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Robust control methods with applications to steer-by-wire systems [Elektronische Ressource] / vorgelegt von Naim Bajçinca

188 pages
Naim Baj¸cincaRobust Control Methods withApplications to Steer-by-Wire Systems- PhD Thesis -Elektrotechnik und InformatikTechnische Universit¨at BerlinJanuary, 2006Robust Control Methods with Applications toSteer-by-Wire Systemsvorgelegt vonDiplom-Ingenieur, Diplom-PhysikerNaim Bajcinca¸aus Prishtinavon der Fakult¨at IV - Elektrotechnik und Informatikder Technischen Universitat¨ Berlinzur Erlangung des akademischen GradesDoktor der Ingenieurwissenschaften- Dr.-Ing. -genehmigte DissertationPromotionsausschuss:Vorsitzender: Prof. Dr.-Ing. S. BernettBerichter: Prof. Dr.-Ing. D. NauninBerichter: Prof. Dr.-Ing. J. AckermannBerichter: Prof. Dr.-Ing. R. HanitschTag der wissenschaftlichen Aussprache: 26. Oktober 2005Berlin 2006D 83Prind¨erve t¨e miAcknowledgementThisthesisistheoutgrowthofmyresearchcarriedoutattheInstituteofRoboticsandMecha-tronics at German Aerospace Center (Deutsches Zentrum fur¨ Luft und Raumfahrt - DLR) inOberpfaffenhofen. I gratefully acknowledge the DAAD (Deutscher akademischer Austauschdi-enst) for the support in pursuing my PhD studies.I am deeply indebted to Professor Dietrich Naunin for his friendly support, help and con-tinuous encouragement throughout my work. Professor Naunin invited me at TU Berlin, andoffered me great opportunities for my research work. I am especially grateful to ProfessorJurg¨ en Ackermann for his supervision and helpful discussions.
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Naim Baj¸cinca
Robust Control Methods with
Applications to Steer-by-Wire Systems
- PhD Thesis -
Elektrotechnik und Informatik
Technische Universit¨at Berlin
January, 2006Robust Control Methods with Applications to
Steer-by-Wire Systems
vorgelegt von
Diplom-Ingenieur, Diplom-Physiker
Naim Bajcinca¸
aus Prishtina
von der Fakult¨at IV - Elektrotechnik und Informatik
der Technischen Universitat¨ Berlin
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr.-Ing. S. Bernett
Berichter: Prof. Dr.-Ing. D. Naunin
Berichter: Prof. Dr.-Ing. J. Ackermann
Berichter: Prof. Dr.-Ing. R. Hanitsch
Tag der wissenschaftlichen Aussprache: 26. Oktober 2005
Berlin 2006
D 83Prind¨erve t¨e miAcknowledgement
ThisthesisistheoutgrowthofmyresearchcarriedoutattheInstituteofRoboticsandMecha-
tronics at German Aerospace Center (Deutsches Zentrum fur¨ Luft und Raumfahrt - DLR) in
Oberpfaffenhofen. I gratefully acknowledge the DAAD (Deutscher akademischer Austauschdi-
enst) for the support in pursuing my PhD studies.
I am deeply indebted to Professor Dietrich Naunin for his friendly support, help and con-
tinuous encouragement throughout my work. Professor Naunin invited me at TU Berlin, and
offered me great opportunities for my research work. I am especially grateful to Professor
Jurg¨ en Ackermann for his supervision and helpful discussions. He gave many useful comments
and suggestions in improving this thesis.
I would like to express my sincere gratitude also to Professor Gerd Hirzinger (Head of the
Institute), Dr. Alfred Jaschinski (Head of the Laboratory) and Dr. Johann Bals (Head of the
Department) for the generous support of my work in the lab.
Thanks to numerous colleagues at DLR for the help and cooperation in various ways. I
hereby want to especially emphasize Markus Hauschild for his remarkable engagement in the
lab, and Rui Cortes˜ao for the fruitful cooperation. I am also thankful to Thomas Hulin and
AngelikaPeerfortheirengagementandcooperation. SpecialthankstomyofficemateNikolaus
Schurma¨ nn for the pleasant ambience in our office.
I am indebted to the Secretary of the Department Mrs Astrid Jaschinski for her enormous
support in the everyday department’s life, to Mrs and Mr Herz from Gilching for having me
as a part of their family, and to family Govori from Oberpfaffenhofen for the provision of the
native vicinity.
DeepestacknowledgmenttomanyprofessorsandteachersatFacultyofElectricalEngineer-
ing and Faculty of Natural Sciences of the University of Prishtina for their great inspiration
and education during my studies.
Finally, I would like to thank my family in Prishtina, in particular my parents Fahrije and
Isa Baj¸cinca, as well as my girlfriend Ardiana Jashari for their understanding and patience.
Oberpfaffenhofen, 6th July, 2005Abstract
This thesis includes mainly theoretical and methodological design contributions on robust
control with applications to steer-by-wire vehicle systems. The main contributions are:
1) A complete mathematical paradigm based on singular frequencies is developed for the
computation of the region in an affine parameter space where certain system properties such
as stability are guaranteed. The essential advantage of the method is that non-convex regions
are constructed using simple convex polyhedral slices. This approach is useful for solving the
difficultproblemoffixedordercontrol. AwidelyspreadcontrollerofthisartisPID.Asoftware
toolbox is developed for fast computation of robust stable regions in PID parameter space.
2) A two degree-of-freedom control structure for dynamic inversion and tracking tasks is
introduced. The structure integrates the feedforward exact inversion and high-gain feedback
principles. This structure is further extended for use in model reference control. In all cases,
robust performance is provided due to the presence of the high-gain term. A mathematical
framework is developed to guide the design of systems with imperfections.
3) Steer-by-wire control problems with uncertainties such as force feedback and road-wheel
actuation, as well as the coupling of the two with respect to some given reference dynamics
are addressed. A detailed robustness design and analysis of force feedback actuation with
regard to uncertainties in the human operator bio-impedance is completed. Different steer-
by-wire representations (admittance, impedance, hybrid) are discussed and compared. Using
the methods introduced in 1) and 2) several control structures providing model-matching and
model-reference control for steer-by-wire are developed. Robustness analysis is performed
in the parameter space constituted by relevant uncertain physical parameters. Therefore a
methodformappingofpositivityboundsoftransferfunctionmatricesinaloworderparameter
space is introduced.Contents
1 Introduction............................................................. 1
1.1 Thesis motivation ...................................................... 1
1.2 Problem definition ..................................................... 3
1.2.1 Steer-by-wire task level ............................................ 3
1.2.2 actuation level ....................................... 4
1.3 Key contributions...................................................... 4
1.3.1 Robust design based on singular frequencies .......................... 4
1.3.2 Inverse disturbance observer........................................ 5
1.3.3 Actuation control ................................................. 5
1.3.4 Steer-by-wire control ............................................. 5
1.3.5 Other contributions ............................................... 6
1.4 Thesis structure ....................................................... 6
2 Robust design based on singular frequencies ............................. 7
2.1 Problem definition ..................................................... 8
2.2 Singular frequencies .................................................... 9
2.3r Γ-curves ...................................................... 10
2.4 Robustness............................................................ 11
2.5 An observation: Hurwitz stability ........................................ 12
2.6 γ Space............................................................... 13
2.6.1 γ -Vector ........................................................ 141
2.6.2 γ -Vector ........................................................ 152
2.6.3 γ ×γ -Subspace ................................................. 161 2
2.6.4 Higher order γ-vectors............................................. 16
2.7 Polyhedral spaces ...................................................... 16
2.8 Decoupling............................................................ 18
3 Robust stability of three-term polynomials............................... 21
3.1 Three-term polynomials................................................. 21
3.2term decoupling.................................................. 22
3.2.1 Hurwitz-stability ................................................. 23
3.2.2 Γ-stability ....................................................... 25
3.2.3 σ−Stability ...................................................... 26XII Contents
3.2.4 Schur-stability.................................................... 27
3.2.5 Γ-Circles ........................................................ 27
3.3 Stable polygons........................................................ 28
3.3.1 Inner polygons ................................................... 28
3.3.2 Singular line transitions ........................................... 28
3.3.3 Types of singular frequencies ....................................... 31
3.3.4 Automatic detection of inner polygons ............................... 33
3.4 Stable gridding intervals ................................................ 34
3.4.1 Hurwitz-stability ................................................. 34
3.4.2 Stability peaks ................................................... 38
3.4.3 Schur-stability.................................................... 39
3.5 Robust multi-model control ............................................. 40
3.5.1 PID control ...................................................... 41
3.5.2 Three-term control................................................ 41
4 Extension to selected topics ............................................. 47
4.1 Three-term quasipolynomials ............................................ 48
4.2 High-frequency behavior ................................................ 50
4.2.1 High singular frequencies .......................................... 50
4.2.2 Infinity root boundaries............................................ 50
4.2.3 Singular line transition ............................................ 51
4.3 Relevant frequency range ............................................... 51
4.4 Stable gridding intervals ................................................ 52
4.5 Case study: PID control ................................................ 54
4.6 Transformation equations ............................................... 56
4.7 γ -Space .............................................................. 571
4.8 Case study: bilinear nonlinearity ......................................... 58
4.8.1 Hurwitz transformation............................................ 59
4.8.2 σ− Transformation ............................................... 60
4.8.3 Circle transformation.............................................. 60
5 Inverse disturbance observer............................................. 63
5.1 The basic idea......................................................... 63
5.2 Internal stability....................................................... 65
5.2.1 Plants with right-half-plane zeros ................................... 67
5.2.2 Plants with righplane poles ................................... 67
5.3 Imperfect inversion models .............................................. 67
5.4 Robustness against imperfection ......................................... 68
5.5 Tracking performance .................................................. 70
5.6 Loopshaping by Q ..................................................... 72
5.7 Realization............................................................ 73
5.8 Robustness notes ...................................................... 74
5.9 Loopshaping notes ..................................................... 76
5.9.1 Resonant IDOB structure .......................................... 76