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Technical Brief

State and Extended Disturbance Observer for Sliding Mode Control of Mismatched Uncertain Systems

[+] Author and Article Information
Divyesh Ginoya

Department of Instrumentation and Control,
College of Engineering Pune,
Pune 411 005, India
e-mail: dlginoya007@gmail.com

P. D. Shendge

Department of Instrumentation and Control,
College of Engineering Pune,
Pune 411 005, India
e-mail: pds.instru@coep.ac.in

S. B. Phadke

Department of Instrumentation and Control,
College of Engineering Pune,
Pune 411 005, India
e-mail: sbp.instru@coep.ac.in

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 6, 2014; final manuscript received December 20, 2014; published online February 9, 2015. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 137(7), 074502 (Jul 01, 2015) (7 pages) Paper No: DS-14-1315; doi: 10.1115/1.4029568 History: Received August 06, 2014; Revised December 20, 2014; Online February 09, 2015

In this paper, a state and extended disturbance observer (DO) is designed for mismatched uncertain systems. Apart from system states and disturbances, the proposed observer estimates the derivatives of the disturbances and thereby improves the accuracy of estimation of disturbances as well as the states. No knowledge of bounds of disturbances or their derivatives is assumed. An observer–controller combination for a sliding mode controller that requires the estimates of the derivatives of disturbances is described, and the ultimate boundedness of the overall system is proved. The proposed observer is illustrated by simulation of a numerical example and a rotary hydraulic actuator. The proposed observer–controller combination is validated on a serial flexible joint manipulator in laboratory.

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Figures

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Fig. 1

Schematic of the proposed scheme

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Fig. 6

Experimental setup

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Fig. 2

Comparison of the proposed scheme (solid line) with the GESO based control (dashed line): (a) z = x1, (b) x1-x∧1, (c) x2-x∧2, and (d) x3-x∧3

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Fig. 3

Comparison of the proposed scheme (solid line) with the GESO based control (dashed line): (a) d1-      d∧1 and (b) d3-      d∧3

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Fig. 4

Effect of observer order on state estimation errors: observer order 1 (dashed), observer order 2 (black), and observer order 3 (red in online version, gray in print version). (a) x1-x∧1, (b) x2-x∧2, and (c) x3-x∧3.

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Fig. 5

Effect of observer order on disturbance estimation errors: observer order 1 (dashed), observer order 2 (black), and observer order 3 (red in online version, gray in print version). (a) d1-      d∧1 and (b) d2-      d∧2.

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Fig. 7

State estimation of the flexible joint system. (a) x1 (solid line), x∧1 (dashed line), and reference (dotted line) in rad, (b) x∧2 in rad/s, (c) x3 (solid line) and x∧3 (dashed line) in rad, and (d) x∧4 in rad/s.

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Fig. 8

Disturbance estimation. (a)       d∧2, (b)        d·∧2, and (c)       d∧4.

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