© The Institution of Engineering and Technology
A non-linear unknown input observer (UIO) is designed for systems with non-linearities having lower bonds on their slopes. The observer is constructed such that the non-linearity in the observer error system satisfies a sector property. Based on this property rather than the Lipschitz property, an algorithm not limited by Lipschitz constant is proposed. Further, all the parameters in the proposed non-linear UIO can be calculated by solving a linear matrix inequality. The UIO is also extended to an adaptive one for a class of uncertain non-linear systems in which the arguments of non-linear terms are perturbed by unknown parameters. Finally, simulations of electric driving system are used to illustrate the effectiveness of the UIOs.
References
-
-
1)
-
J. Chen ,
R.J. Patton ,
H.Y. Zhang
.
Design of unknown input observers and robust detection filters.
Int. J. Control
,
1 ,
85 -
105
-
2)
-
Witczak, M., Korbicz, J., Puig, V.: `An LMI approach to designing observers and unknown input observers for non-linear systems', Proc. IFAC SAFEPROCESS 2006, 2007, Beijing, China, p. 198–203.
-
3)
-
M. Darouach ,
M. Zasadzinski ,
S.J. Xu
.
Full-order observers for linear systems with unknown inputs.
IEEE Trans. Autom. Control
,
3 ,
607 -
609
-
4)
-
X. Fan ,
M. Arack
.
Observer design for systems with multivariable monotone nonlinearities.
Syst. Control Lett.
,
319 -
330
-
5)
-
Chen, W., Saif, M.: `Unknown input observer design for a class of non-linear systems: an LMI approach', Proc. ACC’2006, 2006, Minneapolis, USA, p. 834–838.
-
6)
-
X.G. Yan ,
C. Edwards
.
Nonlinear robust fault reconstruction and estimation using a sliding mode observer.
Automatica
,
1605 -
1614
-
7)
-
M. Hou ,
P.C. Müller
.
Disturbance decoupled observer design: A unified viewpoint.
IEEE Trans. Autom. Control
,
6 ,
1338 -
1341
-
8)
-
Koenig, D., Mammar, S.: `Design of a class of reduced order unknown inputs non-linear observer for fault diagnosis', Proc. ACC’2001, 2001, Arlington, USA, p. 2143–2147.
-
9)
-
T.G. Park
.
Estimation strategies for fault isolation of linear systems with disturbances.
IET Control Theory Appl.
,
12 ,
2781 -
2792
-
10)
-
Y. Guan ,
M. Saif
.
A novel approach to the design of unknown input observers.
IEEE Trans. Autom. Control
,
5 ,
632 -
635
-
11)
-
Z. Gao ,
S.X. Ding
.
Sensor fault reconstruction and sensor compensation for a class of nonlinear state-space systems via a descriptor system approach.
IET Control Theory Appl.
,
3 ,
578 -
585
-
12)
-
J. Chen ,
R.J. Patton
.
(1999)
Robust model-based fault diagnosis for dynamic systems.
-
13)
-
F. Zhu ,
Z. Han
.
A note on observers for Lipschitz nonlinear systems.
IEEE Trans. Autom. Control
,
1751 -
1754
-
14)
-
B. Marx ,
D. Koenig ,
J. Ragot
.
Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis.
IET Control Theory Appl.
,
5 ,
1487 -
1495
-
15)
-
S.-H. Wang ,
E.J. Davison ,
P. Dorato
.
Observing the states of systems with unmeasurable disturbance.
IEEE Trans. Autom. Control
,
5 ,
716 -
717
-
16)
-
Seliger, R., Frank, P.M.: `Fault diagnosis by disturbance decoupled non-linear observers', Proc. 30th IEEE CDC, 1991, Brighton, UK, p. 2248–2255.
-
17)
-
C.H. Huang ,
P.A. Ioannou ,
J. Maroulas ,
M.G. Safonov
.
Design of strictly positive real systems using constant output feedback.
IEEE Trans. Autom. Control
,
3 ,
569 -
573
-
18)
-
Yaz, E.E., Azemi, A.: `Actuator fault detection and isolation in non-linear systems using LMIs and LMEs', Proc. ACC’1998, 1998, Philadelphia, USA, p. 1590–1594.
-
19)
-
M. Arcak ,
P.V. Kokotović
.
Nonlinear observers: a circle criterion design and robustness analysis.
Automatica
,
1923 -
1930
-
20)
-
Pertew, A.M., Marquez, H.J., Zhao, Q.: `Design of unknown input observers for Lipschitz non-linear systems', Proc. ACC’2005, 2005, Portland, USA, p. 4198–4203.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2011.0611
Related content
content/journals/10.1049/iet-cta.2011.0611
pub_keyword,iet_inspecKeyword,pub_concept
6
6