# ARMD 10.40 (Torque-Based Anti-Jerk Function)

See the funktionsrahmen for the following diagrams:

armd-armd Main function

armd-kifz Subfunction KIFZ (amplification of vehicle model)

armd-flrar Subfunction FLRAR (amplification factor for modelling of external load)

armd-fdar Subfunction FDAR (amplification factor for anti-jerk intervention)

armd-nmoti Subfunction NMOTI

armd-ndfil Subfunction NDFIL (filtered engine speed difference)

armd-frgar Subfunction FRGAR

armd-iniarv Subfunction INIARV

armd-kup gw Subfunction KUPGW

armd-dmar Subfunction DMAR (delta torque anti-jerk)

ARMD 10.40 Function Description

Function purpose

The anti-jerk function detects oscillations of the power train and damps them out by applying opposing-phase torque interventions. The torque intervention is converted into an ignition angle offset by the torque interface.

Desired phase position of the torque intervention

In order to damp the power train oscillation efficiently, the torque intervention should counteract engine speed oscillations. Thereby the same effect is achieved as if the attenuation coefficient of the drive shaft is increased.

Operation pattern of anti-jerk function

Basic idea: a reference speed without oscillation and corresponding to the driver’s demand is evaluated. The difference between desired and actual engine speed isolates the oscillation. A counteracting delta torque is set which is proportional to this oscillation.

The function is realized by a simple vehicle model consisting of an integrator with the constant kifz_w. The input to this integrator is the difference between the driver’s predetermined clutch torque mkar_w and the load torque mlast_w. The output from the integtrator is the modelled engine speed nmod_w. The engine speed difference ndiff_w between the modelled engine speed nmod_w and the actual engine speed nmot_w now forms the basis for the torque intervention as well as for the calculation of the load torque. The load torque is evaluated proportional to the engine speed difference and the factor flrar is taken from the corresponding characteristic line. The engine speed difference ndiff_w contains another offset besides the oscillation part. This offset is filtered on a 50 ms scan timescale through a discrete second order low pass filter. (Coefficients of the nominator polynomial are denoted A0, A1 and A2 and of the denominator polynomial 1, B1 and B2.

The filtered offset ndfil_w is substracted from the differential engine speed and gives the engine speed oscillation ndar_w. Proportionally to this engine speed and using the factor fdar, a delta torque as a torque intervention is calculated. If this intervention lays between the limits KFDMDARU and KFDMDARO, it is set to zero.

Activation Conditions

The model is always active, just the intervention can be switched off.

Application Notes

Conditions for calibration of anti-jerk

The basic calibration of the vehicle must have been done. This includes the transition compensation and all functions for the torque interface.

1. Evaluation of the integrator constant kifz_w and flrar

Coarse application:

Drive on the road (flat surface, no hills) at a constant speed in respective gear with the anti-jerk function deactivated (fdar=0). Then execute a change in load and register the calculated coupling torque mkar_w and the engine speed nmot_w.

Evaluation of integrator constant as follows: at a load step the torque jump is approximately delta M (in %) and the speed approximately rises with constant gradient gradn (in RPM/s). Kifz_w is then calculated from the expression gradn/(delta M). A typical value for second gear is 4.6 x 100/MDNORM [RPM/(sx%)].

Fine application:

Driving on flat surface. Set the product kifz_w x flrar to a fixed value (recommendation: 15). Realization of load jumps with registration of mkar_w, mlast_w, nmot_w and ndiff_w. Vary the couple kifz_w and flrar (maintaining the product constant!) until ndiff_w remains approximately constant during a load jump.

In principle the following process is valid for the amplification factor flrar: high factors cause a reduction of the offset ndfil_w, but also a big phase advance of ndiff_w.

2. Evaluation of filter parameters

For a low pass filter with 50 ms scan rate, the transmission function has the form G(z) = Z(z)/N(z) where

Z(z) = A0 + A1z-1 + A2z-2

N(z) = 1 + B1z-1 + B2z-2

Select one of the low pass filters listed in the table below, according to the appearing jerk frequency:

 TP No. Limit freq. A0 A1 A2 B1 B2 1 0.67 Hz 0.0095 0.0191 0.0095 -1.7056 0.7437 2 0.80 Hz 0.0134 0.0267 0.0134 -1.6475 0.7009 3 1.00 Hz 0.0201 0.0402 0.0201 -1.5610 0.6414

Low pass filter No. 3 is recommended. The attenuation of the jerk frequency is determined by the margin between the jerk frequency and the filter cut-off frequency. The bigger the filter cut-off frequency, the smaller the time the filter needs to stabilize.

Warning: modification of a single coefficient of G(z) is not permitted!

3. Evaluation of fdar

Recommendation is fdar = 0.67 x 100/MDNORM (%/RPM). Increase of attenuation by enlargement of fdar, reduction of fdar decreases the attenuation.

4. Thresholds KFDMDARO and KFDMDARU

In case the delta torque for the intervention is within these thresholds, it is set to zero. This avoids undesired ignition angle instability. Typical values are: KFDMDARU = -5 x 100/MDNORM [%], KFDMDARO = 5 x 100/MDNORM [%].

Abbreviations