A VIRTUAL-CAM BASED CONTROL METHODOLOGY FOR FREE-PISTON ENGINES CHAO YONG. Dissertation. Submitted to the Faculty of the

Transcription

1 A VIRTUAL-CAM BASED CONTROL METHODOLOGY FOR FREE-PISTON ENGINES By CHAO YONG Dissertation Submitted to the Faulty of the Graduate Shool of Vanderbilt University in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mehanial Engineering August 2011 Nashville, Tennessee Approved: Professor Eri J. Barth Professor Mihael Goldfarb Professor Nilanjan Sarkar Professor Robert J. Webster Professor George E. Cook i

2 To my parents ii

3 ACKNOWLEDGEMENTS My deepest and sinerest thanks go to Dr. Eri J. Barth, who has been a great mentor and friend during this work. He always provided me with insightful understandings of the researh and inspired me with his innovative ideas. He was patient during my fruitless researh period. This work and my personal life would never ome to this point without his enouragement and help through all these years. Dr. Barth is also a great friend of everyone in room 504. He reates a relaxing and friendly researh environment in the lab where oming to work beomes a joy for all lab members. Working with Dr. Barth and the department of mehanial engineering has beome my preious memory and it will be herished for the rest of my life. I would like to thank other ommittee members (Dr. Mihael Goldfarb, Dr. Nilanjan Sarkar, Dr. Robert Webster, and Dr. George Cook.) and Suzanne Weiss, Myrtle Daniels, and Jean Miller for their help and aring for the graduate students and the department. I would also like to thank my friends: Mark Hofaker, Alex Pedhenko, Andy Willhite, Jose Riofrio and many others. They bring me so muh help in the lab and many joys in the life. Thanks to Ms. Helen Bird, my friends Nola and Kira. It is my honor to be a friend of yours. Finally, I would like to thank Andy and Jose who did terrifi works on free-piston engines that make my work possible. Thanks to the National Siene Foundation and the Center for Compat and effiient Fluid Power for their finanial support of this work. iii

4 TABLE OF CONTENTS DEDICATION... ii ACKNOWLEDGEMENTS...iii LIST OF FIGURES AND TABLES...vii ABSTRACT... I CHAPTER I. FREE-PISTON ENGINES AND CONTROL....1 HISTORY OF FREE PISTON ENGINES....1 UNIQUE FEATURES OF FREE-PISTON ENGINES... 4 Free-piston dynamis Frequeny ontrol Free-piston engine loads Combustion proess in free-piston engines... 8 CONTROL OF FREE-PISTON ENGINES...8 II. VIRTUAL-CAM BASED CONTROL FOR FREE-PISTON ENGINES. 13 VIRTUAL CAM FOR FREE-PISTON ENGINE CONTROL Virtual-am onstrution Virtual-am based ontrol struture. 19 VIRTUAL CAM REPEATING INDEX BUILD Fuel injetion ontrol Exhaust timing ontrol PRESSURE-BASED CONTROL APPROACH CONCLUSIONS III. MODELING AND SIMULATION OF A FREE LIQUID PISTON ENGINE COMPRESSOR A FREE LIQUID PISTON ENGINE COMPRESSOR (FLPEC).. 39 DYNAMIC MODELS OF THE FLPEC 41 Modelling of the ombustion proess.. 44 Combustion valve dynamis Exhaust valve dynamis Free-piston inertia dynamis...48 iv

5 SIMULATION RESULTS AND VALIDATION.. 48 CONCLUSION...52 IV. SIMULATION RESULTS BASED ON VIRTUAL CAM CONTROL CONTROL OBJECTIVES. 53 VIRTUAL CAM CONSTRUCTION. 54 INTEGRATED VIRTUAL-CAM CONTROL.. 57 SIMULATION RESULTS. 61 CONCLUSIONS V. A HIGH INERTANCE FREE LIQUID PISTON COMPRESSOR...69 INTRODUCTION.. 69 BASIC OPERATION OF THE HIFLPC PROTOTYPE FABRICATIONS AND EXPERIMENTAL SETUP OF THE HIFLPC Critial physial parameters of prototype Injetion iruit and ontrol Experimental test setup EXPERIMENTAL RESULTS WITH FIXED TIMINGS. 83 Experimental results.. 83 Effiieny and power alulation.. 84 DISCUSSION OF THE EXPERIMENTAL RESULTS WITH BEST TUNED PARAMETERS VI. EXPERIMENTAL RESULTS OF THE VIRTUAL-CAM BASED CONTROL METHODOLOGY ON THE HIFLPC MODIFICATIONS OF THE GENERAL CONTROL LAWS. 92 Modifiations of the injetion ontrol law. 92 Modifiations of the exhaust ontrol law VIRTUAL-CAM BASED CONTROL STRUCTURE.. 98 Control struture Dynami adjustment of the repeating indexes EXHAUST AND INJECTION CONTROL RESULTS Exhaust ontrol results Injetion ontrol results FULL ENGINE CONTROL RESULTS Effiieny assessment Wide range of operation Frequeny ontrol CONCLUSIONS VII. CONCLUSIONS v

6 REFERENCES APPENDIX. 132 vi

7 LIST OF FIGURES AND TABLES Page Figure 1.1. Piston dynamis of single piston free-piston engine.. 5 Figure 1.2. Charateristis of free-piston engine loads 7 Figure 2.1. Comparison between physial am and virtual am shemes Figure 2.2. Cam and valve. 15 Figure 2.3. Basi am onfiguration..16 Figure 2.4. Delay and dynami response Figure 2.5. Physial amshaft and virtual amshaft.. 18 Figure 2.6. Virtual-am based free-piston engine ontrol struture..20 Figure 2.7. A simplified illustration of the free-piston engine. 22 Figure 2.8. States of the ombustion hamber.. 24 Figure 2.9. Expansion ratio and fuel mass ontrol 30 Figure Cyle-to-yle exhaust timing ontrol.. 33 Figure Pressure dynamis and power of the expansion hamber in FLPEC Figure 3.1. The free liquid-piston engine ompressor onfiguration Figure 3.2. Shemati of the lumped-parameter dynami model of the FLPEC. 42 Figure 3.3. Free-body diagram of the ombustion valve.. 47 Figure 3.4. Free-body diagram of the exhaust valve.48 Figure 3.5. Simulation results and experimental data of the ombustion pressure.. 50 Figure 3.6. Heat release during the ombustion (simulated) 51 Figure 3.7. Validation of the overall system dynamis for FLPEC. 51 Figure 4.1. Command signals in Simulations Figure 4.2. Virtual ams onstruted by the ommand signals 56 Figure 4.3. The kinemati equivalent virtual am lobes 56 Figure 4.4. States in the exhaust valve ontrol. 58 Figure 4.5. Diagram of the proposed ontrol struture using virtual ams Figure 4.6. Simulation results of FLPEC in three yles Figure 4.7. Virtual-am ommands and their referene ommands Figure 4.8. Overall system dynamis in Simulations.63 vii

8 Figure 4.9. Simulated volume of the ompression hamber Figure Simulated reservoir pressure dynamis Figure Simulated injetion durations onvergene Figure Simulated engine effiienies Figure Frequeny ontrol in the simulations Figure 4.14.Simulated volume of the ompression hamber during the frequeny ontrol. 67 Figure Simulated engine effiienies during the frequeny ontrol...67 Figure 5.1. Shemati of the High Inertane Free Liquid Piston Compressor (HIFLPC).70 Figure 5.2. (a) Shemati of HIFLPC at effetive TDC. (b) Shemati of HIFLPC at effetive BDC Figure 5.3. Assembled HIFLPC prototype Figure 5.4. Air and fuel injetion iruit...76 Figure 5.5. Bosh CNG fuel injetor Figure 5.6. Fuel pressure ontrol iruit Figure 5.7. HIFLPC test onfiguration Figure 5.8 Signal timings for the prototype operation.. 82 Figure 5.9. Measured pressures for HIFLPC operation at 4 Hz for (a) Combustion hamber, (b) Compression hamber, and () Reservoir Figure Single yle reservoir pressure gain Figure Fuel iruit buffer tank pressure for one yle Figure 6.1. Reservoir pressure (a) and Breathe-in durations (b) Figure 6.2. Breathe-in durations vs. pressure gain in the reservoir Figure 6.3. Exhaust ontrol sheme for HIFLPC Figure 6.4. Compression and reservoir pressure dynamis Figure 6.5. Control ommands for the HIFLPC Figure 6.6. Exhaust ontrol results: (a) Exhaust open timings (b) Exhaust lose timings () Reservoir pressures Figure 6.7. Individual adjustments of the exhausting timings: (a) Initial exhaust timings; (b) Post-adjustment exhaust timings Figure 6.8. Injetion ontrol experimental results: (a) Measured breathe-in durations; (b) Injetion duration adjustment viii

9 Figure 6.9. Engine ontrol and its dynamis: (a) Control signals; (b) Pressure dynamis Figure Experimental results with full ontrol: (a) Combustion pressures; (b) Compression pressures; () Reservoir pressures; (d) Breathe-in durations; (e) Injetion durations; (f) Propane pressures in the buffer tank; (g) Exhaust valve timings Figure Low pre-ombustion pressure results: (a) Combustion pressures; (b) Compression pressures; () Reservoir pressures; (d) Breathe-in durations; (e) Injetion durations; (f) Propane pressures in the buffer tank; (g) Exhaust valve timings Figure High effiieny over a wide reservoir pressure range: (a) Reservoir pressures; (b) Breathe-in durations; () Injetion durations; Figure Upper limit for pump: (a) Reservoir pressures; (b) Breathe-in durations; () Injetion durations Figure Frequeny ontrol results: (a) 2 Hz; (b) 4 Hz; () Frequeny adjustment Table 5.1. Physial parameter overview of HIFLPC prototype Table 6.1. Constant gains used in ontrol laws Table 6.2. Effiieny and reservoir pressure gain results Table 7.1. Energeti omparison between domains ix

10 ABSTRACT The free-piston engine has been widely investigated and variety of free-piston engines have been developed for a number of appliations due to their advantages in omparison to onventional internal ombustion (IC) engines: 1) the free-piston redues the mehanial frition losses from side loading of piston due to the rank. 2) The engine an be started/stopped on demand so that the engine s fuel effiieny an be improved by eliminating the idle operation in onventional IC engines. 3) The absene of a rankshaftonneting rod mehanism gives the engine variable stroke lengths to allow the ontroller for optimizing the engine effiieny by using variable ompression/expansion ratios. In onventional internal ombustion engines, valves are opened and losed using a am surfae. The am positions are kinematially related to the piston positions through the rankshaft and timing belt. In ontrast, there is no rankshaft or kinemati am surfae in a free-piston engine to physially realize this mehanism beause the piston is not onneted to a rank and am. In addition, a free-piston engine has variable stroke lengths and therefore it presents a hallenge for ative piston motion and preise stroke length ontrol. Inspired by the rank and am mehanism in onventional engines, this work proposes a virtual-am based approah to onnet free-piston motion to valve ontrols in an eletroni ontrol ontext. The primary funtionality of the virtual am ontrol framework is to reate repetitive but variable indies for the exhaust/injetion valves and spark timing similar to the funtion of physial ams in onventional engines. Sine the am is virtually reated, it an be dynamially rebuilt to omply with yle-toyle variations suh as engine load and stroke length. This index rebuilding proedure is I

11 based on a yle-to-yle adjustment method that uses the information obtained from previous yles to adjust the am parameters. Measurement of the piston position in free-piston engines is often diffiult, whereas the ylinder pressure an be more easily measured. From a ontrol s perspetive, pressure, power and energy of a ontrol volume diretly represent the dynamis of the engine and the piston. Therefore, this work investigates using pressure measurements and pressure dynamis in the virtual-am ontrol approah. Speifi details of this method suh as measurement of ritial positions, e.g. Top Dead Center (TDC) and Bottom Dead Center (BDC), are shown. Moreover, a novel term of breathe-in duration is used for evaluating the pump performane for a free-piston engine air ompressor so that measurement of the stroke length and alulation of expansion ratio are replaed by it. A omprehensive lumped-parameter model of an experimental Free Liquid-Piston Engine Compressor (FLPEC) was built and validated. The proposed ontrol method was first demonstrated in simulation of the FLPEC. The simulation results were promising, thus an experimental evaluation of the proposed ontrol sheme was onduted on a High Inertane Free Liquid Piston Compressor (HIFLPC). Experimental results of the injetion ontrol, exhaust ontrol and overall engine operation presented within this manusript showed an overall satisfatory engine performane, espeially: 1) overall engine effiieny was signifiantly improved from experimental results of manually tuned tests; 2) wide operation range in terms of the reservoir pressure was ahieved; 3) the ontroller was shown to be apable of adjusting the engine operational frequeny upon request. Based on the experimental results, this ontrol framework should be apable of serving as a favourable ontrol sheme for other free-piston engines. II

12 Chapter I FREE-PISTON ENGINES AND CONTROL The free-piston engine has been widely investigated sine it was first proposed by R.P. Pesara in A variety of free-piston engines have been developed for a number of appliations due to their advantages in omparison to onventional internal ombustion (IC) engines. Some of these advantages are: 1) the free-piston redues the mehanial frition losses from side loading of piston due to the rank. In some onfigurations, suh as the free liquid-piston engine developed by Riofrio and Barth [2][3], the piston frition is largely eliminated by using a liquid free-piston. 2) The engine does not require idle yles. In other words, it an be started/stopped upon request so that the engine s fuel effiieny an be improved by eliminating the idle operation in onventional IC engines. 3) The absene of a rankshaft-onneting rod mehanism gives the engine variable stroke lengths. This feature will allow the ontroller to optimize the engine effiieny by using variable ompression/expansion ratios. However, in addition to these advantages, the unique features of the free-piston engine also present a ontrol hallenge due to the non-rank mehanism. In this hapter, a brief review of the free-piston engine onept and appliations is provided, followed by a disussion of the ontrol hallenges. 1.1 Free-piston engines A free-piston engine is typially a linear ombustion engine. The piston used in the engine is alled free beause it is not onneted to a rankshaft and not kinematially 1

13 limited in its motion as in onventional ombustion engines. Based on the piston/ylinder onfiguration, free-piston engines are typially divided into three ategories: single piston, dual piston and opposed piston. A less ommon fourth ategory, gas generators, is also disussed in some literature. For a more detailed desription of these onfigurations, one an refer to a omprehensive review reently provided by R. Mikalsen and A.P. Roskilly [4]. In the early 1930 s, a German ompany named Junkers developed a free-piston air ompressor that was used by the German navy during World War 2 to provide ompressed air for submarines [5]. Later, a US ompany alled Worthington ontinued this Junker design without major design hanges [6]. In 1950 s, the automobile industry onduted researh on utilizing the advantages of the free-piston engine onept, aiming for automobile sale appliations. For instane, General Motors (GM) developed two free-piston gas generators [7]. However, the results of their test were quite disappointing. Aording to Speht [8], the problems inluded ontrol diffiulties and high maintenane osts but they did not dismiss the free-piston engines as a onept. Ford arried out similar efforts in free-piston engine developments in 1950 s without suess [9]. An important reason for these efforts being unsuessful was the lak of a proper mehanial ontrol mehanism, sine eletroni ontrol was not available at the time. Further researh on the free-piston engines was largely abandoned in the mid-20 th entury partially beause of these unsuessful attempts. Along with the advane in modern ontrol tehnologies, however, the free-piston engine onept has again drawn the interest of a number of researh groups. Control systems and their implementation 2

14 have gained more popularity in reported modern free-piston engine development, as opposed to earlier approahes that foused primarily on engine design. Ahten et al. [10] at Innas reported the implementation of an advaned ontrol system for a hydrauli freepiston engine pump, whih has a 20% fuel effiieny inrease ompared to onventional engines due to the redution of frition losses from rank and ative loads. However, the simpliity of the mehanial design set high requirements for the ontrol system. To investigate the ontrol hallenge, Tikkanen et al. [11-12] desribed the design and ontrol of a dual hydrauli free-piston engine pump. In a more reent approah, Kværner ASA developed a modern two-stroke high-speed diesel free-piston engine aimed at marine appliations [13]. By using modern eletroni ontrol tehnologies, experimental results on the single ylinder of the diesel ombustion unit were reported in [14], showing that Top Dead Center (TDC) and Bottom Dead Center (BDC) were ontrolled to be stabilized at their set-points. Authors of [13-14] onluded that the modern eletri ontrol tehnology provides the required proessing apaity and resolution to implement the required ontrol system funtionality of modern free-piston engines. Mikalsen and Roskilly [4] desribed more free-piston engines appliations in a omprehensive overview. They onluded that sine the free-piston engine is "restrited to the two-stroke operating priniple", and therefore heavily reliant on savenging in order to ahieve proper ombustion harateristis, "aurate ontrol of piston motion urrently represents one of the biggest hallenges for developers of free-piston engines." In order to investigate the ontrol hallenges of free-piston engines, a disussion of their unique features is arried out in the next setion. 3

15 1.2 Unique features of free-piston engines In order to ontrol the stroke length and the piston dynamis, the sum fores on either side of the piston (mainly from the pressures on the piston) need to be ontrolled. However, aurate pressure ontrol, espeially ombustion pressure ontrol is diffiult. To address the ontrol hallenge imposed by these diffiulties, the knowledge of the piston dynamis is utilized in the ontroller. Therefore, the free piston dynamis are first disussed in the next sub-setion Free-piston dynamis In onventional engines, the piston is onneted by the rank to the flywheel. This mehanism serves as a mehanial piston motion ontrol system. The inertia of the flywheel ats as energy storage that provides power for the ompression stroke. It laks ontrol flexibility but provides full piston motion and position ontrol. Moreover, the rank mehanism also defines the boundary of the piston motion, i.e. TDC and BDC. This onfiguration allows a fixed stroke and onsequently a fixed expansion ratio. Conversely, in the free-piston engine, the piston is free and its stroke length is not restrited by the rank mehanism. It gives the free-piston engine more ontrol flexibility for omplying with different loads. However, it also presents a ontrol hallenge for aurate piston motion ontrol. Typially, a ombustion hamber and a load hamber (or boune hamber) will be on opposite sides of the piston, as shown in Figure 1.1 (a). The moment when the piston is at TDC is the initial point of ombustion. During the power stroke, high pressure resulting from the ombustion pushes the piston to the load side, thereby sending power 4

16 to the load and pressurizing the boune hamber; during the return stroke, the pressurized boune hamber or some other type of returning fore ats on the piston to ensure a reiproating motion of the piston. BDC is defined as the piston position at whih the piston stops at the end of the power stroke. TDC and BDC together define the stroke length. If a boune devie other than a gas boune hamber is used, the piston motion harateristi is slightly different but the same priniple will remain appliable. P C P Load Combustion Chamber Free Piston Load Chamber (a) A simplified single piston engine F f P C Stroke Length F load x TDC BDC (b) Piston dynamis and stroke Figure 1.1 Piston dynamis of single piston free-piston engine By using pressure sensors, the piston dynamis an be modelled based on the measured pressures together with the fritions and loads ating on the piston. Figure 1.1(b) shows the fores ating upon the piston. Applying Newton s seond law to the moving piston, the dynamis an be desribed as, 5

17 d x 2 Fi mp 2 i dt P A F C f F load (1.1) where P C is the ombustion pressure, A is ross setional area of the piston, F f is the frition fore and F load is the fore from the load, x denotes the position of the mover (piston). The stroke length during the power stroke is x x. BDC TDC Eq. (1.1) implies that preise piston motion ontrol requires aurate pressure ontrol of P C and ontrol of the load fore F load. However, sine the ombustion proess is not diretly ontrollable, the ombustion pressure dynamis are also not diretly ontrollable. TDC and BDC, as shown in Figure 1.1, are not fixed positions as in onventional engines. For stroke length ontrol or expansion (ompression) ratio ontrol, more speifially, ontrolling the piston to reah partiular positions of TDC and BDC is of more interest than the preise piston motion profile ontrol along the piston path. Development of pratial TDC/BDC ontrol methods for suh purpose is more important for good thermodynami effiieny, avoiding piston-wall ollision and so on, whih is the fous in this work Frequeny ontrol In onventional engines, the stroke length is fixed. Thus, the frequeny ontrol in suh engines is essentially speed ontrol. For a free-piston engine using a gas boune hamber or a spring-like return devie, the period of an engine yle is strongly influened by its passive dynamis of the spring-mass nature. The ombustion proess only has slight impat on the engine frequeny in free-piston engines. Therefore, the frequeny of the free-piston engine is typially limited in a small range. However, free- 6

18 Load fore Combustion Fore piston engines do not have idle yle as onventional engines do, and therefore the piston an be ontrolled to stop at the end of the return yle. In this way, the engine frequeny an be ontrolled by stopping the engine for a ertain amount of time before the next power stroke, i.e. postpone the ombustion for next yle Free-piston engine loads Combustion Pressure Linear alternator Air ompressor x Hydrauli pump 1 2 Figure 1.2 Charateristis of free-piston engine loads [15]. x The position-varying loads ating on the piston of a given free-piston engine are different and therefore it also present a ontrol hallenge. As shown in Figure 1.2 [15], the load fores for the same ombustion pressure dynamis (top) in different free-piston 7

19 engine appliations. It is desired to have a linear load, more ontrollable load as seen with the hydrauli pump, so that the piston dynamis is relatively easier to ontrol. Therefore, the diffiulty lies in developing a proper expansion ratio (stroke length) ontrol for devies with non-linear loads Combustion proess in free-piston engines The ombustion proess in free-piston engines, as reported by different researhers, has shown: 1) it is signifiantly faster than that in the onventional ombustion engines due to the diret oupling of the ombustion ylinder to the low inertia moving omponents; 2) it has leaner emissions for a spark ignited free-piston engine than rankshaft engines; 3) the in-ylinder heat transfer is also different from onventional engines. Refer to [4] for more detailed disussions. From a ontrol perspetive, a partiular feature of free-piston engines is that the ombustion proess strongly influenes the stroke length. The amount of fuel injetion determines the stroke length and the energy delivered to the loads. For optimal effiieny, the energy input is desired to math the energy output requirement. Therefore, fuel mass injetion ontrol is a ruial ontrol input for engine effiieny and stroke length ontrol. 1.3 Control of free-piston engines Combustion expansion ratio ontrol is the most important ontrol objetive for free-piston engines. This ontrol objetive is a ombination of TDC and BDC positions ontrol. As shown in Eq. (1.2), TDC and BDC together define the expansion ratio, x BDC (1.2) xtdc 8

20 TDC is the initial piston position in the power stroke. Even small variations in the initial volume of the ombustion hamber lead to large hanges in the expansion ratio. On the other end of the stroke, the BDC position also affets the ompression ratio, but does so muh less than TDC position. In order to ontrol TDC, BDC and the resulting stroke length, a variety of approahes in the past have been attempted by regulating one or more of the following ontrol inputs: 1) amount of air/fuel injetion; 2) exhaust opening timing; 3) exhaust losing timing; 4) ignition timing and 5) load. Load, however, is not diretly ontrollable in most free-piston appliations, and it is therefore not onsidered as a ontrollable input in this work. The four onsidered ontrol inputs listed above will be addressed in order. The amount of the fuel mass is the energy input to the engine whih is onverted to energy output in the form of work done on the load. This amount needs to be regulated in suh a way that the engine will orrespondingly output the power required by ertain loads. S. Tikkanen reported a ontrol approah for this purpose whih is applied to a dual hydrauli free-piston engine [12]. The ontroller is based on energy balane, i.e., the input energy (result of fuel ombustion) equals the output energy, in the form of the piston mehanial energy and ompression energy. In this approah, timing/estimation of the valve and injetion, expansion ratio and engine operation are ontrolled based on energy onservation. Simulation results show good ontrol performane, but experimental tests were not performed on the real devie. This ontrol approah requires full knowledge of the engine, inluding frition and load. This requirement makes the energy-balane-based method diffiult to pratially implement. Moreover, the 9

21 measurement of the load energy is possible for the hydrauli engine pump but not always feasible for other appliations suh as air ompressors. Some free-piston engines, suh as the free-piston engine generator developed by Mikalsen and Roskilly [4], have a savenging port for exhausting. Ative exhaust ontrol is not required for suh engines. By eliminating the exhaust port design, there is more stroke flexibility. However, this requires an aurate exhaust valve ontrol dealing with variable BDC positions. A good example is the ontrol strategy for a free-piston gas generator developed by the Norwegian ompany Kværner ASA. Johansen T.A. et al [13][14]. The authors developed an eletroni am and rankshaft based ontrol strategy dealing with the ontrol of a free-piston diesel engine. The ontrol target is a multiylinder free-piston diesel engine that onsists of a free-piston gas generator, a turboharger and a power turbine. This engine has 8 ylinders with 8MW total power output. The ontrol system in their work inludes valve and injetor timing, piston motion ontrol and a supervisory ontrol. During the engine operation, the piston position and pressures are measured in real time. An estimator is then used to predit piston motion so that the valve timing ontroller an send the ontrol signals in advane to ompensate the time delays of the atuators and injetor. Piston motion ontrol deals with the TDC and BDC position ontrol. Experimental results show a satisfatory level of engine performane ontrolled when using this method. The timing ontrol and piston motion ontrol used by T.A. Johansen et al are based on estimations of the piston position and the gas mass in the power hamber. Therefore, the auray of suh ontrol method is strongly influened by that of the estimator. The authors did not show the performane 10

22 of these estimators and how the estimation auray affets the timing ontrol. The feasibility of estimating piston and pressure dynamis may beome a more ruial question for muh smaller sale than this 8MW engine. Besides piston motion ontrol, engine speed or frequeny ontrol is also one of the ontrol goals. For instane, for hydrauli free-piston engines to allow flow ontrol, they require a wide speed range. For suh purpose, Ahten et al [10] reported a Pulse Pause Modulation sheme for frequeny ontrol of hydrauli free-piston engines. This ontrol method pauses the piston at BDC by using a ontrollable hydrauli ylinder as rebound devie. Only when the hydrauli rebound devie is released, upwards motion of the piston an be resumed. The stored energy in the rebound hamber is released for ompression. This type of frequeny ontrol in free-piston engines is possible beause the piston position in eah stroke is not frequeny-dependent. In a very reent work, Mikalsen and Roskilly [17][18] investigated the feasibility of lassial ontrol strategies for the free-piston engine generator developed at Newastle University. The ontrol strategies inlude deentralized PID ontrol, pseudo-derivative feedbak ontrol and disturbane feedforward ontrol. They onluded further researh into free-piston engine ontrol is required to solve the signifiant ontrol hallenges assoiated with suh engines. As one an see, the reported ontrol approahes are typially appliation speifi and thus, the feasibilities of these reported methods are limited to partiular engines. For instane, aurate estimation of piston dynamis used in [17] [18] is not always ahievable; full knowledge of the engine dynamis and ontrolled loads are not available 11

23 for appliations other than hydrauli pumps [12]. In ontrast, in onventional ombustion engines the rankshaft mehanism provides a universal piston motion and valve timing ontrol framework. Injetion, ompression, and valve timings stritly orrespond to ertain piston positions, ontrolled by the rankshaft and ams regardless of the load and ylinder pressure variations. Inspired by rank and am mehanism in onventional engines, the purpose of this work is to develop a general ontrol framework for freepiston engine ontrol that mimis this rankshaft mehanism without losing ontrol flexibility. Using omputer/eletroni ontrol, the rank and am mehanism an be virtually reated and dynamially adjusted to fulfill the ontrol objetives suh as optimizing the engine effiieny and expansion ratio. In the next hapter, the development of suh a framework is desribed in detail. 12

24 Chapter II VIRTUAL-CAM BASED CONTROL FOR FREE-PISTON ENGINES The term of virtual am used here refers to the repetitive but variable timing ontrol indies in a omputer/eletroni based ontroller. Modern omputer tehnology provides a onvenient way to eletronially ontrol intake/exhaust valves. In the engine ontrol ommunity, researhers have been interested in ontrol of amless engine whih would yield higher effiieny [19]. The amless valve atuation systems offer potential benefits sine valve positions an be ontrolled independently rather than using an engine-dependent amshaft [20]. The free-piston engine an easily take advantage from suh tehnology by its amless nature. The proposed virtual-am based ontroller has a primary funtionality of opening/losing valves similarly to the physial am of onventional engines. That is, ams trigger the open/lose atuations of the ontrol valves at ertain piston positions. In onventional engines, the piston is onneted by the rank to the flywheel. This mehanism mehanially serves as the piston motion ontrol system. The rank mehanism also defines the boundary of the piston motion, i.e. TDC and BDC. The rotary dynamis of the rankshaft are fully onstrained by the piston dynamis. This mehanism an drive the rankshaft to rotate a full revolution beause the onneted piston travel distane is fixed during one engine yle. As illustrated in Figure 2.1 (a), the piston position is used to generate am timing in onventional engines, but this mehanism is not available in free-piston engines. The 13

25 piston motion is now atively ontrolled and absolute positions of the piston an no longer be used to trigger the valve atuations. The proposed virtual am mehanism uses a self-driven rankshaft that loates the virtual ams at relative positions (TDC/BDC for instane) for valve timings. The am harateristis are adjusted based on the measurement of the engine dynamis and the evaluation of the engine performane, as shown in Figure 2.1(b). The angular speed of the virtual amshaft determines the period of a yle. The operational frequeny of the engine an be manually input or an be automatially adjusted by the system level ontroller based on evaluation of the engine performane. Cam (x) Valves x (Piston position) Engine Dynamis (a) Physial am ontrol sheme in onventional engines Modify Cam Desired Engine Frequeny Cam (t) Low Level Controller Valves System Level Controller Engine Dynamis (b) Virtual-am based ontrol sheme for free-piston engines Figure 2.1 Comparison between physial am and virtual am shemes 14

26 2.1 Virtual-am for free-piston engine ontrol Virtual am onstrution Valve displaement Figure 2.2 Cam and valve By definition, a am is a projeting part of a rotating wheel or a shaft that strikes a lever at one or more points in its irular path, as shown in Figure 2.2. In automobile engines, timing belts are used to onnet the rankshaft with the amshaft so that rotary motion of the engine is translated into the reiproating motion of the am to operate the intake and exhaust valves. Cams in engine ontrol an be haraterized by their displaement diagrams, whih reflet the hanging position the valve would make as the am rotates about a fixed axis. The valve displaement is fully defined by the displaement diagram (the shape of its periphery) of the orresponding am. Figure 2.2 shows the valve displaement from lose position (left) to open position (right) along with the am rotation. During the open/lose motion, the am shape and the rotary motion of the am together haraterize the dynamis of the valve. 15

27 e e s s (a) Virtual am position (b) Virtual am shape Figure 2.3 Basi am onfigurations Based on above disussion, one an see that a am has two basi properties: 1) position, inluding start and end positions; 2) shape of its periphery that defines the orresponding valve open/lose dynamis. The position of a am, denoted by s, e, defines the time to open and lose the orresponding valve. The am starts to push valve open at opening angle s and loses the valve at losing angle e. Figure 2.3(a) illustrates a am lobe whih would produe a square-wave shape that only defines the timings for opening/losing the valve at s, e. In Figure 2.3(b), its periphery is designed and shaped to generate ertain valve response dynamis while the am duration is still s, e. Furthermore, the am position is advaned by a low level ontroller to ompensate for valve lifter dynamis and ignition delay if they are known or measured in the previous engine yles. To illustrate, onsider Figure 2.4(a) whih shows the ommand signals sent to a free liquid-piston engine [2-3]. The solid line is the air/fuel injetion ommand, the dashed line is the spark signal and the dotted line is the exhaust valve ommand signal. Valve lift dynamis are shown in Figure 2.4(b). In order to ahieve desired dynami response of the valve lifter, the low-level ontroller an 16

28 Valve response Command signals (on/off) ontrol the shape of the am s periphery. Speifially, the voltage for ontrolling the valve lifting and landing forms the shape of the virtual am. 1.5 Injetion Spark Exhaust Time (s) (a) Control ommands 1.5 Injetion Spark Exhaust Time (s) (b) Atual system responses to the ontrol ommands Figure 2.4 Delay and dynamis response Conventional engines have multiple valves and every valve has a dediated am. All the ams are typially fabriated on a amshaft, whih is a ylindrial rod running the length of the ylinder bank with a number of oblong lobes or ams protruding from it, one for eah valve, as shown in Figure 2.5(a). The ams fore the valves to open by pressing on a valve, or on some intermediate mehanism, as they rotate. In the virtual 17

29 am ontext, all ams an be similarly projeted on one rotating virtual amshaft, as illustrated in Figure 2.5(b). Sine this amshaft is virtually reated, it is self-spinning at an angular veloity. One revolution of this virtual amshaft orresponds to one engine yle. If f engine is the operational frequeny of the engine, the following equation holds, f engine (2.1) 2 Hene, the operating frequeny of the engine ould be simply modulated by ontrolling the angular veloity while using a onstant R. When the angular veloity is hanged to hange the engine frequeny from f to 1 f 2, the new virtual am positions 2 under the new operational frequeny need to be orresponding hanged by 2 f21 f1. Thus, the timings are kept same in the time domain. R (a) A typial amshaft (b) Virtual amshaft Figure 2.5 Physial amshaft and virtual amshaft As a summary, the working priniples of the proposed virtual am ontrol sheme are: 1) one revolution of the virtual amshaft orresponds to one engine yle, thus the frequeny of the engine is ontrolled by the angular veloity of the virtual amshaft; 2) 18

30 the opening/losing timing of eah valve is defined by the valve s virtual am position duplex, s e ; 3) the shape of a virtual am defines the ontrol output, suh as voltage (or urrent) for eletroni valves; 4) all the virtual am and amshaft parameters are redefined at the end of eah engine yle. Thus all timings an be adjusted by hanging the am parameters. Based on the proposed virtual am framework, a ontrol strategy is required to adaptively adjust am funtion from yle to yle. In the next setion, the ontroller design will be disussed in detail Control struture The yle-to-yle rebuilding of the virtual am struture provides a onvenient way for repetitive/iterative engine ontrol strategies. The repeating timing indies are now represented by am parameters s, e at a ertain amshaft angular speed. The main ontrol task for the virtual am is to adaptively modify the am geometry over the engine yles to omply with varying strokes, loads, et. For general engine ontrol, a number of inputs and outputs to the system need to be defined. Typially, main inputs to the engine inlude the signals to the air/fuel injetion system, whih determine fuel injetion timing and the mass of fuel to be injeted, and the signals to the exhaust valve(s), the timings of whih affet the stroke length and expansion (ompression) ratio. The main disturbane for free-piston engines is the engine load, whih is onsidered unontrollable in this work. On the high level ontrol, a system level ontrol is required to optimize the engine performane with respet to fuel effiieny and exhausting timings for a given operating 19

31 point. In onventional engines, this is ahieved by adjusting fuel injetion timing and valve timings. For free-piston engines, optimization of the engine performane also inludes expansion (ompression) ratio, i.e. stroke length ontrol. System-level ontrol Low-level ontrol Timing ontrol Frequeny Control Valve Dynamis Delay Compensation Cam position Camshaft angular veloity Shape of am periphery Advane am position Virtual Camshaft Compression ratio Engine effiieny Free-piston Engine Valve dynamis Delays Figure 2.6 Virtual-am based free-piston engine ontrol struture By using the onept of the virtual am and amshaft, the ontrol struture is illustrated in Figure 2.6. The key part of the ontrol struture is the virtual amshaft that inludes multiple virtual-ams for multiple valves. The system level ontroller ditates the opening/losing timings for valves and the engine frequeny, whih are virtual am position s, e and amshaft angular speed, respetively. The low level ontroller deals with the valve lifter dynamis ontrol and delay ompensation. At the end of eah engine yle, the virtual ams are rebuilt and the resulting ontrol outputs are sent to the free-piston engine. The rebuilding method is based on the analysis of the engine performane inluding stroke length, engine effiieny and other fators that will be 20

32 disussed further in the next setion. Meanwhile, valve response dynamis and delays are measured and fed bak to the low-level ontroller. This struture of the ontrol mehanism naturally bridges system level ontrol with lower level ontrol. Consider an eletromehanial valve atuator in amless engines, whih has been studied by numerous researhers [19][20]. The ontrol design for an eletromehanial valve atuator is the virtual am design in our ontext. The system level ontroller sends out the open/lose ommands, i.e., s e. The orresponding am is then shaped by the low level ontroller to realize desired effets suh as the soft landing of the valve [21]. 2.2 Virtual am repeating index rebuild Sine the low-level ontrol is engine and valve speifi, it will be omitted from the disussion of the general ontrol methodology of the virtual-am framework. This work thus fouses on the system-level ontrol for virtual-am rebuilding. In a typial free-piston engine, optimizing the amount of the fuel mass injeted and the exhaust valve timings are the main ontrol objetives. These objetives are ontrolled to ahieve desired engine effiieny and stroke length. Similar to onventional IC engines, a free-piston engine typially has at least one ombustion hamber, providing energy input for the power stroke, and a load hamber (or a boune hamber), as shown on the left in Figure 2.6. A load hamber is used to deliver energy to loads and a boune hamber is used to assist returning piston bak. For diret air/fuel injetion engines suh as some HCCI free-piston engines, the air/fuel mixture is diretly injeted into the ombustion hamber through an injetion valve. 21

33 Upon ombustion, the piston is pushed towards the load (boune) side by the highpressure ombustion produts. This is alled a power stroke, at the end of whih the piston stops at BDC, as shown on the right in Figure 2.7. The initiation of return stroke is indiated by the return of the piston towards the ombustion side. During the return stroke, the exhaust valve should be opened so that the ombustion produts an be exhausted. Using this simplified model desribed here, the system-level ontrol method an be developed based on the thermodynami analysis of the engine. Air/fuel Injetion Air/fuel Injetion Exhaust Power (ombustion) Load (boune) Exhaust TDC BDC Figure 2.7 A simplified illustration of the free-piston engine Fuel injetion ontrol In onventional IC engines, the mass of fuel injetion per yle influenes the engine speed and power output. This is likewise the ase in free-piston engines. The mass of injeted fuel also affets the stroke length and the expansion ratio in the ombustion hamber. Varying the mass of fuel injeted will not only influene the ombustion energy that will be delivered to the load and stored in the boune hamber, but it will also affet the TDC and BDC positions. 22

34 The fuel injetion ontrol is neessary to optimize the energy input for a speifi load and to ahieve a ertain stroke length so that the optimal engine effiieny an be ahieved. Generally, the overall engine effiieny is given by, E out f (2.2) Ein where E in is the energy input per yle and E out is the energy output per yle. The original amount of hemially stored energy in the injeted mass of air/fuel mixture is given by, E in m H (2.3) r where m is the mass of the fuel injeted into the ombustion hamber and H r is omputed from the lower heating value of the stoihiometri ombustion of the fuel. By using an eletroni on/off valve, the energy investment is proportional to the mass of the fuel injeted, given by Eq. (2.4), E in H r t inj 0 m dt (2.4) Therefore, regulating the duration of the injetion t inj an ontrol the input energy for eah yle. In order to derive the ontrol law for the injetion ontrol, an energy analysis in the ombustion hamber was arried out. The power stroke of the ombustion hamber an be divided into two stages as: 1) air/fuel injetion period; 2) ombustion and expansion period, or alled power period. The states of the ombustion hamber are illustrated in Figure 2.8. The initial time is 23

35 denoted by t 0 when the injetion begins, the end of the injetion or the beginning of the power period is at time t 1, and the end of the power stroke is at time t 2. Air/fuel Injetion Exhaust TDC BDC P V T P V T P V T 0, 0, 0 1, 1, 1 2, 2, 2 t 0 Injetion t1 Power 2 Period Period t t Figure 2.8 States of the ombustion hamber A power balane equates the energy storage rate to the energy flux rate rossing the ontrol volume (CV) of the ombustion hamber boundaries. The rate form of the first law of thermodynamis is given as follows: U H Q W (2.5) where U is the rate of hange of internal energy, H is the net enthalpy flow rate into the CV, Q is the net heat flux rate into the CV, and gas in the CV. Expressions for H and W are given as, p T in out in / out m / W is the rate of work done by the H (2.6) W PV (2.7) where m is the mass flow rate entering (positive sign) or leaving (negative sign) the CV, and T in / are the onstant-pressure speifi heat and the temperature of the out / p in out 24

36 substane entering or leaving the CV, respetively, P, V and T are the pressure, volume and temperature in the CV, respetively, v is the onstant-volume speifi heat of the substane in the CV, and is the ratio of speifi heats of the substane in the CV. During injetion period, assuming the temperature hange is negligible, i.e. T 0 T 1 onst, the hange of the internal energy an be alulated by, t t 0 t1 t1 U dt m T dt PV dt (2.8) 1 1 t 0 p 1 During the power period after ombustion, there is no mass flow in/out the ombustion hamber, i.e. m 0, if the exhaust valve is losed. Therefore, the internal energy hange is given by, t t 1 2 t 0 t2 t2 U dt Q dt PV dt (2.9) 2 t 1 Assuming the ombustion effiieny is denoted by, the energy released by ombustion is proportional to the total fuel mass injeted, given by, t t 1 2 t 1 t1 Q dt H m H m dt (2.10) r Based on the assumption of onstant temperature of T 1 0 during the injetion period, Integrating Eq. (2.5) over the entire period from t 0 to t 2 yields, t 2 t1 t2 t1 t1 t2 U dt U dt U dt m T dt H m dt PV dt (2.11) t 0 t 0 1 t 1 2 The fundamental internal energy equation in the ombustion hamber is given by, t 0 p r t 0 r t 0 t 0 U m T m T (2.12) v v Integrating both sides of the equation yields, 25

37 t t 0 t2 t2 U dt m T dt m T dt (2.13) 2 t 0 During the injetion period, the temperature is assumed to be onstant, whih yields, t t 0 1 v t 0 v m T dt 0 (2.14) v During the power period, there is no mass flow in/out the ombustion hamber, whih gives, Therefore, Eq. (2.13) an be written as, t t t 1 2 m T dt 0 (2.15) v 2 t2 t1 U dt m T dt m T dt (2.16) t 0 Equating the right sides of Eq. (2.11) and Eq. (2.16) yields, t t 1 2 t 1 v t 0 t1 t1 t1 t2 m T dt m T dt m T dt H m dt PV dt (2.17) Rearranging Eq. (2.17) yields, v t 0 v 1 t t1 t2 ( v p ) T 1 H r m dt mvt dt 0 p v r t 2 P Vdt (2.18) t0 t1 t0 Two terms at the right side of Eq. (2.18) an be replaed as following. The net energy inrease in the ombustion hamber, bounded by onstant mass, is only a funtion of its net temperature inrease. 0 t t 0 U 2 t t 1 2 m T dt m T m T (2.19) v 2 v 1 v 2 where T 1 is the temperature at the end of injetion period and T 2 is the temperature in the final state, respetively. During the power period, the internal energy hange of the ombustion hamber an be alulated using, 26

38 U 2 P 1V 1 V 1 V 2 1 k 1 1 (2.20) where the expansion ratio of the ombustion hamber V R is alulated by, 2 R (2.21) V 1 The PV work done by the ombustion gas is delivered to the load by the piston. Thus, t t2 fload( t) x pdt (2.22) t0 2 P Vdt t 0 where f load (t) is the fore from the load and x p is the piston position, and x V A. p The load fore is proportional to the piston displaement. Therefore, the larger expansion of the ombustion hamber results in more energy being delivered to the load. Letting the onstant into Eq. (2.18) yields, k m ( ) T H and substituting Eq. ( ) v p 1 r k m t t 0 1 t k 1 R 1 2 m dt P V f ( t) x dt (2.23) 1 1 Using Eq. (2.23), the ontrol law for fuel mass injetion an be derived. First, the fuel mass influenes the expansion ratio of the ombustion hamber. A larger piston displaement (or a larger stroke length) is ahieved by injeting a larger mass of fuel under a ertain load. Seond, a higher loading fore requires more energy input for the piston to move a ertain stroke length. It is also important to note that the physial onfiguration of the engine limits the maximum stroke length. Hene, the basi idea behind the ontrol of fuel mass injetion is to injet the minimum mass of fuel per yle while ahieving the desired expansion ratio or stroke length. t 0 load p 27

39 The ontrol input is the injetion duration of t0 t1, whih essentially determines the quantity of the fuel mass injeted or the energy input to the engine. The energy output is represented by two terms on the right side of Eq. (2.23). The primary goal of the fuel mass ontrol is to balane Eq. (2.23) so that the energy input in eah yle is suffiient but not exessive to ahieve a ertain stroke length under a ertain load. Rearranging Eq. (2.23) yields, t1 t0 m dt k P V 1 t 1 k 1 x 2 x f ( ) 1 1 load t xpdt (2.24) t0 mv 1 A km where the piston position at the end of power stroke x 2 defines the BDC position and A is the ross setion area of the piston. In the written as, th k engine yle, the above equation an be m [ k] E [ k] x k 1 k 1 x[ k] x[ k] E [ k] L[ ] 2 1 L k (2.25) where P [ k] V [ k] E (2.26) 1 1 x[ k] 1 k 1 kmv 1[ k] A 1 EL[ k] (2.27) k m t L[ k] 2 fload[ k]( t) x pdt (2.28) t0 Eq. (2.25) quantifies the fuel mass required for desired stroke length of x2[ k] x 1[ k] under the load profile of L [k] in the th k yle. Therefore, a desired onstant stroke length is first set for the ontroller, denoted by x d. Then the amount of energy neessary to push the piston to travel for the desired stroke length an be 28

40 alulated. For an air ompressor, this position is where the ompression hamber has zero volume, meaning all of the air in the ompression hamber is pumped out. During engine operation, the load varies from yle to yle. Thus, the fuel mass injeted should be aordingly adjusted to aommodate these variations. In order to adaptively rebuild the virtual am for the fuel mass injetion, this work proposes a yle-to-yle based dynami ontrol method. The adjustment of the fuel mass is based on the evaluation of the engine performane in the previous yle and the urrent loads (or predited loads in the next yle). A linear formulation of the dynami ontrol algorithm reads as, m [ k 1] m [ k] E ( x x [ k]) E ( L[ k 1] L[ k]) (2.29) f where m f [k] is the fuel mass injeted in the x stroke [k] is the measured stroke length in the stroke length error. The weighting onstant f x d stroke L th k yle, x d is the desired stroke length, th k yle, E ( xd xstroke[ k]) x is the weighted E x has the same order of magnitude and unit as E x [k] in Eq. (2.26). L [k] is the load in the th k yle; [ k 1] L is the predited load in the next yle. E L ( L[ k 1] L[ k]) weights the load variation with the onstant E L whih has the same order of magnitude and unit as E L [k] in Eq. (2.27). The ontrol priniple is illustrated in Figure

41 0 xtdc Desired stroke length xbdc Load Fuel mass Cyle n-1 n n+1 n+2 Expansion ratio is lower than desired, inrease fuel mass Expansion ratio reahes desired, load inreases, inrease fuel mass Expansion ratio reahes desired, load dereases, derease fuel mass Expansion ratio is lower than desired, load inreases, inrease fuel mass Figure 2.9 Expansion ratio and fuel mass ontrol The amount of air/fuel mixture used per yle is determined by adaptively adjusting the injetion duration for a desired stroke length and the load based on how it is expeted to vary in the next yle. The adjustment is made effetive by hanging the orresponding virtual am parameters of s, e fuel, i.e., a longer duration of fuel injetion is ahieved by inreasing for a given operating frequeny. s e Exhaust timing ontrol Exhaust valve timings an strongly influene TDC of free-piston engines. At the end of the power stroke, it is desired to open the exhaust valve of the ombustion hamber so that the ombustion produts an be immediately exhausted. In some freepiston engines [5-10], savenge ports are used for this purpose. In more reently developed free-piston engines, suh as [19] [24], ative on/off exhaust valves are used to ahieve better ontrollability. If the exhaust valve is not opened when the return stroke begins, the trapped ombustion produts in the ombustion hamber will be ompressed and will at as a gas spring resisting the return of the piston. This will ause a portion of 30

42 the energy (stored in the boune hamber or other return devie) to be wasted on ompressing the ombustion gas. The return stroke length is thus shorter, resulting in a larger initial TDC, and onsequently, a smaller expansion ratio in the next yle. For most free-piston engines, ombustion and expansion happen very quikly, so the ontrol proess needs to be fast enough to omply with the rapid engine operation. However, sensor measurements and operations onduted on these signals are delayed by filters. Furthermore, solenoid eletroni valves annot be instantaneously opened/losed fully as there are restrited by their response dynamis. These fats make it impossible to use a given engine yle s sensor data to time the opening/losing of the valve in that yle. When the TDC/BDC is determined, the time at whih the ontrol ommand needs to be sent out has already passed. Therefore, ontrol an not be arried out in real-time. These kinds of delay problems have been investigated in onventional engine ontrol [19] [20]. A potential solution is to predit the dynamis of the piston in real-time, allowing for the ontrol ommands to be aordingly sent out in advane to ompensate for the delays [13-14]. This method, however, requires additional intensive omputations and handles disturbanes poorly. Therefore, an adaptive ontrol algorithm is proposed in this work for adjusting virtual am parameters from yle to yle. As mentioned before, the virtual am for eah subsequent yle is rebuilt at the end of yle preeding it. This allows delays and dynami response to be integrated into the rebuilding proess in whih the am lobes are aordingly adjusted. Therefore, based on the knowledge of previous ontrol results, the virtual am parameters an be gradually adjusted at the end of eah yle suh that the timings approah their ideal values. 31

43 At the end of a return stroke, the ideal exhaust valve timing oi, i ex an be obtained by measuring the time when the piston reahes TDC and BDC, whih an be determined by measuring piston positions diretly. The ideal virtual am positions are denoted by oi for open and i for lose. Meanwhile, the atual time when the open/lose ontrol signals are sent to the engine are also known, denoted by oa, a ex. Diretly applying the ideal timings in previous yle to the next yle is not pratial due to the yle-to-yle variations that inlude different TDC/BDC and onsequently ideal exhaust timings. Thus, the exhaust timing adjustment is arried out in a first order proportional ontrol manner, given by [ k 1] [ k] ( [ k] [ k]) (2.30) oa oa o oi [ k 1] [ k] ( [ k] [ k]) (2.31) a a where ( [ k] [ k]) weights the previous exhaust valve open timing error, o oi oa ( [ k] [ k]) weights the previous exhaust valve lose timing error. i a In Equations (2.30) and (2.31), if 1 and 1, it will be diretly applying o the optimal timings ahieved in urrent yle to the next yle. It is not pratial due to the reason mentioned above. Hene, a gradual adjustment, with, 1, is used to redue [ k] [ k] and [ k] [ k] with suessive yles without ausing the oi oa i a system to undergo sudden hanges. Figure 2.10 illustrates the working priniple of the proposed exhaust ontrol strategy. The errors between atual and ideal opening/losing timings are measured in the urrent yle and redued in the following yle by Equations ( ). i oa a o 32

44 Air/fuel Injetion Exhaust For variable strokelength, TDC/BDC are not fixed. TDC i error oi BDC oa oi Ideal Timings error i a a oa Atual Timings Figure 2.10 Cyle-to-yle exhaust timing ontrol 2.3 Pressure-based ontrol approah In order to use those ontrol laws derived above, piston position measurement is required. However, this measurement is not always available in all free-piston engines. For instane, the free liquid-piston engine ompressor [2][3] has no piston rod, and the piston s position is ontrolled by trapping it between two varying ontrol volumes. In its ase, pressure dynamis an be used to infer piston dynamis as the latter is diffiult to pratially measure. For many deades, ylinder pressure has been used by engineers for various appliations of internal ombustion engines. J. D. Powell [22] disussed how to address the air/fuel ratio ontrol problem by using ylinder peak pressure, and showed the benefits of using ylinder pressure for timing and engine ontrol. Additionally, the use of ylinder pressure for ombustion misfire detetion was also disussed by [22]. P. Yoon et al. [23] presented a losed-loop ontrol of spark advane and air/fuel ratio in SI engines 33

45 using the ylinder pressure. The peak pressure and the time at whih it ourred in eah yle were analyzed and used for ontrolling the air/fuel ratio and spark timing. The hamber pressure provides an alternative way to examine the piston dynamis and using pressure for free-piston engine ontrol purpose has never been reported. The fast response of modern eletroni pressure sensors and the omputational apabilities of miroproessors allow the use pressure as a fundamental engine variable for engine ontrol. Hene, this work will be the first to investigate the possibility of using pressures for assisting the proposed virtual-am based ontrol method. During the power stroke while the exhaust valve is losed, pressure dynamis are diretly aused by ompression and expansion in the boune hamber and the ombustion hamber. The fundamental internal energy equation of a gas is given by, whih states that the net energy inrease mass m) is only a funtion of its net temperature inrease U m T (2.32) g v U g in a ontrol volume (bounded by onstant T, assuming that no heat or enthalpy fluxes our. For a ontrol volume that is hanging its states, above equation an be expanded to, U m T m T (2.33) g v o v f where T o is the temperature at the initial state and T f is the temperature at the final state, respetively. Applying the ideal gas law, Eq. (2.33) an be written as, mrt mrt o f U g (2.34)

46 where R and are the gas onstant and the ratio of speifi heats of the gas, respetively. Further, using the ideal gas law, the following substitution an be made, where P o and V o are the original pressure and volume, and Pf V f PoV o U g (2.35) 1 1 Pf and V f are the pressure and volume at the final state, respetively. For a free-piston air ompressor, the final state is when the pump pressure exeeds the reservoir pressure and the pump begins. Assuming this proess is adiabati, the following expression holds, PV P V o 0 f f (2.36) By substituting Eq. (2.36) to Eq. (2.35) and rearranging the terms yields following two equations, 1 P ov V o f U g 1 (2.37) 1 Vo 1 P ov P o f U g 1 (2.38) 1 Po Sine V f V o is the expansion ratio of the ombustion hamber, Eq. (2.37) shows the relation between the expansion energy and the expansion ratio of the ombustion hamber. Eq. (2.38) shows the relation between expansion energy and pressure ratio. These two equations orrelate the pressure dynamis to the ontrol target, that is, the expansion ratio (proportional to the stroke length). Differentiating both sides of Eq. 35

47 (2.36) yields the instantaneous power P w done by the ontrol volume at the final state (or at any time), P w 1 1 Po Vo Pf P f (2.39) Using Equations ( ) and analyzing the engine performane in term of energy and power, the proper timings for engine ontrol an be obtained. As shown in Eq. (2.39), the power of a ontrol volume is related to its pressure dynamis. When P f beomes zero, power is at its maximum or minimum for a given stroke. The gas stops doing work on the piston so that the veloity of the piston beomes zero ( x 0 ) as well. In this way, Eq. (2.39) orrelates the power of gas to the dynamis of the piston. When the piston s x 0, it is typially BDC or TDC whih are of interest to the piston ontroller. When the hamber is not sealed, the above relationship between pressure dynamis and piston dynamis are still true, i.e. P 0 while x 0. In all above equations, (for adiabati proess) an be replaed by a onstant k if it is a polytrophi proess. To illustrate above disussion, the following onsider example of apturing interested piston positions using energy and power analysis. When the piston reahes either BDC or TDC, kineti energy of the piston beomes zero. Therefore, the piston stops doing work on the ontrol volume, and the ontrol volume starts to do work on the piston. This an be seen from the power P w rossing zero and swithing its diretion, as shown in Figure This figure shows the pressure dynamis in the ombustion f piston piston 36

48 Pressure and Power hamber and the work done by the ombustion produts. The data is from simulations of the free liquid-piston engine ompressor (FLPEC), whih will be introdued in the next hapter. When the piston omes to the BDC, pressure reahes its peak (loal maximum) and power rosses zero from negative to positive and P 0 while x 0. f piston 5 x Pressure Power BDC Time(s) Figure 2.11 Pressure dynamis and power of the expansion hamber in FLPEC [2] [3] Most opening/losing valve atuations our at ritial positions suh as BDC and TDC. By opening the exhaust valves, gas in previously sealed ontrol volume is quikly released in the form of mass flowing out of the hamber. Upon savenging, energy in a ylinder is released so that this ontrol volume an redue its negative work on the piston. In this way, the piston an move more freely without being pushed by the ompressed air in the ylinder. In additional to pinpointing ritial positions suh as TDC and BDC, pressure dynamis an be used to analyze piston dynamis influened by ontrol or disturbanes. 37

49 2.4 Conlusions This hapter introdued the working priniples of the virtual-am based ontrol struture. A yle-to-yle based dynami adjustment method for the am parameters was proposed for the injetion ontrol and exhaust ontrol. Control laws for injetion and exhaust were derived in a general free-piston engine ontrol ontext. In addition, the possibility of using pressure dynamis for free-piston engine ontrol was also disussed. Before implementing the proposed ontrol struture on a real devie, it will be tested and validated in simulation. Therefore, the next hapter introdues modeling of a Free Liquid- Piston Engine Compressor (FLPEC). The simulation test results of the ontroller will be provided in hapter 4. 38

50 Chapter III MODLEING AND SIMULATION OF A FREE-PISTON ENGINE COMPRESSOR In this hapter, a prototype of an experimental free-liquid piston engine ompressor [24] is introdued and its modeling and simulation are provided. The proposed virtual-am ontrol framework is tested and validated in simulation of this devie first. Experimental testing of the ontrol method was onduted on a later version the free-piston engine ompressor prototype [25]. 3.1 Free-Liquid Piston Engine Compressor (FLPEC) Motivated by high energy and power densities, pneumati power supply and atuation systems are being investigated by various researhers [26][27] for untethered roboti appliations requiring ontrolled human-sale power motion output. Suh systems utilize linear pneumati atuators that have approximately an order of magnitude better volumetri power density and five times better mass speifi power density than state of the art eletrial motors [28]. Regarding power supply, on-board air supply has shown to be a non-trivial issue, sine standard air ompressors are too heavy for the intended target sale, as are portable tanks with enough ompressed air (stored energy) to supply the atuators for a useful duration of time. To address this problem, a free liquid-piston engine ompressor (FLPEC) with a separated ombustion hamber has been developed by Riofrio and Barth [24] to provide an on-board supply of ompressed air. The FLPEC disussed in this hapter is a ompat internal ombustion engine with a free-piston onfiguration, dynamially arranged to math the load of ompressing 39

51 and pumping air. The ombined benefits of a high-energy density fuel, the effiieny of the devie, the ompatness and low weight of the devie, and the use of the devie to drive lightweight linear pneumati atuators (as ompared with similar power eletri motors) is projeted to provide at least an order of magnitude greater total system energy density (power supply and atuation) than state of the art power supply (batteries) and atuators (eletri motors) appropriate for human-sale power output [24]. (a) Coneptual model of the FLPEC (b) Fabriated engine Figure 3.1 The free liquid-piston engine ompressor onfiguration [24] 40

52 The FLPEC is shown in Figure 3.1. It onsists of a ombustion hamber, an expansion hamber, a liquid piston, and a ompression/pumping hamber. The ombustion hamber is separated from the expansion hamber by a magnetially lathing valve that seals in the fae of high pressure air and fuel injeted into the hamber, and opens in the fae of higher pressure ombustion produts. The expansion hamber allows for the ombustion produts to perform PV work on a free-piston onsisting of a liquid slug trapped between two high-temperature elastomeri diaphragms. Please refer to [24] for more details. 3.2 Dynami system model of the FLPEC The FLPEC was modeled as a lumped-parameter model with a level of fidelity appropriate for only those states of interest, and with auray adequate for ontrol purposes. Therefore the system is simplified as the fored mass-spring-damper system shown in Figure 3.2. A ontrol volume (CV) approah was taken to model the pressure and temperature dynamis in the ombustion onstant-volume hamber (subsript ), the expansion hamber (subsript e ), and the ompression hamber (subsript p ). Mass flow rates were modeled through all six hannels: 1) air/fuel injetion mass flow through a ontrolled on/off valve ( m inj ), 2) breathe-in hek-valve inlet mass flow into the ombustion hamber ( m 1 ), 3) mass flow through the magnetially-lathed ombustion valve between the ombustion and expansion hambers ( m 2 ), 4) mass flow through the exhaust valve of the expansion hamber ( m 3 ), and 5) inlet ( m 4 ) and 6) outlet ( m 5 ) hek-valve mass flow of the ompression hamber. The arrows in Figure 2 indiate the diretions of the mass flow, where m 2 and m 3 are modeled as two-way flow 41

53 dependent upon time varying upstream and downstream pressures. Finally, the inertial dynamis of the liquid piston and the ombustion valve were inluded to relate the timebased behavior of all three ontrol volumes. P S Patm m inj m 1 P V P atm m 2 m 3 P e V e M k P p V p m 4 m 5 P P S atm Figure 3.2 Shemati of the lumped-parameter dynami model of the FLPEC A power balane equates the energy storage rate to the energy flux rate rossing the CV boundaries. The rate form of the first law of thermodynamis is given as follows: U j H Q W (3.1) j j j where j is a subsript (, e or p) indiating eah of the three CVs, U is the rate of hange of internal energy, H is the net enthalpy flow rate into the CV, Q is the net heat flux rate into the CV, and W is the rate of work done by the gas in the CV. Expressions for H, W and U are given as: T H (3.2) j mj pin / out j in / out j W PV (3.3) j j j U j m j T m T 1 PV PV v j j j v j j 1 j j j j j (3.4) where m is an individual mass flow rate entering (positive sign) or leaving (negative sign) the CV, and T in / are the onstant-pressure speifi heat and the temperature out / p in out of the substane entering or leaving the CV, respetively, P, V and T are the pressure, 42

54 volume and temperature in the CV, respetively, v is the onstant-volume speifi heat of the substane in the CV, and is the ratio of speifi heats of the substane in the CV. Combining Equations ( ), the following differential equations an be obtained for the pressure and temperature dynamis: P j j 1 m j p T in out j 1 in / out / j j V j Q j PV j j j (3.5) T j m T j[ pin / out j in / out j v m j v j T ] PV j j j j Q j (3.6) The mass flow rates rossing all six valves depend on the upstream and the downstream pressures where a positive sign onvention indiates mass flow into the CV. Upstream and downstream pressure roles will swith for the two two-way mass flow rates shown ( m 2 and m 3 ) as the pressures P and P e hange dynamially aording to Eq. (3.5). The following equations give the mass rate under subsoni and soni onditions [28]: Pu Cda jc1 Pd T if P u r Pu m j j Pu, Pd (3.7) 1 u u 1 u P u Pd Pd Pd C da jc2 1 if Pr Tu Pu Pu Pu where C d is a nondimensional disharge oeffiient of the valve, a is the area of the valve orifie, P u and P d are the upstream and downstream pressures, T u is the upstream temperature, u is the ratio of speifi heats of the upstream substane, and C 1, C 2 and P r are substane-speifi onstants given by, 43

55 C 1 2 u 1 Ru u 1 1 u u (3.8) C 2 2 u R 1 u u (3.9) P r 2 1 u u 1 u (3.10) where R u is the gas onstant of the upstream substane. The valve orifie areas of the ombustion and exhaust valves ( a 2 and a 3 ) are dynamially determined by the inertial dynamis of their respetive valve stems Modeling of the ombustion proess Sine the expansion and pumping proesses our very quikly, heat lost during these two proesses is negleted. That is Q Q 0. However, the heat flux rate for the e pressure and temperature dynamis of the ombustion hamber is primarily determined by the heat released during the ombustion. The ombustion proess is oupled to the temperature dynamis in the ombustion CV. Given that the PV work term in Eq. (3.6) hanges on a time-sale of the same order as the ombustion proess, a model of the heat release rate during ombustion must be inluded. The total energy stored in the air/fuel p mixture at the time of the spark an be omputed by E H rm t, where spark m is the total mass in the ombustion hamber, and H r is omputed from the lower heating value for the stoihiometri ombustion of propane, 44

56 H r kj 1kg fuel kg fuel kg air/fuel mixture kj 2787 kg air/fuel mixture (3.11) given by, The rate at whih heat is released by ombustion in the ombustion hamber is Q H m (3.12) r where m is the mass of the ombustion produts. In the ombustion researh ommunity, the Arrehnius law [29] is often used to ompute the reation rate. Using this method, the following equation is obtained giving the reation rate of the temperature dependent ombustion, Ea RT Ke / mu (3.13) m where m is the rate of emergene of ombustion produts, E a is the ativation energy, and K is the pre-exponential fator. The mass of unombusted material m u in the ombustion hamber is given by, t m m m dt (3.14) u tspark In the Laplae domain, Equations (3.12), (3.13) and (3.14) an be more ompatly represented by the following, Q E s 1 (3.15) where 45

57 1 (3.16) Ea / RT Ke The Arrehnius law assumes that the fuel is homogeneously ombusted and the temperature is same within all regions of the ombustion hamber. However, the ombustion is spark-ignited in the FLPEC. Hene, the first order model will not adequately apture the spatial propagation dynamis of the ombustion proess. Instead, a seond-order model is applied to aount for the omplexities assoiated with ombustion flame propagation and temperature distribution within the hamber. The overall heat release rate is then given as, Q E 2 s (3.17) s Given that the reation is assumed irreversible, the damping ratio must satisfy 1. The Ea / RT temperature-dependent rate is still given by the Arrehnius law: Ke. Q is regarded as the effetive heat release rate whih ontributes to pressure and temperature dynamis as shown in Equations (3.5) and (3.6). simplified as, an be further (3.18) A T Ke / where K and A are empirially obtained onstants Combustion valve dynamis Sine the ombustion valve has dynami harateristis that influene its flow area, it has to be properly modeled so that Eq. (3.7) an be omputed in real-time. Figure 3.3 shows the free-body diagram of this valve. 46

58 Applying Newton's seond law, the valve dynamis are thus given: m _ v x P A F P A (3.19) v _ v M e _ v P A _ v F M P e A _ v Figure 3.3 Free-body diagram of the ombustion valve where m _ v is the mass of the valve, v x is the position of the valve, F M is the magneti fore generated by the permanent magnet, respetively, and A _ is the ross-setional v area of the valve head. Furthermore, the valve flow area a 2 x v an be desribed by the following: a x min 2 r x, r r v (3.20) v v v v _ stem where r v and r _ are the radii of the valve head and valve stem, respetively. v stem Exhaust valve dynamis The dynamis of the exhaust valve, as shown in Figure 3.4, are given similarly to the ombustion valve as follows, m 2 Patm Pe Ae _ v ke _ v( xe v xe v be vx 0 _ e _ v Fsolenoid (3.21) e _ vxe _ v ) where x _ is the displaement of the exhaust valve into the expansion hamber side, e v A e _ v is the ross-setional area of the exhaust valve, e v b _ is the effetive visous frition, x e _ v0 is the pre-ompressed spring fore giving the valve returning fore, and F solenoid is the fore exerted on the exhaust valve by the solenoid valve ontroller. 47

59 F spring P A atm e _ v F solenoid P A e e _ v where r ex and Figure 3.4 Free-body diagram of the exhaust valve Similarly, the valve flow area a 3 x ex an be desribed by the following: ex stem a x min 2 r x, r r ex (3.22) ex ex ex ex _ stem r _ are the radii of the exhaust valve head and stem, respetively Free-piston inertial dynamis The liquid slug trapped between the elastomeri diaphragms essentially onstitutes a mass-spring-damper system, where the fluid mass M and diaphragms' stiffness k an be seleted for a desired resonant frequeny. The dynamis given by the liquid piston are modeled by the following differential equation: V 1 2 e Pe Pp A kve bv e kve _ rlx (3.23) M where V e is the volume in the expansion side, A is the ross-setional area of the liquidpiston, b is the effetive visous frition assumed for a 50% overshoot, and V _ is the e rlx "relaxed" volume in the expansion hamber when the diaphragms are unstrethed. 3.3 Simulation results and validation This setion shows experimental model validation of three proesses inside the ombustion hamber: 1) pressure dynamis inside the hamber during the injetion of the air/fuel mix, 2) the dynamis of heat release during ombustion and the resulting influene on pressure, and 3) the opening of the ombustion valve and its effets on the 48

60 pressure. Figure 3.5 shows the simulated and experimentally measured pressure and displaement of the ombustion valve in the ombustion hamber during the injetion of the air/fuel mixture. The engine dynamis, when ombusted under different injetion pressures of 80 psig, 62 psig and 45 psig respetively, are shown in Figure 3.5. The model is given by Equations (3.5) and (3.7). The only parameter empirially determined was the oeffiient of disharge C d in Eq. (3.7). Sine the temperature during the ombustion is diffiult to measure on the real devie, only the pressure dynamis an be ompared between simulated and experimental data. As introdued in hapter 2, the system-level ontroller is based on pressure dynamis. Therefore, it is important to validate the pressure dynamis in all three CVs, espeially in the ombustion hamber given that it provides all of the driving power to the remainder of the system. The devie was tested as an open system, where the expansion hamber was not attahed to the ombustion hamber; that is, the ombustion valve was exposed to the atmosphere. The results show the pressure in the ombustion hamber immediately after the spark. The dynamis of heat release during ombustion ause a rapid rise in pressure, and the opening of the ombustion valve auses the pressure drop. The two onstants K and A in Eq. (3.18), and the magnitude of F M in Eq. (3.19) were empirially adjusted to fit the overall ombustion hamber pressure dynamis to the experimental results of the ombustion pressure. The eletromagneti fore eletromagnet was not utilized in this experiment. F EM in Eq. (3.19) was set to zero as this 49

61 Pressure (psi), Displaement (100=10mm) Pressure (psi), Displaement (100=10mm) Pressure (psi), Displaement (100=10mm) Combustion Pressure (Simulation) Combustion Pressure (Experimental) Valve Displaement (Simulation) Valve Displaement (Experimental) Time (s) Combustion Pressure (Simulation) Combustion Pressure (Experimental) Valve Displaement (Simulation) Valve Displaement (Experimental) Time (s) Combustion Pressure (Simulation) Combustion Pressure (Experimental) Valve Displaement (Simulation) Valve Displaement (Experimental) Time (s) Figure 3.5 Simulation results and experimental data of the ombustion pressure dynamis and the displaement of the ombustion valve in the ombustion hamber. 50

62 Pressure (kpa) Pressure (kpa) Figure 3.6 Heat release during the ombustion (simulated) Combustion Pressure Expansion Pressure Pump Pressure Reservoir Pressure Time (s) Combustion Pressure Expansion Pressure Pump Pressure Reservoir Pressure Time (s) Figure 3.7 Validation of the overall system dynamis for FLPEC 51

63 Figure 3.6 shows the total heat released by ombustion as desribed by Eq. (3.17). The total heat E stored in the air/fuel mixture is kj for this ombustion event. However, in mathing the simulated pressure dynamis to the experimentally obtained data, the values of K and A yield an effetive heat release E of 93.8 kj, whih means that the experimental ombustion lost 36.4 kj to some ombination of inomplete ombustion and heat losses through the ombustion hamber walls. Figure 3.7 shows the overall system dynamis validation. Pressures in four CVs are shown, whih are ombustion pressure, expansion pressure, pump pressure and reservoir pressure respetively. It an be seen that the simulated pressure dynamis in these CVs have a very good orrelation to the experimental data. 3.4 Conlusions This hapter presented the modeling and simulation of an experimental prototype of a free liquid-piston engine ompressor. The ombustion proess was modeled as a seond order dynami with the heat release rate governed by the Arrhenius law. The dynamis of three ontrol volumes, the ombustion hamber, the expansion hamber and the pump hamber respetively, were modeled. The mass flows in/out of these ontrol volumes were also modeled. The simulation results for the pressures in the ombustion hamber show good agreement with the experimentally measured pressure. Therefore, the simulation models of the FLPEC provide an aurate platform for testing the ontrol algorithm. 52

64 Chapter IV SIMULATION RESUTLS BASED ON VIRTURAL CAM CONTROL The mathematial model and simulation of the FLPEC prototype exhibit a lose orrelation with experimental data. Hene, the validity of the proposed virtual-am based ontrol struture is ready to be tested in simulation. 4.1 Control objetive The ontrol objetive is to drive the system in an effiient manner by extrating the maximum possible amount of PV work from the ombustion produts. The ontroller should be able to dynamially adjust the ontrol variables, i.e., the fuel injetion duration and valve timings. For instane, the pressure in the reservoir an be inreased by ontinuous pumping, or dereased by supplying air to the end appliation. This results in varying fuel injetions and loads, sine the pressures in the reservoir are different. The duration of air/fuel injetion must be adaptively ontrolled so that optimal effiieny an be ahieved and the ompressor an be kept running in a desired way under varying operating onditions. Furthermore, proper timing of all of the valves is ritial in ahieving the best performane of the FLPEC. Like in most other free-piston appliations, the period from yle to yle ould be hanged for the devie. Hene, the ontroller should also be able to ahieve operational frequeny ontrol. Figure 3.7 shows the simulated dynamis of the ombustion pressure, expansion pressure, ompression pressure and reservoir pressure. It an be seen that the ombustion pressure rises rapidly upon the ignition of the air/fuel mixture. The free-liquid piston is 53

65 then pushed by high pressure on the expansion hamber side, whih results in pumping. Suessful pumping is manifested by a slightly higher ompression hamber pressure P p than the reservoir pressure P s. The pumping proess begins at the time when P p is inreasing and beomes greater than P s. It is imperative that the duration of the air/fuel injetion is long enough to ahieve desired stroke length and full pump under a ertain load. However, exessive air/fuel injeted into the ombustion hamber may result in unutilized energy, whih onsequently dereases the FLPEC s effiieny. In order to ompress the air in the ompression hamber to a ertain pressure, the piston needs to travel ertain stroke length. Therefore, the stroke length ontrolled by the air/fuel mass injetion is ritial for suessful pumping. By putting the ontrol in the virtual am ontext, the virtual am and amshaft are reated in the first yle and adaptively adjusted in the following yles. 4.2 Virtual am onstrution There are three virtual ams orresponding to three valves: 1) Air/fuel valve am; 2) Exhaust valve am of the expansion hamber; 3) Spark ignition am. As previously mentioned, eah ontrol ommand sent by a given virtual am will result as a duplex of { s, e}, whih defines the timings for opening and losing a given valve. This struture results in five ontrol variables being ontrolled by three virtual ams. Three pairs of parameters for three virtual ams an be written as Cam inj (injetion valve inj _ b, inj _ e ontrol), Cam (exhaust valve ontrol) and Cam ex ex _ b, ex _ e sp (spark sp _ b, sp _ e ontrol). The values of these pairs influene five ontrol variables: 1) The amount of 54

66 Command signals(on/off) air/fuel mixture injeted for eah yle, or the time duration of the air/fuel injetion proedure; 2) The initiating time of air/fuel injetion; 3) The timing of the spark; 4) The time at whih the exhaust valve opens; 5) The duration for whih the exhaust valve is open. The ommands for a sample engine yle are shown in Figure 4.1. The orresponding virtual ams on the wheel are built based on these ommands, as shown in the left figure of Figure 4.2, an equivalent virtual am lobes sketh is shown on the right. By hanging the angular veloity of the wheel, the period or the engine operational frequeny an be adjusted as needed. When the frequeny is hanged, the stored am parameters need to be aordingly hanged so that the timings in the time domain remain unhanged. Assuming the original frequeny is f and the new frequeny is 1 f 2, a new am parameter an be found by saling the old parameter by 2 f21 f1. If any of these parameters exeed 2, i.e. some timings an not be arried out within one yle, then the desired frequeny is too high to be implemented and a lower frequeny should be onsidered. 1 Injetion ontrol Spark ontrol Exhaust ontrol Time(s) Figure 4.1 Command signals in Simulation 55

67 Figure 4.2 Virtual ams onstruted by ommand signals Dynami Response Time Delay Ignition Delay Figure 4.3 The kinemati equivalent virtual am lobes With delay and valve dynamis, the atual system behavior will be different from that shown in Figure 4.1. Comparing Figure 4.3 with the original ommand lobe edges in the right figure of Figure 4.2, now valve timings are shifted and are not the same as those ditated by high level ontrol. Hene, the low-level am onstrution funtion should be able to ompensate for these delays and valve response dynamis. These system delays 56

68 and dynami response an be either experimentally measured or modeled using empirial data. The speifi method of addressing these topis is not the fous of this work. Figure 4.3 shows the kinemati equivalent virtual am lobes whih illustrate the effet of inluding delays and valve dynamis. 4.3 Integrated virtual am ontrol In simulation test, an engine operational frequeny of 20Hz is hosen, i.e. angular veloity of the virtual amshaft is 40.The yle-to-yle based dynami ontrol requires information obtained in the previous yles to adaptively adjust the virtual am parameters. However, for the very first yle, there is no prior information to use, and hene, preseleted initial virtual ams are used, 3 Cam inj[0] 0, (4.1) Cam ex[0], (4.2) Cam spark[0], (4.3) 5 5 By applying the above initial virtual ams to the target engine ontroller, the following yles will always use the proposed ontrol laws to adaptively adjust the am parameters. For the injetion am, Cam inj, injetion of air/fuel mixture always starts as soon as a new yle is initialized, whih is k 1) ( k) 0. The duration of the inj_ b( inj_ b next injetion is alulated based on by Eq. (2.29) and the exhaust valve timing ontrol is given by Equations (2.30) and (2.31). The pressure-based ontrol approah is used in the simulation. As previously introdued in hapter 2, TDC and BDC measurement an be 57

69 Pressure (kpa) onduted using pressure dynamis in the ombustion hamber or ompression hamber. However, sine the ombustion pressure sensor is ostly and the pressure measurement is normally assoiated with some problems like drifting and noise, in the simulations and future experimental tests only pump side pressure will be used for both injetion duration ontrol and exhaust ontrol. Next, the exhaust valve ontrol will be first disussed by only using the ompression pressure dynamis Combustion Pressure Expansion Pressure Pump Pressure Reservoir Pressure Time (s) oi oa i a Figure 4.4 States in the exhaust valve ontrol The ideal time to open the valve is when the piston reahes BDC and the ideal time to lose the exhaust valve thus is when the piston reahes TDC. TDC/BDC an be obtained by measuring the ompression hamber pressure P P and the reservoir pressure 58

70 P : 1) BDC is where ompression hamber pressure P 0 and P Ps, whih refers to s P the instant at whih the pump pressure begins to drop and will go below the reservoir pressure). 2) TDC is where pump pressure and expansion pressure both drop down to atmospheri pressure and P 0. P The exhaust ontrol timings annot be implemented in time due to the delays mentioned before, so the ontrol law desribed by Equations ( ) is used here. The required variables for the exhaust ontrol are illustrated in Figure 4.4: ideal am position to open exhaust valve is denoted as oi, that is when piston reahes BDC; ideal am position to lose exhaust valve is denoted as o, that is when piston returns to TDC. The atual time when the exhaust valve is opened is denoted as oa and the atual lose time is denoted as a. At the end of the th k yle, the errors between atual timings and ideal timings are alulated by ( [ k] [ k]) and ( [ k] [ k]). By the ontrol oi oa algorithm desribed by Equations ( ), the valve timings for the next yle, [ k 1] and [ k 1], are ontrolled to approah the ideal timings in the urrent yle, o [k] oi and i[k]. The fuel injetion ontrol essentially is to optimize the energy input for speifi load and to ahieve stroke length so that the optimal engine effiieny an be ahieved. The original amount of hemially stored energy in the injeted mass of the air/fuel mixture is given by, E i m e (4.4) in 0 where m 0 is the mass of the fuel injeted into the ombustion hamber, is the a 59

71 ombustion effiieny and e is omputed from the lower heating value of the stoihiometri ombustion of propane. The duration of the air/fuel injetion is proportional to the mass of the fuel, given by Eq. (4.5), E in e t inj 0 m dt (4.5) fuel Therefore, the input energy for eah yle is ontrolled by regulating the air/fuel injetion duration. To do so, the virtual am responsible for the air/fuel injetion valve is built to 1) maximize the pump energy; Speifially for the FLPEC, this means maximizing the power stroke length to the physial limit of the engine (volume of the ompression hamber is ideally zero at the end of pumping); 2) adjust the mass of the fuel injeted aording to the load variations. The load of the free-piston engine air ompressor is the reservoir pressure. Air in the ompression hamber an be pumped into the reservoir only if the pump pressure beomes higher than the reservoir pressure. Thus, a higher reservoir pressure upon pumping is onsidered as a higher load in a given yle. The adjustment of the fuel injetion parameters is desribed by Eq. (2.29). The stroke length ontrol is arried out by Ex ( xd xstroke[ k]), where x d is the desired stroke length. The term of ( L[ k 1] L[ k]) adjusts the fuel mass aording to the load variation from the E L th k yle to the next yle. With the disussions above, the following diagram illustrates the virtual am based ontrol struture. In the simulation, noises are added to the ombustion pressure and the ompression pressure. Therefore, a filter is used and intended to ause some delays as in real experimental measurements. 60

72 Valve Response Command signals(on/off) Pressures Filter (Differentiator) System Level Control Time(s) Low Level Controller Time(s) Performane Evaluation Figure 4.5 Diagram of the proposed ontrol struture using virtual ams 4.4 Simulation results The initial pressures and temperatures in the three hambers (ombustion, expansion and reservoir) were all set to atmospheri pressure and ambient temperature, the free piston started at its relaxed position, and all the valves were set to be initially losed. Figure 4.6 shows the simulation results of the exhaust valve ontrol for three yles under the ontrol signals (voltages for eletroni exhaust valve, shown in Figure 4.7). In the first yle, virtual am parameters are given as Eq. ( ). At the end of the first yle, new referene exhaust ommands are generated based on the observed system dynamis in this yle. Sine there is no prior data, the initial ommands are very different from preferred referene ones. As a result, the expansion energy of the expansion hamber is low, indiated by the low peak expansion pressure. Using yle-toyle adjustment, atual ommands begin to get lose to referene ommands on the seond yle. The third yle has a strong pump (large amount of ompression energy in 61

73 Pressures (psi) the ompression hamber) due to the lose-to-ideal timings of the exhaust valve, whih inreases the ompression ratio for the next yle. This simulation shows the ontroller is apable of optimizing the exhaust valve timings in only few yles. Thus, the simulation results indiate that the ontroller an adjust virtual am parameters to optimal referenes quikly Time(s) Figure 4.6 Simulation results for FLPEC in three yles Time(s) Figure 4.7 Virtual am ommands and their referene ommands Figure 4.8 shows the overall system performane. Sine the initial onditions for 62

74 Pressures (psig) exhaust valve timings and injetion duration are preset (not optimal), non-optimal ompression ratio results in poor pumping performane in the few yles at the very beginning. One the virtual ams parameters onverge to those optimal values, the system runs well and the reservoir pressure inreased quikly from strong pumps. For the FLPEC, the ideal BDC is where the pump volume is zero. That is, all the air in the ompression hamber is pumped into the reservoir. However, this is not pratially ahievable due to the limitation of hek valve dynamis and the piston inertane. It is beause the hek valve an not provide a large enough opening for long enough to allow the fast moving piston to push all of the air in the ompression hamber into the reservoir. Therefore, in the simulations, desired BDC is set to be a small volume of m. As shown in Figure 4.9, the volume of the ompression hamber reahes its physially limited maximum TDC and approahes the desired BDC in few yles Time(s) Figure 4.8 Overall system dynamis in Simulations 63

75 Pump hamber volume (m 3 ) 14 x Time(s) Figure 4.9 Simulated volume of the ompression hamber The reservoir pressure dynamis are shown in Figure It an be seen that the reservoir loses its pressure beause it outputs air for the injetion without reeiving air from pumping during the first two yles. Figure 4.11 shows the injetion ontrol input. The injetion duration is inreased for the seond yle beause the ompression ratio in the ompression hamber is small in the first yle, requiring more fuel to be injeted. One suessful pumping is maintained and the ompression ratio approahes the desired value, the injetion duration only inreases slowly along with the inreased reservoir pressure (load for pumping). The engine effiieny approahes its theoretial optimum value as the ontrol parameters are adjusted over time, as shown in Figure

76 Injetion Duration (s) Reservoir Pressure (psig) Time(s) Figure 4.10 Simulated reservoir pressure dynamis Time(s) Figure 4.11 Simulated injetion durations onvergene 65

77 Pressures (psig) Engine Effiieny (%) Time(s) Figure 4.12 Simulated engine effiienies Time(s) Figure 4.13 Frequeny ontrol in the simulations Frequeny ontrol is ahieved by hanging the angular veloity of the selfspinning virtual amshaft at the end of a given yle. Figure 4.13 shows frequeny ontrol results in simulation. The free-piston engine was operated at 10Hz for three yles, after whih the frequeny was hanged to 20 Hz. When the angular veloity is hanged from f 10 1 Hz to f 20 2 Hz, the virtual am position needs to be 66

78 Engine Effiieny (%) Pump hamber volume (m 3 ) orrespondingly adjusted by 2 f 21 f1 21. For instane, if the injetion duration was,0.5 0 with 10Hz frequeny, it will be adjusted to, Thus, the timings are kept onstant in the time domain. 0 with 20Hz frequeny. The injetion and exhaust ontrols are based on a yle-to-yle adjustment method. They are not affeted by the operating frequeny. The adjustment of the engine effiieny and the ompression ratio are ahieved along with frequeny ontrol, as shown by Figure 4.14 and Figure x Time(s) Figure 4.14 Simulated volume of the ompression hamber during the frequeny ontrol Time(s) Figure 4.15 Simulated engine effiienies during the frequeny ontrol 67

79 4.5 Conlusions In this hapter, the virtual-am based ontrol method was tested in the simulation of the FLPEC. The pressure-based ontrol sheme for this devie was developed to ontrol 1) The duration of the air/fuel injetion for eah yle; 2) The timing of the air/fuel injetion; 3) The spark timing; 4) The timing and duration of the exhaust valve. Simulation results showed a good dynami performane of the engine. Therefore, the next step is to implement the proposed ontrol sheme on the real devie and test its performane. 68

80 Chapter V A HIGH INERTANCE FREE LIQUID PISTON COMPRESSOR In the previous hapter, simulation results have shown the validity of the proposed ontrol methodology. However, prototype one (FLPEC) presents some diffiulties for implementing the ontroller. That is, the separated ombustion hamber design auses savenging problem resulting in intermittent firing and inomplete ombustion. The seond prototype, a high inertane free liquid piston ompressor (HIFLPC), was designed and fabriated by Andy Willhite and then experimentally tested by myself and Andy Willhite [34-35]. Therefore, the proposed ontrol method was implemented on this devie and experimentally tested for the performane assessment. 5.1 Introdution The work of Riofrio, et al. [2-3] presented a unique design of a free liquid-piston engine ompressor (FLPEC). By utilizing the free liquid piston, the FLPEC demonstrated a solution for an effiient, ompat onversion of fuel to pneumati potential. Performane of the FLPEC was haraterized in [3], with a measured effiieny of 2.01%, orresponding to 931 kj of ool gas pneumati potential per kilogram of fuel. The FLPEC has a unique design of a separated ombustion hamber, whih is sealed by a ombustion valve from the expansion hamber. Upon ombustion, the highpressure ombustion produts fore open the ombustion valve so that high pressure ombustion produts vent into the expansion hamber and expand the expansion hamber. Sine the ombustion hamber is separated and sealed by the ombustion valve, it an hold the high-pressure air/fuel mixture in the ombustion hamber before 69

81 ombustion ours. This design eliminated the intake and ompression strokes in onventional IC engines by diretly injeting high-pressure air/fuel mixture into the ombustion hamber. However, it presented a problem for savenging the ombustion produts from the separated ombustion hamber, leading to intermittent firing. Andy Willhite [34] also pointed out some other problems assoiated with this design. They inlude flow losses around the ombustion valve, inomplete ombustion and so on. All of these problems were assoiated with either the separated ombustion hamber apparatus on the engine side or the pump hek valve on the ompressor side. The pump stroke of the FLPEC was too fast leading to the neessity of the separated ombustion hamber in the engine setion. For instane, without the separated ombustion hamber, diret injetion of air/fuel mixture into a ombined ombustion and expansion hamber will result in pushing the diaphragm signifiantly during injetion. If the piston is too fast or too light, the initial ombustion hamber volume upon ombustion will be very large, resulting in poor expansion ratio. Pump Chek Valve Compression Chamber High inertane setion of the liquid piston Piston Diaphragm Combustion Head Compressor Setion Liquid Piston Combustion Setion Liquid Piston Figure 5.1 Shemati of the High Inertane Free Liquid Piston Compressor (HIFLPC) 70

82 Exhaust Solenoid Elasti Diaphragm Intake Chek Valve Compression Chamber TDC Fuel Injetor Liquid Piston (a). Shemati of HIFLPC at effetive TDC Exhaust Valve Elasti Diaphragm BDC Spark Plug To Reservoir Pump Chek Valve (b). Shemati of HIFLPC at effetive BDC Figure 5.2 Shemati of HIFLPC Sine the FLPEC utilized a liquid piston, the property of liquid inertane ould inrease the system s effetive inertia by exploiting the liquid piston s geometry. The dynamis of the system ould be made slower without neessarily adding mass to the system. With a high enough inertane, the dynami load of the piston ould be suffiient to eliminate the need of the FLPEC s separated ombustion hamber altogether by 71

83 dynamially holding the air/fuel pressure high enough during injetion to maintain a high pre-ombustion pressure. Also, slower flow rate of air during the pump stroke allows for a smaller hek valve that is faster relative to the power stroke duration that an mitigate bakflow while not ausing unaeptable flow losses. Andy Willhite et al. [34-35] presented a design whih exploits these high-inertane effets, the High Inertane Free Liquid Piston Compressor (HIFLPC), as shown shematially in Figure Basi operation of the HIFLPC The shemati onfigurations of the high inertane free liquid piston ompressor (HIFLPC) are illustrated in Figure 5.2 at effetive TDC (a) and BDC (b), respetively. Before an engine yle is started, the diaphragms are at their relaxed positions where the diaphragm on ombustion side fully ontats with the ombustion head, leaving nearly (or ideally) zero volume in ombustion hamber. This is analogous to TDC in onventional engines. On the pump side, the ompression hamber is at atmospheri pressure while the intake hek valve (from outside to the ompression hamber) and pump hek valve (from the ompression hamber to the reservoir) are both shut. The power stroke starts with the injetion of air and fuel for a short duration. The air/fuel injetion sheme will be disussed later. During the air/fuel injetion, the diaphragms are pushed toward the pump side, resulting in an inrease of the ombustion hamber volume. By utilizing the high-inertane liquid piston, the diaphragms are expanded very little during injetion suh that the ombustion hamber an dynamially hold the highpressure air/fuel mixture until ombustion ours. Combustion of the air/fuel mixture onverts the stored hemial energy into kineti energy of the liquid-piston through 72

84 expansion work. Therefore, the piston rapidly moves toward the pump side and ompresses the air in the ompression hamber. One the ompression pressure exeeds the reservoir pressure, the pump hek valve opens and mass flow into the reservoir ours. At the end of pumping, one the piston begins to retrat, the ompression pressure drops to where it is equal to the reservoir pressure. The piston position at this moment is analogous to BDC in onventional engines, as illustrated by Figure 5.2(b). At this position, the ombustion exhaust valve is opened and the piston begins to move bak toward the ombustion side by releasing the energy stored in the diaphragms during the power yle. One the piston has returned to its original TDC position, one engine yle is over as soon after the ombustion exhaust valve is losed. The lak of a ompression stroke allows the engine ompressor to fire on demand - that is, there is no need to have a starting routine or maintain an idle yle. This allows the HIFLPC to operate at varying frequenies by ontrolling the delay between TDC and the ommand for air/fuel injetion. 5.3 Prototype fabriations and experimental setup of the HIFLPC An experimental prototype of the HIFLPC devie, shown in Figure 5.3, was fabriated for performane evaluation and ontrol testing. The devie as onfigured for testing has an approximate weight of 2.6 kg, with a footprint of around 18 by 18 with the liquid piston onfiguration shown. 73

85 Compression (pump) setion Liquid Piston Combustion (engine) setion Figure 5.3 Assembled HIFLPC prototype Critial physial parameters of prototype Table 5.1: Physial parameter overview of HIFLPC prototype: Parameter Value Desription A 1, A Cross-setional area of hemispherial liquid piston 3 region that mates to ombustion hamber with diaphragm. A Cross-setional area of high-inertane tube of liquid 2 piston L Length of high-inertane tube of liquid piston 2 I kg/ mm Calulated inertane of liquid piston D 50.8 mm Diaphragm working diameter diaphragm D 50.8 mm Combustion hamber inner diameter omb D 50.8 mm Compressor hamber diameter omp V omp V res 5.40 mm Compressor hamber initial volume 5.17 mm Volume of reservoir 74

86 Table 5.1 lists ritial physial parameters of prototype omponents. The liquid piston dimensions were sized based on an optimization disussed in Andy Willhite [35] Injetion iruit and ontrol In the appliation of a free-piston engine ompressor, high-pressure air is always on hand. Suh a system presents the opportunity of ombining the high-pressure injetion of fuel with high-pressure air. Suh a sheme allows an engine to bypass the onventional intake and ompression strokes; the simultaneous introdution of high-pressure air and fuel presents a high-pressure mixture diretly before ombustion that is equivalent to the end of a onventional ompression stroke. Utilizing high pressure for the air/fuel injetion is proposed here for small sale free-piston engine ompressors. Conventional air/fuel ratio ontrol for internal ombustion engines ommonly inludes an inner-loop ontroller based on the deviation of the estimated three-way atalyst stored oxygen state [36-37]. In ontrast, the proposed system diretly injets a high-pressure air and fuel to the ombustion hamber through separate air and fuel lines, assisted by high upstream driving pressures. Fuel is firstly injeted into the ombustion hamber. As soon as the fuel injetion is finished, air is then injeted into the ombustion hamber. Therefore, part of the ontrol strategy is to ommand the air and fuel injetion durations to ahieve a ertain air/fuel ratio. The proposed system onsists of two supply lines: the air line and the fuel line. Figure 5.4 shows the injetion sheme of the proposed design. The air used for the mixture injetion omes from the HIFLPC s air reservoir. On the other line, the fuel 75

87 Combustion Chamber soure is a 0.5kg bottle of propane, whih at room temperature has a vapor pressure of about 1 MPa (154 psia). Note that there is a fuel buffer ylinder between the fuel valve and the fuel injetor, as shown in Figure 5.4. Its funtion will be disussed in the ontrol setion. Propane Buffer Valve Buffer tank Fuel Injetor Air P buff Air Injetor P air Eletroni On/Off Valve Cylinder Chek valve Pressure sensor Figure 5.4 Air and fuel injetion iruit The mass flow rates through all valves or any flow restrited areas depend on the upstream and the downstream pressures. The following equations give the mass rate m under subsoni and soni onditions [28]: m j a CdC 2 j P, P P u T u u C d d C Pd Pu 1 P u T 1 u u Pd 1 Pu u 1 u if if Pd P u Pd P u P P r r (5.1) where C d is a nondimensional disharge oeffiient of the valve, a is the area of the valve orifie, P u and P d are the upstream and downstream pressures, T u is the upstream 76

88 temperature, u is the ratio of speifi heats of the upstream substane, and C 1, C 2 and P r are substane-speifi onstants given by C 1 2 u 1 Ru u 1 1 u u (5.2) C 2 2 u R 1 u u (5.3) P r 2 1 u u u 1 (5.4) where R u is the gas onstant of the upstream substane. The speifi heat ratio of the air is 1. 4 and the speifi heat ratio of the propane is Given the orifie areas a of the air and fuel injetors ( a a and instantaneously, injeted air and fuel mass are given as, f a f ) and assuming injetors are opened and losed ta 1 a ta0 where P a is the air upstream pressure, m a P, P (5.5) t a a a ad f 1 m f a f f Pf, Pfd (5.6) t f 0 P f is the fuel upstream pressure and P ad and are the downstream pressures for air injetion and fuel injetion respetively. In Figure 5.4, P a is the air pressure in the reservoir; air/fuel mixture ratio is given by, P fd P f is the fuel pressure in the buffer tank; the ta1 m aa a Pa, Pad a ta0 af (5.7) t f 1 m f a P, P t f 0 f f f fd 77

89 where t f 0 to t f 1 is the injetion duration of fuel, t a0 to t a1 is the injetion duration of air, and t f 1 ta0. For the HIFLPC air and fuel injetion valves, the Bosh CNG fuel injetor (see Figure 5.5) was hosen due to its fast response time (less than 5ms), adequate full-open flow rate, and speifi design for gaseous fuel (as opposed to standard automobile liquid fuel injetors). Figure 5.5 Bosh CNG fuel injetor Propane is supplied to the fuel injetor via the injetion iruit, as shown in Figure 5.6. The propane soure is a standard 16.4 oz. propane tank for small outdoor stoves (Coleman model #5103B164T.) An intermediate buffer tank is used for the propane supply upstream of the injetor. This buffer tank has a volume of 75 that is small enough to give a good resolution of pressure drop (for fuel onsumption measurement) in a typial injetion yle and is big enough to avoid pressure flutuation (a fairly onstant upstream fuel pressure) during the fuel injetion. A 2-way solenoid valve (Parker Series 9), driven by a simple on/off ontroller, regulates the buffer tank propane pressure (measured by a Festo SDE-16-10V sensor.) 78

90 Butter tank pressure sensor Propane soure Buffer tank On/off valve Figure 5.6 Fuel pressure ontrol iruit The reservoir tank not only reeives pressurized air from the ompressor, it also routes a portion of that air bak to the air injetor on the engine to be mixed with fuel. Sine both air and fuel use the same Bosh injetors, the effetive ross-setional area of the air and fuel injetor is taken to be 2 aa/ F aa a f 1. 82mm. Therefore, the ontrollable variables in this setup are the injetion durations and the upstream pressures on the air and fuel lines. A simple ontrol method is used to ahieve a ertain air/fuel ratio and quantity of the mixture of eah injetion. Fuel is first injeted from t f 0 to t f 1 at a ontrollable upstream fuel pressure, followed by the air injetion over t a0 to t a1, see Figure 5.8. The minimum response time of the injetor is a little less than 5ms. Hene, the fuel injetion duration is ontrolled to last for t f 1 t f 0 5ms. If the fuel is diretly injeted from the propane tank that has a vapor pressure around 154 psia for 5ms, the engine will reeive muh more fuel investment than required for its onfiguration (size of ombustion hamber, power output and so on). As a result, upstream pressure of the fuel 79

91 needs to be relatively low in order to avoid exessive fuel injetion for suh a small engine. As shown in Figure 5.6, a fuel buffer tank is added on the fuel injetion line so that the buffer tank pressure an be ontrolled to be muh lower than the vapor pressure out of propane bottle. Moreover, it is onvenient to measure the pressure drop in the buffer tank to alulate the fuel investment for the effiieny assessment. By reading the buffer tank pressure P buff, the eletroni on/off valve only opens when Pbuff Pdesired, i.e. the propane pressure buff P is lower than the desired pressure. The ontrol law for the eletroni fuel valve is desribed as, Fuel On Off P buff P desired otherwise (5.8) The air injetion duration is muh longer than the fuel injetion duration beause the stoihiometri ratio for propane is about 16.3:1. Therefore, the injetion duration in the next setions refers to the air injetion duration. Moreover, the fuel injetion duration is set to be fixed at 5 ms and the fuel amount is governed by setting the buffer tank pressure P buff. Given the air injetion duration, in order to ahieve a ertain ratio, the fuel mass an be ontrolled by regulating the fuel upstream pressure (the buffer tank pressure P buff ) to a desired pressure P desired. Corresponding desired fuel upstream pressures, P desired, for ertain air injetion durations and pressures are experimentally examined. Given a reservoir pressure of 60 psig and injetion duration of 15 ms, the buffer tank pressure of propane is 16 psig for a lean ombustion. It is experimentally obtained by lowering the propane pressure, under a onstant reservoir pressure 60 psig, to where onsistent ombustion is still ahievable. However, if the air upstream pressure 80

92 rises to 80 psig, the buffer tank pressure should be adjusted to 18 psig for 15ms injetion duration beause more air is injeted under higher air upstream pressure. As a result, the injetion ontroller adjusts the buffer tank pressure as a funtion of the pressure hange in the reservoir. The simple ontrol strategy is given by, P desired P K P P ) (5.9) prop_ r p( res _ r res where P prop _ r is the referene buffer tank pressure, 16 psig; res r P _ is the referene reservoir pressure, 60 psig; P desired is the desired propane buffer tank pressure, whih is ahieved by ontrolling the eletroni on/off fuel valve, as desribed in Eq. (5.8); P res is the reservoir pressure measured in real-time; finally, K p is a onstant gain for adjusting propane buffer tank pressure Experimental test set-up Reservoir Propane injetion iruit Figure 5.7 HIFLPC test onfiguration. The HIFLPC system was assembled with reservoir and air/fuel injetion iruit as shown in Figure 5.7. Three pressures are used for measuring the engine dynamis: 1) the ombustion pressure is measured by an Optrand AutoPSI pressure sensor (model 81