The results presented in this thesis are planned to be extended. The extension targets first of all the controller design and its improvement to cover a wider range of parameter uncertainty.
The applied assumptions in case of dynamic hybrid model should be revised in order to further increase the accuracy of this model. Moreover model parameter calibration/identification should be considered in order to increase the accuracy of the developed models. In particular, the following topics are planned for future research.
• Consideration of nonlinear model in case of magnetic relation. As the applied current increases the effect of the nonlinearity and the hysteresis of the magnetization curve increases as well, thus this phenomenon should be included into the detailed model description.
• In order to increase the accuracy of the models a detailed model parameter calibra-tion/identification should be executed using special test cases.
• Consideration of wider uncertainty range of the dead volume of the chamber (Vchd) and the stiffness of the clutch mechanism (∂Fl/∂xpst) in order the control system can fulfill the requirements during the whole lifetime of the clutch.
• Based on Fig. 4.1 it seems that the system has pitchfork bifurcation, since the system has three equilibrium point along a trajectory for
d
dxpstFl(x∗pst) + p∗chA2pst
Vchd +Apstx∗pst <0 and one for
d
dxpstFl(x∗pst) + p∗chA2pst
Vchd +Apstx∗pst >0.
In order to prove this conjecture an exhaustive bifurcation analysis is needed [96].
• Consideration of wider uncertainty range of SMV parameters. The production of the SMV has spread within a given tolerance limit and this causes parameter uncertainty.
The parameter change of the SMV has a large effect on the mass flow rate control, therefore some sort of feedback or long time adaptation should be considered.
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Appendix A
Figures and Tables
Figure A.1: Friction disc, clutch mechanism and concentric clutch actuator from ZF SACHS
Figure A.2: Engine, gearbox and clutch system
Figure A.3: Clutch systems applied with forked lever- (left) and concentric type (right) EPC actuators
Table A.1: List of parameters
Parameter name 1Symbol Value Unit 2Confidence
Adiabatic exponent κ 1.4 − K
Permeability of vacuum µ0 4π·10−7 V s/Am K
Specific gas constant R 287.14 J/kgK K
Drain to source on resistance rDS(on),xx 0.071 Ω PK
Effective breakdown voltage UBR,xx 71 V PK
Inlet diameter ofsxSMV dsx 0.0015 m PK
Inlet diameter ofbxSMV dbx 0.0035 m PK
Armature diameter ofsxSMV darm,sx 0.010 m PK
Armature diameter ofbxSMV darm,bx 0.012 m PK
Stiffness ofsxSMV spring ssx 489 N/m PK
Stiffness ofbxSMV spring sbx 567 N/m PK
Pretension of sxSMV spring xsx,0 0.0102 m PK
Pretension of bxSMV spring xbx,0 0.0063 m PK
Mass ofsxSMV armature msx 0.012 kg PK
Mass ofbxSMV armature mbx 0.016 kg PK
Solenoid turns ofsxSMVs Nsx 600 − PK
Solenoid turns ofbxSMVs Nbx 910 − PK
Electric resistance of sxSMVs Rsx 11.3 Ω PK
Electric resistance of bxSMVs Rbx 9.1 Ω PK
Contraction coefficient of SMVs αxx 0.6 − UK
Magnetic loop resistance of SMVs Rxx 12000000 A/V s UK
Stroke limiting stiffness of SMVs cxx 107 N/m UK
Damping coefficient of SMVs kxx 30 N s/m UK
Stiffness of helper spring chsp 1·104 N/m PK
Pretension stroke of helper spring xhsp0 0.06 m PK
Area of piston Apst 0.0227 m2 PK
Dead volume of chamber Vchd 5.5982·10−4 m3 PK
Lumped mass mpst 9.3922 kg PK
Heat transfer coefficient of chamber kht 8.25 W/m2K UK
Heat transfer area of chamber Aht 0.0689 m2 UK
Friction coefficient of piston µpst 0.1391 − UK
Damping coefficient of piston kpst 2251.3825 N s/m UK Stroke limiting stiffness of piston cpst 108 N/m UK
1In case of power stage / valve model parameterssxcorresponds to the small-,bxcorresponds to the big- and xxcorresponds all power stage / valve.
2K: known, PK: partially known, UK: unknown