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Research Papers

A Note on Observer-Based Frequency Control for a Class of Systems Described by Uncertain Models

[+] Author and Article Information
Nirvana Popescu

Computer Science Department,
University Politehnica, Bucharest,
313, Splaiul Independentei,
Bucharest 060042, Romania
e-mail: nirvana.popescu@cs.pub.ro

Mircea Ivanescu

Mechatronic Department,
University of Craiova,
13, Cuza Street,
Craiova 200585, Romania
e-mail: ivanescu@robotics.ucv.ro

Decebal Popescu

Computer Science Department,
University Politehnica, Bucharest,
313, Splaiul Independentei,
Bucharest 060042, Romania
e-mail: decebal.popescu@cs.pub.ro

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 14, 2016; final manuscript received July 4, 2017; published online October 3, 2017. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 140(2), 021008 (Oct 03, 2017) (9 pages) Paper No: DS-16-1316; doi: 10.1115/1.4037528 History: Received June 14, 2016; Revised July 04, 2017

This paper focuses on the robust control problem for a class of linear uncertain systems by using frequency techniques. The controller/observer dynamics are analyzed using Lyapunov techniques, in terms of the state and state estimation error, for an uncertainty constrained over a specified range. A Popov-type criterion, a “circle criterion,” defined as the Popov frequency condition and the uncertainty circle, is formulated. It is proved that the closed-loop system is robustly stable if the Popov condition holds at all frequencies. The proposed method is validated against a robust controller for a balancing robot (BR).

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Figures

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Fig. 1

Circle criterion for uncertain systems

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Fig. 3

Uncertain domain of a21i for λ∈[3;7], μ∈[0.1;0.5]

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Fig. 4

Uncertain domain of a22i for λ∈[3;7], μ∈[0.1;0.5]

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Fig. 5

Uncertain domain of bi for λ∈[3;7], μ∈[0.1;0.5]

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Fig. 6

Popov plot-margin of stability for β

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Fig. 7

Trajectories: x1(t), x̂1(t)

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Fig. 8

Trajectories: x˙1(t), x˙̂1(t)

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Fig. 9

Skyhook control system

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Fig. 10

Popov plot for skyhook control

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