnear functon of the SOC). Smultaneously the maxmum force of IP/TP wll ncrease as well as ts possble duraton because of the smple fact that there s more ol n the accumulator to effectuate the movement. The onlne optmzaton algorthm must therefore determne the optmal polcy s opt, for each perod n a way that the throttle losses, whch are descrbed by the objectve functon E Loss are as low as possble. The Dynamc Programmng optmzaton method /10/ supposes the crtera of Bellman descrbng a polcy n a perod as optmal f t mnmzes the objectve functon of the same perod and the one of the succeedng perod +1. { } ( h V ) mn E ( h, V ) + E [ T ( h V )] E Loss, mn,, IP, Loss, IP Loss,mn, + 1, IP, = (8) s opt, s the soluton for equaton (8) and mnmzes E Loss, whch are throttle losses and result from the dfference of maxmal forces of the states and the load at each perod. Due to the dependence of the maxmal force on the SOC V IP, and the dependence of the load on the poston h of the pston the objectve functon E Loss, depends on both parameters whch are varables descrbng the states at the begnnng and end of each perod. The throttle losses E Loss at the stage and the throttle losses at the succeedng stage +1 need to be lnked to calculate the mnmum at. Ths lnk s done here wth the transton functons T[h,V IP, ] whch descrbe the lnkng of the SOC V IP and the pston poston h of two perods: h = h + s +1 (9) V IP, 1 = VIP, + s APston, + (10) As the accumulator s beng charged or dscharged n dependency of whch swtchng state s presently used, the pston surface A Pston and ts sgn depend on the present stage. Wth the easy ntal calculaton of the optmum length of the swtchng state at the last stage usng the estmated fnal poston h 7
s opt, 6 h7 h6 = (11) equaton (8) can be solved top down calculatng s opt, for each perod untl arrvng at ndex 1 wth the ntal state varables h 1 and V IP,1 whch are measured and therefore known. The results for s opt, are functons whch depend on the state varables h and V IP, of each perod and are stored n a table. If the ntal state varables h 1 and V IP,1 change, the optmum swtchng sequence s adapted mmedately by recalculatng bottom up all values s whch makes ths optmzaton algorthm very fast and determnstc as t does not approach teratvely the optmum but t calculates t analytcally n a sngle run. F,SOC Throttle losses (objectve functon ) F max, HP/TP (2) F max, IP/TP F max, HP/TP F Load, max F max, HP/IP F max, HP/IP (2) F Load, predcted F max, IP/IP h SOC F Load F Load, actual perods: 1 2 3 4 5 6 polcy: s 1 s 2 s 3 s 4 s 5 s 6 states: h 1,V IP,1 h 2,V IP,2 h 3,V IP,3 h 4,V IP,4 h 5,V IP,5 h 6,V IP,6 h 7,V IP,7 h predcton horzon Fgure 8: Prncple of onlne optmzaton wth Dynamc Programmng 3.3 Smulaton results A bg advantage of the onlne optmzaton algorthm s the determnstc calculaton of global mnma. The equatons are smple as the used mathematcal models to descrbe load and accumulator behavour are lnear. For each swtchng state of the lftng cylnder exsts one equaton whch s stored n the controller of the system. At each calculaton cycle of the controller the nput data lke pston loads, pston postons and ntermedate pressure are transformed nto loads, forces and SOC and the equatons are solved. Ths very smple and fast onlne optmzaton algorthm s programmed nto a Programmable Logc Controller (PLC) whch wll plot the system of the expermental vehcle. Before beng appled on the machne, the program code s tested n a smulaton envronment frst. For ths purpose a smulaton model was created and valdated wth measurng data from the wheel loader. In order to make the vrtual test envronment as realstc as possble and to have an effcent tool to mprove the program code of the PLC, the smulaton model was connected drectly
to the program code va an Object Lnkng and Embeddng for Process Control (OPC) nterface as descrbed n /11/. Ths enables an nterchange of data between program algorthm of the PLC and the smulaton model. A realstc system behavour can be acheved allowng a frst valdaton f the onlne optmzaton s workng and how the system does mprove the effcency of the system. Fgure 9 shows the smulaton results of four succeedng Load & Carry cycles. In ths smulaton the duty cycle s not known by the control algorthm, the controller need to fnd the optmal swtchng decson at any nstant. Thanks to the onlne optmzaton algorthm the swtchng sequence s very close to the one found wth the offlne optmzaton method and an mprovement of effcency of 13% compared to a LS system could be determned. Fgure 9: Results of smulaton run of four cycles showng effcency mprovement 4 SUMMARY AND OUTLOOK The paper presents the dea of an energy effcent actuaton of hydraulc cylnders n a constant pressure system when another lne wth ntermedate pressure s used. Ths allows an ntegrated hybrd hydraulc system wth secondary controlled hydraulc rotary drves and standard hydraulc cylnders whch are operated at dfferent pressure potentals between hgh pressure, ntermedate pressure and tank pressure. An optmum sequence for a chosen specfc duty cycle s determned by the use of a mult objectve optmzaton. An onlne control algorthm was developed usng the Dynamc Programmng method and tested n smulaton showng an effcency mprovement of 13% compared to LS.
The control algorthm whch wll be used for the logc controller wll be tested and mproved by the help of software-n-the-loop smulatons /11/. The wheel loader s equpped wth valve blocks and accumulators for HP lne and IP lne as shown n Fgure 10. The fuel consumpton of the new system wll be compared to the one of the LS system to prove the overall effcency. accumulator HP lne accumulator IP lne valve blocks Fgure 10: Results Test machne wth mounted valve blocks and accumulators 5 ACKNOWLEDGEMENTS The project was performed by the Char of Moble Machnes (Mobma) at the Karlsruhe Insttute of Technology (KIT) n cooperaton wth ARGO-HYTOS GmbH, FLUIDON GmbH and Hermann Paus Maschnenfabrk GmbH. The project s fnanced by the Federal Mnstry of Educaton and Research (BMBF) and supervsed by the German Aerospace Center (DLR). The authors thank the BMBF and the DLR for the support of ths project.
6 REFERENCES /1/ Dreher, T.: The Capablty of Hydraulc Constant Pressure Systems wth a Focus on Moble Machnes, 6 th FPNI PhD Symposum, West Lafayette 2010, proceedngs p. 579-588. /2/ Haas, H.-J.: Sekundärgeregelte hydrostatsche Antrebe m Drehzahl- und Drehwnkelregelkres, PhD thess, RWTH Aachen, 1989 /3/ Fscher, H. Stegerwald, T. & Godzg, M.: Hydraulc Systems for Deep-Sea Applcatons, 7 th Internatonal Flud Power Conference, Aachen, 2010. /4/ Lnjama et. al.: Secondary Controlled Mult Chamber Cylnder, 11 th Scandnavan Internatonal Conference on Flud Power, Lnköpng, 2009. /5/ Bshop, E. D.: Dgtal Hydraulc Transformer Approachng theoretcal Perfecton n Hydraulc Drve Effcency, 11 th Scandnavan Internatonal Conference on Flud Power, Lnköpng, 2009. /6/ Dengler P. et. al.: Effcency Improvement of a Constant Pressure System Usng an Intermedate Pressure Lne, 8 th Internatonal Flud Power Conference, Dresden, Germany, 2012. /7/ Böckl, M.: Adaptves und prädktves Energemanagement zur Verbesserung der Effzenz von Hybrdfahrzeugen, PhD Thess, Unversty of Venna, Austra, 2008. /8/ Kohmäscher, T, Jähne, H., Deters, H.: Moderne voll- und telhydrostatsche Fahrantrebe Untersuchung und Weterentwcklung von Antrebsstrangkonzepten mobler Arbetsmaschnen, O+P 5, 2006. /9/ Back, M.: Prädktve Antrebsregelung zum energeoptmalen Betreb von Hybrdfahrzeugen, PhD Thess, Unversty of Stuttgart, Germany, 2005. /10/ Snedovch, M.: Dynamc Programmng: Foundatons and Prncples, CRC Press, 2011. /11/ von Dombrowsk R., Dengler P.: KonZw Effzenzstegerung durch ene Zwschendruckletung, SIMPEP Kongress für Smulaton m Produktentstehungsprozess, Vetshöchhem, Germany, 2011.