robust-adaptive control of nonlinear singlevariable mechatronic systems and robots nemline´aris

139 Pages·2010·1.34 MB·English

Budapest University of Technology and Economics
Department of Control Engineering and Information Technology
Budapest, Hungary
ROBUST-ADAPTIVE CONTROL OF NONLINEAR
SINGLEVARIABLE MECHATRONIC SYSTEMS
AND ROBOTS
Ph. D. Thesis
(cid:19) (cid:19) (cid:19)
NEMLINEARIS EGYVALTOZOS MECHATRONIKAI
(cid:19)
RENDSZEREK ES ROBOTOK ROBUSZTUS-
(cid:19) (cid:19) (cid:19) (cid:19)
ADAPTIV IRANYITASA
Ph. D. E(cid:19)rtekez(cid:19)es
Lo}rinc M(cid:19)arton
In Partial Ful(cid:12)llment of the Requirements for
the Degree of Doctor of Philosophy
Supervisor:
Dr. B(cid:19)ela Lantos
Dept. of Control Engineering and Information Technology
Budapest University of Technology and Economics
January, 2006

Delclaration
Undersigned, Lo}rinc Ma(cid:19)rton, hereby state that this Ph.D. Thesis is my own work wherein I have
used only the sources listed in the Bibliography. All parts taken from other works, either in a word
for word citation or rewritten keeping the original contents, have been unambiguously marked by a
reference to the source.
Nyilatkozat
Alul(cid:19)(cid:16)rott Ma(cid:19)rton Lo}rinc kijelentem, hogy ezt a doktori (cid:19)ertekez(cid:19)est magam k(cid:19)esz(cid:19)(cid:16)tettem (cid:19)es abban csak a
megadott forra(cid:19)sokat haszna(cid:19)ltam fel. Minden olyan r(cid:19)eszt, amelyet szo(cid:19) szerint, vagy azonos tartalom-
ban, de a(cid:19)tfogalmazva ma(cid:19)s forra(cid:19)sbo(cid:19)l a(cid:19)tvettem, egy(cid:19)ertelmu}en, a forra(cid:19)s megada(cid:19)sa(cid:19)val megjelo(cid:127)ltem.
Budapest, 2005. 12. 01.
Ma(cid:19)rton Lo}rinc
The reviews of this Ph.D. Thesis andthe record of defense will be available later in the Dean O(cid:14)ce of
the Faculty of Electrical Engineering and Informatics of the Budapest University of Technology and
Economics.
Az (cid:19)ertekez(cid:19)esro}l k(cid:19)eszu(cid:127)lt b(cid:19)(cid:16)ra(cid:19)latok (cid:19)es a jegyzo}ko(cid:127)nyv a k(cid:19)eso}bbiekben a Budapesti Mu}szaki (cid:19)es Gaz-
dasa(cid:19)gtudoma(cid:19)nyi Egyetem Villamosm(cid:19)erno(cid:127)ki Kara(cid:19)nak D(cid:19)eka(cid:19)ni Hivatala(cid:19)ban el(cid:19)erheto}ek.
i
Acknowledgements
ThisthesisistheresultofmyPhDresearchworkconductedatBudapestUniversityofTechnology and
Economics, Department of Control Engineering and Information Technology. Parts of the work were
(cid:12)nished at Sapientia Hungarian University of Transylvania, Department of Electrical Engineering.
I would like to thank Professor Dr. B(cid:19)ela Lantos, my supervisor at the Department of Control
Engineering and Information Technology, Budapest University of Technology and Economics for his
professional guidance during the research work. Without his lead and support, my work would not
have been possible.
I would like to thank Professor Dr. P(cid:19)eter Arato(cid:19), head of Department of Control Engineering and
Information Technology, all of my colleagues from the Department and from the Intelligent Robotics
Laboratory for their encouragements andworking conditions provided duringmy work. I am thankful
to Dr. Ba(cid:19)lint Kiss for his professional support and useful advices during my work, and to Dr. Istva(cid:19)n
Harmati and Dr. Zsolt Kem(cid:19)eny for their help and advices during my PhD studies.
Also, I would like to express my sincere gratitude to Professor Dr. La(cid:19)szlo(cid:19) Da(cid:19)vid, head of Depart-
ment of Electrical Engineering, Sapientia Hungarian University of Transylvania for rising my interest
in the science of modern control theory during my undergraduate studies and for his support and
help during my research work. I would like to acknowledge Nimro(cid:19)d Kutasi, Andra(cid:19)s Kelemen, Zolta(cid:19)n
Nagy and all of my colleagues from the Department of Electrical Engineering, Sapientia Hungarian
University of Transylvania for the given help and support during the research work.
I would like to thank for the research support of the Hungarian National Research Program under
grant number OTKA T042634. Finally, I thank the Institute of Research Programmes, Sapientia
University for the (cid:12)nancial support, and the Hungarian Ministry of Education for the scholarship
provided during my PhD studies.
ii
Ko(cid:127)szo(cid:127)netnyilv(cid:19)an(cid:19)(cid:16)t(cid:19)as
A jelen PhD (cid:19)ertekez(cid:19)es a Budapesti Mu}szaki (cid:19)es Gazdasa(cid:19)gtudoma(cid:19)nyi Egyetem Ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)stechnikai (cid:19)es
Informatikai Tansz(cid:19)ek(cid:19)en folytatott doktori kutato(cid:19)i munka(cid:19)m eredm(cid:19)enye. A munka egyes r(cid:19)eszeit a Sapi-
entia Erd(cid:19)elyi Magyar Tudoma(cid:19)nyegyetem Villamosm(cid:19)erno(cid:127)ki Tansz(cid:19)ek(cid:19)en fejeztem be.
Elso}sorbanko(cid:127)szo(cid:127)netet szeretn(cid:19)ek mondani Dr. Lantos B(cid:19)ela professzoru(cid:19)rnak, doktori konzulensem-
nek, aki nem csak a doktori iskola ha(cid:19)rom (cid:19)eve alatt, de az azuta(cid:19)ni kutato(cid:19) munka(cid:19)mnak is ta(cid:19)mogato(cid:19)ja,
szakmai vezeto}je volt. Az O} vezet(cid:19)ese n(cid:19)elku(cid:127)l a munka(cid:19)m nem lett volna lehets(cid:19)eges.
Ko(cid:127)szo(cid:127)net illeti a Budapesti Mu}szaki (cid:19)es Gazdasa(cid:19)gtudoma(cid:19)nyi Egyetem Ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)stechnikai (cid:19)es Infor-
matikai Tansz(cid:19)ek(cid:19)enek vezeto}j(cid:19)et, Dr. Arato(cid:19) P(cid:19)eter professzor urat, az Ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)stechnikai (cid:19)es Informatikai
Tansz(cid:19)ek kollekt(cid:19)(cid:16)va(cid:19)ja(cid:19)t, valamint az Intelligens Robotok Laborato(cid:19)riumbanmindenkoll(cid:19)ega(cid:19)mat a doktori
munka(cid:19)mhoz nyu(cid:19)jtott seg(cid:19)(cid:16)ts(cid:19)egu(cid:127)k(cid:19)ert. Ku(cid:127)lo(cid:127)n ko(cid:127)szo(cid:127)net illeti Dr. Kiss Ba(cid:19)lintot, a doktori munka sora(cid:19)n
nyu(cid:19)jtott hasznos tana(cid:19)csai(cid:19)ert, szakmai ta(cid:19)mogata(cid:19)sa(cid:19)(cid:19)ert, valamint Dr. Harmati Istva(cid:19)nt (cid:19)es Dr. Kem(cid:19)eny
Zsoltot a doktori tanulma(cid:19)nyaimhoz (cid:19)es a doktori munka v(cid:19)egleges(cid:19)(cid:16)t(cid:19)es(cid:19)ehez nyu(cid:19)jtott seg(cid:19)(cid:16)ts(cid:19)egu(cid:127)k(cid:19)ert.
Ko(cid:127)szo(cid:127)nettel tartozom Dr. Da(cid:19)vid La(cid:19)szlo(cid:19) professzor u(cid:19)rnak, a Sapientia Erd(cid:19)elyi Magyar Tu-
doma(cid:19)nyegyetemVillamosm(cid:19)erno(cid:127)kiTansz(cid:19)ekvezeto}j(cid:19)enek, akima(cid:19)razegyetemitanulma(cid:19)nyaimalattfelkel-
tette(cid:19)erdeklo}d(cid:19)esemet akorszeru} ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)stechnikaira(cid:19)nt(cid:19)esadoktorimunka(cid:19)mhozseg(cid:19)(cid:16)ts(cid:19)eget, ta(cid:19)mogata(cid:19)st
nyu(cid:19)jtott.
Ko(cid:127)szo(cid:127)no(cid:127)mKutasiNimro(cid:19)dnak, Kelemen Andra(cid:19)snak,Nagy Zolta(cid:19)nnak, valamint aSapientia Erd(cid:19)elyi
Magyar Tudoma(cid:19)nyegyetem Villamosm(cid:19)erno(cid:127)ki Tansz(cid:19)ek(cid:19)en dolgozo(cid:19) minden koll(cid:19)ega(cid:19)mnak a kutata(cid:19)si
munka(cid:19)mhoz nyu(cid:19)jtott seg(cid:19)(cid:16)ts(cid:19)eget (cid:19)es hasznos tana(cid:19)csokat.
Ko(cid:127)szo(cid:127)netemet fejezem ki a a magyar Orsza(cid:19)gos Tudoma(cid:19)nyos Kutata(cid:19)si Alapprogram kutata(cid:19)si
ta(cid:19)mogata(cid:19)sa(cid:19)(cid:19)ert az OTKAT042634 t(cid:19)ema keret(cid:19)eben. A kutata(cid:19)s tova(cid:19)bbi anyagi ta(cid:19)mogata(cid:19)sa(cid:19)(cid:19)ert ko(cid:127)szo(cid:127)net
illeti a Sapientia Egyetem Kutata(cid:19)si Programok Int(cid:19)ezet(cid:19)et (cid:19)es a Magyar Ko(cid:127)zta(cid:19)rsasa(cid:19)g Oktata(cid:19)si Miniszt(cid:19)e-
riuma(cid:19)t a doktori o(cid:127)szto(cid:127)nd(cid:19)(cid:16)j(cid:19)ert, amelyet a doktori tanulma(cid:19)nyaim alatt biztos(cid:19)(cid:16)tott.
iii
Abstract
The PhD thesis deals with the tracking control of nonlinear mechatronic systems with unknown
parameters. In order to deal with possible modelling errors and external disturbances, the robustness
of the control is increased by variable structure or supervisor control algorithms. To obtain the
unknown parameters, parameter estimation algorithms are applied. The stability of the closed loop
systems and the tracking performance are guaranteed using Lyapunov techniques. The applicability
and performances of the developed control algorithms are demonstrated through simulations and
experimental measurements.
If in the adaptive control systems there are large modelling uncertainties, due to the imperfect
estimationofthenonlinearities,highunimplementablecontrolsignalcanappear(singularityproblem),
which can lead to poor control performances or even instability in the closed loop system. A modi(cid:12)ed
adaptive control law is presented in which the singularity problem is avoided, but it modi(cid:12)es the
control signal only if the adaptation works poor. The developed algorithm can be applied for the
control of mechatronical systems with unknown parameters.
For adaptive control systems in which the modelling error has a large in(cid:13)uence on the quality of
the control, a supervisor control law is elaborated to guarantee the stability of the adaptive closed
loop system.
One of the major source of uncertainty in mechatronic systems is represented by the friction
phenomenon, because the friction force can be modelled with di(cid:14)culty and the frictional parameters
are slowly varying in time. A general friction model is proposed, which describes well the nonlinear
and dynamic behavior of friction and at the same time can easily be introduced in adaptive control
algorithms. A parameter identi(cid:12)cation method for the developed model is introduced. Based on the
model, a friction compensation algorithm is developed, which guarantees high tracking accuracy in
the presence of dominant frictional e(cid:11)ects and can easily be implemented in simple industrial control
architectures and embedded systems.
An adaptive tracking control algorithm is proposed for robotic systems to solve simultaneously
the friction compensation and payload estimation problem. Thedeveloped control law is based on the
dynamic model of the robot and it can guarantee a prescribed tracking accuracy in the presence of
unknown frictional parameters and payload mass.
iv
Kivonat
A PhD (cid:19)ertekez(cid:19)es nemlinearita(cid:19)sokat tartalmazo(cid:19), ismeretlen param(cid:19)eterekkel rendelkezo} mechatronikai
rendszerek ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)sa(cid:19)val foglalkozik. A kifejlesztett algoritmusok a pa(cid:19)lyako(cid:127)vet(cid:19)es feladata(cid:19)ra o(cid:127)sszpon-
tos(cid:19)(cid:16)tanak. Az ismeretlen rendszerparam(cid:19)eterek meghata(cid:19)roza(cid:19)sa(cid:19)ra adapt(cid:19)(cid:16)v param(cid:19)eterbecsl(cid:19)esi algoritmu-
sokatalkalmazunk, ugyanakkorazira(cid:19)ny(cid:19)(cid:16)ta(cid:19)s robusztussa(cid:19)ga(cid:19)tmodellbizonytalansa(cid:19)gokkal(cid:19)esazira(cid:19)ny(cid:19)(cid:16)tott
rendszerre hato(cid:19) ku(cid:127)lso} zajokkal szemben va(cid:19)ltozo(cid:19) struktu(cid:19)ra(cid:19)ju(cid:19) ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)si algoritmusokkal, felu(cid:127)gyelo}
szaba(cid:19)lyozo(cid:19)struktu(cid:19)ra(cid:19)val(cid:19)erju(cid:127)kel. Aszaba(cid:19)lyoza(cid:19)sstabilita(cid:19)sa(cid:19)t, azel(cid:19)erheto}pa(cid:19)lyako(cid:127)vet(cid:19)esipontossa(cid:19)gotLya-
punov mo(cid:19)dszerekkel tanulma(cid:19)nyozzuk, a kidolgozott algoritmusok alkalmazhato(cid:19)sa(cid:19)ga(cid:19)t, hat(cid:19)ekonysa(cid:19)ga(cid:19)t
szimula(cid:19)cio(cid:19)kkal (cid:19)es valo(cid:19)s ideju} m(cid:19)er(cid:19)esekkel igazoljuk.
Amennyiben az adapt(cid:19)(cid:16)v ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)si rendszerben nagy modellbizonytalansa(cid:19)ggal kell sza(cid:19)molnunk, a
nemlinearita(cid:19)sok helytelen becsl(cid:19)ese nagy, nem implementa(cid:19)lhato(cid:19) beavatkozo(cid:19) jelhez vezethet (szingu-
larita(cid:19)s probl(cid:19)ema(cid:19)ja). Ez instabilita(cid:19)st, a szaba(cid:19)lyoza(cid:19)s helytelen mu}ko(cid:127)d(cid:19)es(cid:19)et okozhatja. Olyan mo(cid:19)dos(cid:19)(cid:16)tott
adapt(cid:19)(cid:16)v ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)si algoritmust fejlesztettu(cid:127)nk ki, amely seg(cid:19)(cid:16)ts(cid:19)eg(cid:19)evel a szingularita(cid:19)s probl(cid:19)ema(cid:19)ja
elkeru(cid:127)lheto}, de a beavatkozo(cid:19) jelet csak akkor mo(cid:19)dos(cid:19)(cid:16)tja, ha az adapta(cid:19)cio(cid:19) helytelenu(cid:127)l mu}ko(cid:127)dik. Meg-
mutatjuk, hogyakidolgozott ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)sialgoritmusalkalmazhato(cid:19) ismeretlenparam(cid:19)eterekkel rendelkezo}
mechatronikai rendszerek ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)sa(cid:19)ra.
Felu(cid:127)gyelo} szaba(cid:19)lyozo(cid:19) struktu(cid:19)ra(cid:19)t dolgozunk ki olyan adapt(cid:19)(cid:16)v ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)si rendszerek, stabilita(cid:19)sa(cid:19)nak
garanta(cid:19)la(cid:19)sa(cid:19)ra, amelyekben a modellbizonytalansa(cid:19)gok hata(cid:19)ssal vannak az adapt(cid:19)(cid:16)v param(cid:19)eterbecsl(cid:19)esi
algoritmusokra is.
Mechatronikai rendszerekben a su(cid:19)rlo(cid:19)da(cid:19)si ero} jelenti az egyik legnagyobb bizonytalansa(cid:19)gi t(cid:19)enyezo}t,
mivel nehezen modellezheto} (cid:19)es a su(cid:19)rlo(cid:19)da(cid:19)si param(cid:19)eterek ido}ben va(cid:19)ltoznak. Olyan su(cid:19)rlo(cid:19)da(cid:19)si modellt
javasolunk, amely egyr(cid:19)eszt pontosan le(cid:19)(cid:16)rja a nemlinea(cid:19)ris (cid:19)es dinamikus su(cid:19)rlo(cid:19)da(cid:19)si hata(cid:19)sokat, ma(cid:19)sr(cid:19)eszt
ko(cid:127)nnyen beillesztheto} adapt(cid:19)(cid:16)v ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)si algoritmusokba. Identi(cid:12)ka(cid:19)cio(cid:19)s elja(cid:19)ra(cid:19)st vezetu(cid:127)nk bea kidolgo-
zott modell param(cid:19)etereinek meghata(cid:19)roza(cid:19)sa(cid:19)ra. A kidolgozott modellre alapozva su(cid:19)rlo(cid:19)da(cid:19)skompenza(cid:19)la(cid:19)si
algoritmust dolgozunk ki, amely nagy pa(cid:19)lyako(cid:127)vet(cid:19)esi pontossa(cid:19)got biztos(cid:19)(cid:16)t, (cid:19)es az iparban alkalmazott
bea(cid:19)gyazott rendszereken is ko(cid:127)nnyen implementa(cid:19)lhato(cid:19).
Ipari robotok ira(cid:19)ny(cid:19)(cid:16)ta(cid:19)sa(cid:19)ra, su(cid:19)rlo(cid:19)da(cid:19)skompenza(cid:19)la(cid:19)sra (cid:19)es a robot a(cid:19)ltal mozgatott hasznos teher
to(cid:127)meg(cid:19)enek becsl(cid:19)es(cid:19)ere alkalmasadapt(cid:19)(cid:16)vira(cid:19)ny(cid:19)(cid:16)ta(cid:19)sialgoritmustvezetu(cid:127)nkbe. Azalgoritmusarobotkarok
dinamikus modellj(cid:19)et haszna(cid:19)lja (cid:19)es ismeretlen su(cid:19)rlo(cid:19)da(cid:19)si param(cid:19)eterek (cid:19)es mozgatott to(cid:127)meg mellett k(cid:19)epes
garanta(cid:19)lni egy elo}re megadott pa(cid:19)lyako(cid:127)vet(cid:19)esi pontossa(cid:19)got.
v
Contents
1 Introduction 1
1.1 Control of mechanical systems. A short presentation . . . . . . . . . . . . . . . 1
1.1.1 Modelling of mechanical systems . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Control methods for position control and tracking . . . . . . . . . . . . . 3
1.2 Goal and methodology of the research work . . . . . . . . . . . . . . . . . . . . 5
1.3 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Improved Adaptive Control Algorithms for Single Input Nonlinear Systems 8
2.1 Tracking control of Single Input nonlinear systems . . . . . . . . . . . . . . . . . 9
2.1.1 The controlled system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 The control task and control law . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Previous works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 A method to avoid the singularity problem in adaptive control systems . . . . . 16
2.4 Adaptive Ball and Beam control . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Model based adaptive control law . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Supervisor control law in the presence of large modelling errors . . . . . . . . . . 31
vi
Contents vii
2.5.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3 Friction Modelling, Identi(cid:12)cation and Compensation in Positioning Systems 43
3.1 Previous works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2 Friction model for adaptive compensation . . . . . . . . . . . . . . . . . . . . . . 48
3.2.1 Piecewise linearly parameterized Striebeck friction model . . . . . . . . . 50
3.2.2 Properties of the introduced model . . . . . . . . . . . . . . . . . . . . . 52
3.2.3 Incorporating the dynamic e(cid:11)ects . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Practical identi(cid:12)cation method for Striebeck friction . . . . . . . . . . . . . . . . 57
3.4 Robust adaptive friction compensation . . . . . . . . . . . . . . . . . . . . . . . 60
3.4.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5.1 The experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5.2 Friction measurement and identi(cid:12)cation . . . . . . . . . . . . . . . . . . 69
3.5.3 Friction compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4 Friction Compensation and Payload Estimation in Robotic Systems 78
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.2 Previous works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Robot modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3.1 Dimensional analysis of the model . . . . . . . . . . . . . . . . . . . . . . 84
4.4 Adaptive friction compensation and payload estimation . . . . . . . . . . . . . . 86
viii Contents
4.4.1 The e(cid:11)ect of modelling errors on control . . . . . . . . . . . . . . . . . . 90
4.5 Modi(cid:12)ed control for dynamic friction . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A Some Notions from Stability Theory i
A.1 L Function Spaces and the Barbalat Lemma . . . . . . . . . . . . . . . . . . . i
p
A.2 Lyapunov Theory and Practical Stability . . . . . . . . . . . . . . . . . . . . . . ii
B Friction Modelling vi
B.1 Static friction models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
B.2 Dynamic friction models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
C Dynamic Modelling of Robotic Arms xv
Bibliography xvii