The use of multiple surface sliding controllers for robust control of nonlinear systems with mismatched uncertainties has produced a number of impressive applications, but also raised a few theoretical questions. Among the latter are the use of numerical differencing to obtain derivatives of desired trajectories, robustness to uncertainties in the gain terms and the common practice of filtering desired trajectories for implementation. This paper seeks to address these issues through the concept of a Dynamic Surface Controller, in which filters form an integral part of the structure. This filtering removes the need for numerical differencing and guarantees a certain smoothness, enabling other assumptions of smoothness to be relaxed. In this paper, the Dynamic Surface Controller is coupled with a sequential design procedure that carves a system workspace out of the state space. Within this bounded region, bounded tracking performance can be rigorously guaranteed in the presence of uncertainties and constraints such as rate limits and saturation can be systematically avoided. The design of a Dynamic Surface Controller and the advantages of the workspace concept are demonstrated in the context of engine speed control.

Issue Section:
Technical Papers
Keywords:
nonlinear control systems, robust control, controllers
Topics:
Control equipment, Design, Errors, Filters, Uncertainty, Nonlinear systems, Trajectories (Physics)
1.
Green, J. H., and Hendrick, J. K., 1990, “Nonlinear speed control for automotive engines,” in: Proceedings of the 1990 American Control Conference. pp. 2891–2897.
2.
Barmish
,
B. R.
, and
Leitmann
,
G.
,
1982
, “
On ultimate boundedness control of uncertain systems in the absence of matching conditions
,”
IEEE Trans. Autom. Control
,
26
, No.
5
, pp.
153
–
157
.
3.
Barmish
,
B. R.
,
Corless
,
M.
, and
Leitmann
,
G.
,
1983
, “
A new class of stabilizing controllers for uncertain dynamical systems
,”
SIAM J. Control Optim.
,
21
, pp.
246
–
255
.
4.
Slotine
,
J. J.
, and
Sastry
,
S. S.
,
1983
, “
Tracking control of non-linear, systems using sliding surfaces with application to robot manipulators
,”
Int. J. Control
,
38
, No.
2
, pp.
465
–
492
.
5.
Utkin, V. I., Drakunov, S. V., and Izosimov, D. B., 1984. “A hierarchical principle of control system decomposition based on motion separation,” in: 9th World IFAC Conference, Budapest, Hungary, July 2–6.
6.
Drakunov
,
S. V.
,
Izosimov
,
D. B.
,
Luk’yanov
,
A. G.
,
Utkin
,
V. A.
, and
Utkin
,
V. I.
,
1990
, “
The block control principle I.
,”
Autom. Remote Control (Engl. Transl.)
,
51
, No.
5
, pp.
601
–
608
.
7.
Drakunov
,
S. V.
,
Izosimov
,
D. B.
,
Luk’yanov
,
A. G.
,
Utkin
,
V. A.
, and
Utkin
,
V. I.
,
1990
, “
The block control principle II
,”
Autom. Remote Control (Engl. Transl.)
,
51
, No.
6
, pp.
737
–
746
.
8.
Slotine
,
Jean-Jacques E.
, and
Hedrick
,
J. Karl
,
1993
, “
Robust input-output feedback linearization
,”
Int. J. Control
,
57
, No.
5
, pp.
1133
–
1139
.
9.
Kanellakopoulos
,
I.
,
Kokotovic
,
P. V.
, and
Morse
,
A. S.
,
1991
, “
Systematic design of adaptive controllers for feedback linearizable systems
,”
IEEE Trans. Autom. Control
,
36
, No.
11
, pp.
1241
–
1253
.
10.
Freeman
,
R. A.
, and
Kokotovic
,
P. V.
,
1993
, “
Design of ‘softer’ robust nonlinear control laws
,”
Automatica
,
29
, No.
6
, pp.
1425
–
1437
.
11.
Krstic, M., Kanellakopoulos, I., and Kokotovic, P., 1995. Nonlinear and Adaptive Control Design, Wiley Interscience, New York.
12.
Swaroop, D. V. A. H. G., Gerdes, J. C., Yip, P. P., and Hedrick, J. K., 1997, “Dynamic surface control of nonlinear systems,” in: Proceedings of the 1997 American Control Conference, Albuquerque, NM.
13.
Levant
,
A.
,
1993
, “
Sliding order and sliding accuracy in sliding mode control
,”
Int. J. Control
,
58
, pp.
1247
–
1263
.
14.
Bartolini
,
G.
,
Ferrara
,
A.
, and
Usai
,
E.
,
1998
, “
Chattering avoidance by second order sliding mode control
,”
IEEE Trans. Autom. Control
,
43
, No.
2
, pp.
241
–
246
.
15.
Bartolini, G., Ferrara, A., Levant, A., and Usai, E., 1999, “On second order sliding mode controllers,” in: Variable Structure Systems, Sliding Mode and Nonlinear Control K. D. Young and U. Ozguner Eds. Springer-Verlag, New York.
16.
Choi, S. B. and Hedrick, J. K., 1992, “Experimental implementation of sliding controls on automotive engines.” in: Proc. 1992 ACC, Chicago, IL.
17.
Alleyne, A., 1994, “Nonlinear and Adaptive Control with Applications to Vehicle Suspensions.” PhD thesis UC Berkeley.
18.
McMahon, D. H., Hedrick, J. K., and Shladover, S. E., 1990. “Vehicle modeling and control for automated highway systems.” In: Proc. 1990 ACC, San Diego, CA. pp. 297–303.
19.
Gerdes
,
J. C.
, and
Hedrick
,
J. K.
,
1997
, “
Vehicle speed and spacing control via coordinated throttle and brake actuation
,”
Control Engineering Practice
,
5
, No.
11
, pp.
1607
–
1614
.
20.
Herrmann, A., Spurgeon, S., and Edwards, C., 1999, “Discretization of sliding mode based control schemes,” in: Proceedings of the 38th CDC, Phoenix, AZ. pp. 4257–4262.
21.
Gerdes, J. C., 1996, “Decoupled Design of Robust Controllers for Nonlinear Systems: As Motivated by and Applied to Coordinated Throttle and Brake Control for Automated Highways,” PhD thesis. University of California at Berkeley.
22.
Kokotovic
,
Petar V.
,
1992
, “
The joy of feedback: Nonlinear and adaptive
,”
IEEE Control Syst. Mag.
,
pp.
7
–
17
.
23.
Esfandiari, F. and Khalil, H. K., 1989, “Observer-based control of uncertain linear systems: recovering state feedback robustness under matching condition,” in: Proceedings of the 1989 American Control Conference. pp. 931–936.
24.
Aubin, J-P, 1991, Viability Theory, Birkhauser. Boston.
25.
Swaroop
,
D.
,
Hedrick
,
J. K.
,
Yip
,
P. P.
, and
Gerdes
,
J. C.
,
2000
, “
Dynamic surface control for a class of nonlinear systems
,”
IEEE Trans. Autom. Control
,
45
, No.
10
, pp.
1893
–
1899
.
Copyright © 2002
 by ASME
You do not currently have access to this content.