In this paper, a new approach to estimation of unknown inputs and faults in a class of nonlinear systems is presented. The approach is based on the design of a cascade connection of two sliding mode observers. The first observer is used for the estimation of state and unknown inputs and the second is used for the fault detection and isolation. An important feature of the proposed approach is that the state trajectories do not leave the sliding manifold even in the presence of unknown inputs and faults. This allows for faults and unknown inputs to be completely reconstructed based on the information retrieved from the equivalent output injection signals. The proposed approach is tested on a nonlinear model of single link flexible joint robot system.

References

1.
Beard
,
R. V.
,
Failure Accommodation in Linear Systems Through Self-Reorganization
(
Department of Aeronautic and Astronautics, MIT
,
Cambridge, MA
, 1971).
2.
Frank
,
P. M.
and
Ding
,
X.
, 1997, β€œ
Survey of Robust Residual Generation and Evaluation Methods in Observer-Based Faults Detection Systems
,”
J. Process Control
,
7
(
6
), pp.
403
–
424
.
3.
Gertler
,
J. J.
, 1987, β€œ
Survey of Model-Based Failure Detection and Isolation in Complex Plants
,”
IFAC Symposium on Microcomputer Applications to Process Control
, Istanbul,
Turkey
.
4.
Massoumnia
,
M. A.
,
Verghese
,
G. C.
,
and Willsky
,
A.S.
, 1989, β€œ
Failure Detection and Identification
,”
IEEE Trans. Autom. Control
,
34
(
3
), pp.
316
–
321
.
5.
Seliger
,
R.
,
and Frank
,
P. M.
, 1991, β€œ
Fault Diagnosis by Disturbance Decoupled Nonlinear Observers
,”
30th IEEE Conference on Decision and Control
,
Brighton, England
.
6.
Hammouri
,
H.
,
Kinnaert
,
M.
, and
El Yaagoubi
,
E. H.
, 1999, β€œ
Observer-Based Approach to Fault Detection and Isolation for Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
44
(
10
), pp.
1879
–
1884
.
7.
Koenig
,
D.
, and
Mammar
,
S.
, 2001, β€œ
Design of a Class of Reduced Order Unknown Inputs Nonlinear Observer for Fault Diagnosis
,”
Proceedings of American Control Conference
,
Arlington, VA
.
8.
Persis
,
C. D.
, and
Isidori
,
A.
, 2001, β€œ
A Geometric Approach to Nonlinear Fault Detection and Isolation
,”
IEEE Trans. Autom. Control
,
46
(
6
), pp.
853
–
865
.
9.
Besancon
,
G.
, 2003, β€œ
High-Gain Observation With Disturbance Attenuation and Application Robust Fault Detection
,”
Automatica
,
39
, pp.
1095
–
1102
.
10.
Xiong
,
Y.
, and
Saif
,
M.
, 2001, β€œ
Sliding Mode Observer for Nonlinear Uncertain Systems
,”
IEEE Trans. Autom. Control
,
46
(
12
), pp.
2012
–
2017
.
11.
Koshkouei
,
A. J.
, and
Zinober
,
A. S. I.
, 2004, β€œ
Sliding Mode State Observation for Nonlinear Systems
,”
Int. J. Control
,
77
(
2
), pp.
118
–
127
.
12.
Sreedhar
,
R.
,
Fernandez
,
B.
, and
Masada
,
G. Y.
, 1993, β€œ
Robust Fault Detection in Nonlinear Systems Using Sliding Mode Observers
,”
2nd IEEE Conference on Control Applications
,
Vancouver, BC, Canada
.
13.
Levant
,
A.
, 2003, β€œ
Higher-Order Sliding Modes: Differentiation and Output Feedback Control
,”
Int. J. Control
,
76
(
9–10
), pp.
924
–
941
.
14.
Tan
,
C. P.
, and
Edwards
,
C.
, 2003, β€œ
Sliding Mode Observers for Robust Detection and Reconstruction of Actuator and Sensor Faults
,”
Int. J. Robust Nonlinear Control
,
13
(
5
), pp.
443
–
463
.
15.
Floquet
,
T.
,
Barbot
,
J. P.
,
Perruquetti
,
W.
, and
Djemai
,
M.
, 2004, β€œ
On the Robust Fault Detection via a Sliding Mode Disturbance Observer
,”
Int. J. Control
,
77
(
7
), pp.
622
–
629
.
16.
Edwards
,
C.
,
Fridman
,
L.
, and
Thein
,
M. -W. L. L.
, 2007, β€œ
Fault Reconstruction in a Leader/Follower Spacecraft Using Higher Order Sliding Mode Observers
,”
American Control Conference
,
New York
.
17.
Fridman
,
L.
,
Shtessel
,
Y.
,
Edwards
,
C.
,
Yan
,
X.-G.
, 2008, β€œ
Higher-Order Sliding-Mode Observers for State Estimation and Input Reconstruction in Nonlinear Systems
,”
Int. J. Robust Nonlinear Control
,
18
, pp.
399
–
412
.
18.
Isidori
,
A.
,
Nonlinear Control Systems
(
Springer
,
New York
, 1996).
19.
Kwatny
,
H. G.
, and
Blankenship
,
G. L.
,
Nonlinear Control and Analytical Mechanics: A Computational Approach
(Birkhauser,
Boston
, 2000).
20.
Wang
,
J.
,
Qu
,
Z.
,
Hull
,
R. A.
, and
Martin
,
J.
, 2007, β€œCascaded Feedback Linearization and its Application to Stabilization of Nonholonomic Systems,”
Systems & Control Letters
,
56
(
4
), pp.
285
–
295
.
21.
Khalil
,
H. K.
,
Nonlinear Systems
(
Prentice-Hall
,
Englewood Cliffs, NJ
, 2002).
22.
Drakunov
,
S. V.
, 1992, β€œ
Sliding-Mode Observer Based on Equivalent Control Method
,”
31st Conference on Decision and Control
,
Tucson, AZ, IEEE
.
23.
Edwards
,
C.
, and
Spurgeon
,
S. K.
,
Sliding Mode Control
(
Taylor & Francis
,
London
, 1998).
24.
Edwards
,
C.
, and
Spurgeon
,
S. K.
,
Sliding Mode Control: Theory and Applications
(
Taylor & Francis
,
London
, 1998).
25.
Sanchis
,
R.
, and
Nijmeijer
,
H.
, 1998, β€œ
Sliding Controller-Sliding Observer Design for Nonlinear Systems
,”
Eur. J. Control
,
4
(
3
), pp.
197
–
208
. Cote INIST:26357,35400007291595.0030Cote INIST:26357,35400007291595.0030
26.
Utkin
,
V. I.
,
Sliding Modes in Control Optimization
(
Springer-Verlag
,
Berlin
, 1992).
27.
Ben-Israel
,
A.
, and
Greville
,
T. N. E.
, 2002, β€œ
Generalized inverses: Theory and Applications
,”
Canadian Mathematical Society
(
Springer
,
New York
).
28.
Marconi
,
L.
,
Isidori
,
A.
, and
Serrani
,
A.
2002, β€œ
Autonomous Vertical Landing on an Oscillating Platform: An Internal-Model Based Approach
,”
Automatica
,
38
, pp.
21
–
32
.
29.
Persis
,
C. D.
,
Santis
,
R. D.
, and
Isidori
,
A.
, 2001, β€œ
Nonlinear Actuator Fault Detection and Isolation for a VTOL Aircraft
,”
Proceedings of the American Control Conference
,
Arlington, VA
.
30.
Jankovic
,
M.
,
Fontaine
,
D.
, and
Kokotovic
,
P.
, 1996, β€œTORA Example: Cascade- and passivity-based control designs,”
4
(
3
), pp.
292
–
297
.
31.
Bartolini
,
G.
,
Ferrara
,
A.
, and
Stotsky
,
A. A.
,1999, β€œ
Robustness and Performance of an Indirect Adaptive Control Scheme in Presence of Bounded Disturbances,”
44
(
4
), pp.
789
–
793
.
32.
Raghavan
,
S.
, and
Hendrick
,
J. K.
, 1994, β€œ
Observer Design for a Class of Nonlinear Systems
,”
Int. J. Control
,
59
(
2
), pp.
515
–
528
.
You do not currently have access to this content.