Compound Control Methodology for Flight Vehicles

270 Pages·2013·5.248 MB·English

by  Yuanqing Xia, Mengyin Fu (auth.)

LLeecctture Notes in Control

and Information Sciences
438
Yuanqing Xia
Mengyin Fu
Compound Control
Methodology for
Flight Vehicles
123
Lecture Notes in Control and Information Sciences
Volume 438
SeriesEditors
M.Thoma,Hannover,Germany
F.Allgöwer,Stuttgart,Germany
M.Morari,Zürich,Switzerland
SeriesAdvisoryBoard
P.Fleming
UniversityofSheffield,UK
P.Kokotovic
UniversityofCalifornia,SantaBarbara,CA,USA
A.B.Kurzhanski
MoscowStateUniversity,Russia
H.Kwakernaak
UniversityofTwente,Enschede,TheNetherlands
A.Rantzer
LundInstituteofTechnology,Sweden
J.N.Tsitsiklis
MIT,Cambridge,MA,USA
Forfurthervolumes:
http://www.springer.com/series/642
·
Yuanqing Xia Mengyin Fu
Compound Control
Methodology for Flight
Vehicles
ABC
Prof.YuanqingXia Prof.MengyinFu
SchoolofAutomation SchoolofAutomation
BeijingInstituteofTechnology BeijingInstituteofTechnology
Beijing Beijing
China China
ISSN0170-8643 ISSN1610-7411 (electronic)
ISBN978-3-642-36840-0 ISBN978-3-642-36841-7 (eBook)
DOI10.1007/978-3-642-36841-7
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013932786
(cid:2)c Springer-VerlagBerlinHeidelberg2013
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.
PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations
areliabletoprosecutionundertherespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub-
lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany
errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect
tothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
To Weibing Gao
(1925-1994)
who made great contributions to Sliding Mode Control
To Jingqing Han
(1937-2008)
who invented Active Disturbance Rejection Control
Preface
Advantages of sliding mode control (SMC). It is well known that SMC is a
robust method to control nonlinear and uncertain systems which has attrac-
tivefeaturestokeepthesysteminsensitivetotheuncertaintiesonthesliding
surface. The conventional SMC design approach consists of two steps. First,
aslidingmanifoldisdesignedsuchthatthesystemtrajectoryalongtheman-
ifold acquires certain desired properties. Then, a discontinuous controller is
designed such that the system trajectories reach the manifold in finite time.
As a general designtool for control systems, SMC has been well established,
andtheprimaryadvantagesofwhichare:I)fastresponseandgoodtransient
performance; II) robustness against a large class of perturbations or model
uncertainties; and III) the possibility of stabilizing some complex nonlinear
systemswhicharedifficulttobestabilizedbycontinuousstatefeedbacklaws.
Advantages of active disturbance rejection control (ADRC). In this ap-
proach, the error resulting from unmodelled dynamics and disturbances are
estimated using an extended state observer (ESO) and compensated during
eachsamplingperiod.Sinceuncertaintiesanddisturbancesareestimatedand
canceledviaESO,thereisnoneedforintegralcontrol.ADRCwasdeveloped
by Professor Jingqing Han. The proposed ADRC control system consists of
thetrackingdifferentiator(TD),ESOandanonlinearproportionalderivative
(PD) controller.It is designedunder the assumptionof highdegree of model
uncertainties.Thecontrollerisdesignedtobeinherentlyrobustagainstplant
variations. Once it is set up for the problem within a predetermined range
of variation in system variables, no tuning is needed for start up, or to com-
pensate for changes in the system dynamics and disturbance. This method,
becauseofitsrobustnessanddisturbancerejectioncapabilities,isparticularly
suitable for control of uncertain systems.
VIII Preface
However, SMC will suffer chattering, which may bring poor performance,
and the uncertainties and disturbances can not be observed by ESO per-
fectly, especially, when the uncertainties and disturbances are beyond the
observability of ESO, they can not be compensated completely by ADRC.
Compound control is composed of advantages of SMC and ADRC, it con-
sists of two steps: I) When the trajectory of controlled systems is far away
from the equilibrium point, SMC is applied; and II) When the trajectory
is near equilibrium point, ADRC is adopted. Therefore, the performance of
compoundcontrolis significant.Certainly, othermoderncontroltheoriesare
also applied as parts of compound control according to the charactersof un-
certainties and disturbances. Therefore, compound control methodology is
proposed to flight vehicle control, which is of great importance.
Chapter 1 of this book is an overview of recent development of SMC.
In Chapter 2, some recent developments of ADRC are reviewed. ADRC in-
herits the advantages of proportional-integral-derivative (PID) control and
overcomesthe shortcomingsof the PID control. ADRC puts forwarda novel
concept, unlike most existing methods, to solve the control problems. The
scope of the applications shown in this book includes motion control, ship
control, vehicle control, servo system control, robotics, wind energy conver-
sion system, MEMS gyroscopes, super conducting magnetic energy storage,
boiler-turbine unit control and others.
In Chapter 3, an overview of flight vehicle control is presented. In Chap-
ter 4, flight vehicle motion and attitude description methods are described,
the quaternion is introduced, and attitude dynamics equations are given by
Momentum Theorem. In Chapter 5, a novel approach combining SMC and
ESO is proposed for attitude control of a missile model which is nonlinear
in aerodynamics.Combiningthe back-steppingtechnique, the corresponding
SMC law is designed to guarantee the state variables of the closed loop sys-
tem to converge to the reference state with the help of ESO by estimating
the unknown variable.
The problem of attitude stabilization for a spacecraft system which is
nonlinear in dynamics with inertia uncertainties and external disturbances
is investigated in Chapter 6. An adaptive law is applied to estimating the
disturbances, by which a SMC law is designed to force the state variables
of the closed loop system to converge to the origin. Then, the spacecraft
system subjected to control constraints is further considered and another
adaptive SMC law is designed to achieve the attitude stabilization. No prior
knowledge of inertia moment is required for both of the proposed adaptive
controllaws,which implies that the designedcontrolschemescanbe applied
in aircraftsystems with largeparametric uncertainty existing in inertial ma-
trix or even unknown inertial matrix. The problem of attitude control for a
aircraft model which is nonlinear in dynamics with inertia uncertainty and
Preface IX
external disturbances is investigated in Chapter 7. Three novel nonsingular
terminal sliding mode (NTSM) controllers are designed to make the space-
craftsystemconvergetoitsequilibriumpointinfinitetimeoraregionaround
its equilibrium point, which are shown by rigorous proof. Furthermore, the
proposed adaptive controllers require no information on uncertainties and
disturbances, then they can be used widely in the practical systems. Due to
nonlinear TSM, the designed controllers not only provide faster and higher
control precision, but also are singularity-free.
In Chapter 8, the problem of attitude tracking for a flight vehicle model
which is nonlinear in dynamics with inertia uncertainty and external distur-
banceshas beeninvestigated.Adaptivelaw andESOareappliedto estimate
the disturbances, by which sliding mode controllers are designed combining
thetwoapproachesrespectivelytoforcethestatevariablesoftheclosedloop
system to converge to the reference attitude states. In Chapter 9, the atti-
tude tracking control problem of a spacecraft nonlinear model with external
disturbancesandinertiauncertaintiesisaddressed.First,anewslidingmode
controller is designed to ensure the asymptotic convergence of the attitude
and angular velocity tracking errors against external disturbances and in-
ertia uncertainties by using a modified differentiator to estimate the total
disturbances. Second, an adaptive algorithm is applied to compensating the
disturbances, by which another sliding mode controller is successfully de-
signedtoachieveahighperformanceontheattitudetrackinginthepresence
of the inertia uncertainties, external disturbances and actuator saturations.
In Chapter 10, the problem of missile interception is investigated. SMC
with finite-time convergence is proposed for the design of guidance laws.
Specially, the control design consists of the estimation of the target accel-
eration by ESO and thus it achieves the decrease of undesired chattering
effectively. InChapter11,the problemofmissile interceptionis investigated.
ASMClawisdevelopedtoachievetheinterceptioninthepresenceoftheun-
known target acceleration. Then, actuator faults are further considered and
new fault-tolerantcontrolschemeswithfinite-time convergenceareproposed
for the design of guidance laws. In Chapter 12, the problem of optimal guid-
ance laws for cooperative attack of multiple missiles based on the optimal
control theory is investigated. Although neither SMC nor ADRC technique
isadoptedinthis chapter,itisinterestingtopresentnewguidancelawssuch
that multiple missiles attack a single target simultaneously. Simulation re-
sults show the effectiveness of the proposed algorithms. This chapter can be
viewed as a complementary part of this book.
We would like to acknowledge the collaborations with PH.D candidates:
Zheng Zhu, Wen Xie, Kunfeng Lu, Zhufeng Xie, Chunming Wang, Xiao Sun
and Professor Zhihong Deng for their great contribution in this monograph.
The supports fromthe National BasicResearchProgramofChina (973 Pro-
gram) (2012CB720000), the National Natural Science Foundation of China
X Preface
(61225015,60974011),ProgramforNewCenturyExcellentTalentsinUniver-
sity of China (NCET-08-0047), the Ph.D. Programs Foundation of Ministry
of Education of China (20091101110023,20111101110012),and Programfor
Changjiang Scholars and Innovative Research Team in University, and Bei-
jing Municipal Natural Science Foundation (4102053,4101001), respectively,
are gratefully acknowledged.
School of Automation, Beijing Institute of Technology, Beijing, China,
Yuanqing Xia
School of Automation, Beijing Institute of Technology, Beijing, China,
Mengyin Fu
April 2012
Symbols and Acronyms
A system matrix
A−1 inverse of matrix A
AT transpose of matrix A
A≥0 symmetric positive semi-definite
A>0 symmetric positive definite
A≤0 symmetric negative semi-definite
A<0 symmetric negative definite
(cid:2)AM the largest eigenvalue of matrix A
(ATA) induced norm of a matrix A∈Rn×n
M
A⊥B E{ABT}=0
α,β angle of attack and sideslip angle
α˙,β˙ angular velocity of attack and sideslip angle
C field of complex numbers
C measurement matrix
i
det(A) determinant of matrix A
δ Kronecker delta function
kj
δ ,δ ,δ deflection angles
x y z
δ˙ ,δ˙ ,δ˙ deflection angular velocity
x y z
g gravity acceleration
γ bank angle
c
γ (k) a stochastic sequence that takes values on 1 and 0 with
i
Bernoulli distribution, which is used to describe the missing
of measurements of Sensor i
I identity matrix
J ,J ,J moments of inertia
x y z
lim limit
LMI linear matrix inequality
L reference length
λ(A) eigenvalue of matrix A
λ (A) minimum eigenvalue of matrix A
min
λ (A) maximum eigenvalue of matrix A
max