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Research Papers

Parameter Design in Optimal Control Problems for Linear Dynamic Systems Using a Canonical Form

[+] Author and Article Information
Ui-Jin Jung

Department of Mechanical Engineering,
Hanyang University,
Seoul, South Korea, 133-791
e-mail: christmas@hanyang.ac.kr

Gyung-Jin Park

Professor
Department of Mechanical Engineering,
Hanyang University,
Ansan, South Korea, 426-791
e-mail: gjpark@hanyang.ac.kr

Sunil K. Agrawal

Professor
Department of Mechanical Engineering,
Columbia University,
New York, NY 10027
e-mail: Sunil.Agrawal@columbia.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received October 27, 2011; final manuscript received July 22, 2013; published online October 15, 2013. Assoc. Editor: Nader Jalili.

J. Dyn. Sys., Meas., Control 136(1), 011014 (Oct 15, 2013) (8 pages) Paper No: DS-11-1336; doi: 10.1115/1.4025455 History: Received October 27, 2011; Revised July 22, 2013

Control problems in dynamic systems require an optimal selection of input trajectories and system parameters. In this paper, a novel procedure for optimization of a linear dynamic system is proposed that simultaneously solves the parameter design problem and the optimal control problem using a specific system state transformation. Also, the proposed procedure includes structural design constraints within the control system. A direct optimal control method is also examined to compare it with the proposed method. The limitations and advantages of both methods are discussed in terms of the number of states and inputs. Consequently, linear dynamic system examples are optimized under various constraints and the merits of the proposed method are examined.

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References

Figures

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Fig. 1

A flow chart for the direct optimal control method

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Fig. 2

A flow chart for the proposed method

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Fig. 3

A spring-mass system with 4-states and 1-input

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Fig. 10

Optimum trajectory of the proposed method (j = 5)

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Fig. 9

Optimum trajectory of the direct optimal control method (j = 5)

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Fig. 8

Initial trajectory of 8-states and 2-inputs system

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Fig. 7

A spring-mass system with 8-states and 2-inputs

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Fig. 6

Optimum trajectory of the proposed method (j = 5)

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Fig. 5

Optimum trajectory of the direct optimal control method (j = 5)

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Fig. 4

Initial trajectory of 4-states and 1-input system

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