This paper investigates the applicability of two state feedback controllers for a class of uniformly controllable and observable nonlinear systems. The first one is based on an appropriate high gain control principle that has been developed by duality from the high gain observer principle. The state feedback control gain is particularly provided by a synthesis function satisfying a well-defined condition, leading thereby to a unification of the high gain control designs. The second one is a backstepping controller that has been developed from a suitable combination of the backstepping control approach bearing in mind the high gain control principle pursued for the first controller design. A common engineering design feature that is worth to be mentioned consists in properly formulating their underlying control problems as a regulation problem involving a suitable reference model with respect to the structure of the system as well as the control design principle under consideration. Of fundamental interest, the involved reference model is systematically derived thanks to the flatness and backstepping principles using an appropriate Lyapunov approach. An experimental evaluation is carried out to illustrate the efficiency of the proposed nonlinear controllers.

References

References
1.
Smaoui
,
M.
,
Brun
,
X.
, and
Thomasset
,
D.
,
2006
, “
A Study on Tracking Position Control of an Electropneumatic System Using Backstepping Design
,”
Control Eng. Pract.
,
14
(
8
), pp.
923
933
.
2.
Turki
,
K.
,
Smaoui
,
M.
,
Thomasset
,
D.
,
Mnif
,
F.
, and
Derbel
,
N.
,
2008
, “
Nonlinear Passivity Based Control Law With Application to Electropneumatic System
,”
17th International Federation of Automatic Control World Congress, Seoul, South Korea, July 6–11
, pp.
1827
1832
.
3.
Girin
,
A.
,
Plestan
,
F.
,
Glumineau
,
A.
, and
Brun
,
X.
,
2009
, “
High Order Sliding Mode Controllers of an Electropneumatic Actuator: Application to an Aeronautic Benchmark
,”
IEEE Trans. Control Syst. Technol.
,
17
(
3
), pp.
633
645
.
4.
Ameur
,
O.
,
Massioni
,
P.
,
Scorletti
,
G.
,
Brun
,
X.
, and
Smaoui
,
M.
,
2016
, “
Lyapunov Stability Analysis of Switching Controllers in Presence of Sliding Modes and Parametric Uncertainties With Application to Pneumatic Systems
,”
IEEE Trans. Control Syst. Technol.
,
24
(
6
), pp.
1953
1964
.
5.
Ayadi
,
A.
,
Hajji
,
S.
,
Smaoui
,
M.
,
Chaari
,
A.
, and
Farza
,
M.
,
2017
, “
Experimental Sensorless Control for Electropneumatic System Based on High Gain Observer and Adaptive Sliding Mode Control
,”
Int. J. Adv. Manuf. Technol.
,
93
(
9–12
), pp.
4075
4088
.
6.
Ayadi
,
A.
,
Smaoui
,
M.
,
Aloui
,
S.
,
Hajji
,
S.
, and
Farza
,
M.
,
2018
, “
Adaptive Sliding Mode Control With Moving Surface: Experimental Validation for Electropneumatic System
,”
Mech. Syst. Signal Process.
,
109
, pp.
27
44
.
7.
Shearer
,
J. L.
,
1956
, “
Study of Pneumatic Processes in the Continuous Control of Motion With Compressed Air—I
,”
Trans. ASME
,
78
, pp.
233
242
.
8.
Shearer
,
J. L.
,
1956
, “
Study of Pneumatic Processes in the Continuous Control of Motion With Compressed Air—II
,”
Trans. ASME
,
78
, pp.
243
249
.
9.
Farza
,
M.
,
M'Saad
,
M.
, and
Sekher
,
M.
,
2005
, “
A Set of Observers for a Class of Nonlinear Systems
,”
International Federation of Automatic Control World Congress
, Prague, Czech Republic, July 3–8.
10.
Seshagiri
,
S.
, and
Khalil
,
H.
,
1996
, “
Robust Output Feedback Regulation of Minimum-Phase Nonlinear Systems Using Conditional Integrators
,”
Automatica
,
41
(
1
), pp.
43
54
.
11.
Hajji
,
S.
,
Chaari
,
A.
,
M'Saad
,
M.
, and
Farza
,
M.
,
2007
, “
Output Feedback Controller for a Class of Nonlinear Systems
,”
European Control Conference (ECC)
, Kos, Greece, July 2–5, pp.
3831
3837
.
12.
Hajji
,
S.
,
Farza
,
M.
,
M'Saad
,
M.
, and
Kamoun
,
M.
,
2008
, “
Observed-Based Output Feedback Controller for a Class of Nonlinear Systems
,”
IFAC Conference on Control Systems Design (CSD2008)
, Seoul, South Korea, July.
13.
Agrawal
,
S. K.
, and
Sira-Ramirez
,
H.
,
2004
,
Differentially Flat Systems
,
Taylor and Francis Group
, Boca Raton, FL.
14.
Fliess
,
M.
,
Levine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1999
, “
A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
44
(
5
), pp.
922
937
.
15.
Sepulchre
,
R.
,
Jankovič
,
M.
, and
Kokotovič
,
P.
,
1997
,
Constructive Nonlinear Control
,
Springer
, London.
16.
Fliess
,
M.
,
Levine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1995
, “
Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples
,”
Int. J. Control
,
61
(
6
), pp.
1327
1361
.
17.
Isidori
,
A.
,
1995
,
Nonlinear Control Systems
,
3rd ed.
,
Springer
, London.
18.
Krstič
,
M.
,
Kanellakopoulos
,
I.
, and
Kokotovič
,
P.
,
1995
,
Nonlinear and Adaptive Control Design
,
Wiley
, New York.
19.
Åström
,
K. J.
,
2000
, “
Limitations on Control System Performance
,”
Eur. J. Control
,
6
(
1
), pp.
2
20
.
20.
Kanellakopoulos
,
I.
,
Kokotovic
,
P.
, and
Morse
,
A.
,
1991
, “
Systematic Design of Adaptive Controllers for Feedback Linearizable Systems
,”
IEEE Trans. Autom. Control
,
36
(
11
), pp.
1241
11253
.
21.
Besançon
,
G.
,
2000
, “
Remarks on Nonlinear Adaptive Observers Design
,”
Syst. Control Lett.
,
41
(
4
), pp.
271
280
.
22.
Fliess
,
M.
, and
Kupka
,
I.
,
1983
, “
A Finiteness Criterion for Nonlinear Input-Output Differential Systems
,”
SIAM J. Control Optim.
,
21
(
5
), pp.
721
728
.
23.
Gauthier
,
J.
,
Hammouri
,
H.
, and
Othman
,
S.
,
1992
, “
A Simple Observer for Nonlinear Systems—Application to Bioreactors
,”
IEEE Trans. Autom. Control
,
37
(
6
), pp.
875
880
.
24.
Farza
,
M.
,
M'Saad
,
M.
, and
Rossignol
,
L.
,
2004
, “
Observer Design for a Class of MIMO Nonlinear Systems
,”
Automatica
,
40
(
1
), pp.
135
143
.
25.
Ayadi
,
A.
,
Hajji
,
S.
,
Smaou
,
M.
,
Chaari
,
A.
, and
Farza
,
M.
,
2016
, “
Dynamic High-Gain Observer to Estimate Pneumatic Actuator Temperatures
,”
ASME J. Dyn. Syst. Meas. Control
,
138
(
2
), p.
024503
.
26.
Belgharbi
,
M.
,
Thomasset
,
D.
,
Scavarda
,
S.
, and
Sesmat
,
S.
,
1999
, “
Analytical Model of the Flow Stage of a Pneumatic Servodistributor for Simulation and Nonlinear Control
,”
Sixth Scandinavian International Conference on Fluid Power
, Tampere, Finland, May 26–28, pp.
847
860
.
27.
Brun
,
X.
,
Belgharbi
,
M.
,
Sesmat
,
S.
,
Thomasset
,
D.
, and
Scavarda
,
S.
,
1999
, “
Control of an Electropneumatic Actuator: Comparison Between Some Linear and Non-Linear Control Laws
,”
Proc. Inst. Mech. Eng., Part I
,
213
(
5
), pp.
387
406
.
28.
Smaoui
,
M.
,
Brun
,
X.
, and
Thomasset
,
D.
,
2008
, “
High-Order Sliding Mode for an Electropneumatic System: A Robust Differentiator-Controller Design
,”
Int. J. Robust Nonlinear Control
,
18
(
4–5
), pp.
481
501
.
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