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Research Papers

Four-Bar Mechanism's Proportional-Derivative and Neural Adaptive Control for the Thorax of the Micromechanical Flying Insects

[+] Author and Article Information
Romulus Lungu

Electrical, Energetic, and
Aerospatiale Engineering Department,
University of Craiova,
107 Decebal Street,
Craiova 200440, Romania
e-mail: romulus_lungu@yahoo.com

Lucian Sepcu

Electrical, Energetic, and
Aerospatiale Engineering Department,
University of Craiova,
107 Decebal Street,
Craiova 200440, Romania
e-mail: lsepcu@elth.ucv.ro

Mihai Lungu

Electrical, Energetic, and
Aerospatiale Engineering Department,
University of Craiova,
107 Decebal Street,
Craiova 200440, Romania
e-mail: Lma1312@yahoo.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 21, 2014; final manuscript received July 27, 2014; published online December 10, 2014. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 137(5), 051005 (May 01, 2015) (13 pages) Paper No: DS-14-1032; doi: 10.1115/1.4028793 History: Received January 21, 2014; Revised July 27, 2014; Online December 10, 2014

The paper focuses on the dynamics and control of the nondeformable and deformable four-bar mechanism (three of the bars are mobile and one is fixed), this being a subsystem of the micromechanical flying insects' (MFIs) thorax. The control of the mechanism (six-order system described by Lagrange equations) is initially achieved by using a proportional-derivative (PD) control law, a Newton–Raphson type algorithm, and the Lyapunov theory. Because the thorax's dynamics is strongly nonlinear and is characterized by fast time varying coefficients, the PD control law cannot always guarantee small overshoot and angular rates; to overcome this drawback, over the control law PD component we superpose a neural adaptive component which compensate the error of the global nonlinearity's approximation associated to the thorax's dynamics. The two obtained control systems are validated by complex numerical simulations.

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Figures

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Fig. 1

The four-bar mechanism

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Fig. 2

The mechanical model associated to the mechanism with four elastic bars

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Fig. 3

The neutral and the extreme orientation positions of the mechanism's bars

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Fig. 4

Time histories θ(t), φ(t), ψ(t)

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Fig. 5

Structure of the system for the automatic control of angle θ with PD control law

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Fig. 6

The block diagram, with transfer operators, associated to the system in Fig. 5

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Fig. 7

The adaptive system for the control of the MFI's thorax

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Fig. 8

The characteristics obtained for the system in Fig. 6 for a step type input

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Fig. 9

The characteristics obtained for the system in Fig. 6 for a sinusoidal type input

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Fig. 10

matlab/simulink model of the system in Fig. 7

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Fig. 11

The characteristics obtained for the system in Fig. 7 for a step type input

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Fig. 12

The characteristics obtained for the system in Fig. 7 for a sinusoidal type input

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