This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.

References

1.
Shamma
,
J. S.
, and
Athans
,
M.
,
1991
, “
Guaranteed Properties of Gain Scheduled Control for Linear Parameter Varying Plants
,”
Automatica
,
27
(
3
), pp.
559
564
.
2.
Packard
,
A.
,
1994
, “
Gain Scheduling Via Linear Fractional Transformations
,”
Syst. Control Lett.
,
22
(
2
), pp.
79
92
.
3.
Becker
,
G.
, and
Packard
,
A.
,
1994
, “
Robust Performance of Linear Parametrically Varying Systems Using Parametrically Dependent Linear Dynamic Feedback
,”
Syst. Control Lett.
,
23
(
3
), pp.
205
215
.
4.
Apkarian
,
P.
, and
Gahinet
,
P.
,
1995
, “
A Convex Characterization of Gain-Scheduled H Controllers
,”
IEEE Trans. Autom. Control
,
40
(
9
), pp.
853
864
.
5.
Apkarian
,
P.
, and
Adams
,
R. J.
,
1998
, “
Advanced Gain-Scheduling Techniques for Uncertain System
,”
IEEE Trans. Control Syst. Technol.
,
6
(
1
), pp.
21
32
.
6.
Wu
,
F.
,
Yang
,
X. H.
,
Packard
,
A.
, and
Becker
,
G.
,
1996
, “
Induced L2 Norm Control for LPV Systems With Bounded Parameter Variation Rates
,”
Int. J. Robust Nonlinear Control
,
6
(
9/10
), pp.
983
998
.
7.
Shamma
,
J. S.
, and
Cloutier
,
J. R.
,
1993
, “
Gain-Scheduled Missile Autopilot Design Using Linear Parameter Varying Transformations
,”
AIAA J. Guid. Control Dyn.
,
16
(
2
), pp.
256
263
.
8.
Wu
,
F.
,
Packard
,
A.
, and
Balas
,
G.
,
2002
, “
Systematic Gain-Scheduling Control Design: A Missile Autopilot Example
,”
Asian J. Control
,
4
(
3
), pp.
341
347
.
9.
Marcos
,
A.
,
Veenman
,
J.
, and
Scherer
,
C. W.
,
2010
, “
Application of LPV Modeling, Design and Analysis Methods to a Re-Entry Vehicle
,”
AIAA
Paper No. AIAA-8192.
10.
Mohammadpour
,
J.
, and
Scherer
,
C. W.
, eds.,
2012
,
Control of Linear Parameter Varying Systems With Applications
,
Springer
,
New York
.
11.
Rugh
,
W. J.
, and
Shamma
,
J. S.
,
2000
, “
Research on Gain Scheduling
,”
Automatica
,
36
(
10
), pp.
1401
1425
.
12.
Rugh
,
W. J.
,
1991
, “
Analytical Framework for Gain-Scheduling
,”
IEEE Control Syst. Mag.
,
11
(
1
), pp.
79
84
.
13.
Nichols
,
R. A.
,
Reichert
,
R. T.
, and
Rugh
,
W. J.
,
1993
, “
Gain Scheduling for H-Infinity Controllers: A Flight Control Example
,”
IEEE Trans. Control Syst. Technol.
,
1
(
2
), pp.
69
79
.
14.
Lawrence
,
D. A.
, and
Rugh
,
W. J.
,
1995
, “
Gain Scheduling Dynamic Linear Controllers for a Nonlinear Plant
,”
Automatica
,
31
(
3
), pp.
381
390
.
15.
Kaminer
,
I.
,
Pascoal
,
A. M.
,
Kargonekar
,
P. P.
, and
Thompson
,
C.
,
1995
, “
A Velocity Algorithm for the Implementation of Gain Scheduled Controllers
,”
Automatica
,
31
(
8
), pp.
1185
1191
.
16.
Lawrence
,
D. A.
, and
Sznaier
,
M.
,
2004
, “
Nonlinear Compensator Synthesis Via Linear Parameter-Varying Control
,”
American Control Conference
,
Boston, MA
, pp.
1356
1361
.
17.
Isidori
,
A.
, and
Byrnes
,
C. I.
,
1990
, “
Output Regulation of Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
35
(
2
), pp.
131
140
.
18.
Gajic
,
Z.
,
2003
,
Linear Dynamic Systems and Signals
,
Prentice Hall
,
Upper Saddle River, NJ
.
19.
Wu
,
F.
,
1995
, “
Control of Linear Parameter Varying Systems
,” Ph.D. dissertation, University of California, Berkeley, CA.
20.
Lee
,
L. H.
,
1997
, “
Identification and Robust Control of Linear Parameter-Varying Systems
,” Ph.D. dissertation, University of California, Berkeley, CA.
21.
Hauser
,
J.
,
Sastry
,
S.
, and
Kokotovic
,
P. V.
,
1992
, “
Nonlinear Control Via Approximate Input-Output Linearization: The Ball and Beam Example
,”
IEEE Trans. Autom. Control
,
37
(
3
), pp.
392
398
.
22.
Song
,
X.
,
Ren
,
Z.
, and
Wu
,
F.
,
2013
, “
Gain-Scheduling Compensator Synthesis for Output Regulation of Nonlinear Systems
,”
American Control Conference
, (
ACC
)
Washington, DC
, June 17–19, pp.
6078
6083
.
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