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Research Papers

Adaptive Control for Fractional-Order Micro-Electro-Mechanical Resonator With Nonsymmetric Dead-Zone Input

[+] Author and Article Information
Xiaomin Tian

Key Laboratory of Measurement
and Control of CSE,
School of Automation,
Ministry of Education,
Southeast University,
Nanjing 210096, China
e-mail: tianxiaomin100@163.com

Shumin Fei

Key Laboratory of Measurement
and Control of CSE,
School of Automation,
Ministry of Education,
Southeast University,
Nanjing 210096, China
e-mail: smfei@seu.edu.cn

1Corresponding author.

Manuscript received October 6, 2014; final manuscript received January 3, 2015; published online June 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(6), 061022 (Nov 01, 2015) (6 pages) Paper No: CND-14-1238; doi: 10.1115/1.4029604 History: Received October 06, 2014; Revised January 03, 2015; Online June 09, 2015

This paper deals with the adaptive control of fractional-order micro-electro-mechanical resonator system (FOMEMRS) with nonsymmetric dead-zone nonlinear input. The slope parameters of the dead-zone nonlinearity are unmeasured and the parameters of the controlled systems are assumed to be unknown in advance. To deal with these unknown parameters, some fractional versions of parametric update laws are proposed. On the basis of the frequency distributed model of fractional integrator and Lyapunov stability theory, a robust control law is designed to prove the stability of the closed-loop system. The proposed adaptive approach requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. Finally, simulation examples are given to verify the robustness and effectiveness of the proposed control scheme.

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Figures

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Fig. 1

A schematic picture of MEMRS

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Fig. 2

The strange attractors of system (7) with different q: (a) q = 54, (b) q = 0.7, (c) q = 0.8, and (d) q = 0.9

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Fig. 3

Nonsymmetric dead-zone nonlinearity

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Fig. 4

The state trajectories of system (8) with q = 0.54

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Fig. 5

The time evolutions of estimated parameters in system (8)

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Fig. 6

The state trajectories of system (8) with different q: (a) q = 0.7, (b) q = 0.8, and (c) q = 0.9

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