Sage Journals: Discover world-class research

Abstract

This paper presents a robust control method, combining sliding mode control (SMC) and quantitative feedback theory (QFT) to track the tip of an inverted pendulum, subject to base excitation. A non-linear inverted pendulum (IP) model is considered to analyse tracking control characteristics through computer simulation in order to demonstrate the effectiveness of the proposed control methodology. The sliding mode control is used to track the trajectory of the tip of the inverted pendulum. However, when the system enters into sliding regime, chattering occurs due to switching delays as well as base vibrations. The chattering is eliminated with the introduction of QFT inside the boundary layer to ensure smooth tracking. Problems with noise amplification, resonances, presence of uncertainties, and unmodelled high-frequency dynamics can largely be avoided with the use of QFT over other optimization methods. In addition, the QFT design methodology guides design evolution rather than replacing human intervention as would appear to be the case in some control synthesis methodologies.

Keywords

non-linear modelling sliding surface feedback control tracking error stability time varying surface boundary layer chattering error dynamics first order filter model uncertainty

Get full access to this article

View all access options for this article.

References

Jean-Jacques

E. S.

Weiping

Applied non-linear control, 1991 (Prentice-Hall, Inc., Englewood Cliffs, New Jersey).

Roberge

J. K.

The mechanical seal. Bachelor's thesis, 1960, Massachusetts Institute of Technology, USA.

Dorf

R. C.

Modern control systems, 1967, pp. 276–279 (Addison-Wesley, Reading, Massachusetts).

Ogata

Modern control engineering, 1970, pp. 277–279 (Prentice-Hall, Englewood Cliffs, New Jersey).

Higdon

D. T.

Cannon

R. H.

ASME J. Cntrl Unstable Multiple-Output Mech. Syst., 1963, ASME Publication 63-WA-148, 1963, New York.

Truxal

J. G.

State models, transfer functions, and simulation, 1965, Monograph 8, Discrete Systems Concept Project.

Lundberg

K. H.

Roberge

J. K.

Classical dualinverted-pendulum control In Proceedings of the IEEE CDC 2003, Maui, Hawaii, 2003, pp. 4399–4404.

Taha

E. Z.

Happawana

G. S.

Hurmuzlu

Quantitative feedback theory (QFT) for chattering reduction and improved tracking in sliding mode control (SMC)

ASME J. Dynamic Syst. Measmt, and Cntrl, 2003, 125, 665–669.

Phillips

L. C.

Control of a dual inverted pendulum system using linear-quadratic and H-infinity methods. Master's thesis, 1994, Massachusetts Institute of Technology, USA.

10.

Siebert

W. McC.

Circuits, signals, and systems, 1986 (MIT Press, Cambridge, Massachusetts).

11.

Hedrick

J. K.

Gopalswamy

Nonlinear flight control design via sliding method, 1989 (Dept. of Mechanical Engineering, Univ. of California, Berkley).

12.

Bondarev

A. G.

Bondarev

S. A.

Kostylyova

N. Y.

Utkin

V. I.

Sliding modes in systems with asymptotic state observers

Autom. Remote Contr., 6, 1985.

13.

Shieh

L. S.

Control of uncertain systems. In Proceedings IEEE, 1993, 99–110.

14.

Doyle

J. C.

Feedback control theory, 1992 (Macmillan, New York).

15.

Sanchez-Pena

R. S.

Sznaier

Robust systems theory and applications, 1998 (John Wiley & Sons, New York).

16.

Zames

Input-output feedback stability and robustness

IEEE Control Syst., 1996, 16 (3), 61–66.

Suppression of base vibrations and tracking of the tip of an inverted pendulum using sliding mode control and quantitative feedback theory

Abstract

Abstract

Keywords

Get full access to this article

References