DE102018217111B4 - Method for determining a rotational angle position of a crankshaft of an internal combustion engine - Google Patents

Abstract

Method for determining a rotational angle position of a crankshaft of an internal combustion engine which is coupled directly or with a gear ratio to an electrical machine (110, 210) comprising a rotor and a stator, which has a rectifier and voltage regulator circuit (120, 220) and a battery (140 , 240) are connected downstream, at least one signal (320, 330) of the electrical machine (110, 210) each having one or more characteristic values which each occur at least once per revolution of the rotor, characterized in that a system consisting of the electrical machine (110, 210), the rectifier and voltage regulator circuit (120, 220) and the battery (140, 240) is described with the aid of a theoretical model (400, 500, 600), as a boundary condition (411, 412) for the theoretical model (400, 500, 600) an inductance (411) of the electrical machine (110, 210) and a theoretical open circuit voltage (412) of the electrical machine (110, 210) are given as input variables (421, 422, 423) for the theoretical model (400, 500, 600) current values of a time difference (421) between two characteristic values of the at least one signal (320, 330) of the electrical machine (110, 210 ), a voltage (422) of the battery (140, 240) and a short-circuit voltage (423) of the rectifier and voltage regulator circuit (120, 220) can be specified with the aid of the theoretical model (400, 500, 600) depending on the boundary conditions (411, 412) and the input variables (421, 422, 423) a pole wheel angle (431, 531, 633) is determined and the rotational angle position of the crankshaft is determined as a function of the pole wheel angle (431, 531, 633).

Description

The present invention relates to a method for determining a rotational angle position of a crankshaft of an internal combustion engine as well as a computing unit and a computer program for its implementation.

State of the art

The angle of rotation position and the speed of the crankshaft of an internal combustion engine are essential input variables for many functions of the electronic engine control. To determine them, markings can be provided at equal angular intervals on a body rotating with the crankshaft of the internal combustion engine. The passing of a marking as a result of the rotation of the crankshaft can be detected by a sensor and passed on to evaluation electronics as an electrical signal.

This electronics determines the respective stored signal for the marking for the respective angular position of the crankshaft or measures a time difference between two markings and can determine the angular speed and the rotational speed based on the known angular distance between two markings. In motor vehicles, in particular ATV (All Terrain Vehicle), motorcycles, mopeds or motorcycles, the markings can be provided, for example, by teeth of a metallic gear, a so-called transducer wheel, which cause a change in the magnetic field through their movement in the sensor. A gap of a few teeth can serve as a reference mark for recognizing the absolute position.

While 60-2 teeth are mostly used in cars (even distribution of 60 teeth, two being left out), 36-2, 24-2 or 12-3 teeth are also used in motorcycles or motorcycles, for example. With this indirect principle of determining the rotational speed or the rotational angle position of the crankshaft, the resolution of the rotational speed signal or the absolute detection of the rotational angle position is determined by the number of teeth and by reliable detection of the reference mark.

Every modern vehicle with an internal combustion engine has a built-in generator that is driven by the rotation of the crankshaft and supplies electrical signals that are used to supply the vehicle with electrical energy and to charge the vehicle battery. The intended operation of a vehicle without this generator is not possible or only possible for a short time.

A use of the electrical output variables of an electrical machine (generator) driven via the crankshaft is for example in the DE 10 2014 206 173 A1 used to determine the speed. For this purpose, one or more signals from the electrical machine are evaluated, each of which has one or more values that occur at least once per revolution of the rotor of the electrical machine. The speed is calculated by calculating a time difference between two times when values occur.

Furthermore, in the DE 10 2016 221 459 A1 discloses using such electrical output variables for determining a rotational angle position of a crankshaft of an internal combustion engine. For this purpose, a time of occurrence of at least one value of a phase signal of the electrical machine, which occurs at least once per revolution of the rotor, is used to determine a rotational angle position of the rotor. The angular position of the crankshaft is calculated from the angular position and an angular offset.

Disclosure of the invention

Against this background, a method for determining a rotational angle position of a crankshaft of an internal combustion engine as well as a computing unit and a computer program for its implementation with the features of the independent claims are proposed. Advantageous configurations are the subject of the subclaims and the description below.

The internal combustion engine is coupled directly or with a gear ratio to an electrical machine comprising a rotor and a stator. The electrical machine is also followed by a rectifier and voltage regulator circuit and a battery.

At least one signal from the electrical machine has one or more characteristic values that occur at least once per revolution of the rotor. In particular, such a signal can be a speed signal of the electrical machine or an output voltage at the output of the electrical machine. Characteristic values are, for example, zeros, maxima or minima.

In the context of the present method, a system consisting of the electrical machine, the rectifier and voltage regulator circuit and the battery is described with the aid of a theoretical model. An inductance of the electrical machine, in particular an inductance of a generator string, and a theoretical Open-circuit voltage or an ideal open-circuit voltage of the electrical machine specified. In particular, these boundary conditions are assumed to be constant.

In particular, an ohmic resistance of the inductance or the generator string can also be specified as a boundary condition. In a simple approximation, however, this ohmic resistance can expediently also be assumed to be negligibly small.

Current values of a time difference between two characteristic values of the at least one signal of the electrical machine, a voltage of the battery and a short-circuit voltage of the rectifier and voltage regulator circuit are specified as input variables for the theoretical model.

With the aid of the theoretical model, a pole wheel angle or a current value of a pole wheel angle is determined depending on the boundary conditions and the input variables. The angle of rotation position of the crankshaft is determined as a function of the pole wheel angle or the current value of the pole wheel angle.

Due to the fixed coupling of the crankshaft of the internal combustion engine and the rotor of the electrical machine, if the rotational angle position of the rotor is known, conclusions can be drawn about the rotational angle position of the crankshaft. In the case of an unloaded electrical machine, the exact rotational angle position of the rotor can be read directly from the open circuit voltage of the electrical machine, since the relative phase position of the open circuit voltage corresponds to the rotational angle position of the rotor. However, this relationship does not apply to a loaded electrical machine, since the flow of current leads to a shift in the phase position and accordingly the output voltage of the electrical machine, which corresponds to the phase voltage of at least one phase of the electrical machine, no longer corresponds to the angular position of the rotor. This offset of the angular position between the output voltage of the electrical machine and the actual angular position of the rotor of the electrical machine is commonly referred to as the pole wheel angle.

Thus, by determining the rotor angle and the phase voltage of a phase of the electrical machine, it is possible to determine the rotational angle position of the crankshaft with improved accuracy and thus higher quality. Consequently, a high-resolution determination of the rotational angle position of the crankshaft can be provided directly from the internal signals of the electrical machine, whereby a corresponding encoder wheel for determining the rotational angle position or the speed and the associated sensors can be dispensed with. This enables costs to be saved, which is particularly advantageous in relation to cheaper mopeds or light motorcycles. In addition, the control functions, such as. B. the position calculation of the injection, torque calculation or learning functions for precise determination of the TDC position and the like can be significantly improved.

The present method provides a possibility of a model-based determination of the pole wheel angle of the electrical machine for calculating the crankshaft variables of the internal combustion engine. With the help of the theoretical model, the system consisting of the electrical machine, the rectifier and voltage regulator circuit and the battery can be described or approximated in a simple manner. A calculation rule for the current pole wheel angle is expediently derived from the model, which can be implemented as simply and efficiently as possible in order to be able to determine the crankshaft position several times per revolution with great accuracy and as little calculation effort as possible.

If sufficient computing power is available, any precise model of the electrical components electrical machine, rectifier, voltage regulator, battery and vehicle electrical system can be used to determine the dynamic behavior of the pole wheel angle of the electrical machine and also, in particular, its speed. Depending on the computing power available, the model can expediently also be simplified by approximations or by quantities assumed to be negligibly small. In particular, the number of boundary conditions and input variables as well as the complexity of the model and the determination of the pole wheel angle can be reduced. Available input variables for the simulation model are in particular variables which are usually determined in the course of regulating or controlling the electrical machine, in particular the battery voltage, the behavior of the output voltage of the electrical machine, possibly the switching state of the rectifier or voltage regulator, various states of the electrical system.

The current value for the time difference between two zero crossings of the at least one signal of the electrical machine is advantageously specified as the input variable, preferably the time difference between two zero crossings of an output voltage or an output current of the electrical machine. The mechanical angular speed of the electrical machine and the mechanical rotor angle, i.e. the variables related to the machine shaft, result from the Division of the electrical quantities by the number of pole pairs p of the electrical machine. The electrical or mechanical angular velocity of the electrical machine expediently results from the time between two zero crossings of the current or the output voltage and the electrical or mechanical angle swept between them. The rotational frequency on which the mechanical angular velocity is based (f = ω _mech / (2π)) is referred to as the rotational speed of the crankshaft. The swept angle results from the electrical (180 °) or mechanical (180 ° / p) distance between two signal edges and the change in the electrical or mechanical rotor angle that occurred in between.

According to an advantageous embodiment, the pole wheel angle is determined by using the theoretical model to determine a course of a current at the output of the electrical machine and the pole wheel angle is determined as an angular offset between this course of the current and an ideal induced voltage of the electrical machine. The rotor angle represents in particular a phase offset or angular offset between the ideal induced voltage U _i (t) and the current curve i (t) at the output of the electrical machine. If the output is loaded with an ohmic load or a passive rectifier and voltage regulator circuit, is in addition, the real output voltage U _{out of} the electrical machine, in particular in phase with the current i (t). In this case, the pole wheel angle also represents an angular offset between the ideal induced voltage U _i (t) and the real output voltage U _out . This angular offset or the pole wheel angle corresponds in particular to an angle between a zero crossing of the ideal induced voltage U _i (t) and a subsequent zero crossing of the current curve i (t) or the real output voltage U _out .

U_i (t) = ω *U_i0*sin(ωt) ist dabei die ideale induzierte Spannung der idealen Spannungsquelle ist mit der idealen Leerlaufspannung U_i0 für ω = 1. $U_L\left(t\right)=L\ast \frac{di\left(t\right)}{dt}$

ist der Spannungsabfall an der Spule.
U_R(t) = R*i(t) ist der Spannungsabfall an dem Widerstand.
U_r(t) ist der Spannungsabfall an der Gleichrichter- und Spannungsreglerschaltung.A differential equation is preferably determined as the theoretical model, which mathematically describes an equivalent circuit diagram of the system comprising the electrical machine, the rectifier and voltage regulator circuit and the battery. In particular, the electrical machine can be assumed to be an ideal voltage source, which is followed in series by a coil and a resistor which represent the inductance or the internal resistance of the strand of the electrical machine. Switches of the rectifier, for example diodes or semiconductor switches (for example MOSFET), can in particular be regarded as ideal switches. The equivalent circuit diagram can in particular be described using the following equation: $$U_i\left(t\right)=U_{\mathrm{L.}}\left(t\right)+U_{\mathrm{R.}}\left(t\right)+U_r\left(t\right)$$

U _i (t) = ω * U _i0 * sin (ωt) is the ideal induced voltage of the ideal voltage source with the ideal open-circuit voltage U _i0 for ω = 1. $U_{\mathrm{L.}}\left(t\right)=\mathrm{L.}\ast \frac{di\left(t\right)}{dt}$

is the voltage drop across the coil.
U _R (t) = R * i (t) is the voltage drop across the resistor.
U _r (t) is the voltage drop across the rectifier and voltage regulator circuit.

By rearranging the above equation, the following differential equation in particular results, which describes the equivalent circuit diagram of the system: $$\omega \ast U_{i0}\ast sin\left(\omega t\right)-U_r\left(t\right)=\mathrm{L.}\ast \frac{di\left(t\right)}{dt}+\mathrm{R.}\ast i\left(t\right)$$

If the internal resistance of the electrical machine is assumed to be negligibly small, the term UR (t) or R * i (t) can in particular be omitted.

A course of a current at the output of the electrical machine is preferably determined as the solution of the differential equation. From the course of the current and the corresponding course of the ideal voltage U _i (t), the pole wheel angle can expediently be determined as the phase offset of these two signals. These calculations can be used, in particular, in an algorithm on a control unit to obtain information about the pole wheel angle and speed.

The pole wheel angle 9 is thus preferably a function of the inductance L of the electrical machine, the theoretical or ideal open-circuit voltage U _{i0 of} the electrical machine, the voltage Ubat of the battery, the short-circuit voltage U _{reg of} the rectifier and voltage regulator circuit and the time difference Δt between two zero crossings of the real output voltage of the electrical machine: $$\vartheta =f\left(\mathrm{L.},U_{i0},U_{bat},U_{reG},\Delta t\right)$$

Furthermore, an internal resistance of the electrical machine or of the generator train is preferably specified as a boundary condition for the theoretical model. This is particularly the case if the internal resistance cannot be assumed to be negligibly small and if the term UR (t) or R * i (t) is expediently also taken into account in the above differential equation. Thus, the rotor angle θ is also a function of the internal resistance R of the electrical machine: $$\vartheta =f\left(\mathrm{R.},\mathrm{L.},U_{i0},U_{bat},U_{reG},\Delta t\right)$$

An angular velocity of the ideal voltage source of the electrical machine and a point in time of a characteristic value of the at least one signal, in particular the point in time of a zero crossing of the real output voltage of the electrical machine, are preferably also determined with the aid of the theoretical model. The determination of these variables can be necessary in particular if a speed of the electrical machine and / or a state of the rectifier or voltage regulator cannot be assumed to be constant and also have an effect on the current rotor angle.

The angular velocity of the ideal voltage source of the electrical machine, the point in time of the characteristic value of the at least one signal and the pole wheel angle are preferably fed back as input variables for the theoretical model. The determination of the pole wheel angle is therefore expediently carried out iteratively. _{The current values for the angular velocity ω n} , the time t _{n of} the characteristic value and the pole wheel angle ϑ _n determined in the course of a current iterative n-th step are fed back as further input variables for the next (n + 1) -th iterative step, see above that the rotor angle is also determined as a function of these fed back input variables: $$\vartheta =f\left(\mathrm{R.},\mathrm{L.},U_{i0},U_{bat},U_{reG},\Delta t,t_n,{\omega }_n,{\vartheta }_n\right)$$

In this case, an initial angular velocity ω _{0 of} the ideal voltage source of the electrical machine, an initial time t _{0 of} the characteristic value of the at least one signal and an initial pole wheel angle ein _{0 can} be estimated or approximately determined as input variables for the theoretical model for an initial calculation step .

It is also conceivable to specify further useful input variables for the theoretical model, advantageously a pressure, in particular an ambient pressure, and / or a temperature, in particular an ambient temperature and / or a temperature of the internal combustion engine.

If the electric machine is not rigidly coupled to the crankshaft of the internal combustion engine, for example via a belt with slippage, the rotational angle position of the crankshaft is advantageously determined as a function of the pole wheel angle and also as a function of this slip of the belt. To determine the slip, the speeds of both shafts, generator and crankshaft, must be known. One possibility for this can be the use of a camshaft position / speed sensor, with the signal of which a reference is available for determining the slip. As an alternative or in addition to the information from the camshaft sensor, the generator can be used to supplement further position and speed information and thus in particular a crankshaft sensor can be dispensed with.

A computing unit according to the invention, for example a control unit of a motor vehicle, is set up, in particular in terms of programming, to carry out a method according to the invention.

The implementation of a method according to the invention in the form of a computer program with program code for performing all method steps is advantageous, since this causes particularly low costs, especially if an executing control device is used for other tasks and is therefore available anyway. Suitable data carriers for providing the computer program are, in particular, magnetic, optical and electrical memories, such as hard drives, flash memories, EEPROMs, DVDs, etc. A program can also be downloaded via computer networks (Internet, intranet, etc.).

Further advantages and embodiments of the invention emerge from the description and the accompanying drawing.

The invention is shown schematically in the drawing using exemplary embodiments and is described below with reference to the drawing.

Figure list

• 1 shows schematically a system comprising an electrical machine, a rectifier and voltage regulator circuit, a battery and a computing unit, which can be the basis of a preferred embodiment of a method according to the invention.
• 2 shows schematically an equivalent circuit diagram a system comprising an electrical machine, a rectifier and voltage regulator circuit and a battery, which can be determined in the course of a preferred embodiment of a method according to the invention.
• 3 shows schematically time profiles of signals of an electrical machine, which can be determined in the course of a preferred embodiment of a method according to the invention.
• 4th to 6th each show schematically as a block diagram a theoretical model of a system comprising an electrical machine, a rectifier and voltage regulator circuit and a battery according to a preferred embodiment of a method according to the invention.

Embodiment (s) of the invention

In 1 is schematically a system 100 from an electric machine 110 , a rectifier and voltage regulator circuit 120 , a battery 140 and a computing unit 150 , which is set up to carry out a preferred embodiment of a method according to the invention, shown.

The electric machine 110 is designed in particular as a generator in a motor vehicle, for example as a three-phase alternator or as a so-called starter generator, and is coupled to a crankshaft of an internal combustion engine of the vehicle, which for reasons of clarity in 1 is not explicitly shown. For example, the electrical machine 110 be designed as a two-phase permanent magnet electrical machine, in which two voltage signals phase-shifted by 180 ° are induced. The battery 140 is designed in particular as a motor vehicle battery and can be part of an on-board network.

The rectifier and voltage regulator circuit 120 assigns a variety of here as diodes 121 , 122 , 123 , 124 trained switches, by means of which the polyphase output voltage of the electrical machine 110 rectified and to supply the vehicle battery 140 or the on-board network can be provided. A (simple) regulator with two additional diodes is provided here to regulate the on-board electrical system voltage 125 , 126 and a switch designed here as a MOSFET 130 has, by means of which a short circuit of the rectifier and voltage regulator circuit 120 can be generated.

An output voltage at an output of the electrical machine is in 1 labeled U _out. Voltage drops at the individual diodes or at the MOSFET 130 are designated with U _Diode or U _Mosfet . The voltage of the battery 140 is labeled Ubat.

The arithmetic unit 150 is designed as a control device and in particular for controlling the rectifier and voltage regulator circuit 120 and also provided in particular for controlling the internal combustion engine. The control unit 150 is also set up to determine a pole wheel angle and, as a function of the pole wheel angle, a rotational angle position of the crankshaft of the internal combustion engine. This is the purpose of the control unit 150 , in particular in terms of programming, set up to carry out a preferred embodiment of a method according to the invention, which is described below in relation to 2 to 6th is explained.

As part of the procedure, the system 100 from the electrical machine 110 , the rectifier and voltage regulator circuit 120 and the battery 140 described with the help of a theoretical model. For this purpose the system 100 advantageously described with the help of an equivalent circuit diagram. Such an equivalent circuit diagram of the system 100 out 1 is schematic in 2 shown and with 200 designated.

In this equivalent circuit diagram 200 is the electric machine 210 as an ideal voltage source 211 approximated which in series is a coil 212 and a resistance 213 are connected downstream, which is the inductance L or the internal resistance R of the winding of the electrical machine 210 represent.

U _i denotes an ideal induced voltage of the ideal voltage source 211 , U _{L is} the voltage drop across the coil 212 and U _{R is} the voltage drop across the resistor 213 .

In the rectifier and voltage regulator circuit 220 can be a short circuit across the mosfet 130 can be represented by the choice of the voltage of the U _{bat /} U _{reg of} the model, where U _{reg is} a short-circuit voltage. Instead of the battery voltage Ubat, a lower voltage is selected in particular, which reduces the voltage drop across the MOSFET 130 represents. If a linear voltage regulator is used instead of a switching voltage regulator, a constant voltage U _{bat /} U _{reg can be} assumed.

The diodes 121 to 126 can be seen as ideal switches, for example. In order to take into account the voltage drop across the diodes, this voltage drop can be added to the value U _{bat /} U _reg . For power diodes, for example, a voltage drop of around 1V per diode can be assumed. The voltage U _{bat /} U _reg usually adds a 2V voltage drop across the rectifier diodes 220 (approx. 1V voltage drop per power diode of a branch with a correspondingly high current flow).

In 3 is a diagram 300 with schematic time curves of signals from the electrical machine 110 according to the equivalent circuit diagram 200 shown.

Curve 310 shows schematically the ideal induced voltage U _i (t) of the ideal voltage source 211 . Curve 320 however, shows the real one Output voltage U _out (t) at the output of the electrical machine 110 and curve 330 the associated real output current i (t) at the output of the electrical machine 110 . By the rectifier 220 subsequent battery 240 becomes the output voltage U _out (t) of the electrical machine 110 limited. This results in a real output voltage U _out (t), which can be approximated by a rectangular signal curve.

The zero crossings (here corresponds to the rising and falling edges) of the output voltage U _out (t) 320 or the corresponding zero crossings of the output current i (t) 330 represent characteristic values of the respective signal, which in each case at least once per revolution of the rotor of the electrical machine 110 occur.

The point in time at which the rising edge of the output voltage U _out (t) or the rising zero crossing of the output current i (t) occurs is in 3 denoted by t _n. The point in time at which the falling edge of the output voltage U _out (t) or the falling zero crossing of the output current i (t) occurs is designated as t _{n + 1.}

Δt describes the time interval between the two times t _n and t _{n + 1} and thus the time interval between two characteristic values of these signals 320 , 330 of the electric machine 110 .

ω _n and ω _{n + 1} , each denote the electrical angular velocity of the electrical machine 110 at times t _n and t _{n + 1.} ϑ _n and ϑ _{n + 1} each denote the electrical pole wheel angle of the electrical machine 110 at times t _n and t _{n + 1} .

This mechanical angular velocity as well as this mechanical rotor angle, i.e. the one on the shaft of the electrical machine 110 related variables are obtained by dividing the electrical variables by the number of pole pairs p of the electrical machine 110 .

As in 3 the rotor angle ϑ represents the angular offset between the ideal induced voltage U _i (t) and the real output voltage U _out (t) or the associated current curve i (t).

ϑ _n corresponds to the angle between the first zero crossing of the ideal induced voltage U _i (t) 310 and the following rising zero crossing of the current i (t) 330 or the rising edge of the real output voltage U _out (t) 320 . ϑ _n-1 corresponds to the angle between the second, descending zero crossing of the ideal induced voltage U _i (t) 310 and the subsequent descending zero crossing of the current i (t) 330 or the falling edge of the output voltage U _out (t) 320 .

The electrical or mechanical angular velocity results from the time between two zero crossings of the current i (t) 330 or two edges of the output voltage U _out (t) 320 and the electrical or mechanical angle swept between them. _{The rotational frequency (f = ω mech} / (2π)) on which the mechanical angular velocity is based is also referred to as the rotational speed n of the generator shaft or crankshaft. The swept angle results from the electrical (180 °) or mechanical (180 ° / p) distance between two signal edges and the change in the electrical or mechanical rotor angle that occurred in between.

In order to determine the rotor angle 9 with the aid of the theoretical model in the context of the present method, the equivalent circuit diagram 200 out 2 described by the following equation: $$U_i\left(t\right)=U_{\mathrm{L.}}\left(t\right)+U_{\mathrm{R.}}\left(t\right)+U_r\left(t\right)$$

By rearranging this equation, the following differential equation results, which is the equivalent circuit diagram 200 of the system 100 describes: $$\omega \ast U_{i0}\ast sin\left(\omega t\right)-U_r\left(t\right)=\mathrm{L.}\ast \frac{di\left(t\right)}{dt}+\mathrm{R.}\ast i\left(t\right)$$

Solving this differential equation results in a calculation rule for calculating the temporal current profile i (t).

According to the in 3 The signal curves shown are derived from the curve of the current i (t) 330 and the underlying course of the ideal voltage U _i (t) 310 the rotor angle ϑ is determined as the phase offset of these two signals. The rotational speed of the generator shaft or the angular speed are determined in turn as a function of the determined pole wheel angle 9, and ultimately the rotational angle position of the crankshaft of the internal combustion engine is determined.

The theoretical model and thus the above differential equation can be simplified by approximations or quantities assumed to be negligibly small. In particular, the number of boundary conditions and input variables as well as the complexity of the model and the determination of the pole wheel angle can be reduced, as follows with reference to the 4th to 6th is explained.

In 4th is a theoretical model 400 of the system 100 or the equivalent circuit diagram 200 according to a preferred embodiment of the Method according to the invention shown schematically as a block diagram

In this case, the internal resistance becomes R of the electric machine 110 as negligibly small compared to the inductance 411 assumed, so that the term U _R (t) or R * i (t) is omitted in the above differential equation. Furthermore, the rotational speed is assumed to be constant for the observed period of time Δt and it is assumed that there is no change in the state of the voltage regulator either in the considered period of time Δt or sufficiently long beforehand 120 takes place, so that U _reg is also assumed to be constant.

In this case the theoretical model will be used 400 as the first boundary condition 411 the inductance of the electrical machine 110 and as a second boundary condition 412 the ideal no-load voltage U _i0 specified.

As the first input 421 the time difference Δt between two edges of the real output voltage U _out (t) 320 given. As a second input variable 422 becomes the voltage Ubat of the battery 140 and as a third input variable 423 the short-circuit voltage U _reg at the MOSFET 130 the rectifier and voltage regulator circuit 120 .

As a starting point 431 of the theoretical model 400 the pole wheel angle is 9 as a function of these boundary conditions 411 , 412 and these input variables 421 , 422 , 423 certainly: $$\vartheta =f\left(\mathrm{L.},U_{i0},U_{bat},U_{rOG},\Delta t\right)$$

U_r ergibt sich dabei abhängig davon, ob die Ausgangsspannung U_out gerade U_bat oder U_reg entspricht.To calculate the pole wheel angle 9, the mathematical equation for the current curve, which results from the above differential equation taking into account the specified simplifications, is set to zero, since this allows the occurrence time of the zero crossing of the current to be determined. The assumption of constant speed results in the following calculation rule for the rotor angle: $$\vartheta ={\text{cos}}^{-1}\left(\frac{U_r}{U_{i0}}\ast \frac{\Delta t}{2}\right)$$

U _r results depending on whether the output voltage U _out corresponds to U _bat or U _reg.

In 5 is a theoretical model 500 of the system 100 or the equivalent circuit diagram 200 according to a further preferred embodiment of the method according to the invention shown schematically as a block diagram.

In this example, the internal resistance R of the electrical machine is not neglected, so that this internal resistance R is a further boundary condition 511 the model 500 is fed. The other boundary conditions 411 , 412 and input variables 421 , 422 , 423 are analogous to the example of 4th fed.

As a starting point 531 of the theoretical model 500 the rotor angle 9 is also determined as a function of the internal resistance: $$\vartheta =f\left(\mathrm{R.},\mathrm{L.},U_{i0},U_{bat},U_{rOG},\Delta t\right)$$

A, B, C und D sind dabei Funktionen, die von R, L, U_i0, ω, U_reg und U_bat abhängen. ω steht für die Winkelgeschwindigkeit und ergibt sich bei konstant angenommener Drehzahl insbesondere zu: $$\omega =\frac{\pi }{\Delta t}$$

To calculate the rotor angle ϑ, the mathematical equation for the current curve, which results from the above differential equation, taking into account the specified simplifications, is set to zero: $$\left(\mathrm{A.}\text{cos}\left(\omega t_1\right)-\mathrm{B.}\text{sin}\left(\omega {\text{t}}_1\right)\right)\ast \left(1+e^{\mathrm{C.}}\right)-\mathrm{D.}\ast \left(1-e^{\mathrm{C.}}\right)=0$$

A, B, C and D are functions that depend on _{R, L, U i0} , ω, U _reg and U _bat. ω stands for the angular velocity and results in particular from: $$\omega =\frac{\pi }{\Delta t}$$

_{The occurrence time t 1} for the zero crossing of the current curve, which can be determined by this equation, simultaneously represents the time elapsed since the last zero crossing of the ideal induced voltage, since this occurs at time t = 0 according to the definition of the differential equation.

From the time between the zero crossings and the time Δt, the electrical pole wheel angle θ can be calculated in particular using the following formula: $$\vartheta =\frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102018217111B4\_0022.png"\; state="\{\{state\}\}">t</figure-callout>}}_1}{2\Delta t}\ast 360°$$

The mechanical pole wheel angle related to the shaft of the electrical machine is obtained in particular by dividing the electrical pole wheel angle by the number of pole pairs p (ϑ _mech = ϑ _el / p).

In 6th is another theoretical model 600 of the system 100 or the equivalent circuit diagram 200 according to a further preferred embodiment of the method according to the invention shown schematically as a block diagram.

If one of the assumptions does not apply, that the speed and / or the state of the voltage regulator 120 are constant, this affects the rotor angle Pol. In areas of high speed dynamics or electrical transient processes due to voltage regulator interventions, their influences can be taken into account.

In this case, the theoretical model can also be used to determine the angular velocity ω of the ideal voltage source 211 and the times t at which the characteristic values or the signal edges of the output voltage U _out (t) 320 occur, determined and fed back as input variables.

In 6a is an example of the case that with a corresponding theoretical model 600 an initialization of the corresponding algorithm is carried out in an initial calculation step.

For this purpose, as a first additional input variable 621 an initial point in time t ₀ at which a first edge of the output voltage U _out (t) 320 occurs as the second additional input variable 622 an initial angular velocity ω _{0 of} the ideal voltage source 211 and as a third additional input variable 623 an initial pole wheel angle ϑ _{0 is} estimated or approximately determined in the model.

As the first output 631 of the model 600 the time t _{n of} the current edge of the output voltage U _out (t) 320 determined as the second output variable 632 the current angular velocity ω _{n of} the ideal voltage source 211 and as a third output variable 633 the current rotor angle ϑ _n .

In 6b shows an example of how the values determined in the current calculation step for the time t _n , the current angular velocity ω _n and the current pole wheel angle ϑ _n are fed back as input variables for the subsequent calculation step.

Thus, with the help of the theoretical model 600 The pole wheel angle 9 in the course of the current iterative step is also determined as a function of the values determined in the previous step for the angular velocity ω _n , the time t _{n of} the output voltage flank and the pole wheel angle: _n: $$\vartheta =f\left(\mathrm{R.},\mathrm{L.},U_{i0},U_{bat},U_{reG},\Delta t,t_n,{\omega }_n,{\vartheta }_n\right)$$

Since a constant speed is no longer assumed, a distinction must be made between the speed at time t _n and t _{n + 1} .

There are also different pole wheel angles ϑ _n and ϑ _{n + 1} for these points in time. The difference between these two values is denoted by Δϑ.

E, F, H, G, I und J sind dabei insbesondere Funktionen, die von R, L, U_i0, ω, Δϑ, U_reg und U_bat abhängen.If, as in the previous case, the solution of the above differential equation is set to zero, the pole wheel angle difference Δϑ results from the following equation: $$\begin{array}{l}\mathrm{E.}\text{sin}\left(\left(\frac{\pi +\Delta \vartheta }{\Delta t}\right)\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102018217111B4\_0022.png"\; state="\{\{state\}\}">t</figure-callout>}}_1+\Delta t\right)\right)-\\ -\mathrm{F.}\text{cos}\left(\left(\frac{\pi +\Delta \vartheta }{\Delta t}\right)\left({\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102018217111B4\_0022.png"\; state="\{\{state\}\}">t</figure-callout>}}_1+\Delta t\right)\right)-\mathrm{I.}+\\ +\left(G\text{cos}\left({\omega }_1{\text{t}}_1\right)-H\text{sin}\left({\omega }_1{t}_1\right)+\mathrm{I.}\right)e^{-J\Delta t}=0\end{array}$$

E, F, H, G, I and J are in particular functions that depend on _{R, L, U i0} , ω, Δϑ, U _reg and U _bat.

The equation shows that a solution can only be _{calculated for known t 1} and ω ₁ , i.e. for a known point in time of the current zero crossing t _n and a known angular velocity ω _n from the last calculation run. Therefore, an iterative algorithm structure as in 6b shown required.

$${\vartheta }_{n+1}={\vartheta }_n+\Delta \vartheta$$

$$t_{n+1}=\frac{{\vartheta }_{n+1}}{{\omega }_{n+1}}=\frac{{\vartheta }_n+\Delta \vartheta }{\pi +\Delta \vartheta }\Delta t$$

In particular, the following additional quantities follow from Δϑ: $${\omega }_{n+1}=\frac{\pi +\Delta \vartheta }{\Delta t}$$

$${\vartheta }_{n+1}={\vartheta }_n+\Delta \vartheta$$

$$t_{n+1}=\frac{{\vartheta }_{n+1}}{{\omega }_{n+1}}=\frac{{\vartheta }_n+\Delta \vartheta }{\pi +\Delta \vartheta }\Delta t$$

The rotational angle position of the crankshaft determined according to one of the above methods is then used in particular to control the internal combustion engine, with injection times, ignition times and top dead centers, for example, being determined and speed and position-based control functions calculated and executed as a function of the rotational angle position determined.

Claims (15)

Method for determining a rotational angle position of a crankshaft of an internal combustion engine which is coupled directly or with a gear ratio to an electrical machine (110, 210) comprising a rotor and a stator, which has a rectifier and voltage regulator circuit (120, 220) and a battery (140 , 240) are connected downstream, with at least one signal (320, 330) of the electrical Machine (110, 210) each has one or more characteristic values which each occur at least once per revolution of the rotor, characterized in that a system comprising the electrical machine (110, 210), the rectifier and voltage regulator circuit (120, 220) and the battery (140, 240) is described with the aid of a theoretical model (400, 500, 600), as a boundary condition (411, 412) for the theoretical model (400, 500, 600) an inductance (411) of the electrical machine ( 110, 210) and a theoretical open circuit voltage (412) of the electrical machine (110, 210) are specified as input variables (421, 422, 423) for the theoretical model (400, 500, 600) current values of a time difference (421) between two characteristic values of the at least one signal (320, 330) of the electrical machine (110, 210), a voltage (422) of the battery (140, 240) and a short-circuit voltage (423) of the rectifier and voltage regulator circuit (120, 220 ), a rotor angle (431, 531, 633) is determined with the aid of the theoretical model (400, 500, 600) as a function of the boundary conditions (411, 412) and the input variables (421, 422, 423) and as a function of the rotational angle position of the crankshaft is determined from the pole wheel angle (431, 531, 633). Procedure according to Claim 1 , the current value for the time difference (421) between two zero crossings of the at least one signal (320) of the electrical machine (110, 210), in particular between two zero crossings of an output voltage (320) of the electrical machine (110, 210) being specified as the input variable becomes. Procedure according to Claim 1 or 2 , the pole wheel angle (431, 531, 633) being determined by using the theoretical model (400, 500, 600) to determine a course of a current (330) at the output of the electrical machine (110, 210) and the pole wheel angle ( 431, 531, 633) is determined as an angular offset between this course of the current (330) and an ideal induced voltage (310) of the electrical machine (110, 210). Method according to one of the preceding claims, wherein a differential equation is determined as the theoretical model (400, 500, 600), which is an equivalent circuit diagram (200) of the system (100) comprising the electrical machine (110, 210), the rectifier and voltage regulator circuit (120, 220) and the battery (140, 240). Procedure according to Claim 3 and 4th , the course of the current (330) at the output of the electrical machine (110, 210) being determined as the solution of the differential equation. Method according to one of the preceding claims, wherein an internal resistance (511) of the electrical machine (110, 210) is also specified as a boundary condition for the theoretical model (500, 600). Method according to one of the preceding claims, further comprising, with the aid of the theoretical model (500, 600), an angular velocity (632) of an ideal voltage source (211) of the electrical machine (110, 210) and a point in time (631) of a characteristic value of the at least one Signals (320) of the electrical machine (110, 210) are determined. Procedure according to Claim 7 , the angular velocity (632) of the ideal voltage source (211) of the electrical machine (110, 210), the point in time (631) of the characteristic value of the at least one signal (320) and the pole wheel angle (431, 531, 633) as input variables for the theoretical model (600) can be traced back. Procedure according to Claim 7 and 8th , wherein for an initial calculation step an initial angular velocity (622) of the ideal voltage source (211) of the electrical machine (110, 210), an initial point in time (621) of the characteristic value of the at least one signal (320) and an initial rotor angle (431, 531, 633) can be estimated or approximately determined as input variables for the theoretical model (600). Method according to one of the preceding claims, wherein a pressure, in particular an ambient pressure, and / or a temperature, in particular an ambient temperature and / or a temperature of the internal combustion engine, are also specified as the input variable for the theoretical model (400, 500, 600). Method according to one of the preceding claims, wherein the determination of the rotational angle position of the crankshaft is carried out as a function of the pole wheel angle (431, 531, 633) and further as a function of a slip of a belt. Method according to one of the preceding claims, wherein the internal combustion engine is operated as a function of the determined rotational angle position of the crankshaft. Computing unit (150) which is set up to carry out all method steps of a method according to one of the preceding claims. Computer program that causes a computing unit (150) to perform all method steps of a method according to one of the Claims 1 to 12th to be carried out when it is executed on the processing unit. Machine-readable storage medium with a computer program stored thereon Claim 14 .

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