NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection, and parameter ...

112 Pages·2015·6.18 MB·English

by  Nicola Mimmo

Alma Mater Studiorum – Università di Bologna
DOTTORATO DI RICERCA IN
Automatica e Ricerca Operativa
Ciclo XXVII
Settore Concorsuale di afferenza: 09/G1
Settore Scientifico disciplinare: ING-INF/04
NLGA based Active Control in Aerospace:
fault tolerability, disturbance rejection, and
parameter estimation
Presentata da: Nicola Mimmo
Coordinatore Dottorato Relatore
prof. Daniele VIGO prof. Lorenzo Marconi
Correlatore
prof. Paolo Castaldi
Esame finale anno 2015
"...mais de toutes les sciences la plus absurde, à mon avis, et celle qui est la plus capable
d’étouffer toute espèce de génie, c’est la géométrie. Cette science ridicule a pour objet des
surfaces, des lignes, et des points, qui n’existent pas dans la nature. On fait passer en esprit
cent mille lignes courbes entre un cercle et une ligne droite qui le touche, quoique dans la réalité
on n’y puisse pas passer un fétu. La géométrie, en vérité, n’est qu’une mauvaise plaisanterie."
Voltaire
ALMA MATER STUDIORUM – UNIVERSITA’ DI BOLOGNA
Abstract
School of Engineering and Architecture
Department of Electrical, Electronic and Information Engineering
”Guglielmo Marconi”
Doctor of Philosophy
NLGA based Active Control in Aerospace: fault tolerability, disturbance rejection,
and parameter estimation
by Nicola Mimmo
A new control scheme has been presented in this thesis. Based on the NonLinear Geometric
Approach, the proposed Active Control System represents a new way to see the reconfigurable
controllers for aerospace applications. The presence of the Diagnosis module (providing the
estimation of generic signals which, based on the case, can be faults, disturbances or system
parameters), mean feature of the depicted Active Control System, is a characteristic shared by
three well known control systems: the Active Fault Tolerant Controls, the Indirect Adaptive
Controls and the Active Disturbance Rejection Controls. The standard NonLinear Geometric
Approach(NLGA)hasbeenaccuratelyinvestigatedandthanimprovedtoextenditsapplicability
to more complex models. The standard NLGA procedure has been modified to take account
of feasible and estimable sets of unknown signals. Furthermore the application of the Singular
Perturbations approximation has led to the solution of Detection and Isolation problems in
scenarios too complex to be solved by the standard NLGA. Also the estimation process has
been improved, where multiple redundant measuremtent are available, by the introduction of
a new algorithm, here called “Least Squares - Sliding Mode”. It guarantees optimality, in the
sense of the least squares, and finite estimation time, in the sense of the sliding mode. The
Active Control System concept has been formalized in two controller: a nonlinear backstepping
controller and a nonlinear composite controller. Particularly interesting is the integration, in
the controller design, of the estimations coming from the Diagnosis module. Stability proofs are
provided for both the control schemes. Finally, different applications in aerospace have been
provided to show the applicability and the effectiveness of the proposed NLGA-based Active
Control System.
Acknowledgements
I would like to express deep gratitude to my academic advisor Prof. P. Castaldi for his consistent
encouragement, motivationandguidancethroughoutmystudyatUniversityofBologna. Hehas
provided me with unquenchable enthusiasm, vision, and wisdoms, which inspired me from the
beginning to the end. I also wish to thank Prof. L. Marconi for believing in me since the first
day of my doctorate.
I can’t forget my company tutors Dr. P. Goupil and Dr. R. Dayre for their great support,
availability and congeniality, background of my inestimable technical improvement during my
extraordinary six months in Toulouse.
I would also like to thank all my friends and colleagues at University of Bologna, particularly
Prof. M. Zanzi, Ing. A. Ghetti, Ing. F. Pieri, Dr. P. Baldi and Ing. C. Bezziccheri, with whom I
spent a lot of time both at work and in spare time. They made my years at university’s hangar
labs, in Forlì, enjoyable and memorable.
Last but by no means least, I am most sincerely grateful to my girlfriend, Ofelia, for her love
and support over the years. She has always been a pillar of strength, inspiration and support.
I could never thank my family for their unconditional love, without which I would never have
come so far.
iii
Contents
Acknowledgements iii
Contents iv
List of Figures vi
Abbreviations vii
Symbols viii
1 Introduction and Motivations 1
1.1 Thesis contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 NLGA based Active Control Scheme 9
2.1 NLGA based Detection and Diagnosis Module . . . . . . . . . . . . . . . . . . . . 13
2.1.1 NLGA based Detection and Isolation Technique . . . . . . . . . . . . . . . 14
2.1.1.1 The standard NLGA based Detection and Isolation Technique . 14
2.1.1.2 NLGA Applicability Improvement: Output to Input Mapping
Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1.3 NLGA Applicability Improvement: the Singular Perturbation
Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.1.4 Formulations and Solutions of Detection and Isolation Problems 21
2.1.2 Detection Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.3 Isolation Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.4 Estimation Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.4.1 Least Squares with forgetting factor . . . . . . . . . . . . . . . . 30
2.1.4.2 Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.4.3 A new algorithm: Least Squares - Sliding Mode . . . . . . . . . 34
2.1.5 NLGA based Detection and Diagnosis module: Summary . . . . . . . . . 37
2.2 Nominal Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Backstepping Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.1.1 Active Backstepping Controller Design Concept. . . . . . . . . . 39
iv
Contents v
2.2.1.2 Stability analysis of the Active BackStepping Control . . . . . . 41
2.2.1.3 Stability of the Active Control . . . . . . . . . . . . . . . . . . . 43
2.2.2 Active Composite Controller. . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2.2.1 Generalized Faults Scenario . . . . . . . . . . . . . . . . . . . . . 46
2.2.2.2 Modeling the faulty plant . . . . . . . . . . . . . . . . . . . . . . 46
2.2.2.3 Control problem formulation and solution . . . . . . . . . . . . . 47
2.2.2.4 Feedback Linearization for the Reduced Errors Model . . . . . . 48
2.2.2.5 Feedback Linearization for the Boudary–Layer Error Model . . . 49
2.2.2.6 Stability analysis of the Active Fault Tolerant Composite Control 49
3 Case Studies 56
3.1 Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.1.1 Active Fault Tolerant Control - Case 1 . . . . . . . . . . . . . . . . . . . . 62
3.1.2 Active Fault Tolerant Control - Case 2 . . . . . . . . . . . . . . . . . . . . 64
3.1.3 Active Fault Tolerant Control - Case 3 . . . . . . . . . . . . . . . . . . . . 67
3.1.4 Active Wind Rejection Control . . . . . . . . . . . . . . . . . . . . . . . . 69
3.1.5 FlightParameterEstimationforExtendedGuidanceNavigationandControl 74
3.2 Fixed Wing UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2.1 Active Fault Tolerant Control . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3 Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.1 Active Fault Tolerant Control . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4 Quad Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4.1 Active Disturbance Rejection Control . . . . . . . . . . . . . . . . . . . . 89
4 Conclusions 92
Bibliography 93
List of Figures
2.1 Active Control Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 NLGA based Detection and Diagnosis Module . . . . . . . . . . . . . . . . . . . . 13
3.1 Aicraft simulator structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Estimate fˆ of f fault. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
δe δe
3.3 Estimate fˆ of f fault. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
δ δ
th th
3.4 Aircraft state with and without AFTC scheme: case of fault on δ . . . . . . . . . 64
e
3.5 Aircraft state with and without AFTC scheme: case of fault on δ . . . . . . . . . 65
th
3.6 Estimation of sinusoidal concurrent faults on δ and δ . . . . . . . . . . . . . . . 66
th e
3.7 Aircraft state with and without AFTC scheme: case of concurrent faults on δ
th
and δ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
e
3.8 Distance from the glide slope with and without AFTC scheme: case of concurrent
faults on δ and δ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
th e
3.9 Detection residuals behavior: comparison for isolation. . . . . . . . . . . . . . . . 68
3.10 Fault Estimation: Fˆ estimates F . . . . . . . . . . . . . . . . . . . . . . . . . . 69
V V
3.11 Stateerror,e = [e ,e ]T: thedesignedAFTC,whenengaged,guaranteesfaultless–
1 2
like performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.12 Comparison of the simulated and estimated horizontal wind component. . . . . . 71
3.13 Comparison of the simulated and estimated vertical wind component. . . . . . . . 71
3.14 Comparison of the simulated and estimated rotational wind component. . . . . . 72
3.15 Comparison of the simulated and estimated horizontal wind derivative. . . . . . . 72
3.16 Comparison of the simulated and estimated vertical wind derivative. . . . . . . . 73
3.17 Aircrafttrajectoryinthecaseofthecontrollerwithandwithoutwindcompensation. 73
3.18 State evolutions in the case of the controller with and without wind compensation. 74
3.19 Surface – actuator: j-th system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.20 Airspeed Virtual Sensor: performance . . . . . . . . . . . . . . . . . . . . . . . . 78
3.21 Recursive Detection and Isolation Scheme based on Estimation . . . . . . . . . . 81
3.22 FW-UAV: Estimation and tracking performance . . . . . . . . . . . . . . . . . . . 81
3.23 Satellite simulator scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.24 Satellite: Estimation and tracking performance - case of step faults . . . . . . . . 84
3.25 Satellite: Estimation and tracking performance - case of ramp faults . . . . . . . 85
3.26 Satellite: Estimation and tracking performance - case of sinusoidal faults . . . . . 85
3.27 Quadrotor simulator scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.28 Exogenous disturbance and its estimation. . . . . . . . . . . . . . . . . . . . . . . 88
3.29 Inertial position in the case of the controller with and without disturbances com-
pensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.30 Inertial speed in the case of the controller with and without disturbances com-
pensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
vi
Abbreviations
ADRC Active Disturbance Rejection Control
AFTC Active Fault Tolerant Control
BS BackStepping
CAS Calibrated Air Speed
DD Detection and Diagnosis
DI Detection and Isolation
FL Feedback Linearization
LS Least Squares
LES Locally Exponentially Stable
NED North-East-Down local inertial axes
NLGA NonLinear Geometric Approach
RBF-NN Rarial Basis Functions Neural Network
RPM Revolution Per Minutes
RM Residual Matrix
SM Sliding Mode
SP Singular Perturbations
TAS True Air Speed
UAV Unmanned Aerial Vehicle
o.c.a. observability codistribution algorithm
vii
Symbols
x state vector
x¯ state vector of the first subsystem provided by the NLGA
1
x¯ state vector of the second subsystem provided by the NLGA
2
x¯ state vector of the third subsystem provided by the NLGA
3
y output vector
y¯ output vector of the first subsystem provided by the NLGA
1
y¯ output vector of the second subsystem provided by the NLGA
2
u input vector
f unknown signals vector
f input faults vector
u
f disturbance and system faults vector
sys
f output faults vector
y
f set of undesired signals to be diagnosed
s
d generalized disturbance to be decoupled
s
h(x) output map
n(x) vector field
g(x) input vector field
l(x) f vector field
s
p(x) d vector field
s
ˆ
(·) estimation of (·)
X compact set in the state space
Y compact set in the output space
U compact set in the input space
viii
Symbols ix
F compact set in the input faults space
u
F compact set in the output faults space
y
F compact set in the disturbances and system faults space
sys
N number of minimal detection and isolation sets
r
Smin i-th minimal detection and isolation set
i
R residuals set
Ω residual subset
r analog residuals vector
rd digital residuals vector
J residual evaluation function
r
J residual evaluation function threshold
th
(cid:96) state space dimension
n
(cid:96) output space dimension
m
(cid:96) input space dimension
u
(cid:96) disturbances and system faults space dimension
sys
(cid:96) dimension of f
f
ν dimension of f
s s
ΣP minimal conditioned invariant distribution containing P
∗
P distribution spanned by the columns of p
s
(ΣP)⊥ codistribution orthogonal to ΣP
∗ ∗
Ω∗ maximal observability codistribution contained in (ΣP)⊥
∗
ξ vector of estimation activation signals
ε singular perturbation parameter
m rigid body mass
V inertial speed expressed in body axes
I,B
Ω rotational speed in body axes
B
F external forces expressed in body axes
B
I rigid body inertia matrix