This paper treats the control problem of a class of monodimensional (1D) hyperbolic differential models with nonlinear components by using the boundary controller, the state measuring, and the control action on the boundary of the system. This controller is easy to implement from point of view of measuring techniques and actuation. The proposed algorithm provides the exponential convergence to the desired reference trajectory and rejects the effect of the nonlinear components by using the constraints in state space. A maximum principle of this class of system is inferred in order to evaluate the effect of boundary control. A constructive Lyapunov-based proof of convergence of the control algorithm is carried out. Numerical simulations of a technical model are presented.

References

References
1.
Padhi
,
R.
, and
Faruque Ali
,
Sk.
,
2009
, “
An Account of Chronological Developments in Control of Distributed Parameter Systems
,”
Annu. Rev. Control
,
33
(
1
), pp.
59
68
.
2.
Bensoussan
,
A.
,
Delfour
,
M. C.
,
Da Prato
,
G.
, and
Mitter
,
S. K.
,
2006
,
Representation and Control of Infinite Dimensional Systems
, Vol.
1
,
Birkhauser Verlag
,
Basel, Switzerland
.
3.
Tourre
,
Y.
, and
Rudolph
,
J.
,
2001
, “
Controller Design for Distributed Parameter Systems
,”
Control Systems, Robotics and Automation
, Vol.
XIV
,
Springer
,
Berlin
.
4.
Callier
,
F. M.
, and
Winkin
,
J.
,
1990
, “
Spectral Factorization and LQ-Optimal Regulation for Multivariable Distributed Systems
,”
Int. J. Control
,
52
(
1
), pp.
55
75
.
5.
Callier
,
F. M.
, and
Winkin
,
J.
,
1992
, “
LQ-Optimal Control of Infinite-Dimensional Systems by Spectral factorization
,”
Automatica
,
28
(
4
), pp.
757
770
.
6.
Christofides
,
P. D.
,
2001
,
Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes
,
Birkhauser
,
Boston
.
7.
Christofides
,
P. D.
, and
Daoutidis
,
P.
,
1996
, “
Feedback Control of Hyperbolic PDE Systems
,”
AIChE J.
,
42
(
11
), pp.
3063
3086
.
8.
Maidi
,
A.
,
Diaf
,
M.
, and
Corriou
,
J. P.
,
2009
, “
Boundary Geometric Control of a Heat Equation
,”
European Control Conference (ECC’09)
, Budapest, Hungary, Aug. 23–26, pp.
4677
4682
.
9.
Maidi
,
A.
,
Diaf
,
M.
, and
Corriou
,
J. P.
,
2009
, “
Boundary Control of a Parallel-Flow Heat Exchanger by Input-Output Linearization
,”
European Control Conference (ECC’09)
, Budapest, Hungary, Aug. 23–26, pp.
3246
3253
.
10.
Maidi
,
A.
, and
Corriou
,
J. P.
, 2011, “
Boundary Control of Nonlinear Distributed Parameter Systems by Input-Output Linearization
,” 18th IFAC Congress, Milano, Italy, Aug. 28–30, pp.
10910
10916
.
11.
Ivanescu
,
M.
,
Popescu
,
N.
, and
Popescu
,
D.
,
2010
, “
Frequency Criteria for the Grasping Control of a Hyper-Redundant Robot
,”
IEEE International Conference on Robotics and Automation
, (ICRA 2010), Anchorage, AK, May 3–8, pp.
1542
1549
.
12.
Krstic
,
M.
, and
Smyshlyaev
,
A.
,
2006
,
Boundary Control of PDEs: A Short Course on Backstepping Design,
SIAM, Philadelphia.
13.
Temam
,
R.
,
1997
,
Infinite-Dimensional Dynamical Systems in Mechanics and Physics
,
Springer-Verlag
,
New York
.
You do not currently have access to this content.