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Research Papers

Visualizing Non-Linear Control System Performance by Means of Multidimensional Scaling

[+] Author and Article Information
J. A. Tenreiro Machado

Institute of Engineering,
Polytechnic of Porto,
Department of Electrical Engineering,
Porto 4200-07, Portugal
e-mail: jtm@isep.ipp.pt

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received November 21, 2011; final manuscript received May 6, 2013; published online July 18, 2013. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 8(4), 041017 (Jul 18, 2013) (7 pages) Paper No: CND-11-1222; doi: 10.1115/1.4024540 History: Received November 21, 2011; Revised May 06, 2013

This paper addresses the use of multidimensional scaling in the evaluation of controller performance. Several nonlinear systems are analyzed based on the closed loop time response under the action of a reference step input signal. Three alternative performance indices, based on the time response, Fourier analysis, and mutual information, are tested. The numerical experiments demonstrate the feasibility of the proposed methodology and motivate its extension for other performance measures and new classes of nonlinearities.

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Figures

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Fig. 1

Nonlinearities: Saturation, backlash and the combination of relay, and deadzone

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Fig. 2

Locus (K, θ, X) for the saturation, backlash, and combination of relay and deadzone

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Fig. 3

Two dimensional MDS map of the fifteen control systems for the measure based on signal time correlation and a unit step reference input

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Fig. 4

Three dimensional MDS map of the fifteen control systems for the measure based on signal time correlation and a unit step reference input

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Fig. 5

Shepard diagram for the two dimensional MDS map with fifteen control systems and the measure based on signal time correlation and a unit step reference input

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Fig. 6

Shepard diagram for the three dimensional MDS map with fifteen control systems and the measure based on signal time correlation and a unit step reference input

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Fig. 7

Stress versus number of dimensions of the MDS maps for the fifteen control systems and the measure based on signal time correlation and a unit step reference input

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Fig. 8

Three dimensional MDS map of the fifteen control systems for the measure based on frequency distance and a unit step reference input

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Fig. 9

Three dimensional MDS map of the fifteen control systems for the measure based on the mutual information and a unit step reference input

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Fig. 10

Three dimensional MDS map of the fifteen control systems for the measure based on signal time correlation and a double pulse reference input

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Fig. 11

Three dimensional MDS map of the fifteen control systems for the measure based on frequency distance and a double pulse reference input

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Fig. 12

Three dimensional MDS map of the fifteen control systems for the measure based on the mutual information and a double pulse reference input

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