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Technical Brief

Stability Analysis of Discrete Integral Sliding Mode Control for Input–Output Model

[+] Author and Article Information
Elhajji Zina

Research Unit: Numerical Control of Industrial Processes,
National Engineering School of Gabes,
University of Gabes Tunisia,
Medenine Street,
Gabes 6029, Tunisia
e-mail: zinaelhajji41@gmail.com

Dehri Khadija

Associate Professor
Research Unit: Numerical Control of Industrial Processes,
National Engineering School of Gabes,
University of Gabes Tunisia,
Medenine Street,
Gabes 6029, Tunisia
e-mail: khadija.dehri@gmail.com

Nouri Ahmed Said

Professor
Research Unit: Numerical Control of Industrial Processes,
National Engineering School of Gabes,
University of Gabes Tunisia,
Medenine Street,
Gabes 6029, Tunisia
e-mail: ahmedsaid.nouri@enig.rnu.tn

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 2, 2016; final manuscript received October 6, 2016; published online January 16, 2017. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 139(3), 034501 (Jan 16, 2017) (7 pages) Paper No: DS-16-1073; doi: 10.1115/1.4034949 History: Received February 02, 2016; Revised October 06, 2016

The sliding mode control (SMC) has several advantages in terms of good transient performance and system robustness. However, the sensitivity of this control technique to disturbance before reaching the sliding surface and the existence of the chattering phenomenon can be considered as the major problems in its implementation. To overcome these problems, we propose a new discrete integral sliding mode control (DISMC) for input–output model and compare it with the classical SMC and a recent version of DISMC. Then, a stability analysis is presented. Simulation results are given to illustrate the effectiveness of the proposed method.

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References

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Figures

Grahic Jump Location
Fig. 1

Evolution of the disturbance d(k)

Grahic Jump Location
Fig. 2

Evolution of the output y(k) and the reference input yr(k) (classical DSMC)

Grahic Jump Location
Fig. 3

Evolution of the sliding function S(k) (classical DSMC)

Grahic Jump Location
Fig. 4

Evolution of the control law u(k) (classical DSMC)

Grahic Jump Location
Fig. 5

Evolution of the output y(k) and the reference input yr(k) (DISMC [25])

Grahic Jump Location
Fig. 6

Evolution of the sliding surface S(k) (DISMC [25])

Grahic Jump Location
Fig. 7

Evolution of the control law u(k) (DISMC [25])

Grahic Jump Location
Fig. 8

Evolution of the output y(k) and the reference yr(k) (our proposed DISMC)

Grahic Jump Location
Fig. 9

Evolution of the sliding surface S(k) (our proposed DISMC)

Grahic Jump Location
Fig. 10

Evolution of the control input u(k) (our proposed DISMC)

Grahic Jump Location
Fig. 11

Evolution of the output y(k) and the reference yr(k)

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