WO2014039800A1 - Rapid estimation of piezoelectric fuel injection events - Google Patents

Abstract

Piezoelectric fuel injectors provide a means to reduce fuel consumption, noise and emissions in modern IC engines. Disclosed herein are methods and apparatus for within-an-engine cycle estimation of injected fuel, especially for a "rate shaped" profile. A reduced order model is introduced by simplifying a physically-based, experimentally- validated simulation model. The estimation algorithm is derived from the model by closing a loop of one or more measurable quantities in the system. The resulting estimator runs at a sufficiently short loop time and is able to make an on-line prediction of fuel injection rate, and is also validated to show the improvement on the prediction.

Description

RAPID ESTIMATION OF PIEZOELECTRIC FUEL INJECTION EVENTS

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority to U.S. Provisional Patent

Application Serial No. 61/698,588, filed September 8, 2012, and U.S. Provisional Patent application Serial No. 61/777,595, filed March 12, 2013, both of which are incorporated herein by reference.

FIELD OF THE INVENTION

Various embodiments of the present invention pertain to methods and apparatus for injection of fuel in an internal combustion engine, and in some embodiments to the rapid estimation of fuel injection parameters using an estimator in near real time.

BACKGROUND OF THE INVENTION

High pressure multi-pulse fuel injections with precisely controlled fueling quantity and spacing are useful for cleaner, quieter and more efficient diesel engines. Future improvements will require even more flexibility, including the capability to achieve more complex profiles, such as a process called "rate shaping".

Typically, injection is controlled by the motion of a needle inside the injector body, which, by its movement, starts and stops the flow through spray holes in the nozzle. On electric actuated injectors, needle displacement is driven by

electromechanical devices known as actuators. Piezoelectric stack injectors enable fast needle control, allowing complex injection rate profiles. However, the difficulty comes in the precise control for rate shaping, especially during the "toe". A further challenge is the absence of a means to measure the fuel flow rate from the injector while on the engine, for use in diagnostic flow control algorithms.

Various embodiments of the present invention pertain to a model based flow rate estimation strategy for rate shaping that can run within an operational cycle of the engine - a capability that would allow feedback control in near real-time, and in some embodiments during the injection event itself.

SUMMARY OF THE INVENTION

One aspect of the present invention pertains to an apparatus. Some

embodiments include a fuel system including an electrically actuatable fuel injector operating within a variable volume and receiving fuel at a pressure, said injector capable of providing a fuel flow. Yet other embodiments include a pressure sensor providing a signal corresponding to fuel pressure. Still further embodiments include an electronic controller receiving said signal and operably connected to provide electrical actuation of said injector with a boot-shaped profile.

One embodiment of the present invention includes a control system operated according to an algorithm that includes an estimator design approach for the injector model. The estimator gain of the body volume subsystem is calculated based on the linearized dynamic equation. This is utilized in the nonlinear model to build an estimator which corrects the error of a measurable state variable (such as Pbv) constantly to give a prediction of the injected fuel flow rate.

One aspect of the present invention pertains to an internal combustion engine including an electrically actuatable fuel injector and receiving fuel at a pressure, the injector capable of providing a fuel flow to the engine for combustion in the engine on a cyclic basis. Still other embodiments include an electronic controller operating an algorithm to predict the quantity of fuel injected into the engine and operably connected to said fuel injector to provide an electrical input signal for actuation of said injector, the algorithm being adapted and configured to estimate the quantity of fuel as a function of fuel pressure.

Another aspect of the present invention pertains to a method for operating an internal combustion engine, including a source of fuel at a pressure, an electrically actuatable fuel injector assembly, and an electronic controller operating an algorithm including an estimator of fuel flow from the fuel injector assembly. Other embodiments include providing fuel from the source to the injector at a pressure, and measuring the fuel pressure with the controller. Still further embodiments include calculating a term dependent on the value of measured fuel pressure, and using the term with the estimator to predict fuel flow provided to the engine

It will be appreciated that the various apparatus and methods described in this summary section, as well as elsewhere in this application, can be expressed as a large number of different combinations and subcombinations. All such useful, novel, and inventive combinations and subcombinations are contemplated herein, it being recognized that the explicit expression of each of these combinations is unnecessary.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graphical representation of a boot shaping profile.

FIG. 2 is a schematic representation of a piezoelectric fuel injector according to one embodiment of the present invention.

FIG. 2.8 is a graphical representation of a voltage force relation of piezo stack.

FIG. 2.9 is a graphical representation of a free body diagram of plungers according to one embodiment of the present invention.

FIG. 2.10 is a graphical representation of a free body diagram of injector needle according to one embodiment of the present invention.

FIG. 2.1 1 is a graphical representation of a free Body diagram of injector snubber according to one embodiment of the present invention.

FIG. 2.12 is a graphical representation of flow restrictions from body volume to cylinder according to one embodiment of the present invention.

FIG. 2.13 is a graphical representation of a needle effective flow area.

FIG. 2.16 is a graphical representation of a simulation result of the plunger displacements according to one embodiment of the present invention.

FIG. 2.17 is a graphical representation of a simulation result of the pressures.

FIG. 2.24 is a graphical representation of a stack voltage of multiple pulse at 1000 bar.

FIG. 2.30 is a graphical representation of a stack voltage of boot shaped pulse

1000 bar.

FIG. 3.1 is a graphical representation of a closed loop control strategy for the injector according to one embodiment of the present invention.

FIG. 3.2 is a graphical representation of a two pulse injection rate.

FIG. 3.3 is a graphical representation of a boot shaped injection rate. FIG. 3.4 is a graphical representation of a mass and spring model of the injector needle according to one embodiment of the present invention.

FIG. 3.5 is a graphical representation of a Simulation Result of Needle and Needle Tip Displacement.

FIG. 3.6 is a graphical representation of a nonlinear flow ortb vs. ΔΡ.

FIG. 3.7 is a graphical representation of a nonlinear flow coiof vs. ΔΡ.

FIG. 3.8 is a graphical representation of a nonlinear flow coiof vs needle displacement.

FIG. 3.9 is a graphical representation of an Euler forward differentiation method. FIG. 3.10 is a graphical representation of an estimator output resolution display. FIG. 3.1 1 is a graphical representation of a stack voltage of single pulse 1000 bar.

FIG. 3.12 is a graphical representation of an injection rate of single pulse1000 bar.

Fig 3.13 is a graphical representation of a simulated body volume pressure of single pulse1000 bar.

FIG. 3.14 is a graphical representation of a simulated trapped volume pressure of single pulse1000 bar.

FIG. 3.15 is a graphical representation of a simulated plunger displacement of single pulse1000 bar.

FIG. 3.16 is a graphical representation of a simulated needle displacement of single pulse1000 bar.

Fig 3.17 is a graphical representation of an injection rate of multiple pulse 1000 bar. FIG. 3.18 is a graphical representation of a simulated body volume pressure of multiple pulse 1000 bar.

FIG. 3.19 is a graphical representation of a simulated trapped volume pressure of multiple pulse 1000 bar.

FIG. 3.20 is a graphical representation of a simulated plunger displacement of multiple pulse 1000 bar.

FIG. 3.21 is a graphical representation of a simulated needle displacement of multiple pulse 1000 bar.

FIG. 3.22 is a graphical representation of an injection rate of boot shaped pulse 1000 bar.

FIG. 3.23 is a graphical representation of a simulated body volume pressure of a boot shaped pulse 1000 bar.

FIG. 3.24 is a graphical representation of a simulated trapped Volume pressure of a boot shaped pulse.

FIG. 3.25 is a graphical representation of a simulated plunger displacement of a boot shaped pulse.

FIG. 3.26 is a graphical representation of a simulated Needle displacement of a boot shaped pulse.

FIG. 3.27 is a graphical representation of an Injection rate of boot shaped pulse 1000 bar 40% toe height.

FIG. 3.28 is a graphical representation of an Injection rate of boot shaped pulse 1000 bar 60% toe height.

FIG. 3.29 is a graphical representation of an Injection rate of boot shaped pulse 800 bar. FIG. 3.30 is a graphical representation of an Injection rate of boot shaped pulse 1200 bar.

FIG. 3.31 is a graphical representation of an Injection rate of boot shaped pulse 1400 bar.

FIG. 3.32 is a graphical representation of an Injection rate of boot shaped pulse

1600 bar.

FIG. 3.33 is a graphical representation of real-time estimation results of boot shaped pulse 1000 bar according to one embodiment of the present invention.

FIG. 3.34 is a graphical representation of real-time estimation results of boot shaped pulse 800 bar according to one embodiment of the present invention.

FIG. 3.35 is a graphical representation of real-time estimation results of boot shaped Pulse 1200 bar according to one embodiment of the present invention.

FIG. 3.36 is a graphical representation of real-time estimation results of boot shaped pulse 1400 bar according to one embodiment of the present invention.

FIG. 3.37 is a graphical representation of real-time estimation results of boot shaped pulse 1600 bar according to one embodiment of the present invention.

FIG. 6 is a graphical representation of an injection rate of single pulse.

FIG. 8 is a graphical representation of an Injection rate of multiple pulse l OOObar. FIG. 13 is a graphical representation of an injection rate of single pulse l OOObar. FIG. 14 is a graphical representation of a simulated body volume pressure of single pulse 10OObar according to one embodiment of the present invention.

FIG. 15 is a graphical representation of an injection rate of multiple pulse l OOObar according to one embodiment of the present invention.

FIG. 16 is a graphical representation of a simulated body volume pressure of multiple pulse 10OObar according to one embodiment of the present invention. FIG. 18 is a graphical representation of a simulated body volume pressure of single pulse 10OObar according to one embodiment of the present invention.

FIG. 19 is a graphical representation of an injection rate of boot shaped pulse 1000bar according to one embodiment of the present invention.

FIG. 20 is a graphical representation of an injection rate of boot shaped pulse

1000bar according to one embodiment of the present invention.

FIG. 21 is a graphical representation of an injection rate of boot shaped pulse 800bar according to one embodiment of the present invention.

FIG. 23 is a graphical representation of an injection rate of boot shaped pulse 1400bar.

DESCRIPTION OF THE PREFERRED EMBODIMENT

For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated device, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates. At least one embodiment of the present invention will be described and shown, and this application may show and/or describe other embodiments of the present invention. It is understood that any reference to "the invention" is a reference to an embodiment of a family of inventions, with no single embodiment including an apparatus, process, or composition that should be included in all embodiments, unless otherwise stated. Further, although there may be discussion with regards to "advantages" provided by some embodiments of the present invention, it is understood that yet other

embodiments may not include those same advantages, or may include yet different advantages. Any advantages described herein are not to be construed as limiting to any of the claims. The usage of words indicating preference, such as "preferably," refers to features and aspects that are present in at least one embodiment, but which are optional for some embodiments.

Although various specific quantities (spatial dimensions, temperatures, pressures, times, force, resistance, current, voltage, concentrations, wavelengths, frequencies, heat transfer coefficients, dimensionless parameters, etc.) may be stated herein, such specific quantities are presented as examples only, and further, unless otherwise noted, are approximate values, and should be considered as if the word "about" prefaced each quantity. Further, with discussion pertaining to a specific composition of matter, that description is by example only, and does not limit the applicability of other species of that composition, nor does it limit the applicability of other compositions unrelated to the cited composition.

What will be shown and described herein, along with various embodiments of the present invention, is discussion of one or more tests that were performed, mathematical models that were prepared or mathematical analysis that was prepared. It is

understood that such examples are by way of examples only, and are not to be construed as being limitations on any embodiment of the present invention. It is understood that embodiments of the present invention are not necessarily limited to or described by the specific test, models, or mathematical analysis presented herein.

A dynamic model-based fuel flow estimator has been disclosed in co-pending U.S. patent application 13/515, 204, filed June 1 1 , 2012, titled FLOW RATE

ESTIMATION FOR PIEZO-ELECTRIC FUEL INJECTION incorporated herein in its entirety by reference. In some embodiments, a reduced order model is derived that is capable of predicting single pulse, multiple pulse as well as "boot" profiles (as is illustrated in FIG. 1 ). From this model, an FPGA based within-a-cycle flow estimator according to one embodiment was designed and experimentally validated. As used herein the term "cycle" refers to a cycle of an internal combustion engine (intake, compression, expansion, exhaust), unless otherwise noted.

A model simplification process is outlined. The process includes state reduction and parameter simplification. The resulting reduced order model (also known as the control model) is a simplified description of the injector dynamics, which captures some of the coupling from the system inputs to the output. It has been validated with experimental data in different rail pressures and stack voltages, and also been compared to the simulation model. This shows its capability of predicting the injection rate as accurate as the original detailed model.

Also, a within-a-cycle estimation algorithm is disclosed for improving the performance of the model. Measurable quantities are used as feedback signals to the estimator. For the injector, the measured feedback signal is the pressure inside the injector body volume. In order to calculate the estimation gain, the reduced order model has been analyzed and partially linearized, and the estimator gain has been applied back to the nonlinear model to generate the estimator. The estimator is discretized to be implemented in an FPGA-based system (Nl compactRIO system). The predicted flow rate of the estimator is compared to the reduced order model, showing that the performance is improved by using the estimation strategy, particularly for boot shaped pulse profiles, but also for any type of injection profile.

One embodiment of the present invention pertains to methods and apparatus for controlling the injection of fuel into an internal combustion engine. What will be shown and described are inventions that pertain to characterizing the engine system (including details of the fuel system), modifying that characterization with various simplifying assumptions, and generating a control algorithm that permits complex injection schemes to be implemented in real-time, with the control algorithm itself being modified in real-time to better achieve the desired injection event. Further, it is understood that the techniques described herein are not limited to control of internal combustion engines, but are also applicable to any system in which a liquid is provided to a system, and especially those systems in which the injection event is actuated by a

hydromechanical device with an electric actuator, and especially piezoelectric actuators.

In one embodiment, the apparatus for injecting the fuel or other liquid includes a nozzle for injecting the fuel, a hydromechanical valve for providing fuel to the nozzle, and an electric actuator such as a piezoelectric actuator for controlling the operation of the valve. In some embodiments, this apparatus is adapted and configured to provide an injection event that is less than 10 milliseconds in duration, with some injection events having a more complicated two-step (or boot) profile in which portions of the event are less than about 2 milliseconds in duration. For such short term events, the dynamic response of the valve, in terms of its mechanical, hydraulic, and electrical operation, can impact the actual injection event, and result in the actual event having timing and magnitude errors in comparison to the desired event.

In one embodiment of the present invention, a control algorithm is adapted and configured to accommodate various nonlinearities in the hydraulic, mechanic, and electrical operation of the injector system to improve the fidelity of the actual injection event to the desired injection event. Various embodiments account for the nonlinear changes to the injector system dynamics at about the same time as those changes occur. It has been found that by providing a real-time estimator of injector dynamics that the injection event can be more accurately controlled while the event is occurring. In some embodiments the manner of controlling the injector system is modified in realtime based on one or more observable and measurable inputs or outputs of the system.

As one example, in some embodiments it has been found that the pressure of the fuel provided to the injector can change the dynamic response of the injector system. In such embodiments, a measurement of fuel pressure is provided to a control algorithm as the injection event is occurring. Based on knowledge of this fuel pressure, the control algorithm can generate changes in the algorithm with regards to various control parameters (such as time delays, gains, time constants, and the like). These modified control values are used within the overall control algorithm to better control the injector system. In some embodiments, the apparatus and methods are adapted and configured to be useful in injection events in which it is desired to have fuel flowing at a first rate for a first period of time, followed smoothly by further injection of fuel at a second rate for a second period of time. Such injection events can be of a boot-shape, in which the first event is of a lesser amount of fuel, and the second event is of a greater amount of fuel. However, various embodiments of the present invention pertain to injection profiles of any shape and timing.

During the control of a boot-shaped profile it has been found that various aspects of the injection system dynamics are related to the current state of the injector apparatus (in terms of pressure and voltage, as examples). For example, the injector dynamics can change as the relative position of various internal components change, resulting in one or more internal volumes that vary in time as the injection event occurs. Further, as another example, any of various internal flow resistances (such as at the injection nozzle or an internal orifice) can vary as a result of other injector dynamics. Various embodiments of the present invention can adjust the control algorithms in realtime (such as during an engine cycle) by measuring a characteristic of the injector system (such as fuel pressure or voltage provided to the electric actuator), and change the electronic control signal provided to the actuator during the injection event.

The schematic diagram of an injector 50 is shown in FIG. 2. As is seen in the figure, the injector 50 includes a piezo stack actuator 58, upper and outer plungers 57.1 and 57.2, and the needle 56. The piezo stack of the injector is powered by a driver box 48 that is manufactured from QorTek Inc. The input to the driver box 48 is provided by an electronic engine controller 30. Controller 30 also receives feedback as shown in FIG. 2 as to the voltage actually provided to the piezo stack 58. In those embodiments including an estimator, various aspects of the estimator are mathematically modeled and implemented on a gate array 32, such as a field programmable gate array, although in yet other embodiments these or similar algorithms can be implemented with an ASIC. It is recognized that any of the various input signals provided to controller 30 (such as fuel pressure or received voltage, or others) may also be utilized by gate array 32.

Once piezo stack 58 is electrified, it will expand and force down the plungers below. Fuel at a pressure is provided from a source 52.1 to the injector body volume 59. The downward motion of the outer plunger 57.2 is then translated to the upward motion of the needle 56 through a hydraulic amplification circuit, forcing fuel out of the injector. Upon retraction of piezo stack 58, the needle is forced backwards by the pressure forces and stops the injection. In some applications, the source of fuel pressure for each of the injectors 50 is from a common rail 52.1 that is provided with fuel from a pump (not shown). In some embodiments, a pressure sensor 52.15 is in fluid communication with rail 52.1 and provides a signal corresponding to fuel pressure to the electronic controller 30.

The schematic diagram of one piezoelectric fuel injector is shown in FIG. 2. In the figure, a piezo driver box provides input voltage to the piezo stack. The piezo stack contains 708 stack layers and the maximum voltage that can be applied to the stack without damaging it is about 200 volts. All of the layers are wired parallel to a single driver and the stack is enclosed in a protective housing.

The injector plungers are connected to the piezo stack. When the piezo stack expands, it pushes down the plunger and thus pressurizes the fluid inside the trapped volume. The pressure rising in the trapped volume increases the force acting on the needle bottom area, which forces the needle upward. While the needle is lifting, the fluid inside the control volume is squeezed out to the body volume through the snubber orifice, causing a smooth upward motion of the needle and the injection. When the piezo stack is deactivated, it only retracts the upper plunger and has no effect on the outer plunger. This is because there is no rigid connection between the two plungers, which leads to the result that the needle closing dynamics may differ from the needle opening dynamics. The interacting force between the two plungers could be zero while the needle is closing. The retraction motion for the lower plunger is caused by the trapped volume pressure and the needle return spring. The upward movement of the outer plunger reduces the trapped volume pressure, opens the snubber and increases the pressure in the control volume, which will close the needle quickly.

As long as the piezo stack is supplied by sufficient voltage, the injector will reach its saturation point to deliver injections with a constant peak value for both single and multiple pulse injections. During rate shaping, varying the input voltage affects the expansion of the piezo stack, which in turn affects the degree to which the needle is in its open or closed position. Thus, changing input voltage causes a change in output fuel flow rate.

The control of the stack voltage is done by the controller and the digital I/O module of the Nl cRIO system.

Table 2.1 . Data Acquisition System Specifications

The piezo stack voltage is generated in the QorTeck driver box, and the driver box is linked to the digital output card. From the driver box, a continuous fifty percent duty cycle square wave function with a constant period of 10 μβ is being sent to the input port of the digital I/O card. This signal acts as a synchronizing signal for updating the output voltage of the driver. Once the TTL is on, voltage updating begins and at every rising edge of the sync signal. The driver box receives a calibrated count number from the digital I/O card and sends an output voltage to the piezo stack according to the input count number. The count number varies from 0 to 1023, so the magnitude of output voltage is roughly equal to the fraction of the count number out of its maximum value multiplied by the bus voltage of the driver box.

The injector model mainly includes the piezo stack, the plungers, and the injector needle. These components represent the injector's internal dynamics and simulate its working performance. The coordinates for model development are shown in the table below.

Table 2.2. Coordinates for the Injector Model.

When the piezoelectric material is stressed, charge is accumulated in the material and electric field is built inside. The piezoelectric effect is defined as the electromechanical interaction between the mechanical and electrical state in piezoelectric materials. The piezoelectric effect is a reversible process, meaning that the piezoelectric material can generate a mechanical strain in response to an applied electric field.

From previous studies, it is known that the piezo stack model is non-linear, frequency dependent and hysteretic. However, in an injector, the transient time of the supply voltage is only a small part of the whole on time. For this reason, a quasi-static, constant parameter and frequency-independent piezo stack force model is developed, which is given by

(2.1 ) where k_staCk is the compressive stiffness of the piezo stack material, and f{V_s) is the non-linear force caused by the input stack voltage. The model is based on the piezo material testing results, which shows that the piezo force is linearly related to the stack displacement but not to the applied voltage. The nonlinear relation between the input voltage and the resulting force is plotted in FIG. 2.8. Note that the stack model considers hysteresis effects.

The upper plunger is located beneath the piezo stack. It acts as a link between the injector body and the actuator. The net force on the upper plunger makes it always be in contact with the piezo stack. Therefore, the stack displacement can be directly transferred to the movement of the upper plunger. The structure below the upper plunger is called the outer plunger. Since the outer plunger is not rigidly connected to the upper plunger, there are two possible plunger dynamics while the injector is running. During needle opening and steady-state injection, the two plungers are lumped together so that there is a contact force between them. However, during closing, a separation occurs between the two plungers such that there is no contact force between them. The free body diagrams of the plungers in these two cases are shown in FIG. 2.9.

The left diagram of FIG. 2.9 shows the case when two plungers are connected and regarded as one mass. There are three springs acting on the plungers, as well as the forces from various pressures, the piezo stack and the housing. The reaction force from the injector snubber is neglected, and also the pressure drop through the snubber orifice is assumed to be negligible. From the free body diagram and above assumptions, the equation of motion for the plungers during the connection case (FIG. 2.9 case 1 ) is given by

+ m_ou )u = F_bvl + F_cv + F_tv + F_s2 + F_s3 + F_housmg

— F piezo—F s4—F bv2—F damp\ (2.2) where m_up is the effective mass of the upper plunger including the stack and shim and m_ou is the mass of the outer plunger. F_bv1 is the force body volume pressure acting on the upper plunger. F_bv2, F_cv and F_tv are the pressure forces from body volume, control volume and trapped volume acting on the outer plunger, F_si is the spring force from the h spring. Finally Fp_iez0 is the piezo stack force and F_h0using is the force from the protective housing acting on the plunger. All these forces are given by the following equations

¹ F bvl = ^ Atlink ¹ P bv (2.3)

F cv = A ^{j L}ptop P^± cv (2.5)

F tv - ^ Apbot P tv (2.6)

s3 ^{PL J}ss33 ^{~ k}ss33yS (2.8)

^housing ^~ ^housi g ^s3 ^U (2.10) and

F damp\^~ y (2.1 1 ) where Λ/ is the top link area of the upper plunger, A_ptop is the top area of the outer plunger and A_pbot is the bottom area of the outer plunger. PL_si indicates the preload of the ith labeled spring and k_si \s the corresponding stiffness of the i_th spring. The damping force Fdampi is numbered such that b1 is the total damping coefficient including upper and outer plungers as well as the stack. From injector geometry, A_ptop = A_tn_nk-

With these equations and the piezo force expression from Eq. 2.1 , the equation of motion for the plungers when connected can be derived and written as

PL_tot + A_tlinkP_cv + A_pbot (P^ P_bv ) F_piezo ) k

u eff

^M (2.12) m up + m ou ^m«p ^{+ m}o ^mup ^{+ m}c with

y ^U (2.13) noticing PL_tot represents the sum of all the preloads and k_eff represents the effective stiffness of all the springs.

The right diagram in FIG. 2.9 shows the case when the reaction force between the upper and outer plungers goes below zero. In this case, disconnection occurs and the two plungers move separately until the next time they connect. During this disconnection, the motion of the upper plunger is mainly driven by the piezo force, which is given by the equation mup^{U ~} ^bvl ^~*^~ ^housing ^~ fpiezo ^~ ^s ^~ ^dampl ' (2.14) The motion of the outer plunger is mainly governed by pressure forces, and it is given by m_ouy ⁼ _cv + F_tv + F_s2 + F_s3—F_bv2—F_{damp3 (2 15)}

Fdamp is the damping force, and it can be written as

Fdampl — b₂U (2.16)

Fdampl ^~

(2.17) where b∑ and 63 are the damping coefficient for the upper and outer plungers, and they have the following relationship with bi ¾ 4- !¾ ™ l> _\ .

(2.18)

After substituting all the forces in Eq. (2.14) and (2.15), the equations of motion for the upper and outer plungers during disconnection are represented by

(PL_housing PL_S + A_tlinkP_bv F_piezo) (k_hous

u = ^■u '2 u

m u.p m u„p m u„p

and

.. 4- - — : PL* : Am.....n...k...i.:.P< - - ......:: .^■: A_≠ P_tv - P_bK) ··)·

Noting that the model does not consider the momentum conservation of the plungers when they connect again. It simply equals the displacement and velocity of the outer plunger to the upper plunger when they connect to move together. As is shown in FIG. 2.10, based on the forces acting on the needle, the needle motion equation can be written as ifi need Ϋ— F tv2 -\- F ntip -\- F contact— F cv2— F si— F damp,need (2.21 ) where m_neecj is the needle mass, F_w2, F_nti_P and F_cv2 are the pressure forces acting on the needle bottom, tip and top areas, F_si is the spring force, F_damp_:need is the damping force and Fcontact is the contact force from needle seat. All the forces can be calculated using the following equations

(2.22)

(2.24)

(2.25)

+ A_mcP_m<: otherwise

(2.26)

where A_nbot is the area of the needle bottom, A_nto_P is the area of the needle top, A_nn_P is the area of the needle tip and A_sac is the area of the needle tip exposed to the sac volume, which is the small volume enclosed at the bottom of the injector needle (as is shown on the right of FIG. 2.10). P_sac is the sac volume pressure, k_neecj is the needle stiffness and k_seat is the contact stiffness between the needle and the seat. Notice that xtip indicates whether the needle is open or closed: the needle is open with positive value of x_f/p and closed with negative value of ¾p.

And its value is given by

(2.28)

The snubber valve has two operation states: open and closed. When it is closed, it does contact the outer plunger. According to the free body diagram shown in FIG. 2.1 1 , the equation of motion for the snubber can be simply developed as

where m_sn is the snubber mass and pressure forces are given by

¹ F cv3 = ^ Asnbot¹ P cv (2.30)

F = A P ·

¹ sn ^^Lsntop sn (2.31 ) These two forces are assumed to be the same and can be canceled because the top and bottom areas of the snubber are the same and the pressures above and below (Pcv and Psn) are approximately equal.

The injector Body dynamics are modeled by a coupled continuity and state equation shown in Eq. 2.32, which is derived from the Navier-Stokes equation. (2.32) where ω_ι-_η is the inlet volumetric flow rate to the chamber in the injector body, a)_out is the outlet volumetric flow rate from the chamber, V is the volume of the chamber, ?,_s the fluid bulk modulus, and P is the pressure inside the chamber.

Flows are modeled by orifice equation, which describes the mass flow rate of liquid through an orifice and is represented as p.

(2.33) and the volumetric flow rate is

where C_d is the discharge coefficient, A is the flow area of the orifice and p is the fluid density.

Note that if the pressure difference becomes negative, the direction of the flow will be reversed. Also, during calculation, the temperature of the working fluid is around 80 °C and the change of uid properties is based on the temperature and pressure change.

When the needle is open, fuel is injected from the body volume to sac volume through the orifice between the needle and the seat. The fuel then passes through the spray holes to enter the cylinder. FIG. 2.12 shows two restrictions for the flow that goes from body volume to the cylinder. One is the flow resistance past the needle, which depends on the needle position, and the other is the spray hole resistance.

Recall Eq. 2.33, the mass flow rate from the body volume to the sac volume is (2.35) where C_neecj is the needle discharge coefficient, A_neecj is the effective flow area, and pb_V is the fuel density in the body volume. The CFD result together with the tuned result of needAneed as a function of needle lift is shown in FIG. 2.13, where C_need is assumed to be constant and A_neecj is a function of the needle tip position χ_ϋρ.

Similarly, the mass flow rate from the sac volume to the cylinder is given by

(2.36) where Cash is the spray hole discharge coefficient, A_sh is the flow area of the spray hole, Psac is the fuel density in the sac volume and P_cyi is the cylinder pressure. C_dsh and A_sh are assumed to be constant, and the cylinder pressure is 7 bar. In addition, according to the mass conservation law, the mass flow rate from the body volume to the sac volume and the sac volume to the cylinder should be the same. Since w_/0f_massi = w/₀f_mass2, the sac volume pressure P_sac can be expressed in terms of P_bv and P_cyi by

Thus, the total mass flow rate coming out of the injector is

and the volumetric flow rate from the body volume to the sac volume is

(2.39)

The volumetric flow rate from the control volume to the body volume is given by

and the volumetric flow rate from the rail to the injector body is given by

where C_dsn and C_dran are the related discharge coefficients, A_sn and A_ran are the effective flow areas, and P_ran is the commanded rail pressure.

After deriving equations for the flow rates coming into and out of the injector body, a body volume pressure dynamic equation can be developed from Eq. 2.32 and is given by

(2.42)

This assumes that the change of the body volume is negligible ( is zero) and C_bv = ^ is the body volume fluid capacitance.

The trapped volume is enclosed by the needle and outer plunger such that there is no flow coming into or out of this volume. Thus the dynamic equation can be simply written as

where C_tv ⁼ ^ ^iS the control volume fluid capacitance. According to FIG. 2, relates to the needle and plunger velocities, and is given by

(2.44) Although the trapped volume is enclosed, leakage is likely to occur when the pressure difference between different chambers becomes significantly large. This affects the trapped volume pressure dynamic in Eq. 2.43, and the resultant dynamic equation becomes

where is the leakage coefficient from the trapped volume to the body volume and kieak2 is the leakage coefficient from the trapped volume to the control volume.

For the control volume equation, there is only one flow term coming out of the control volume and the dynamic equation is given by

r

H i

at A

(2.46) where C_cv =— is the control volume fluid capacitance, and V_cv is the size of the control βον

CLVcv

volume.—^- relates to the needle and plunger velocities, which can be represented by the equation

(2.47)

Including the leakage coming from trapped volume, the dynamic equation for the control volume pressure becomes

(2.48)

Table 2.3. States for Simulation Model

State reduction is the process of eliminating states which are unnecessary for the description of plants or can be expressed using other states. Reducing the states will reduce the order of the model directly. The original model has 1 1 states that are listed in table 2.3. These states can be classified as two categories: the motion of components (ύ, u, y, y, z, z, x, x) and the pressure dynamics (P_bv, P_cv, P_tv)- The state reduction process for the simulation model is mainly based on the kinematic and dynamic relations between these states. The upper plunger functions as a link between the stack and outer plunger. It transfers the motion of the piezo stack to the outer plunger. Since the contact between the upper plunger and outer plunger is nonrigid, the simulation model includes the effect of disconnection of the plungers when they lose contact.

The two plungers will not lose connection until the supplying voltage from the driver ends. At that moment, the sudden reduction of the voltage will lead to faster retraction of the upper plunger than the outer plunger, as shown in FIG. 2.16. However, the difference between the displacements is not significant. As such, ignoring disconnection (i.e. assuming that the upper and outer plungers are rigidly connected) is a reasonable simplification. With this assumption, two states can be eliminated (ii, u). The plungers will then behave as they do in the first case of FIG. 2.9.

The snubber valve is located in the control chamber between the injector needle and the outer plunger. In general, it serves to damp the relative motion of the needle and outer plunger through an orifice in the center. Since the flow resistance of the orifice is very small, the snubber valve does not have a significant impact on the pressure change of the control volume. Furthermore, due to its small mass, the dynamic effect from the snubber valve to the rest of the model is negligible. Therefore, the position and velocity states (z, z) that describe the snubber valve in the model can be neglected.

The control volume is the volume above the injector needle, with a flow path to and from the body volume via the snubber orifice. Since the flow resistance of the orifice between the control volume and the body volume is relatively small, the control volume pressure can be similar to the body volume pressure, as is indicated in FIG. 2.17. As such, a reasonable assumption is to set the control volume pressure equal to the body volume pressure. From the process of model reduction, the original 1 1 state simulation model is simplified to a lower order model with just 6 states in some embodiments of the present invention, listed in table 2.4.

Table 2.4. Table of States for Reduced Order Model.

Both the response time and the hardware resources are limited. However a simpler version of model can meet these requirements. A control model that is simplified from the simulation model is helpful, and a model reduction of the injector is disclosed. The process of model simplification can also include simplifications of fuel properties.

The bulk modulus and fuel density vary with different pressures and

temperatures. They are mainly used in the calculation of pressure dynamics and flow rates. Because the relationships between the fluid properties and pressure and temperature are nonlinear, they will add nonlinearities to the model, which makes the model more complex. Several assumptions are made to simplify the fuel properties in the simulation model.

Bulk modulus is a property measuring a fluid's resistance to compression, varying with different operating temperatures and pressures of the fluid. Since the testing fuel temperature is relatively constant (80°C), the change of the fluid bulk modulus is mostly caused by pressure variation. Furthermore, the pressure does not change much within the range of injector operating points. So it is reasonable to assume that bulk modulus in the model is a constant under a certain rail pressure.

Similarly, the fuel density is a function of pressure under a constant temperature. Moreover, the variation of the fuel density with different pressures is small, and it can also be regarded as a constant in the simplified model in the injector volumes.

The control volume is the volume above the injector needle, with a flow path from/to the body volume via the snubber orifice. Since the flow resistance of the orifice between the control volume and the body volume is relatively small, the control volume pressure will be similar to the body volume pressure, as is indicated in FIG. 2.17. Thus in the model, one of them can be replaced by the other.

The dynamic equations of the reduced order model are listed herein. Simulated results of the higher order model and the reduced order model are compared against the experimental data. The validation is under different running conditions, including single pulse, multiple pulses and boot shaped pulse cases. Starting with the single pulse injection, the driver box gives a 155 volt single pulse wave with an on-time of 2.5ms, as is shown in FIG. 3.1 1 , while the rail pressure is 1000bar (100A//mm²).

The comparison of the injection rate between simulation and the experimental results is shown in FIG. 6. In the figure, the original higher order model is denoted as "Simulation Model" and the simplified model is denoted as "Reduced Order Model".

The simulation model captures the start and steady state of the injection rate. The experimental result shows slight oscillations on the curve. Since negative flow into the injector is impossible, these oscillations are not physical representation of the injected flow, and it is likely that they are caused by the pressure measurement due to the rate tube measurement principle.

As for the reduced order model, it captures the start of the injection, and at steady state the injection rate slightly drops during the on-tie of the injection. It may be caused by the discrepancy between the simulated and measured body volume pressure. And it can be resolved by developing an estimator with measurement variable. Additionally, the reduced order model performs better than the simulation model in the falling edge of injection. This could be because that in the reduced order model, the outer plunger is connected rigidly to the upper plunger and it retracts together with the upper plunger (which is faster) when the needle closes.

The stack voltage for the two pulse case is shown in Fig, 7, with 155 volt high,

2.5ms injection on-time and 1 ms pulse-to- pulse separation time. The corresponding injection rate is plotted in FIG. 8.

Another case for model validation is the boot shaped pulse injection. The stack voltage in this case has the same peak value, 155 volt, but also has a step from the "toe" to the "shank", as is shown in FIG. 9. The injection on-time is 4.5 ms and the toe duration is about 1 .5ms.

The corresponding injection rate for the boot shaped case is plotted in FIG. 3.1 1 . As is shown in the figure, since the toe height of the stack voltage is lower than the shank height (peak value), the injection rate does not reach full size and is also lower at the toe duration. And after toe duration, it is the same as the case of single pulse injection.

The on-engine measurable variable (line pressure - an approximation for the body pressure) is coupled with a model-based estimator, enabling the accurate calculation of estimated flow rate.

A physically-based, simplified and experimentally-verified model is helpful in understanding the input/output relationships and the internal states of the injector. Moreover, in order to design a closed-loop controller for the injection system, feedback is helpful. It is difficult to measure this injection rate in real-world diesel engines directly due to space and cost consideration. In one embodiment an estimation approach is introduced, which is coupled with the on-engine measurable variable (line pressure - an approximation for the body pressure), enabling calculation of estimated flow rate. The estimator output is feedback for the closed-loop controller.

One control scheme for the injector is shown in FIG. 3.1 . In the figure, the input stack voltage enters the estimator and the plant, and the on-engine measurable body volume pressure enters the estimator. The estimated injection rate goes back to the controller as a feedback signal. The estimator can make a better estimation of the injection rate than the simulation model.

For single and multiple pulses (FIG. 3.2), injection happens when the needle is typically open so that it can be quantified by on-time (OT), pulse dwell (D) and pulse quantity (Q). However, for boot shaped injection profiles (FIG. 3.3), not only do the three parameters need to be considered, but so does the profile information such as toe height (TH), toe duration (TD) and shank duration (SD) is taken into consideration.

An estimator according to one embodiment of present invention can provide the updated output profile to the controller constantly during an engine or injection cycle (within-a-cycle estimation), so that the control strategy is able to correct the error for reference tracking constantly.

An estimator in one embodiment is a combination of a model, inputs, and measurable variables that can produce a desired output. It is used to calculate an estimate of a given quantity based on observed data. In one embodiment the body volume pressure is a system state and it is assumed observable by approximating the line pressure to the body pressure. It should be noted that although the line pressure measurement is available in some cases, in other cases it may not be available. With such engines, other embodiments of the present invention contemplate the use of estimators based on yet other observed data.

For the injector system, full-order state estimators are one strategy that is relatively easy to implement. State estimators often use linear models. However, the injector model can be highly nonlinear. In some embodiments, a linearized subsystem that includes the measurable variable (body volume pressure) as state output is used.

One simplified model has 6 states, represented in the state space form as below.

^X\ — ^X2 (3.1 )

^• __^ l v _ _J__V eed _v ⁱtop ώοί , ₂ ( 3 > 5 ) ^~ ^sl

4 - l 3 4 5 6 (3.4)

^need ^need ^need ^need ^need ^need

where /1(u1), /2(x3; x5) are nonlinear forces. Rrail is the flow resistance from rail to the body volume which is given by

and Rtot(x3) is the total resistance from the body volume to the cylinder, which includes the needle resistance and the spray hole resistance. It is given by

Since the needle effective flow area changes with needle position, the total resistance is a function of the needle position.

The system inputs are the stack voltage (u1 ) and the commanded rail pressure (u2). The cylinder pressure is considered as a fixed system parameter because it keeps the same value (7 bar) while the rig is running. The system output (y) is the volumetric flow rate from the sac volume to the cylinder (where the experimental value is measured).

The state variables are listed in Table 3.1 .

Table 3.1 . State Variables

The simulation model is able to capture the measurable quantity of injection rate, as well as complex internal variables such as intermediate pressures and

displacements. An estimator is used in some embodiments in order to get a better prediction of the injection flow rate.

Generally, an estimator includes system inputs, a mathematical model, and measurable variables. One measurable variable in the injector system is the body volume pressure, which is a state of the injector model, the design of the estimator is by means of partially linearizing the model to calculate the estimation gain and then applying to the nonlinear equation.

For continuous time linear system

x - ,4x + .Bu _{(1 )} - Cx 4- Dii ₍₂₎ aan $D«i $nr where x £ " is the state vector, u G ^Jl is the input vector, and y e ^Λ is the output vector. The estimator state space equations have an additional term, which is calculated by subtracting the estimator outputs from the measured system and then multiplying by an estimator gain matrix L. The state space equations are given below. x = Ax - L ( — vi 4- Bu

^" " (3) y =. C\ - DVL ₍₄₎ where x £ is the state vector of the estimator, and y £ ^" is the output vector of the estimator. And the estimator state error is e = x— x , and from Eqn. Ill-A the dynamic equation of the error can be derived as

e ~ (,4 - LC)e (₅)

The eigenvalues of the matrix A-LC can be made by selecting an appropriate estimator gain L. Particularly, it can be made Hurwitz and the estimator error e→ 0 when time t→ oe.

The injector model is nonlinear in some embodiments, and it is difficult to utilize the linear estimator design to the whole system. One way to linearize a subsystem is measure an output such as body volume pressure, and then calculate the estimator gain based on the subsystem and use it for the nonlinear system. Based on the linear estimator design strategy, a proper estimation gain L for the estimator is calculated. Then the dynamic equation of body volume pressure with estimation becomes

One state space model for the piezoelectric fuel injector is nonlinear, and it can be difficult to utilize the linear estimator design for the whole system. Another way is to apply the method in some embodiments to a subsystem with its measurable outputs, namely body volume pressure for the injector system, and then calculate the estimator gain based on the subsystem and use it for the nonlinear system.

The measurable variables in one injector system are the stack voltage and the body volume pressure. Since the stack voltage is regarded as the input to the system, a usable measurement for the estimator design is the body volume pressure.

The state space equation of the injector gives the equation of the body volume pressure (Eq. 3.5). Based on this equation, a subsystem describing the body volume dynamics can be developed with the rail pressure and the needle displacement as inputs and the body volume pressure as the output (to the remaining system). The nonlinear state space equation is developed as ή . (3.15)

= 3¾ (3,16) where inputs u2 = Prail, u3 = x3 and the output y5 = x5 (using same subscript as the state variable). Note that for the injector model, the total flow resistance is a function of needle tip displacement rather than a function of the needle displacement x3. They are different because the needle can be compressed due to material compliance (as shown in FIG. 3.4). Although geometrically the difference is small (FIG. 3.5), it can affect the flow since the flow resistance is very sensitive to the needle tip position, such as when the needle is not totally open. While calculating the estimator gain, however, this difference is negligible and the needle resistance can be treated solely as a function of x3.

Since the body volume dynamic is nonlinear, it can be linearized before applying the estimator design method.

As is shown in the nonlinear state space equation of the body volume pressure (Eq. 3.15), the dynamic equation has two nonlinear terms: the volumetric flow rate from the rail to the injector body divided by the body volume capacitance and the volumetric flow rate from the injector body to the sac volume divided by the body volume capacitance. One linear approximation can be made for these two terms by picking a suitable operating pressure region. It is to be noted that the linear approximation is used in calculating the estimator gain.

For the first term, the flow resistance Rrail is constant. The flow rate nonlinearity is caused by the square root of the pressure difference from the rail to the body. And it can be simply approximated by a linear function of the pressure difference. FIG. 3.6 displays the linearization, resulting in the linearized equation given by

where a1 is the slope of the approximated linear function.

For the second term, the flow rate coming from the body volume to the sac volume is also nonlinear, but the nonlinearity comes not only from the square root of the pressure difference but also from the flow resistance. These two nonlinearities are coupled, and both of them affect the nonlinear flow simultaneously. The flow equation is regarded as a nonlinear function of two variables: the pressure difference from the body to the cylinder and the needle displacement. One method to linearize the nonlinear flow equation is finding the variable having the stronger linear relationship to the flow equation. FIG. 3.7 and FIG. 3.8 show the relationship of the nonlinear flow rate to the two variables respectively.

FIG. 3.8 shows that the needle displacement has a different relationship with the flow rate than the pressure difference. This can be verified by looking at the flow rate equation. Since the cylinder pressure is almost 0, the variation of the pressure difference mainly depends on the drop of the body volume pressure. The drop-off value is relatively small compared to its initial value, which is the commanded rail pressure. Thus the square root of the pressure difference is about the square root of the rail pressure, which is constant. The needle resistance varies with needle position and therefore it affects the flow rate directly. Moreover, since the needle dynamics depend on the body volume pressure, using needle lift as a variable to linearize the flow rate from the body volume to the sac volume can also include the effect of pressure change to the flow rate.

According to the above analysis, the second term can be linearized as described below

where a 2 is the slope of the approximation line in FIG. 3.8.

Writing the state space equation in form of matrices, x5 and y5 are given by

One output is the state of the body volume pressure x5 in this subsystem because it is the measurable variable. Recalling section 3.1 .2 with a defined estimator gain L = [I5], the estimation error dynamic of the body volume pressure

is given by

If the error approaches zero, the estimated body volume pressure will then follow its measurement. The characteristic equation is

s

k - 0, (3,221

I*

Since is positive, the linearized system has a single LHP pole s =

The time constant of the system is given by

With a desired time constant ^{> d}, the estimator gain is calculated by

1 o I

(3.24)

. In one embodiment, an estimation time constant would be Ι Ομβ, giving the estimator gain 15 - 100.

The estimator gain calculated from the linearized system is applied to the nonlinear system. The linearized equation of the subsystem is used for calculating the estimator gain. The calculated estimator gain will be applied to one or more nonlinear equations.

With the addition of the estimator gain and error, the body volume dynamic equation is therefore corrected and given by

p .

y ¾ - ¾

3.25

3.26

The estimator discussed above is a continuous-time model in the form of differential equations. It can be discretized with a certain time step before implementing into a computer-based system such as the Nl cRIO system.

Discretization uses a numerical analysis method which is based on the approximations of time derivatives of the differential equations. Two commonly used discretizing methods are Euler forward and backward differentiation method. The Euler forward method is known as the Euler method, and it is the most basic explicit method for numerical integration of differential equations. The backward method is somewhat more accurate than the forward method, but it is implicit and more difficult to use. For simplicity, in this estimator, a method of Euler forward mixed with backward is being implemented. A graphical visualization of the Euler method is shown in FIG. 3.9.

The forward method is based on the following approximation of the time derivation ^ ^{' k } ~ h} (7) where h is the time step and index k stands for the current moment. The name "forward" stems from the --^lk ' ¹ term in the equation. Solving for ifk—i and reducing the time index by one gives y(t_k) - (i_k^ i ) + hy( tk)

(8)

Replacing the notation t _k by k, Eq. 8 can be written as y(k) = y(k ---- 1) -f

(9)

Similarly, the backward approximation of the time derivation is

K y(tk) - V(tk-l)

y\ ) ^™ — ^···

(10) and the expression of i^) will be

If the current time derivative of the function ^ is known, Euler backward method can be applied; otherwise the forward method is used by calculating the previous time derivative of

In the case of a reduced order estimator according to one embodiment, the highest order of the differential equation is two. The second order time derivative term is calculated from the previous time step as where / (k— 1 ) is a function of variables at k— 1 time step, and it can be either linear or nonlinear. Thus from Eq. 9, the first order time derivative describing ^ ^" is given by (k)™ y(k ~~ 1) -f~ hy(k— 1)

(13) i_ll /.' !

Then applying the Euler backward method in Eq. 1 1 , ^' ' is solved as y{k )—^■ y(k - 1} -r hy(k) = y(k - 1) - hy{k - 1)

- -h²y(k— 1 )

And for the differential equation with orders less than two, the Euler forward method is used. The time step of the discrete estimator based on the design

requirements and system limitations.

High resolution flow rate analysis is helpful in engine control systems. Accurate rate shape and needle position estimates should to be calculated in a short enough time to inform control action prior to the upcoming engine cycle. This is helpful, especially in case of complex injection profiles such as the boot shaping.

A figure of an injection rate profile is shown in FIG. 3.10. The profile is divided by vertical lines with a certain resolution, which gives a sense of how much resolution is enough to represent the profile. A sampling time of about 10μ^ is used in some embodiments in order to capture the details in the flow rate profile.

Moreover, for the discrete model, it is also known that the stability will be different from the continuous model. As is shown in FIG. 3.9, the discretization method is a way of numerical approximation. Once the time step increases, approximation error will propagate and thus the system can lose stability. The critical time step for stability can be calculated for linear models. However, since the injector model includes complex nonlinear parts, it cannot be directly calculated. A feasible way to get the critical time step of the estimator is simulating the model with different time steps, which yields that it should be less than about 8 μ$.

The real-time estimation is done in the FPGA module in a cRIO system. FPGA is short for Field-programmable gate array, and it is a reprogrammable silicon chip with an ultra-high processing speed. Largely the estimator is compiled in the FPGA and simulated under the real-time clock of the FPGA. Although the time-loop frequency of the FPGA can be as fast as 40 MHz, i.e. 0.025 μβ, the estimator time loop is far slower because the differential equation is very complex. After optimizing the FPGA VI, the smallest loop time for running the estimator is 4.7 μβ. TABLE II

TIME STEP LIMITS

Under the consideration of all the above things (listed in Table II), the time step of the estimator is designed to be 6 μβ. This value satisfies both the estimation requirements and the hardware limitation. The estimator model is discretized with time step h = δμβ. The discrete estimator model is applicable to the computer-based system and is able to provide a good estimation of the output flow rate for the piezoelectric fuel injector.

The resulting discrete estimator is realized in hardware using FPGA to reduce the loop computation time and provide a platform for within-a-cycle control. Estimator results are compared against both open-loop simulation results as well as experimental data from the rig for a variety of flow profiles at different toe heights and different operating rail pressures and show notable improvement over the pure open loop simulation results.

For single pulse, the injector is tested under the same stack voltage as is shown in FIG. 3.1 1 , and the rail pressure is 1000bar. The measurable injection rate and body volume pressure are plotted together with the simulated results of the reduced order model and the estimator, as is shown in FIG. 13 and 14. From the body volume pressure comparison, it is known that the model predicted body volume pressure is different from the measurement value. After implementing the estimation strategy, the estimated body volume pressure can follow the measurement value, leading to a better prediction of the injection rate in FIG. 13. The estimated injection profile has a steady state value during the on-time, and a falling edge closer to the experimental results (compared to the model without estimation). It should be noted that the falling edge drops a little earlier for the estimator than experimental result. The reason might be that the plunger simplification makes the needle close faster than actual situation, and thus it influences the ending time of injection.

The stack voltage is shown in FIG. 2.24, and the rail pressure is also 1000bar. Injection rate and body volume pressure are plotted in FIG. 15, 16. As is seen from the figure, the pulse-to- pulse bleeding problem doesn't appear for the estimated injection rate because the body volume pressure is "corrected" in the estimator.

Estimation plays a role for the boot shaped case. The measurable results are plotted in FIG. 3.22 and FIG. 18. Similarly, the improvement of injection rate is shown in the estimator results comparing to the reduced order model.

In addition, more cases of boot shaped injection are illustrated for the purpose of verifying the estimator. Two more cases at 1000bar with different toe height are shown in FIG. 19 and 20. Results of different rail pressures at 800bar, 1200bar, 1400bar and 1600bar are in FIG. 21 , 22, 23, 24 respectively.

A summary of the percentage error between measurement and the predicted fueling amount of the toe duration (TD) as well as total on-time (OT) is shown in table 3.3. Note that the percentage error is calculated by comparing the fueling amount of the model/estimator prediction to the experimental measurement, and the fueling amount is integrated from the fuel flow rate over a certain time duration.

Table 3.3. Estimator Prediction Error Summary.

The simulation results demonstrated that the estimator performs accurately for a wide range of different profiles and rail pressures, and can run "within-an-engine cycle" at time step of about 6 μβ. Furthermore, the real-time estimation more accurately predicts the flow rate than the open-loop model and this improvement is evident for the boot profile cases (FIGS. 3.27 to 3.32).

Estimator simulation results are compared against both open-loop simulation results and experimental data from the rig for a variety of flow profiles at different operating rail pressures. There is a notable improvement of the simulation results with the estimation algorithm over the pure open-loop simulation results. Real-time estimation results are plotted and validated with experimental data. Estimation plays a role in the boot shaped injection events. The results of body volume pressure and flow rate are plotted in FIG. 3.33 for a rail pressure of 1000 bar. Note that in the figure, the estimated body pressure follows its experimental value, and the estimated flow rate matches the experimental result well.

Furthermore, more cases of boot shaped injections are illustrated for the purpose of verifying the estimator. Results of different rail pressures at 800 bar, 1200 bar, 1400 bar and 1600 bar are in FIGS. 3.34, 3.35, 3.36, 3.37, respectively.

A piezoelectric fuel injector model simplification process is disclosed. The process includes state reduction and parameter simplification. The resulting reduced order model (also known as the control model) is a simplified description of the injector dynamics, which captures the essential coupling from the system inputs to the output. It has been validated with experimental data in different rail pressures and stack voltages.

A within-a-cycle estimation algorithm is described which improves the

performance of the model. The measured body volume pressure is coupled with the estimator to provide a better prediction of the fuel flow rate. To calculate the estimation gain, the reduced order model has been divided and partially linearized. After that, the estimator gain is applied back to the nonlinear model to generate the estimator. Also, based on the requirements and limitations, the estimator is discretized to be

implemented in the computer-based system (Nl compactRIO system). The predicted flow rate of the estimator is compared to the reduced order model, showing that the performance has an improvement when using the estimation strategy, for boot shaped pulse profiles. The simulated result of other internal states displays a difference from the estimator to the reduced order model.

Various embodiments of the present invention include for an internal combustion engine a control algorithm using an estimator, which is capable of different injection profiles such as multiple pulse profiles and boot shaping. The controller is incorporated into a fuel injection system, achieving fuel injection control.

The results demonstrated that the estimator has an acceptable performance with a wide range of different profiles and rail pressures. The estimator improvement compared to a simulation model is helpful for the injection profiles with higher rail pressure. It shows the injection rate is systematically ahead of the experimental data, causing a time delay between the estimated value and the measurement value. The reason for that is possibly the measurement delay of the injection rate.

Various aspects of different embodiments of the present invention are expressed in paragraphs X1 and X2 as follows:

X1 . One aspect of the present invention pertains to an apparatus. The apparatus preferably includes an internal combustion engine including a combustion chamber. The apparatus preferably includes a fuel system including an electrically actuatable fuel injector and receiving fuel at a pressure, said injector capable of providing a fuel flow to the engine for combustion in the engine on a cyclic basis. The apparatus preferably includes a pressure sensor providing a data signal corresponding to fuel pressure. The apparatus includes an electronic controller operating an algorithm to predict the quantity of fuel injected into the engine and receiving said signal and operably connected to said fuel injector to provide an electrical input signal for actuation of said injector, the algorithm being adapted and configured to estimate the quantity of fuel as a function of fuel pressure within one combustion cycle of the engine.

Another aspect of the present invention pertains to a method for operating an internal combustion engine. The method preferably includes providing an internal combustion engine, a source of fuel at a pressure, an electrically actuatable fuel injector assembly, and an electronic controller operating an algorithm including an estimator of fuel flow from the fuel injector assembly and including a representation of an actuation characteristic of the fuel injector. The method preferably includes providing fuel from the source to the injector at a pressure. The method preferably includes measuring the fuel pressure with the controller. The method preferably includes calculating a term with the actuation characteristic dependent on the value of measured fuel pressure. The method preferably includes using the term with the estimator to predict fuel flow provided to the engine.

Yet other embodiments pertain to any of the previous statements X1 and X2, which are combined with one or more of the following other aspects.

Wherein the input signal is a boot-shaped voltage profile.

Wherein the input signal is adapted and configured to provide within one combustion cycle a first smaller quantity of fuel to initiate combustion followed by a second greater quantity of fuel, and/or wherein the algorithm estimates the first quantity of fuel.

Wherein said fuel system includes a plurality of electrically actuatable fuel injectors each receiving the fuel from a fuel rail at the pressure, and said pressure sensor is in fluid communication with said fuel rail.

Wherein said injector receives a voltage signal from said controller for actuation, and which further comprises a second sensor providing a second signal corresponding to the received voltage, said electronic controller acquiring the second signal.

Wherein said algorithm is adapted and configured to estimate the quantity of fuel as a function of received voltage within one combustion cycle of the engine.

Wherein said controller includes a gate array and said gate array is programmed with the algorithm. Which further comprises operating the engine on a cyclic basis, and wherein said calculating the term is within one cycle, and said using the term is in the one cycle or the next cycle, and wherein the cycle is a four stroke compression ignition cycle.

Wherein the actuation characteristic is a linearized representation of the fuel injector assembly and said calculating the term is with the linearized representation, and/or wherein the linearized representation is a representation of the filing of the internal volume of the fuel injector with fuel.

Wherein the term is a gain used to adjust the fuel flow predicted by the estimator.

Wherein the estimator includes a non-linear representation of the fuel injector assembly and said using the term is with the linearized representation, and/or wherein the term is a gain and said using the term is in multiplication.

Wherein said providing fuel is with a boot-shaped actuation signal from the controller.

Wherein the actuation signal corresponds to a voltage from the controller to the fuel injector assembly, and/or which further comprises measuring the voltage received at the fuel injector assembly, and/or wherein said calculating the term is dependent on the measured voltage.

Wherein said providing includes a fuel pressure transducer and said measuring is by the pressure transducer.

Wherein said providing includes a plurality of electrically actuatable fuel injectors, said providing fuel from the source is to each of the plurality of fuel injectors from a common rail and the fuel pressure is the pressure of the common rail.

While the inventions have been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only certain embodiments have been shown and described and that all changes and modifications that come within the spirit of the invention are desired to be protected.

Claims

WHAT IS CLAIMED IS:

1 . An apparatus comprising:

an internal combustion engine including a combustion chamber;

a fuel system including an electrically actuatable fuel injector and receiving fuel at a pressure, said injector providing a fuel flow to the engine for combustion in the engine on a cyclic basis;

a pressure sensor providing a data signal corresponding to fuel pressure; and an electronic controller operating an algorithm to predict the quantity of fuel injected into the engine and receiving said signal and operably connected to said fuel injector to provide an electrical input signal for actuation of said injector, the algorithm being adapted and configured to estimate the quantity of fuel as a function of fuel pressure within one combustion cycle of the engine.

2. The apparatus of claim 1 wherein said controller includes a gate array and said gate array is programmed with the algorithm.

3. The apparatus of claim 1 wherein said injector defines a variably sized internal volume, and said algorithm estimates the quantity of fuel as a function of the volume.

4. The apparatus of claim 1 wherein the input signal is a boot-shaped voltage profile.

5. The apparatus of claim 1 wherein the input signal is adapted and configured to provide within one combustion cycle a first smaller quantity of fuel to initiate combustion followed by a second greater quantity of fuel.

6. The apparatus of claim 5 wherein the algorithm estimates the first quantity of fuel.

7. The apparatus of claim 1 wherein said fuel system includes a plurality of electrically actuatable fuel injectors each receiving the fuel from a fuel rail at the pressure, and said pressure sensor is in fluid communication with said fuel rail.

8. The apparatus of claim 1 wherein said injector receives a voltage signal from said controller for actuation, and which further comprises a second sensor providing a second signal corresponding to the received voltage, said electronic controller acquiring the second signal.

9. The apparatus of claim 8, wherein said algorithm is adapted and configured to estimate the quantity of fuel as a function of received voltage within one combustion cycle of the engine.

10. A method for operating an internal combustion engine, comprising:

operating an internal combustion engine, a source of fuel at a pressure, an electrically actuatable fuel injector assembly, and an electronic controller operating an algorithm including an estimator of fuel flow from the fuel injector assembly and including a representation of an internal volume of the fuel injector that is filled with fuel; providing fuel from the source to the injector at a pressure;

calculating a term corresponding to the size of the volume and dependent on the value of fuel pressure; and

using the term with the estimator to predict fuel flow provided to the engine.

1 1 . The method of claim 10 which further comprises operating the engine on a cyclic basis, and wherein said calculating the term is within one cycle, and said using the term is in the one cycle or the next cycle.

12. The method of claim 1 1 which further comprises measuring the fuel pressure with the controller, and said calculating is with the measured fuel pressure.

13. The method of claim 10 wherein the actuation characteristic is a linearized representation of the fuel injector assembly and said calculating the term is with the linearized representation.

14. The method of claim 13 wherein the linearized representation is a representation of the filing of the internal volume of the fuel injector with fuel.

15. The method of claim 13 wherein the term is a gain used to adjust the fuel flow predicted by the estimator.

16. The method of claim 13 wherein the estimator includes a non-linear representation of the fuel injector assembly and said using the term is with the linearized representation.

17. The method of claim 10 wherein the estimator is implemented on a field programmable gate array.

18. The method of claim 10 wherein the term is a gain and said using the term is in multiplication of an output of the estimator.

19. The method of claim 10 wherein said providing fuel is with a boot-shaped actuation signal from the controller.

20. The method of claim 19 wherein the actuation signal corresponds to a voltage from the controller to the fuel injector assembly.

21 . The method of claim 10 which further comprises measuring the voltage received at the fuel injector assembly.

22. The method of claim 10 wherein said calculating the term is dependent on the measured voltage.

23. The method of claim 10 wherein said operating includes a fuel pressure transducer and said measuring is by the pressure transducer.

24. The method of claim 23 wherein said operating includes a plurality of electrically actuatable fuel injectors, said providing fuel from the source is to each of the plurality of fuel injectors from a common rail and the fuel pressure is the pressure of the common rail.