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Modeling and Control of Linear Combustion Engine
Copyright © IFAC Advances in Automotive Control Salemo. Italy, 2004
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocalelifac
MODELING AND CONTROL OF LINEAR COMBUSTION ENGINE N~me~ek Pavel*, ~indelka Michal **, VysokY Ondi'ej
***
Czech Technical University, Karlovo namesti 13, Prague 2,12135, Czech Republic Department of Control engineering, Faculty ofElectrical Eng ineering • tel. : ++42022435 7330 e-mail: [email protected] ··tel. : ++42022435 7330 e-mail: [email protected] *** tel. : ++42022435 7333 e-mail: [email protected]
Abstract: This paper describes modeling and control of a Linear Combustion Engine (LCE). A LCE is a special type of combustion engine representing a new approach concerning the conversion of the chemical energy of hydrocarbon fuel into electrical energy. Unlike conventional engines, this type of engine does not use a crankshaft. and generates electric energy directly by a linear movement of pistons. Copyright © 2004 IFA C
Keywords: Combustion engine, linear combustion engine, LCE, HEV, combustion engine control.
I INTRODUCTION TO THE LCE PROBLEM
order to avoid collision between the piston and the cylinder head. The controller must also detect possible misfires and intervene appropriately. This presents a key problem related to the feasibility of the LCE. The control features should also maximize the electric energy drained from the LCE.
The LCE presented here is a two-stroke, two cylinder combustion engine. Unlike conventional combustion engines, the LCE has no crankshaft. The LCE moving part consists only of two rod-connected pistons, which move from one side to another. The reduced amount of moving parts and strict linear movement of pistons significantly increase the durability of the LCE and simplify the lubrication of pistons. During operation, the pistons are accelerated by a combustion mixture and move from one side to the opposite side. The released energy is partially used to compress the fuel mixture in the opposite cylinder. This action is repeated periodically. The difference between the energy released by the combustion mixture and the energy consumed by mixture compression and mechanical losses is drained from the system as electric energy by a linear motorgenerator which is also used as a starter during the start of LCE. Finally, the motor-generator also allows the prevention of the LCE from stopping when a misfire occurs.
The main drawbacks of a conventional two-stroke engine (e.g., high emissions of pollutants and irregularity at low speed) could be partially eliminated by the use of a precise fuel mixture system (e.g., air assisted fuel injection). A number of papers, which examine a combined linear alternator and combustion engine system, have been published; however, most of these works concern the coupling of a linear alternator and Stirling engine (Holliday, et al., 1986). A configuration with two opposed cylinders and twostroke cycle is described in Clark et al. (1998) and Cawthorne (1999), but these works are focused mainly on simulation, but control is not considered. Another configuration with one piston and spring is discussed by Kos (1991) and expanded by Zhang (1997). This configuration also allows the use of a four-stroke cycle, but in this case external electric energy is needed for steady operation.
Because the motion of a moving part is not constrained by a crankshaft, the controller must provide precise control of a moving part' s position in
305
2 MODEL OF THE LCE
2.1 Mechanical system model
This model describes the conversion of forces pushing the rod-connected pistons to the position of the rod center (x) . State variables velocity and position are the outputs. A simple friction model is employed. Figure 2 shows a global diagram of this model.
The main task of this model is to obtain infonnation about system behavior. Thus, the precise mode ling of phenomena like fuel burning, thennodynamical processes, etc. is not the main goal. Figure 1 shows a simplified LCE diagram. .
.
L •
F.
v.
0
~
1JEliBr
Fig. 2. Mechanical system model
Fig I. Simplified LCE diagram - constants and variables
2.2 Linear motor-generator model
The linear motor-generator provides a bi-directional energy transfer between the mechanical system and the energy accumulators. A single-phase linear motor-generator is considered in this model. The inputs are: desired braking force Fbw(t) and velocity of connecting rod vet). The output is a force that pushes the moving part Fb(t). The linear motorgenerator is driven by an lOBT power bridge, which serves as a PWM modulator. Since the force is proportional to the applied current, not to the voltage, a current control loop must be employed. In this case a proportional controller is used. A complete diagram of the linear motor-generator model is shown in Figure 3.
Variables: x position of connecting rod center v connecting rod velocity F resultant offorces pushing the connecting rod Fb force generated by motor-generator Fbwdesired force generated by motor-generator F, force pushing piston in cylinder I i current through the motor-generator coils Pi pressure in cylinder I sp spark position Pin filling pressure (in-cylinder pressure at time of closing exhaust a and filling channels) Q thermal energy
Constants: D piston diameter S piston area L maximum stroke m total weight of moving parts (incl. pistons, connecting rod, moving generator parts) Xk position of connecting rod center at time of opening and closing intake and exhaust ports Cp specific thermal capacity at constant pressure Cv specific thermal capacity at constant volume R specific gas constant Lv inductance of motor-generator coils Rv resistance of linear motor-generator coils Uo maximal PWM modulator voltage KA motor-generator constant
Fig.3. Linear motor-generator model The saturation represents the PWM bridge transfer characteristic that is linear, but saturated by the value of the motor-generator power supply voltage. Output P(t) represents power supplied tolby (+1-) the system.
The model created is composed of the following parts: • • •
•
2.3 Model of thermodynamic processes
a mechanical system model a linear motor-generator model a thermodynamic processes model derived from the first law of thermodynamics and the gas state equation. a thermal energy production model
This model is based on a simplified description of the thermodynamic processes. It is assumed that the gas is "ideal" and also that all actions, perfonned by the gas, are reversible. ,,Ideal gas" can be described as a gas where: molecules are infInitely small, there are no gravitation forces, and molecule collisions are elastic.
306
Reversible action is one where the gas state equation is valid in every moment. It means the gas is in a steady state during the entire action. The adiabatic exponent, which equals to Cp/CV =1 ,4, is also supposed to be constant. The adiabatic exponent varies during the work cycle. It is caused by the changes in a gas composition and by the changes of temperature. The derivation of the model is based on the fIrst thermodynamic law (I) and the gas state equation (2). Inputs are: connecting rod position x(t), rod velocity vet), and time increment of the delivered thermal energy. System has a single output: force pushing the piston Fi(t).
OQ=dU+oW
(1)
p .dV + V.dp == nR.dT
(2)
energy gained by burning the whole cylinder content) is delivered in infmitely short time, because the volume is a function of time. This idealization fails mainly at high operation speeds of the engine. It is because the burning speed is fInite and depends on pressure, temperature, mixture proportion etc. Generally, the fInite burning speed decreases the p-V area and thus the gained energy and efficiency. The finite burning speed is taken into account in the suggested model. A constant or an actual pressure dependency of the speed can be chosen. When the burning speed is a constant high enough, the thermal energy delivery is almost isochoric. This model does not intend to simulate the processes, which exactly occur in the cylinder. The main goal is to simulate the time scattered energy delivery to the thermodynamic cycle. Inputs of this model are: position of connecting rod x(t), in-cylinder pressure pi(t), flame up position xz(t), and energy quantum generated by the burn out of whole cylinder content Q(t). The output is energy time increment delivered to the thermodynamic cycle. The flame area is supposed to have a spherical shape. The flame propagation is constrained by cylinder and piston. surface and the speed of flame is dependent on in-cylinder pressure. This model has more clearly physical representation then e.g. Wiebe function. The simulation diagram is shown in Figure 5.
Equation (3) was derived under the assumption that compression and expansion are fully adiabatic. This equation, which is easy to implement in Matlab, describes dependency of the in-cylinder pressure on the rod position, rod velocity and, in-system delivered thermal energy.
dp == _l_(R 8QH _ C p. dV) dt CvV dt P dt
(3)
The simulation diagram is shown in Figure 4. Equation (3) also considers the fact, that medium exchange exists, which leads to the implementation of a switch. The closing of intake and exhaust channels was considered to happen simultaneously. The pressure when the channels are closing is an input variable and is named pin. At time when the channels are opened the pressure pin is applied to the output, through the conversion to force.
Fig. 5. Model of thermal energy production 2.5 The global simulation diagram The described models are encapsulated into the subsystems, which put together give a global simulation diagram. The model of the linear electric motor-generator is left out. The global model diagram consists of a mechanical system model, two models of thermo-dynamical processes "Cylinder I" and "Cylinder 2", and two models of combustion "Combustion 1" and "Combustion 2". Also the necessary conversions force - pressure and position volumes are implemented. The modeling of the opposite orientation of the cylinders is done by multiplying the velocity vet) and the position x(t)
Fig. 4. Model of thermodynamic processes 2.4 Model ofthennal energy production The described model of the thermodynamic processes has a thermal energy time increment input. The way how the energy is delivered into the system depends on a level of idealization of the thermodynamic cycle. Often the isochoric energy delivery is considered. It means that the quantum of energy (amount of thermal
307
simulation near the steady operation. The filling pressure is set equal to the atmospheric pressure of 100 kPa. The spark position is set to the value of 17 mm leading to the compression ratio E = 11 , which ensures that the operation is steady. Voltage of the UO source was set to 400V. Maximal stroke volume of the cylinder was 50ccm, maximal stroke L=44 mm. Inductance of the motor-generator coil is Lv=16 mH, its resistance Rv=5.Q. The velocity of flame propagation in the cylinder is considered to be constant and equal to 20 mls. The constants of the motor-generator are K.A=60 NA-l and Kv=54.6 Vsm-l. All mentioned values either have a real grounding or they are given by the component manufacturers. Experimental results are shown in figure 9 and 10.
related to the cylinder 2 by -1. The overall model is a feedback system. The feedback variables are the velocity vet), position x(t) and, for the model of combustion, also pressures pi (t) and p2(t). The model of combustion delivers the time-depending amount of thermal energy to each model of thermodynamic processes. This amount also depends on the rod position, the pressure in cylinder and the energy quannun. The models of thermodynamic processes generate time dependencies of forces, which push the connecting rod. The values of these forces depend on the rod position, in-cylinder pressures, delivered thermal energy and the start compression pressure. These forces together with the braking force are combined in the model of mechanical system. The outputs of this model are the feedback variables - the velocity and position of the connecting rod. The diagram is shown in Figure 6.
4 THE REAL MODEL Real LCE model employs two 50ccm cylinders with direct fuel injectors. These DiTech technology injectors use the air assisted fuel injection method, which allows proper mixture preparation and consequently low emissions. The linear motorgenerator is a product of VUES Company and is driven through a 3-phase IGBT bridge. The control problem is multi-level. Generally, we consider three levels (in case of LCE use in hybrid vehicles). The top level is an energy management of the vehicle, which determines the use of on-board energy sources - batteries (or supercapacitors) and hydrocarbon-electricity converter (LCE in this case). This level is not considered at this time. The middle level controls the amount of the fuel-air mixture to burn according to the power demands. It is done by controlling the fuel injectors, throttle, and spark position. It is also responsible for emissions and keeping the lambda ratio equal to I (approx.). The bottom level controls the movement of rod-connected pistons by keeping the energy drain max efficient. It is done by adequate control of IGBT power bridge. This level is also responsible for overcoming misfires (prevent stopping of LCE due to a misfire) and avoiding collisions between pistons and cylinder heads. Note, that the linear movement has no limits, in comparison to the conventional combustion engine. So the key problem is the collision avoiding. The on-system measured variables are position of the connecting rod, velocity of the rod, intake air pressure, intake mass airflow, and currents flowing through motor-generator coils.
.>
Fig. 6. The global LCE simulation diagram
3 THE SIMULATION CONDITIONS This model performs a simulation of LCE operation. The energy gained in this experiment by the burning of mixture is drained by the linear motor-generator that is represented by the model in chapter 2.2. The experiment did not include any controller. The requested breaking force was derived from the velocity of the connecting rod. The amount of the in system delivered energy was experimentally set to the value corresponding to the steady operation. Steady operation means that there is no energy concentration in the mechanical system. Observed variables were: velocity and position of the connecting rod, pressure in cylinder I and 2, p-V diagram related to cylinder I, electrical power transferred to the source of UO, mechanical power drained from the system, and actual braking force. Mechanical power drained from the system is calculated taking the actual braking force and velocity of the connecting rod. Electrical power is calculated inside the model of the linear generator. The initial velocity of the connecting rod was set to 3,5 mls . This value allows starting the
In this case, for bottom and middle control level is used a powerful Motorola PowerPC based system produced and supplied by DSPACE Company. The modem, high-level design methods utilize Real Time Workshop, Matlab and Simulink for precise real-time control. Main advantage of this high level approach is a short implementation time of control algorithms in comparison to "C" or assembly language based
308
development. Control algorithms, which are tested on the Simulink model, can be also used directly for the real model control.
external electric energy (desired result of the project) was not achieved yet. Main reasons are improper motor-generator parameters (partially due to budget limits). Key problem is low self-braking force (current raised only by inducted voltage seems to be too low). However short-term steady operation was achieved with external electric power source.
The Dspace DSP board contains analog and digital inputs and outputs. An additional hardware had been constructed to provide an interaction with a real model. Block diagram of this hardware is shown in Figure 7.
Two control loops are used to control the movement of the linear motor-generator. Outer loop provides tracking of the desired (sine) trajectory (fixed sine trajectory is not eligible for maximization of energy gained from linear motor-generator, but allow to make some basic experiments on combustion engine). The desired position is compared with the real position, which is sensed by an incremental magnetic sensor. At present a simple PD regulator is used for position control. To obtain better results, a FIR filter is used to approximation of derivation. The output value of this regulator is a desired force, which should be generated by the linear motor-generator. This force is dependent on the actual currents through the motor-generator coils, therefore another regulation loop is necessary to provide the appropriate control. Real phase angle of motor-generator is calculated from the measured position according to the LCE geometry. Then the desired time paths of the currents flowing through two of motor-generator coils are derived from this phase angle (third current is a sum of these two). Amplitude of the currents is derived from desired braking force value and the force constant of linear motor-generator [NI A]
Fig. 7. Block diagram of extension hardware Comparator
IGBT bridge
400V network
To 1inear motor-generator
Fig. 8. Block diagram of power switch
(4)
For experimental phase of development a power switch is used instead of accumulator with corresponding power management. Main function of this circuit is to recognize and control electric energy flow. 3-phase IGBT bridge (driven from dSpace) is powered through rectifier and diode D (Figure 8). Whenever linear motor-generator is in generator mode, voltage on capacitor C2 is higher than voltage on Cl. To avoid the increase of voltage on C2 over its surge voltage, the load resistor is used. If voltage difference UC2-UCI exceeds adjusted limit, energy is routed to this resistor. Power dissipation on it is equal to power gained from LCE. 5
Two PID controllers are used to provide sufficient tracking of the desired values. The outputs of the regulators are used as inputs of PWM modulator. Time path of a third signal is calculated from another two in accordance with the equation
6
THE EXPERIMENTAL RESULTS
Comparisons between experimental and simulated results are show in figures 9 and 10. Step of the pressure in the simulated result is caused by an assumption that the exhaust port opens in infinitely short time. The spark position is obvious on the compression curve. Another fact - the limited speed of flame expansion can be observed.
THE EXPERIMENT ARRANGEMENT
For the experimental purpose the pressure sensor was placed directly into the cylinder head. It enables to obtain p-V diagram and compare it with simulated one. Unfortunately steady operation without need of
309
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8 REFERENCES
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Cawthorne, W.R. (1999), Optimization of a Brushless Permanent Magnet Linear Alternator for Use With a Linear Internal Combustion Engine. PhD Thesis, West Virginia University.
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Fig. 10. Simulated and experimental time behavior of in-cylinder pressure during one cycle
Clark, N.N. (1998), P. Famouri, Modeling and development of a linear engine. In 1998 Spring Technical Conference of the ASME Internal Combustion Engine Division, vol. 30-2.
7 CONCLUSION
Holliday, lC. (1986), S.G.Howell , M. Richter, FreePiston Linear Alternator Solar Stirling Engine Concept. Proceedings of the 21 st Intersociety Energy Conversion Engineering Conference, 468-473.
Nevertheless a simplification in model, simulations results show a good correspondence between model and real system. Although simulation indicates, that system can supply electric power into the load resistor, this aim wasn't still achieved. The main reasons are improper motorgenerator parameters. Solution could be using of the linear motor-generator with more suitable parameters. At present we work on modifications of mechanical construction, which allow using of new linear motorgenerator. Other problem is the irregularity of the particular combustions (can be suppressed by the sophisticated control algorithm).
Kos, J.F. (1991), Computer optimized hybrid engine. United States Patent 5002020. Zhang, X. (1997), Modeling and simulation of a hybrid engine. Master's thesis, University of Regina.
Here are some pictures of the real model. They show the LCE generator and the power switch replacing an accumulator pack for the purpose of our experiments.
310
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocalelifac
MODELING AND CONTROL OF LINEAR COMBUSTION ENGINE N~me~ek Pavel*, ~indelka Michal **, VysokY Ondi'ej
***
Czech Technical University, Karlovo namesti 13, Prague 2,12135, Czech Republic Department of Control engineering, Faculty ofElectrical Eng ineering • tel. : ++42022435 7330 e-mail: [email protected] ··tel. : ++42022435 7330 e-mail: [email protected] *** tel. : ++42022435 7333 e-mail: [email protected]
Abstract: This paper describes modeling and control of a Linear Combustion Engine (LCE). A LCE is a special type of combustion engine representing a new approach concerning the conversion of the chemical energy of hydrocarbon fuel into electrical energy. Unlike conventional engines, this type of engine does not use a crankshaft. and generates electric energy directly by a linear movement of pistons. Copyright © 2004 IFA C
Keywords: Combustion engine, linear combustion engine, LCE, HEV, combustion engine control.
I INTRODUCTION TO THE LCE PROBLEM
order to avoid collision between the piston and the cylinder head. The controller must also detect possible misfires and intervene appropriately. This presents a key problem related to the feasibility of the LCE. The control features should also maximize the electric energy drained from the LCE.
The LCE presented here is a two-stroke, two cylinder combustion engine. Unlike conventional combustion engines, the LCE has no crankshaft. The LCE moving part consists only of two rod-connected pistons, which move from one side to another. The reduced amount of moving parts and strict linear movement of pistons significantly increase the durability of the LCE and simplify the lubrication of pistons. During operation, the pistons are accelerated by a combustion mixture and move from one side to the opposite side. The released energy is partially used to compress the fuel mixture in the opposite cylinder. This action is repeated periodically. The difference between the energy released by the combustion mixture and the energy consumed by mixture compression and mechanical losses is drained from the system as electric energy by a linear motorgenerator which is also used as a starter during the start of LCE. Finally, the motor-generator also allows the prevention of the LCE from stopping when a misfire occurs.
The main drawbacks of a conventional two-stroke engine (e.g., high emissions of pollutants and irregularity at low speed) could be partially eliminated by the use of a precise fuel mixture system (e.g., air assisted fuel injection). A number of papers, which examine a combined linear alternator and combustion engine system, have been published; however, most of these works concern the coupling of a linear alternator and Stirling engine (Holliday, et al., 1986). A configuration with two opposed cylinders and twostroke cycle is described in Clark et al. (1998) and Cawthorne (1999), but these works are focused mainly on simulation, but control is not considered. Another configuration with one piston and spring is discussed by Kos (1991) and expanded by Zhang (1997). This configuration also allows the use of a four-stroke cycle, but in this case external electric energy is needed for steady operation.
Because the motion of a moving part is not constrained by a crankshaft, the controller must provide precise control of a moving part' s position in
305
2 MODEL OF THE LCE
2.1 Mechanical system model
This model describes the conversion of forces pushing the rod-connected pistons to the position of the rod center (x) . State variables velocity and position are the outputs. A simple friction model is employed. Figure 2 shows a global diagram of this model.
The main task of this model is to obtain infonnation about system behavior. Thus, the precise mode ling of phenomena like fuel burning, thennodynamical processes, etc. is not the main goal. Figure 1 shows a simplified LCE diagram. .
.
L •
F.
v.
0
~
1JEliBr
Fig. 2. Mechanical system model
Fig I. Simplified LCE diagram - constants and variables
2.2 Linear motor-generator model
The linear motor-generator provides a bi-directional energy transfer between the mechanical system and the energy accumulators. A single-phase linear motor-generator is considered in this model. The inputs are: desired braking force Fbw(t) and velocity of connecting rod vet). The output is a force that pushes the moving part Fb(t). The linear motorgenerator is driven by an lOBT power bridge, which serves as a PWM modulator. Since the force is proportional to the applied current, not to the voltage, a current control loop must be employed. In this case a proportional controller is used. A complete diagram of the linear motor-generator model is shown in Figure 3.
Variables: x position of connecting rod center v connecting rod velocity F resultant offorces pushing the connecting rod Fb force generated by motor-generator Fbwdesired force generated by motor-generator F, force pushing piston in cylinder I i current through the motor-generator coils Pi pressure in cylinder I sp spark position Pin filling pressure (in-cylinder pressure at time of closing exhaust a and filling channels) Q thermal energy
Constants: D piston diameter S piston area L maximum stroke m total weight of moving parts (incl. pistons, connecting rod, moving generator parts) Xk position of connecting rod center at time of opening and closing intake and exhaust ports Cp specific thermal capacity at constant pressure Cv specific thermal capacity at constant volume R specific gas constant Lv inductance of motor-generator coils Rv resistance of linear motor-generator coils Uo maximal PWM modulator voltage KA motor-generator constant
Fig.3. Linear motor-generator model The saturation represents the PWM bridge transfer characteristic that is linear, but saturated by the value of the motor-generator power supply voltage. Output P(t) represents power supplied tolby (+1-) the system.
The model created is composed of the following parts: • • •
•
2.3 Model of thermodynamic processes
a mechanical system model a linear motor-generator model a thermodynamic processes model derived from the first law of thermodynamics and the gas state equation. a thermal energy production model
This model is based on a simplified description of the thermodynamic processes. It is assumed that the gas is "ideal" and also that all actions, perfonned by the gas, are reversible. ,,Ideal gas" can be described as a gas where: molecules are infInitely small, there are no gravitation forces, and molecule collisions are elastic.
306
Reversible action is one where the gas state equation is valid in every moment. It means the gas is in a steady state during the entire action. The adiabatic exponent, which equals to Cp/CV =1 ,4, is also supposed to be constant. The adiabatic exponent varies during the work cycle. It is caused by the changes in a gas composition and by the changes of temperature. The derivation of the model is based on the fIrst thermodynamic law (I) and the gas state equation (2). Inputs are: connecting rod position x(t), rod velocity vet), and time increment of the delivered thermal energy. System has a single output: force pushing the piston Fi(t).
OQ=dU+oW
(1)
p .dV + V.dp == nR.dT
(2)
energy gained by burning the whole cylinder content) is delivered in infmitely short time, because the volume is a function of time. This idealization fails mainly at high operation speeds of the engine. It is because the burning speed is fInite and depends on pressure, temperature, mixture proportion etc. Generally, the fInite burning speed decreases the p-V area and thus the gained energy and efficiency. The finite burning speed is taken into account in the suggested model. A constant or an actual pressure dependency of the speed can be chosen. When the burning speed is a constant high enough, the thermal energy delivery is almost isochoric. This model does not intend to simulate the processes, which exactly occur in the cylinder. The main goal is to simulate the time scattered energy delivery to the thermodynamic cycle. Inputs of this model are: position of connecting rod x(t), in-cylinder pressure pi(t), flame up position xz(t), and energy quantum generated by the burn out of whole cylinder content Q(t). The output is energy time increment delivered to the thermodynamic cycle. The flame area is supposed to have a spherical shape. The flame propagation is constrained by cylinder and piston. surface and the speed of flame is dependent on in-cylinder pressure. This model has more clearly physical representation then e.g. Wiebe function. The simulation diagram is shown in Figure 5.
Equation (3) was derived under the assumption that compression and expansion are fully adiabatic. This equation, which is easy to implement in Matlab, describes dependency of the in-cylinder pressure on the rod position, rod velocity and, in-system delivered thermal energy.
dp == _l_(R 8QH _ C p. dV) dt CvV dt P dt
(3)
The simulation diagram is shown in Figure 4. Equation (3) also considers the fact, that medium exchange exists, which leads to the implementation of a switch. The closing of intake and exhaust channels was considered to happen simultaneously. The pressure when the channels are closing is an input variable and is named pin. At time when the channels are opened the pressure pin is applied to the output, through the conversion to force.
Fig. 5. Model of thermal energy production 2.5 The global simulation diagram The described models are encapsulated into the subsystems, which put together give a global simulation diagram. The model of the linear electric motor-generator is left out. The global model diagram consists of a mechanical system model, two models of thermo-dynamical processes "Cylinder I" and "Cylinder 2", and two models of combustion "Combustion 1" and "Combustion 2". Also the necessary conversions force - pressure and position volumes are implemented. The modeling of the opposite orientation of the cylinders is done by multiplying the velocity vet) and the position x(t)
Fig. 4. Model of thermodynamic processes 2.4 Model ofthennal energy production The described model of the thermodynamic processes has a thermal energy time increment input. The way how the energy is delivered into the system depends on a level of idealization of the thermodynamic cycle. Often the isochoric energy delivery is considered. It means that the quantum of energy (amount of thermal
307
simulation near the steady operation. The filling pressure is set equal to the atmospheric pressure of 100 kPa. The spark position is set to the value of 17 mm leading to the compression ratio E = 11 , which ensures that the operation is steady. Voltage of the UO source was set to 400V. Maximal stroke volume of the cylinder was 50ccm, maximal stroke L=44 mm. Inductance of the motor-generator coil is Lv=16 mH, its resistance Rv=5.Q. The velocity of flame propagation in the cylinder is considered to be constant and equal to 20 mls. The constants of the motor-generator are K.A=60 NA-l and Kv=54.6 Vsm-l. All mentioned values either have a real grounding or they are given by the component manufacturers. Experimental results are shown in figure 9 and 10.
related to the cylinder 2 by -1. The overall model is a feedback system. The feedback variables are the velocity vet), position x(t) and, for the model of combustion, also pressures pi (t) and p2(t). The model of combustion delivers the time-depending amount of thermal energy to each model of thermodynamic processes. This amount also depends on the rod position, the pressure in cylinder and the energy quannun. The models of thermodynamic processes generate time dependencies of forces, which push the connecting rod. The values of these forces depend on the rod position, in-cylinder pressures, delivered thermal energy and the start compression pressure. These forces together with the braking force are combined in the model of mechanical system. The outputs of this model are the feedback variables - the velocity and position of the connecting rod. The diagram is shown in Figure 6.
4 THE REAL MODEL Real LCE model employs two 50ccm cylinders with direct fuel injectors. These DiTech technology injectors use the air assisted fuel injection method, which allows proper mixture preparation and consequently low emissions. The linear motorgenerator is a product of VUES Company and is driven through a 3-phase IGBT bridge. The control problem is multi-level. Generally, we consider three levels (in case of LCE use in hybrid vehicles). The top level is an energy management of the vehicle, which determines the use of on-board energy sources - batteries (or supercapacitors) and hydrocarbon-electricity converter (LCE in this case). This level is not considered at this time. The middle level controls the amount of the fuel-air mixture to burn according to the power demands. It is done by controlling the fuel injectors, throttle, and spark position. It is also responsible for emissions and keeping the lambda ratio equal to I (approx.). The bottom level controls the movement of rod-connected pistons by keeping the energy drain max efficient. It is done by adequate control of IGBT power bridge. This level is also responsible for overcoming misfires (prevent stopping of LCE due to a misfire) and avoiding collisions between pistons and cylinder heads. Note, that the linear movement has no limits, in comparison to the conventional combustion engine. So the key problem is the collision avoiding. The on-system measured variables are position of the connecting rod, velocity of the rod, intake air pressure, intake mass airflow, and currents flowing through motor-generator coils.
.>
Fig. 6. The global LCE simulation diagram
3 THE SIMULATION CONDITIONS This model performs a simulation of LCE operation. The energy gained in this experiment by the burning of mixture is drained by the linear motor-generator that is represented by the model in chapter 2.2. The experiment did not include any controller. The requested breaking force was derived from the velocity of the connecting rod. The amount of the in system delivered energy was experimentally set to the value corresponding to the steady operation. Steady operation means that there is no energy concentration in the mechanical system. Observed variables were: velocity and position of the connecting rod, pressure in cylinder I and 2, p-V diagram related to cylinder I, electrical power transferred to the source of UO, mechanical power drained from the system, and actual braking force. Mechanical power drained from the system is calculated taking the actual braking force and velocity of the connecting rod. Electrical power is calculated inside the model of the linear generator. The initial velocity of the connecting rod was set to 3,5 mls . This value allows starting the
In this case, for bottom and middle control level is used a powerful Motorola PowerPC based system produced and supplied by DSPACE Company. The modem, high-level design methods utilize Real Time Workshop, Matlab and Simulink for precise real-time control. Main advantage of this high level approach is a short implementation time of control algorithms in comparison to "C" or assembly language based
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development. Control algorithms, which are tested on the Simulink model, can be also used directly for the real model control.
external electric energy (desired result of the project) was not achieved yet. Main reasons are improper motor-generator parameters (partially due to budget limits). Key problem is low self-braking force (current raised only by inducted voltage seems to be too low). However short-term steady operation was achieved with external electric power source.
The Dspace DSP board contains analog and digital inputs and outputs. An additional hardware had been constructed to provide an interaction with a real model. Block diagram of this hardware is shown in Figure 7.
Two control loops are used to control the movement of the linear motor-generator. Outer loop provides tracking of the desired (sine) trajectory (fixed sine trajectory is not eligible for maximization of energy gained from linear motor-generator, but allow to make some basic experiments on combustion engine). The desired position is compared with the real position, which is sensed by an incremental magnetic sensor. At present a simple PD regulator is used for position control. To obtain better results, a FIR filter is used to approximation of derivation. The output value of this regulator is a desired force, which should be generated by the linear motor-generator. This force is dependent on the actual currents through the motor-generator coils, therefore another regulation loop is necessary to provide the appropriate control. Real phase angle of motor-generator is calculated from the measured position according to the LCE geometry. Then the desired time paths of the currents flowing through two of motor-generator coils are derived from this phase angle (third current is a sum of these two). Amplitude of the currents is derived from desired braking force value and the force constant of linear motor-generator [NI A]
Fig. 7. Block diagram of extension hardware Comparator
IGBT bridge
400V network
To 1inear motor-generator
Fig. 8. Block diagram of power switch
(4)
For experimental phase of development a power switch is used instead of accumulator with corresponding power management. Main function of this circuit is to recognize and control electric energy flow. 3-phase IGBT bridge (driven from dSpace) is powered through rectifier and diode D (Figure 8). Whenever linear motor-generator is in generator mode, voltage on capacitor C2 is higher than voltage on Cl. To avoid the increase of voltage on C2 over its surge voltage, the load resistor is used. If voltage difference UC2-UCI exceeds adjusted limit, energy is routed to this resistor. Power dissipation on it is equal to power gained from LCE. 5
Two PID controllers are used to provide sufficient tracking of the desired values. The outputs of the regulators are used as inputs of PWM modulator. Time path of a third signal is calculated from another two in accordance with the equation
6
THE EXPERIMENTAL RESULTS
Comparisons between experimental and simulated results are show in figures 9 and 10. Step of the pressure in the simulated result is caused by an assumption that the exhaust port opens in infinitely short time. The spark position is obvious on the compression curve. Another fact - the limited speed of flame expansion can be observed.
THE EXPERIMENT ARRANGEMENT
For the experimental purpose the pressure sensor was placed directly into the cylinder head. It enables to obtain p-V diagram and compare it with simulated one. Unfortunately steady operation without need of
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8 REFERENCES
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Cawthorne, W.R. (1999), Optimization of a Brushless Permanent Magnet Linear Alternator for Use With a Linear Internal Combustion Engine. PhD Thesis, West Virginia University.
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Fig. 10. Simulated and experimental time behavior of in-cylinder pressure during one cycle
Clark, N.N. (1998), P. Famouri, Modeling and development of a linear engine. In 1998 Spring Technical Conference of the ASME Internal Combustion Engine Division, vol. 30-2.
7 CONCLUSION
Holliday, lC. (1986), S.G.Howell , M. Richter, FreePiston Linear Alternator Solar Stirling Engine Concept. Proceedings of the 21 st Intersociety Energy Conversion Engineering Conference, 468-473.
Nevertheless a simplification in model, simulations results show a good correspondence between model and real system. Although simulation indicates, that system can supply electric power into the load resistor, this aim wasn't still achieved. The main reasons are improper motorgenerator parameters. Solution could be using of the linear motor-generator with more suitable parameters. At present we work on modifications of mechanical construction, which allow using of new linear motorgenerator. Other problem is the irregularity of the particular combustions (can be suppressed by the sophisticated control algorithm).
Kos, J.F. (1991), Computer optimized hybrid engine. United States Patent 5002020. Zhang, X. (1997), Modeling and simulation of a hybrid engine. Master's thesis, University of Regina.
Here are some pictures of the real model. They show the LCE generator and the power switch replacing an accumulator pack for the purpose of our experiments.
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