Analysis and Synthesis of Delta Operator Systems with Actuator Saturation

419 Pages·2019·7.299 MB·English

by  Hongjiu Yang, Yuanqing Xia, Qing Geng

Studies in Systems, Decision and Control 193
Hongjiu Yang
Yuanqing Xia
Qing Geng
Analysis and
Synthesis of Delta
Operator Systems
with Actuator
Saturation
Studies in Systems, Decision and Control
Volume 193
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Hongjiu Yang (cid:129) Yuanqing Xia (cid:129) Qing Geng
Analysis and Synthesis
of Delta Operator Systems
with Actuator Saturation
123
HongjiuYang YuanqingXia
SchoolofElectricalandInformation SchoolofAutomation
Engineering BeijingInstituteofTechnology
TianjinUniversity Beijing,China
Tianjin,China
QingGeng
InstituteofElectricalEngineering
YanshanUniversity
Qinhuangdao
Hebei,China
ISSN2198-4182 ISSN2198-4190 (electronic)
StudiesinSystems,DecisionandControl
ISBN978-981-13-3659-1 ISBN978-981-13-3660-7 (eBook)
https://doi.org/10.1007/978-981-13-3660-7
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Deltaoperatorsystems(DOSs)dealwithfast
samplingeffectively
Actuatorsaturationappearsinpractical
systemswidely
WedevotetoDOSswithactuatorsaturation
Preface
Saturation is very ubiquitous in practical control systems due to inherent physical
limitations of devices. Actuator saturation may lead to performance degradation
and even instability for a closed-loop system if it is ignored by designers. High-
speedsamplingbringsproductionefficiencyofindustrialequipmentandutilization
ratio of raw materials for control systems. Delta operator discretization methods
avoid numerical instability caused by traditional shift operator methods with the
high-speed sampling. Consequently, it is indispensable to analysis and research
of DOSs with actuator saturation, which has motivated a large amount of works
concerning modeling, stability, and performance analysis. Sampling periods are
explicit parameters in results of the DOSs with actuator saturation, so it is easy
to observe and analyze control effect with different sampling periods. The DOSs
have advantage on better numerical properties in finite word length computers,
especially at high sampling rates. There are many difficulties and challenges on
analysis of null controllable regions, the domain of attraction (DoA), and other
performance analysis of a delta operator system (DOS) with actuator saturation.
It is very important to estimate the DoA under a high-speed sampling condition,
enlargetheDoA,andincreasethespeedofconvergenceintheDoAforaDOSwith
actuatorsaturation.Thisbookaimsattheabovementionedproblemsanddifficulties
toresearchandanalysisofDOSssubjecttoactuatorsaturation.
InChap.1,amotivationontheresearchanditsoverviewonrecentdevelopment
ofDOSswithactuatorsaturationareprovided.
Then,thisbookwillpresentfiveparts:
PartI:SomebasicanalysesforDOSswithactuatorsaturationareintroduced.In
Chap.2,anestimationofnullcontrollableregionsofDOSsisproposed.InChap.3,
a set of equilibrium points in the null controllable regions are obtained based on
an important assumption. In Chap.4, some main results on practical stabilization
vii
viii Preface
onthenullcontrollableregionsareobtainedforaDOSwithactuatorsaturationand
boundeddisturbances.InChap.5,theDoAforDOSsunderapre-designedsaturated
linearfeedbackisestimated.
PartII:TheDoAforDOSssubjecttoactuatorsaturationisenlarged.InChap.6,
we present a lifting technique to improve the feedback property of DOSs with
actuator saturation. In Chap.7, the problems on control for a DOS with nested
actuator saturation are considered. In Chap.8, stability analysis of DOSs by a
saturation-dependent Lyapunov function is proposed. In Chap.9, both analytical
approximation and monotonicity of a maximal invariant ellipsoid are given for
DOSswithactuatorsaturation.
Part III: Performance analysis is designed for DOSs subject to actuator satu-
ration.InChap.10,semi-globalstabilizationwithguaranteedregionalperformance
forDOSssubjecttoactuatorsaturationisgiven.InChap.11,someresultsonoverall
convergenceratearedevelopedtoreduceconservativenessandcomputablematrix
inequalityconditions.InChap.12,aproblemonoutputregulationbystatefeedback
is investigated for linear DOSs subject to actuator saturation. In Chap.13, low-
gain feedbacks via delta operator approaches are given for linear systems subject
toactuatorsaturation.
Part IV: Analysis of the DoA for typical systems in delta domain is presented.
In Chap.14, stabilization problems are solved for two-dimensional (2-D) DOSs
with actuator saturation. In Chap.15, stability analysis is investigated for high-
frequency DOSs with actuator saturation. In Chap.16, both mode-dependent and
mode-independentstatefeedbackcontrollersareproposedforMarkovjumpDOSs
withactuationsaturation.InChap.17,akindofrobustfuzzy-schedulingcontroller
designmethodsisdesignedforTakagi-Sugeno(T-S)fuzzyDOSs.
Part V: With the development of complicated systems, some applications are
investigated for DOSs subject to actuator saturation. In Chap.18, invariance set
conditionsaredevelopedandappliedtoreliablestabilizationproblemsforalinear
DOSsubjecttotime-varyingfaultsandactuatorsaturation.InChap.19,stabilization
for a Markov jump DOS with time-varying delays and actuator saturation is
proposed.InChap.20,localstabilityandstabilizationoflinearperiodicDOSsare
analyzedtoestimatetheDoAbyapplyingperiodicinvariantellipsoids.InChap.21,
sufficient conditions for networked control systems (NCSs) with quantization,
actuatorsaturation,andpacketsdropoutaregiven.
ThesupportsfromtheNationalNaturalScienceFoundationofChinaunderGrant
(61573301), the National Natural Science Foundation Projects of International
CooperationandExchangesunderGrant(61720106010),theFoundationforInno-
vativeResearchGroupsoftheNationalNaturalScienceFoundationofChinaunder
Grant (61621063), the National Science Fund for Distinguished Young Scholars
of Hebei Province under Grant (F2016203148), and the Beijing Natural Science
Foundation underGrant(4161001),respectively,aregratefullyacknowledged. We
would like to acknowledge the collaborations with Professor Peng Shi and PhD
candidatesCeYan,PengLi,HuiLi,HuanhuanYuan,andTingZhangfortheirgreat
contributioninthismonograph.Inaddition,sincerelythankstotheothermembersin
Preface ix
ourresearchgroupwhohaveprovidedtheirhelpforthisbook.Wearealsograteful
toourfamilies.Withouttheirsacrificeandsupport,thisbookwouldnothavebeen
completed.
NankaiDistrict,Tianjin,China HongjiuYang
HaidianDistrict,Beijing,China YuanqingXia
HaigangDistrict,Hebei,China QingGeng
Symbols and Acronyms
T samplingperiod
R fieldofrealnumbers
Rn n-dimensionalrealEuclideanspace
Rn×m spaceofn×mrealmatrices
C fieldofcomplexnumbers
I identitymatrix
O zeromatrix
A systemmatrix
A−1 inverseofmatrixA
AT transposeofmatrixA
A∗ complexconjugatetransposeofmatrixA
A>0 symmetricpositivedefinite
A≤0 symmetricnegativesemi-definite
A<0 symmetricnegativedefinite
tr(A) traceofmatrixA
det(A) determinantofmatrixA
rank(A) rankofmatrixA
λ(A) eigenvalueofmatrixA
λ (A) minimumeigenvalueofmatrixA
min
λ (A) maximumeigenvalueofmatrixA
max
sign(x) signofx
|x| absolutevalue(ormodulus)ofx
(cid:3)x(cid:3) Euclideannorm
(cid:3)·(cid:3) thesecondnormforvectors
(cid:3)·(cid:3)∞ theinfinitenormforvectors
(cid:3)P(cid:3) inducednormsup (cid:3)Px(cid:3)
(cid:4)x(cid:4)=1
∗ symmetrictermsinasymmetricmatrix
∀ forall
∈ belongto
→ tendto,ormappingto(casesensitive)
:= definition
xi