Nonlinear H control synthesis is extended to an output regulation problem for a servomechanism with backlash. The problem in question is to design a feedback controller so as to obtain the closed-loop system in which all trajectories are bounded and the load of the driver is regulated to a desired position while also attenuating the influence of external disturbances. Provided the servomotor position is the only measurement available for feedback, the proposed extension is far from trivial because of nonminimum phase properties of the system. Performance issues of the nonlinear H-output regulator constructed are illustrated in an experimental study.

1.
Isidori
,
A.
, 2000, “
A Tool for Semiglobal Stabilization of Uncertain Non-Minimum-Phase Nonlinear Systems via Output Feedback
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
10
), pp.
1817
1827
.
2.
Byrnes
,
C.
, and
Isidori
,
A.
, 2003, “
Limit Sets, Zero Dynamics, and Internal Model in the Problem of Nonlinear Output Regulation
,”
IEEE Trans. Autom. Control
0018-9286,
48
(
10
), pp.
1712
1723
.
3.
Lagerberg
,
A.
, and
Egardt
,
B.
, 2003, “
Estimation of Backlash With Application to Automotive Powertrains
,”
Proc. of 42th Conference on Decision and Control
,
Maui
, Hawaii,
IEEE
, pp.
4521
4526
.
4.
Aguilar
,
L.
,
Orlov
,
Y.
, and
Acho
,
L.
, 2002, “
Nonlinear H∞-Control of Nonsmooth Time Varying Systems With Application to Friction Mechanical Manipulators
,”
Automatica
0005-1098,
39
, pp.
1531
1542
.
5.
Basar
,
T.
, and
Bernhard
,
P.
, 1990,
H∞ Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach
,
Birkhauser
,
Boston
.
6.
Isidori
,
A.
, and
Astolfi
,
A.
, 1992, “
Disturbance Attenuation and H∞-Control via Measurement Feedback in Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
37
(
9
), pp.
1283
1293
.
7.
Van der Schaft
,
A. J.
, 1992, “
L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback Control
,”
IEEE Trans. Autom. Control
0018-9286,
37
(
6
), pp.
770
784
.
8.
Cadiou
,
J. C.
, and
M’Sirdi
,
N. K.
, 1995, “
Modelization and Analysis of a System With Torque Transmitted Through a Backlash
,”
9th World Congress on the Theory of Machines and Mechanisms
, Milan, pp.
1467
1470
.
9.
Nordin
,
M.
,
Bodin
,
P.
, and
Gutman
,
P. O.
, 2001, “
New Models and Identification Methods for Backlash and Gear Play
,”
Adaptive Control of Nonsmooth Dynamic Systems
,
Gao
,
T.
, and
Lewis
,
F.
, eds.,
Springer-Verlag
,
Berlin
, pp.
1
30
.
10.
Merzouki
,
R.
,
Cadiou
,
J. C.
, and
M’Sirdi
,
N. K.
, 2004, “
Compensation of Friction and Backlash Effects in an Electrical Actuator
,”
J. Systems and Control Engineering
,
218
, pp.
75
84
.
11.
Isidori
,
A.
, 1995,
Nonlinear Control Systems
,
3rd ed.
,
Springer-Verlag
,
Berlin
.
12.
Orlov
,
Y.
, 2005, “
Finite Time Stability and Quasihomogeneous Control Synthesis of Uncertain Switched Systems With Application to Underactuated Manipulators
,”
Proc. of 44th Conference on Decision and Control
,
Seville, Spain
,
IEEE
, pp.
4566
4571
.
13.
Doyle
,
J.
,
Glover
,
K.
,
Khargonekar
,
P.
, and
Francis
,
B.
, 1989, “
State Space Solution to Standard H2 and H∞ Control Problems
,”
IEEE Trans. Autom. Control
0018-9286,
34
(
8
), pp.
831
846
.
14.
Anderson
,
B. D.
, and
Vreugdenhil
,
R.
, 1973,
Network Analysis and Synthesis
,
Prentice Hall
,
Englewood Cliffs, NJ
.
15.
Orlov
,
Y.
,
Acho
,
L.
, and
Solis
,
V.
, 1999, “
Nonlinear H∞-Control of Time Varying Systems
,”
Proc. of 38th Conference on Decision and Control
,
Phoenix
, Arizona,
IEEE
, pp.
3764
3769
.
16.
Canudas de Wit
,
C.
,
Astrom
,
K.
,
Sorine
,
M.
, and
Olsson
,
H.
, 1999, “
Control of Systems With Dynamic Friction
,”
Workshop on Systems with Friction
, Honolulu, Hawaii.
17.
Kelly
,
R.
,
Llamas
,
J.
, and
Campa
,
R.
, 2000, “
A Measurement Procedure for Viscous and Coulomb Friction
,”
IEEE Trans. Instrum. Meas.
0018-9456,
49
(
4
), pp.
857
861
.
You do not currently have access to this content.