Method and device for operating a hybrid drive train of a vehicle

By determining pilot torque based on actual transmission ratios using measured rotational speeds, the method ensures smooth clutch actuation during shifting in hybrid vehicles, addressing abrupt ratio changes and enhancing control.

DE102012219126B4Active Publication Date: 2025-08-21ZF FRIEDRICHSHAFEN AG
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Patent Information

Application Number
DE102012219126
Authority / Receiving Office
DE · DE
Patent Type
Patents
Current Assignee / Owner
Filing Date
2012-10-19
Publication Date
2025-08-21
Estimated Expiration
2032-10-19

AI Technical Summary

Technical Problem

Abrupt changes in transmission ratio during shifting operations in automatic transmissions of hybrid vehicles lead to discomfort and control issues with the clutch between the internal combustion engine and electric machine.

Method used

A method to determine pilot torque for the clutch based on the actual transmission ratio, using measured input and output rotational speeds to ensure a continuous profile during shifting, thereby avoiding abrupt changes in vehicle moment of inertia.

Benefits of technology

This method enables smooth clutch actuation during shifting, maintaining comfort and improving control without losses, applicable to hybrid vehicles with hydraulic or electric clutches.

✦ Generated by Eureka AI based on patent content.

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Abstract

Method for operating a hybrid drive train of a vehicle, wherein the hybrid drive train comprises a drive unit with an internal combustion engine (1) and an electric machine (2) and an automatic transmission (4) connected between the drive unit and an output (3), wherein the internal combustion engine (1) can be coupled to the hybrid drive train by closing the clutch (5) via a clutch (5) between the internal combustion engine (1) and the electric machine (2) and can be decoupled from the hybrid drive train by opening the clutch (5), wherein when the clutch (5) is closed, a pilot control torque (M V ) is determined, with which the clutch (5) is controlled, whereby the pilot torque (M V ) from a vehicle moment of inertia (j F) which is determined by the transmission ratio (i) of the automatic transmission (4) corresponding to the gear engaged in the automatic transmission (4), wherein during a gear shift in the automatic transmission (4) while the vehicle is moving from an actual gear to a target gear, a value for the transmission ratio (i) of the automatic transmission (4) is determined which corresponds to the ratio of a measured input speed (N E ) at the input of the automatic transmission (4) and a measured output speed (N A ) at the output of the automatic transmission (4), and based on this fixed value of the gear ratio (i) the vehicle moment of inertia (j F ) and from this the pre-control moment (M V ) can be determined.
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Description

[0001] The invention relates to a method and a device for operating a hybrid drive train of a vehicle and a corresponding vehicle.

[0002] In the drivetrain of a hybrid vehicle, both an internal combustion engine and an electric motor can be used to generate drive torque. A separating clutch is typically provided between the internal combustion engine and the electric motor. When the clutch is disengaged, the hybrid vehicle can be driven purely electrically via the motor operation of the electric motor. When the clutch is engaged, hybrid driving is achieved, in which both the internal combustion engine and the electric motor are involved. An automatic transmission is typically used to transfer the drive torque generated in the hybrid drivetrain to an output.

[0003] US 2007 / 0 102 205 A1 describes a hybrid vehicle control system. The hybrid vehicle can switch between electric and hybrid operation. For this purpose, a clutch is provided between an internal combustion engine and an electric motor. The electric motor is connected to the input shaft of an automatic transmission, whose output shaft is connected to the drive wheels of the hybrid vehicle.

[0004] DE 199 43 334 A1 describes a method for controlling an electrohydraulically controlled clutch of a transmission. The clutch is controlled using a model-based compensation pressure controller. The compensation pressure controller contains a nonlinear compensation element that corresponds to the inverse model of the clutch or brake control system. An observer estimates clutch control disturbances based on a powertrain model using a state estimation method.

[0005] Torque-dependent pre-control is used to control the clutch between the combustion engine and the electric motor in a hybrid powertrain. This pre-control determines, among other things, a pre-control torque based on the gear ratio of the automatic transmission. This pre-control torque is then used to determine the corresponding clutch control variables so that the clutch is appropriately adjusted depending on the vehicle's operating condition. It is problematic that the gear ratio of the transmission changes abruptly when gearshifts are performed in the automatic transmission, which in turn leads to a jump in the determination of the pre-control torque of the clutch between the combustion engine and the electric motor. This causes problems in clutch control, which can lead to a loss of comfort.

[0006] The object of the invention is therefore to provide a method for operating a hybrid drive train of a vehicle, with which an improved control of the clutch is achieved when carrying out gear shifts of the automatic transmission in the hybrid drive train.

[0007] This object is achieved by the method according to claim 1 and the device according to claim 8. Further developments of the invention are defined in the dependent claims.

[0008] The method according to the invention serves to operate a hybrid drive train comprising a drive unit with an internal combustion engine and an electric motor, as well as an automatic transmission connected between the drive unit and an output. The internal combustion engine can be coupled to the hybrid drive train by engaging the clutch via a separating clutch between the internal combustion engine and the electric motor, or decoupled from the hybrid drive train by disengaging the clutch. When the clutch is engaged, a pilot torque is determined, which is used to control the clutch. The pilot torque depends on a vehicle moment of inertia determined by the gear ratio of the automatic transmission according to the gear engaged in the automatic transmission. The determination of such a pilot torque is known per se. One possible way of calculating such a pilot torque is explained in the detailed description.

[0009] The method according to the invention is characterized in that, during a shift in the automatic transmission while the vehicle is moving from the currently engaged gear to a target gear to be engaged, a value for the transmission ratio of the automatic transmission is determined. This value corresponds to the ratio of a measured input speed at the input of the automatic transmission and a measured output speed at the output of the automatic transmission. Based on this determined value of the transmission ratio, the vehicle's moment of inertia and, from this, the pre-control torque are then determined.

[0010] The method according to the invention enables continuous adjustment of the pilot torque based on the actual gear ratio, even during a gear shift. This gear ratio is determined by measuring the input and output speeds of the automatic transmission. This means that the method according to the invention uses appropriate measuring devices that determine these speeds. The method according to the invention has the advantage that, during gear shifts while the vehicle is moving, the pilot torque of the clutch is adjusted based on a gear ratio profile without any jumps, thereby creating significantly improved clutch control without compromising comfort.

[0011] In a particularly preferred embodiment, the pilot control torque is determined based on a primary moment of inertia on the primary side of the hybrid drivetrain extending from the clutch to the internal combustion engine and a secondary moment of inertia on the secondary side of the hybrid drivetrain extending from the clutch to the electric machine. The secondary moment of inertia comprises the vehicle moment of inertia, which according to the invention is determined during gearshifts based on the actual gear ratio of the automatic transmission. Preferably, the secondary moment of inertia further includes an inertia of the electric machine and / or the clutch components on the secondary side. In contrast, the primary moment of inertia comprises the moment of inertia of the internal combustion engine and, if appropriate, also the moment of inertia of the clutch components on the primary side.The determination of the pre-control torque is based in particular on the condition that the angular accelerations on the primary side and the secondary side are equal.

[0012] In a further preferred embodiment, during a shift in the automatic transmission from an engaged actual gear to a neutral position without traction in the transmission (i.e., without a gear engaged), the pilot torque is set based on a predetermined continuous temporal increase in the gear ratio from the gear ratio of the actual gear to a virtual (high) gear ratio in the neutral position. Analogously, during a shift in the automatic transmission from a neutral position without traction to a target gear to be engaged, the pilot torque is set based on a predetermined continuous temporal decrease in the gear ratio from a virtual (high) gear ratio in the neutral position to the gear ratio of the target gear.

[0013] According to the embodiment just explained, a continuous progression of the gear ratio is ensured even when shifting from or to the neutral position. In order to be able to use the same calculation rule for the pilot torque as for shifting between gears, the gear ratio for the neutral position is set to a virtual value that is very large and, in particular, higher than the gear ratio of all other gears of the automatic transmission. The continuous temporal increase or decrease of the gear ratio can be determined in a suitable manner, e.g., via filtering. This continuous increase or decrease is predetermined and is not determined from the measurement of the input and output speeds.The switching process in the automatic transmission from an actual gear to a neutral position or vice versa just explained relates in particular to a switching process when the vehicle is stationary, but can also refer to a material process while the vehicle is moving, e.g. from or to coasting mode.

[0014] In a further preferred embodiment of the method according to the invention, during a shift in the automatic transmission while the vehicle is moving from an actual gear to a target gear, the specified value of the gear ratio, which corresponds to the ratio of the measured input speed at the input of the automatic transmission and the measured output speed at the output of the automatic transmission, is limited by a minimum value and a maximum value. The minimum value is the minimum of the gear ratio of the actual gear and the gear ratio of the target gear. The maximum value represents the maximum of the gear ratio of the actual gear and the gear ratio of the target gear. The value of the gear ratio is set to the minimum value if the minimum value is undershot and to the maximum value if the maximum value is overshot. In this way, inaccuracies orNoise in the corresponding measurement signal of the speeds is appropriately taken into account.

[0015] The method according to the invention can be used in hybrid drives with any type of clutch between the internal combustion engine and the electric motor. In a preferred embodiment, the clutch is a hydraulic clutch or an electric clutch, or a combination of a hydraulic and electric clutch.

[0016] In addition to the method described above, the invention further relates to a device for operating a hybrid drive train of a vehicle, wherein the hybrid drive train comprises a drive unit with an internal combustion engine and an electric motor, as well as an automatic transmission connected between the drive unit and an output. The internal combustion engine can be coupled to the hybrid drive train via a clutch between the internal combustion engine and the electric motor by closing the clutch, or decoupled from the hybrid drive train by opening the clutch. The device comprises a control device which is designed such that, when the clutch is closed, a pilot control torque is determined, with which the clutch is controlled, wherein the pilot control torque depends on a vehicle moment of inertia which is determined by the gear ratio of the automatic transmission according to the gear engaged in the automatic transmission.The control device is characterized by the fact that, during a shift in the automatic transmission while the vehicle is moving from an actual gear to a target gear, a value for the transmission ratio of the automatic transmission is determined. This value corresponds to the ratio of a measured input speed at the input of the automatic transmission and a measured output speed or output speed at the output of the automatic transmission. Based on this determined value of the transmission ratio, the vehicle's moment of inertia and, from this, the pilot torque are determined by the control device.

[0017] The device according to the invention is preferably designed such that one or more preferred variants of the method according to the invention can be carried out with the device.

[0018] The invention further relates to a vehicle with a hybrid drive train, in particular a motor vehicle, such as a car or a truck, wherein the vehicle comprises the above-described device according to the invention for operating the hybrid drive train.

[0019] Embodiments of the invention are described in detail below with reference to the attached figures.

[0020] They show: Fig. 1 shows a schematic representation of an example of a drive train of a hybrid vehicle that can be operated based on the method according to the invention; Fig. 2 a diagram showing the determination of a gear ratio during shifting operations of the automatic transmission from Fig. 1 between gears according to an embodiment of the invention; and Fig. 3 a diagram showing the determination of a gear ratio during gear shifts of the automatic transmission from Fig. 1 from or into the neutral position according to an embodiment of the invention.

[0021] The method according to the invention is used to operate a hybrid drive train of a vehicle. Fig. Figure 1 shows an exemplary block diagram of a possible powertrain configuration in which the method according to the invention can be used. This is a parallel hybrid powertrain.

[0022] The Fig. The drive train shown in Figure 1 comprises an internal combustion engine 1 and an electric motor 2. An automatic transmission 4 is connected between the hybrid drive formed thereby and an output 3. A clutch 5 is also connected between the internal combustion engine 1 and the electric motor 2, wherein when the clutch 5 is disengaged, the internal combustion engine 1 is decoupled from the output 3. In the embodiment shown, a starting element 6 is connected between the electric motor 2 and the transmission 4, which is designed as a starting element external to the transmission. Instead of a starting element external to the transmission, a starting element internal to the transmission can also be used. The drive train of the Fig. 1 further comprises an electrical energy storage device 7, which supplies the electrical machine 2 with power during motor operation. It is also possible to operate the electrical machine 2 as a generator, in which case mechanical energy is extracted from the drive train by the machine 2 and used to charge the energy storage device 7. The drive train of the Fig. 1 also has a control unit 8 in the form of a so-called HCU (Hybrid Control Unit), via which the individual components of the drive train are controlled or regulated based on a hybrid strategy.

[0023] The hybrid strategy explained below is characterized by a special control of the clutch 5 via a pilot torque M Vwhich adjusts the clutch to suit the engaged position. The actual gear ratio of the automatic transmission is taken into account when shifting between gears, as explained in more detail below.

[0024] The determination of the pre-control moment M V is based on a primary drive torque M P on the side of the drive train extending from the clutch 5 to the combustion engine 1 (also referred to as the primary side) and a secondary drive torque M S on the side of the drive train extending from the clutch 5 to the electric machine 2 (also referred to as the secondary side). A primary moment of inertia j P which results from the moment of inertia j VM of the combustion engine and the moment of inertia j KPof the components of clutch 5 on the primary side. On the secondary side, a secondary moment of inertia j S which results from the moment of inertia j EM of the electrical machine, the moment of inertia j KS the shares of clutch 5 on the secondary side and the vehicle moment of inertia j F The vehicle's moment of inertia depends on the gear ratio i of the automatic transmission 4.

[0025] The pilot torque M V is calculated based on the following equations (1) to (3): jP⋅ω˙P=MP−MV, where jP=jVM+jKP jS⋅ω˙S=MS+MV, where jS=jKS+jEM+jF and jF=jF_konsti2 ω˙diff=ω˙P−ω˙S=0

[0026] Here, ώ P the angular acceleration on the primary side and ώ S the angular acceleration on the secondary side. The term j F_konstrepresents the moment of inertia of the vehicle for a gear ratio of one. According to the above equations, the product of the moment of inertia on the primary side and the angular acceleration on the primary side should be equal to the difference between the drive torque on the primary side and the pilot torque. Furthermore, the moment of inertia on the secondary side multiplied by the angular acceleration on the secondary side should be equal to the sum of the drive torque on the secondary side and the pilot torque. The pilot torque is derived based on the condition that the angular accelerations on the primary and secondary sides are equal. The pilot torque M results from the above equations (1) to (3). V according to the following equation: MV=jSjP+jS⋅MP−jPjP+jS⋅MS

[0027] With the determined pilot torque M VA corresponding control variable for clutch 5 is then determined in a known manner using a conversion. For a hydraulic clutch, a corresponding pressure for the hydraulic system is determined. In contrast, for an electric clutch, a required current for the clutch's electric actuators is determined.

[0028] The determination of the pre-control torque based on equation (4) above is known per se. However, the method according to the invention is characterized by a special determination of the vehicle moment of inertia j F which, according to equation (2) above, is the quotient of the term j F_konst and the square of the gear ratio. The gear ratio is adjusted to the actual gear ratio when shifting between gears. This prevents the moment of inertia j FThe vehicle's torque is abruptly reduced during a gear change from a high to a low gear due to the increase in the gear ratio, or increased during a transition from a low to a high gear due to the decrease in the gear ratio. Such a sudden change in the gear ratio can cause problems in the control of clutch 5.

[0029] To avoid such problems, the input speed N is measured during gear shifts using appropriate measuring devices at the gearbox input and gearbox output. E at the gearbox input and the output speed or output speed N A at the gearbox output. The gear ratio is determined based on the quotient between input speed N E and output speed N A fixed, ie i = N E / N AIn this way, the actual gear ratio is reproduced during gear changes and the jumps mentioned above are avoided.

[0030] Fig. Figure 2 shows the just-explained determination of the gear ratio for gear shifts while the vehicle is moving. Time t is plotted along the abscissa and gear ratio i along the ordinate. The value i1 corresponds to the gear ratio in first gear, the value i2 to the gear ratio in second gear, the value i3 to the gear ratio in third gear, the value i4 to the gear ratio in fourth gear, and the value i5 to the gear ratio in fifth gear. The gear ratio value used to determine the pre-control torque is represented by line L. The gear ratio of the transmission before a gear shift is indicated by a dashed curve and after a gear shift by a dotted curve. First, Fig. Two gear shifts are shown when downshifting from fifth gear to first gear. The next shifts are from first gear to second gear and from second gear to third gear. It can be seen that the gear ratio between the shifts does not jump abruptly from the actual gear ratio to the target gear, but follows a continuous progression corresponding to the ratio of the input speed to the output speed.

[0031] Under certain circumstances, noisy measurements of the input speed N E or the output speed N AIn addition, the quotient of input speed and output speed may be above or below the actual gear ratio or target gear ratio. To avoid such overshoot, in a particularly preferred embodiment, a minimum value and a maximum value are defined for the gear ratio corresponding to the quotient of input speed and output speed. The maximum value is the maximum of the actual gear ratio and target gear ratio, and the minimum value is the minimum of the actual gear ratio and target gear ratio. If the maximum value is exceeded, the gear ratio is set to the maximum value, and if the minimum value is undershot, the gear ratio is set to the minimum value.

[0032] In the embodiment of the invention described here, a sudden change in the pilot control torque M Vwhen changing from a transmission state without traction (so-called neutral position) to first gear or vice versa when the vehicle is stationary. In this case, the actual gear ratio consisting of the input speed and output speed can no longer be used, because the output speed is zero when the vehicle is stationary, which would result in an infinitely large gear ratio. In order to nevertheless determine the pre-control torque based on equation (4) above, a very high (virtual) value for the gear ratio i0 is set when the transmission is in neutral. This value is significantly higher than the gear ratios of all other gears. The transition from first gear to neutral or from neutral to first gear is further modeled by a (virtual) continuous temporal progression of the gear ratio.

[0033] The corresponding change in the gear ratio i or the vehicle moment of inertia j F When the vehicle is stationary, the diagram shows the Fig. 3. Time t is shown along the abscissa of the diagram. The left ordinate i represents the gear ratio, whose course is indicated by the solid line L'. In contrast, the right ordinate represents the vehicle's moment of inertia j. F again, the course of which is indicated by the dotted line L". Fig. Figure 3 initially shows the transition from first gear with the gear ratio i1 to neutral, where no gear is engaged. The gear ratio continuously increases to the virtual value i0. Accordingly, the vehicle's moment of inertia decreases from the value j F1 (y F1 = J F_konst / i1 2 ) with first gear engaged to the smaller value j F0 (y F0 = j F_konst / i02 ) in the neutral position. The transition between first gear and neutral is modeled by a continuous progression of the gear ratio or the vehicle's moment of inertia. Finally, when shifting back to first gear from the state without traction with the virtual gear ratio i0, the gear ratio returns to the value i1 of first gear, while at the same time the vehicle's moment of inertia is reduced to the value i F1 This transition is also modeled by a suitable continuous curve. In contrast to the switching processes of the Fig. 2, the continuous progression of the gear ratios is predetermined and was not determined by a measured input and output speed. Nevertheless, the continuous transition in Fig. 3 ensures that the gear ratio i and the vehicle moment of inertia jF do not change abruptly, thus avoiding problems in the control of clutch 5.

[0034] The method according to the invention has a number of advantages. In particular, during a shift between the gears of an automatic transmission, the actual gear ratio curve is simulated to determine the clutch pre-control torque by using the ratio of the measured input speed to the measured output speed of the automatic transmission as the gear ratio. This enables continuous calculation of the clutch pre-control without interference from a gear step. Furthermore, in a preferred variant, the method according to the invention also enables continuous adjustment of the clutch pre-control torque during a shift from or to the neutral position of the automatic transmission by specifying a (virtual) gear ratio curve during such shifts. Reference symbol 1 combustion engine 2 Electric machine 3 Downforce 4 gearboxes 5 Clutch 6 Starting element 7 Energy storage 8 Control unit Mv pre-control moment N E , N A speeds M P , Ms drive torques j P , j VM , j KP , j S , j EM , j KS , j F Moments of inertia i Gear ratio i0, i1, i2, i3, i4, i5 Gear ratio in neutral position or in gears j F0 , j F1 Moment of inertia of the vehicle in neutral position or in 1st gear L, L', L'' lines t time

Claims

[1] Method for operating a hybrid drive train of a vehicle, wherein the hybrid drive train comprises a drive unit with an internal combustion engine (1) and an electric machine (2) and an automatic transmission (4) connected between the drive unit and an output (3), wherein the internal combustion engine (1) can be coupled to the hybrid drive train by closing the clutch (5) via a clutch (5) between the internal combustion engine (1) and the electric machine (2) and can be decoupled from the hybrid drive train by opening the clutch (5), wherein when the clutch (5) is closed, a pilot control torque (M V ) is determined, with which the clutch (5) is controlled, whereby the pilot torque (M V ) from a vehicle moment of inertia (j F) which is determined by the transmission ratio (i) of the automatic transmission (4) corresponding to the gear engaged in the automatic transmission (4), wherein during a gear shift in the automatic transmission (4) while the vehicle is moving from an actual gear to a target gear, a value for the transmission ratio (i) of the automatic transmission (4) is determined which corresponds to the ratio of a measured input speed (N E ) at the input of the automatic transmission (4) and a measured output speed (N A ) at the output of the automatic transmission (4), and based on this fixed value of the gear ratio (i) the vehicle moment of inertia (j F ) and from this the pre-control moment (M V ) can be determined. [2] Method according to claim 1, characterized by that the pre-control moment (M V ) based on a primary moment of inertia (j P) on the primary side of the hybrid drive train extending from the clutch (5) to the combustion engine (1) and a secondary moment of inertia (j S ) on the secondary side of the hybrid drive train extending from the clutch (5) to the electric machine (2), wherein the secondary moment of inertia is the vehicle moment of inertia (j F ) and preferably further comprises a moment of inertia of the electric machine (2) and / or the clutch components on the secondary side. [3] Method according to claim 1 or 2, characterized by that during a shift in the automatic transmission (4) from an actual gear to a neutral position without traction in the automatic transmission (4), the pilot control torque (M V) based on a predetermined continuous temporal increase of the gear ratio (i) from the gear ratio (i1) of the actual gear to a virtual gear ratio (i0) in the neutral position. [4] Method according to one of the preceding claims, characterized by that during a gear change in the automatic transmission (4) from a neutral position without traction in the automatic transmission (4) to a target gear, the pilot control torque (M V ) based on a predetermined continuous temporal decrease of the gear ratio (i) from a virtual gear ratio (i0) in the neutral position to the gear ratio (i1) of the target gear. [5] Method according to claim 3 or 4, characterized bythat the shifting operation in the automatic transmission (4) from an actual gear to a neutral position without traction in the automatic transmission (4) and / or the shifting operation in the automatic transmission (4) from a neutral position without traction in the automatic transmission (4) to a target gear correspond to a shifting operation when the vehicle is stationary. [6] Method according to one of the preceding claims, characterized by that during a gear change in the automatic transmission (4) while the vehicle is moving from an actual gear to a target gear, the specified value of the gear ratio (i) corresponding to the ratio of the measured input speed (N E ) at the input of the automatic transmission (4) and the measured output speed (N A) at the output of the automatic transmission (4), is limited by a minimum value and a maximum value, wherein the minimum value corresponds to the minimum of the gear ratio (i) of the actual gear and the gear ratio (i) of the target gear and the maximum value corresponds to the maximum of the gear ratio (i) of the actual gear and the gear ratio (i) of the target gear, wherein the value of the gear ratio (i) is set to the minimum value when the minimum value is undershot and to the maximum value when the maximum value is overshot. [7] Method according to one of the preceding claims, characterized by that the clutch (5) between the internal combustion engine (1) and the electric machine (2) is a hydraulic clutch and / or electric clutch. [8] Device for operating a hybrid drive train of a vehicle, wherein the hybrid drive train comprises a drive unit with an internal combustion engine (1) and an electric machine (2) and an automatic transmission (4) connected between the drive unit and an output (3), wherein the internal combustion engine (1) can be coupled to the hybrid drive train by closing the clutch (5) via a clutch (5) between the internal combustion engine (1) and the electric machine (2) and can be decoupled from the hybrid drive train by opening the clutch (5), wherein the device comprises a control device (8) which, when the clutch (5) is closed, generates a pilot control torque (M V ) with which the clutch (5) is controlled, whereby the pilot control torque (M V) is determined by the transmission ratio (i) of the automatic transmission (4) corresponding to the gear engaged in the automatic transmission (4), wherein the control device is designed such that during a gear shift in the automatic transmission (4) while the vehicle is moving from an actual gear to a target gear, a value for the transmission ratio (i) of the automatic transmission (4) is determined which corresponds to the ratio of a measured input speed (N E ) at the input of the automatic transmission (4) and a measured output speed (N A ) at the output of the automatic transmission (4), and based on this fixed value of the gear ratio (i) the vehicle moment of inertia (j F ) and from this the pre-control moment (M V ) can be determined. [9] Device according to claim 8, characterized bythat the device is designed such that a method according to one of claims 2 to 7 can be carried out with the device. [10] Vehicle with a hybrid powertrain, characterized by that the vehicle comprises a device according to claim 8 or 9.

Citation Information

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