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Research Papers

Adaptive Frequency Shaped Linear Quadratic Control of Mechanical Systems: Theory and Experiment

[+] Author and Article Information
An-Chyau Huang

Professor
Department of Mechanical Engineering,
National Taiwan University of Science
and Technology,
Taipei 106, Taiwan
e-mail: achuang@mail.ntust.edu.tw

Ting-Kai Jhuang

Department of Mechanical Engineering,
National Taiwan University of Science
and Technology,
Taipei 106, Taiwan

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 30, 2015; final manuscript received March 18, 2016; published online May 26, 2016. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 138(9), 091003 (May 26, 2016) (7 pages) Paper No: DS-15-1357; doi: 10.1115/1.4033273 History: Received July 30, 2015; Revised March 18, 2016

The traditional linear quadratic (LQ) controller can give optimal performance to a known linear system with weightings in the time domain, while the frequency shaped LQ (FSLQ) controller is able to provide optimal performance to the same class of systems with weightings in the frequency domain. When the system contains uncertainties, both of these two approaches fail. In this paper, an adaptive controller is proposed to an uncertain mechanical system such that LQ performance can be achieved with weightings in the frequency domain. The function approximation technique is applied to represent the uncertainties into a finite combination of a set of known basis functions. This allows the system to be with various nonlinearities and uncertainties without significant impact on the design procedure. The Lyapunovlike analysis is used to ensure convergence of the system output and boundedness of the internal signals. A dual stage is built to evaluate the performance of the proposed scheme experimentally.

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Figures

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Fig. 1

A dual stage system

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Fig. 2

A high-pass filter for the fine motion stage

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Fig. 3

Trajectory of the gross motion stage under proportional-integral-derivative (PID) control

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Fig. 4

Trajectory of the fine motion stage under PID control

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Fig. 5

Control effort of the gross motion stage under PID

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Fig. 6

Control effort of the fine motion stage under PID

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Fig. 7

Trajectory of the gross motion stage under FSLQ

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Fig. 8

Trajectory of the fine motion stage under FSLQ

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Fig. 9

Control effort of the gross motion stage under FSLQ

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Fig. 10

Control effort of the fine motion stage under FSLQ

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Fig. 11

The actual motion of the fine motion stage under FSLQ

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