Control design for multivariable nonlinear systems has cultivated into a mature research area. A variety of control design methodologies have been well established. In most of the approaches, however, it is implicitly assumed that an analytically mathematical model can be available. This is not always feasible since in many practical control problems, system dynamics may be represented by nonanalytical modules, such as look-up tables, c or Fortran codes, etc. As a consequence, conventional methods can only be performed after analytical models are obtained. In this paper, an approach is proposed where the nonanalytical modules can be handled directly. Important results are obtained on optimal control laws and their implementation; robust control is achieved using a new online tuning method; input saturation and stability issues are also discussed. A numerical study is provided to validate the effectiveness of the proposed method.

References

References
1.
Isidori
,
A.
,
1995
,
Nonlinear Control Systems
,
3rd ed.
,
Springer-Verlag
,
Berlin
.
2.
Van der Shaft
,
A. J.
,
1996
,
L2 Gain and Passivity Techniques in Nonlinear Control
,
Springer-Verlag, Heidelberg
,
Germany
.
3.
Byrnes
,
C. I.
,
2000
, “
Toward a Nonequilibrium Theory for Nonlinear Control Systems
,”
Lecture Notes in Control and Information Sciences
,
Springer
,
Berlin
.
4.
Sepulchre
,
R.
,
Jankovic
,
M.
, and
Kokotovic
,
P. V.
,
1997
,
Constructive Nonlinear Control
,
Springer-Verlag
,
New York
.
5.
Block
,
A. M.
,
Baillieul
,
J.
,
Crouch
,
P.
, and
Marsden
,
J.
,
2003
,
Nonholonomic Mechanics and Control
,
Springer
,
New York
.
6.
Mayne
,
D. Q.
,
Rawlings
,
J. B.
,
Rao
,
C. V.
, and
Scokaet
,
P. O. M.
,
2000
, “
Constrained Model Predictive Control: Stability and Optimality
,”
Automatica
,
36
(
6
), pp.
787
814
.
7.
Zhou
,
K.
,
Doyle
,
J. C.
, and
Glover
,
K.
,
1996
,
Robust and Optimal Control
,
Prentice Hall
,
Englewood Cliffs, NJ
.
8.
Kristić
,
M.
,
Sun
,
J.
, and
Kokotović
,
P. V.
,
1996
, “
Robust Control of Nonlinear Systems With Input Unmodeled Dynamics
,”
IEEE Trans. Autom. Control
,
41
(
6
), pp.
913
920
.
9.
Ahmadi
,
M.
,
Mojallali
,
H.
, and
Wisniewski
,
R.
,
2012
, “
Robust H∞ Control of Uncertain Switched Systems Defined on Polyhedral Sets With Filippov Solutions
,”
ISA Trans.
,
51
(
6
), pp.
722
731
.
10.
de Best
,
J.
,
Bukkems
,
B.
,
van de Molengraft
,
M.
,
Heemels
,
W.
, and
Steinbuch
,
M.
,
2008
, “
Robust Control of Piecewise Linear Systems: A Case Study in Sheet Flow Control
,”
Control Eng. Pract.
,
16
(
8
), pp.
991
1003
.
11.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Emami-Naeini
,
A.
,
2002
,
Feedback Control of Dynamical Systems
,
4th ed.
,
Addison-Wesley Longman Publishing
,
Englewood, CO
.
12.
Radke
,
A.
, and
Gao
,
Z.
,
2006
, “
A Survey of State and Disturbance Observers for Practitioners
,”
2006 American Control Conference
, Minneapolis, MN, June 14–16, pp.
5183
5188
.
13.
Li
,
S.
,
Yang
,
J.
,
Chen
,
W.
, and
Chen
,
X.
,
2014
,
Disturbance Observer Based Control: Methods and Applications
,
CRC Press
,
London
.
14.
Choi
,
Y.
,
Yang
,
K.
,
Chung
,
W. K.
,
Kim
,
H. R.
, and
Suh
,
I. H.
,
2003
, “
On the Robustness and Performance of Disturbance Observers for Second-Order Systems
,”
IEEE Trans. Autom. Control
,
48
(
2
), pp.
315
320
.
15.
Choi
,
H. T.
,
Kim
,
B. K.
,
Suh
, I
. H.
, and
Chung
,
W. K.
,
2000
, “
Design of Robust High-Speed Motion Controller for a Plant With Actuator Saturation
,”
ASME J. Dyn. Syst. Meas. Control
,
122
(
3
), pp.
535
541
.
16.
Lee
,
K. B.
, and
Blaabjerg
,
F.
,
2007
, “
Robust and Stable Disturbance Observer of Servo System for Low-Speed Operation
,”
IEEE Trans. Ind. Appl.
,
43
(
3
), pp.
627
635
.
17.
Yang
,
J.
,
Zolotas
,
A.
,
Chen
,
W.
,
Michail
,
K.
, and
Li
,
S.
,
2011
, “
Robust Control of Nonlinear MAGLEV Suspension System With Mismatched Uncertainties Via DOBC Approach
,”
ISA Trans.
,
50
(
3
), pp.
389
396
.
18.
Han
,
J.
,
2009
, “
From PID to Active Disturbance Rejection Control
,”
IEEE Trans. Ind. Electron.
,
56
(
3
), pp.
900
906
.
19.
Zhang
,
Y.
, and
Jiang
,
J.
,
2008
, “
Bibliographical Review on Reconfigurable Fault-Tolerant Control Systems
,”
Annu. Rev. Control
,
32
(
2
), pp.
229
252
.
20.
Jiang
,
J.
, and
Yu
,
X.
,
2012
, “
Fault-Tolerant Control Systems: A Comparative Study Between Active and Passive Approaches
,”
Annu. Rev. Control
,
36
(
1
), pp.
60
72
.
21.
Dey
,
C.
, and
Mudi
,
R.
,
2009
, “
An Improved Auto-Tuning Scheme for PID Controllers
,”
ISA Trans.
,
48
(
4
), pp.
396
409
.
22.
Das
,
S.
,
Saha
,
S.
,
Das
,
S. P.
, and
Gupta
,
A.
,
2011
, “
On the Selection of Tuning Methodology of FOPID Controllers for the Control of Higher Order Processes
,”
ISA Trans.
,
50
(
3
), pp.
376
388
.
23.
Wang
,
J.
,
Hu
,
Z.
, and
Ye
,
Z.
,
2014
, “
Static Feedback Stabilization of Nonlinear Systems With Single Sensor and Single Actuator
,”
ISA Trans.
,
53
(
1
), pp.
50
55
.
24.
Slotine
,
J. J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
,
Englewood Cliffs, NJ
.
You do not currently have access to this content.