Stability Analysis of a Class of Nonlinear Systems Using Discrete Variable Structures and Sliding Mode Control
This paper presents the application of discrete-time
variable structure control with sliding mode based on the 'reaching
law' method for robust control of a 'simple inverted pendulum on
moving cart' - a standard nonlinear benchmark system. The
controllers designed using the above techniques are completely
insensitive to parametric uncertainty and external disturbance. The
controller design is carried out using pole placement technique to find
state feedback gain matrix , which decides the dynamic behavior
of the system during sliding mode. This is followed by feedback gain
realization using the control law which is synthesized from 'Gao-s
reaching law'. The model of a single inverted pendulum and the
discrete variable structure control controller are developed, simulated
in MATLAB-SIMULINK and results are presented. The response of
this simulation is compared with that of the discrete linear quadratic
regulator (DLQR) and the advantages of sliding mode controller over
DLQR are also presented
[1] V. I. Utkin, Sliding Modes and Their Applications in Variable Structure
Systems, Moscow, Nauka, Mir, 1978.
[2] V.I.Utkin, "Variable structure systems with sliding mode", IEEE Trans.
Autom. Control, Vol.AC-22, No.2, pp.212-222, Apr 1977.
[3] J.Y.Hung, W.Gao, and J.C.Hung, "Variable structure control: A survey,"
IEEE Trans. Ind. Electron., Vol.40, No.1, pp.2-21, Feb 1993.
[4] W. B. Gao and J.C.Hung, "Variable structure control of nonlinear
systems: A new approach", IEEE Trans. Ind. Electron, Feb.1993, pp.
45-55.
[5] K.D. Young, V.I.Utkin, and U. Ozguner, "A control engineer-s guide to
sliding mode control", IEEE Trans. Control syst., Vol.7, No.3, pp.328-
342, May 1999.
[6] W. B. Gao, Y.Wang, and A.Homaifa, "Discrete-Time Variable Structure
Control Systems", IEEE Trans. Ind. Electron., Vol.42, No.2, pp.117-
122, Apr 1995.
[7] Juergen Ackerman and Vadim Utkin "Sliding Mode Control Design
Based on Ackerman-s Formula", IEEE Trans. Autom. Control, Vol.43,
No.2, Feb 1998.
[8] Govert Monsees, "Discrete-Time Sliding Mode Control", Ph.D. Thesis,
ISBN 90-77017-83-6, 2002.
[9] Katsuhiko Ogata, Modern Control Engineering, III Edition, Prentice
Hall, Inc., 1997.
[10] Katsuhiko Ogata, Discrete-Time Control Systems, II Edition, Pearson
Education, Inc., Delhi, 2001.
[1] V. I. Utkin, Sliding Modes and Their Applications in Variable Structure
Systems, Moscow, Nauka, Mir, 1978.
[2] V.I.Utkin, "Variable structure systems with sliding mode", IEEE Trans.
Autom. Control, Vol.AC-22, No.2, pp.212-222, Apr 1977.
[3] J.Y.Hung, W.Gao, and J.C.Hung, "Variable structure control: A survey,"
IEEE Trans. Ind. Electron., Vol.40, No.1, pp.2-21, Feb 1993.
[4] W. B. Gao and J.C.Hung, "Variable structure control of nonlinear
systems: A new approach", IEEE Trans. Ind. Electron, Feb.1993, pp.
45-55.
[5] K.D. Young, V.I.Utkin, and U. Ozguner, "A control engineer-s guide to
sliding mode control", IEEE Trans. Control syst., Vol.7, No.3, pp.328-
342, May 1999.
[6] W. B. Gao, Y.Wang, and A.Homaifa, "Discrete-Time Variable Structure
Control Systems", IEEE Trans. Ind. Electron., Vol.42, No.2, pp.117-
122, Apr 1995.
[7] Juergen Ackerman and Vadim Utkin "Sliding Mode Control Design
Based on Ackerman-s Formula", IEEE Trans. Autom. Control, Vol.43,
No.2, Feb 1998.
[8] Govert Monsees, "Discrete-Time Sliding Mode Control", Ph.D. Thesis,
ISBN 90-77017-83-6, 2002.
[9] Katsuhiko Ogata, Modern Control Engineering, III Edition, Prentice
Hall, Inc., 1997.
[10] Katsuhiko Ogata, Discrete-Time Control Systems, II Edition, Pearson
Education, Inc., Delhi, 2001.
@article{"International Journal of Electrical, Electronic and Communication Sciences:58719", author = "Vivekanandan C. and Prabhakar .R. and Prema D.", title = "Stability Analysis of a Class of Nonlinear Systems Using Discrete Variable Structures and Sliding Mode Control", abstract = "This paper presents the application of discrete-time
variable structure control with sliding mode based on the 'reaching
law' method for robust control of a 'simple inverted pendulum on
moving cart' - a standard nonlinear benchmark system. The
controllers designed using the above techniques are completely
insensitive to parametric uncertainty and external disturbance. The
controller design is carried out using pole placement technique to find
state feedback gain matrix , which decides the dynamic behavior
of the system during sliding mode. This is followed by feedback gain
realization using the control law which is synthesized from 'Gao-s
reaching law'. The model of a single inverted pendulum and the
discrete variable structure control controller are developed, simulated
in MATLAB-SIMULINK and results are presented. The response of
this simulation is compared with that of the discrete linear quadratic
regulator (DLQR) and the advantages of sliding mode controller over
DLQR are also presented", keywords = "Inverted pendulum, Variable Structure, Sliding mode
control, Discrete-time systems, Nonlinear systems.", volume = "2", number = "5", pages = "862-7", }