Research Papers

Discrete-Time Sliding Mode Controller With Time-Varying Band for Unfixed Sampling-Time Systems

[+] Author and Article Information
Chidentree Treesatayapun

Department of Robotic and
Advanced Manufacturing,
Ramos Arizpe 25903, Mexico
e-mails: treesatayapun@gmail.com; chidentree@cinvestav.edu.mx

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received October 9, 2017; final manuscript received April 30, 2018; published online June 4, 2018. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 140(11), 111002 (Jun 04, 2018) (10 pages) Paper No: DS-17-1511; doi: 10.1115/1.4040209 History: Received October 09, 2017; Revised April 30, 2018

An adaptive discrete-time controller is developed for a class of practical plants when the mathematical model is unknown and the sampling time is nonconstant or unfixed. The data-driven model is established by the set of plant's input–output data under the pseudo-partial derivative (PPD) which represents the change of output with respect to the change of control effort. The multi-input fuzzy rule emulated network (MiFREN) is utilized to estimate PPD with an online-learning phase to tune all adjustable parameters of MiFREN with the convergence analysis. The proposed control law is developed by the discrete-time sliding mode control (DSMC), and the time-varying band is established according to the unfixed sampling time and unknown boundaries of disturbances and uncertainties. The prototype of direct current-motor current control with uncontrolled-sampling time is constructed to validate the performance of the proposed controller.

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Fig. 1

Sampling and Computing times

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Fig. 2

MiFREN structure of PPD estimation

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Fig. 3

Experimental system: DC motor's current control

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Fig. 4

Membership functions of u(k−1)

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Fig. 5

Membership functions of y(k)

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Fig. 6

Tracking performance: y(k) at initial run

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Fig. 7

s(k) and ωBε(k) at initial run

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Fig. 8

Estimation error: ê(k) at initial run

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Fig. 9

Estimated PPD: θ̂(k) at initial run

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Fig. 10

Adjustable parameters of MiFREN: ||β(k)||2

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Fig. 11

Histogram of actual sampling-time: Ts(k)

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Fig. 12

Tracking performance: y(k) at second run

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Fig. 13

s(k) and ωBε(k) at second run

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Fig. 14

Tracking performance: y(k). Hybrid fuzzy PID [30].

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Fig. 15

Tracking performance: y(k). Higher order sliding mode [10].

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Fig. 16

Tracking performance: y(k) with disturbance



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