This paper presents a structurally stable scheme for nonlinear systems which do not satisfy the so-called FIB conditions for the existence of a linear solution to the structurally stable regulator solution, namely, the case when some necessary detectability condition with respect to the original system’s output does not hold. Under certain additional conditions, it is shown that the proposed scheme guarantees zero output tracking error between the actual output and the desired reference signal, in spite of the presence of parameter variations. Application to the model of a rotary inverted pendulum shows the effectiveness of the proposed scheme.

Issue Section:
Technical Papers
Keywords:
nonlinear control systems, controllers, pendulums, nonlinear systems, regulator theory, structurally stable regulation
Topics:
Control equipment, Errors, Nonlinear systems, Pendulums, Signals, Steady state
1.
Isidori
,
A.
, 1995,
Nonlinear Control Systems
, 3rd ed.,
Springer
,
London
.
2.
Isidori
,
A.
, and
Byrnes
,
C. I.
, 1990, “
Output Regulation of Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
35
(
2
), pp.
131
–
140
.
Crossref
Search ADS
 
3.
Francis
,
B. A.
, 1976, “
The Internal Model Principle of Control Theory
,”
Automatica
0005-1098,
12
, pp.
457
–
465
.
Crossref
Search ADS
 
4.
Francis
,
B. A.
, 1977, “
The Linear Multivariable Regulator Problem
,”
SIAM J. Control Optim.
0363-0129,
15
, pp.
486
–
505
.
Crossref
Search ADS
 
5.
Huang
,
J.
, and
Rugh
,
W. J.
, 1990, “
On the Nonlinear Multivariable Servomechanism Problem
,”
Automatica
0005-1098,
26
, pp.
963
–
972
.
Crossref
Search ADS
 
6.
Huang
,
J.
, 2004,
Nonlinear Output Regulation: Theory and Applications
,
SIAM
,
Philadelphia
.
7.
Huang
,
J.
, and
Lin
,
C-F.
, 1993, “
Internal Model Principle and Robust Control of Nonlinear Systems
,” in
Proceedings of the 32nd IEEE CDC
, pp.
1501
–
1513
.
8.
Hepburn
,
J. S. A.
, and
Wonham
,
W. M.
, 1984, “
Error Feedback and Internal Model on Differentiable Manifolds
,”
IEEE Trans. Autom. Control
0018-9286,
29
, pp.
397
–
403
.
Crossref
Search ADS
 
9.
Byrnes
,
C. I.
,
Delli Priscoli
,
F.
, and
Isidori
,
A.
, 1997,
Output Regulation of Uncertain Nonlinear Systems
,
Birkhauser
,
Boston
.
10.
Huang
,
J.
, 2001, “
Remarks on the Robust Output Regulation Problem for Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
46
(
12
), pp.
2028
–
2031
.
Crossref
Search ADS
 
11.
Huang
,
J.
, 1998, “
K-Fold Exosystem and the Robust Nonlinear Servomechanism Problem
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
120
(
1
), pp.
149
–
153
.
Crossref
Search ADS
 
12.
Huang
,
J.
, and
Chen
,
Z.
, 2004, “
A General Framework for Tackling the Output Regulation Problem
,”
IEEE Trans. Autom. Control
0018-9286,
49
(
12
), pp.
2203
–
2218
.
Crossref
Search ADS
 
13.
Carr
,
J.
, 1981,
Applications of Centre Manifold Theory
,
Springer Verlag
,
New York
.
14.
Castillo-Toledo
,
B.
,
Celikovsky
,
S.
, and
Di Gennaro
,
S.
, 2004, “
Generalized Immersion and Nonlinear Robust Regulation Problem
,”
Kybernetika
0023-5954,
40
(
2
), 2004, pp.
207
–
220
.
15.
Spong
,
M. W.
, and
Viyasagar
,
M.
, 1989,
Robot Dynamical and Control
,
Wiley
,
New York
.
16.
Knobloch
,
H. W.
,
Isidori
,
A.
, and
Flockerzi
,
D.
, 1993,
Topics in Control Theory
,
Birkhauser Verlag
,
Berlin
.
17.
Castillo-Toledo
,
B.
, 1990, “
Almost Tracking Trough Singular Points via the Nonlinear Regulator Theory
,” in
Proceedings of the IV Latin American Congress on Automatic Control
,
Puebla
,
México
, Vol.
2
, pp.
590
–
594
.
18.
Huang
,
J.
, and
Rugh
,
W. J.
, 1992, “
An Approximation Method for the Nonlinear Servomechanism Problem
,”
IEEE Trans. Autom. Control
0018-9286,
37
, pp.
1395
–
1398
.
Crossref
Search ADS
 
Copyright © 2006
 by American Society of Mechanical Engineers
You do not currently have access to this content.