Sliding Mode Control with Perturbation Estimation (SMCPE) is a recent control routine which steers uncertain dynamic systems with disturbances to follow a desired trajectory. It eliminates the conventional requirement for the knowledge of uncertainty upper bound. A perturbation estimation scheme provides a tool for robustness. This text offers an additional robustizing mechanism: selection of time-varying sliding functions utilizing frequency shaping techniques. Frequency shaping together with sliding mode control introduces a behavior for selectively penalizing tracking errors at certain frequency ranges. This combination provides two advantages concurrently: (a) It filters out certain frequency components of the perturbations therefore eliminating the possible excitation on the unmodelled dynamics, and (b) it drives the state to the desired trajectory despite perturbations. The crucial point is that a priori knowledge of the perturbation upper bound is not necessary to eliminate the perturbation effects at the designated frequencies. Numerical examples prove the effectiveness of this novel scheme.

1.
Dorling
C. M.
, and
Zinober
A. S. I.
,
1986
, “
Two Approaches to Hyperplane Design in Multivariable Structure Control Systems
,”
International Journal of Control
, Vol.
44
, No.
1
, pp.
65
82
.
2.
Elmali
H.
, and
Olgac
N.
,
1992
, “
Sliding Mode Control with Perturbation Estimation (SMCPE): A New Approach
,”
International Journal of Control
, Vol.
56
, No.
4
, pp.
923
941
.
3.
Gupta
N. K.
,
1980
, “
Frequency-Shaped Cost Functionals: Extension of Linear-Quadratic-Gaussian Design Methods
,”
Journal of Sound and Vibration
, Vol.
3
, No.
6
, pp.
529
535
.
4.
Slotine
J. J.
, and
Sastry
S. S.
,
1983
, “
Tracking Control of Nonlinear Systems Using Sliding Surfaces, With Application to Robot Manipulators
,”
International Journal of Control
, Vol.
38
, No.
2
, pp.
465
492
.
5.
Utkin
V. I.
,
1977
, “
Variable Structure Systems with Sliding Modes
,”
IEEE Transactions on Automatic Control
, Vol.
AC-22
, No.
2
, pp.
212
222
.
6.
Yoshikawa, T., 1990, Foundations of Robotics Analysis and Control, MIT Press.
7.
Young
K. D.
, and
O¨zgu¨ner
,
1993
, “
Frequency Shaping Compensator Design for Sliding Mode
,”
International Journal of Control
, Vol.
57
, No.
5
, pp.
1005
1019
.
This content is only available via PDF.
You do not currently have access to this content.