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Research Papers

Robust Stochastic Sampled-Data H Control for a Class of Mechanical Systems With Uncertainties

[+] Author and Article Information
S. Dharani

Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: sdharanimails@gmail.com

R. Rakkiyappan

Department of Mathematics,
Bharathiar University,
Coimbatore 641046, Tamil Nadu, India
e-mail: rakkigru@gmail.com

Jinde Cao

Department of Mathematics and
Research Center for Complex Systems and
Network Sciences,
Southeast University,
Nanjing 210096, Jiangsu, China;
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: jdcao@seu.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 15, 2014; final manuscript received June 5, 2015; published online July 21, 2015. Assoc. Editor: Umesh Vaidya.

J. Dyn. Sys., Meas., Control 137(10), 101008 (Jul 21, 2015) Paper No: DS-14-1333; doi: 10.1115/1.4030800 History: Received August 15, 2014

This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical results.

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Figures

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Fig. 5

State trajectories of displacement and velocity of controlled mechanical system with randomly occurring uncertainties

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Fig. 6

State trajectories of displacement and velocity of uncontrolled mechanical system with randomly occurring uncertainties

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Fig. 7

Stochastic parameter h of Example 1

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Fig. 8

Stochastic parameter h of Example 2

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Fig. 9

Time evolutions of δ(t) ; δ(t) switch from values 0 and 1 according to their expectations in Example 3

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Fig. 1

State trajectories of displacement and velocity of controlled nominal system

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Fig. 2

State trajectories of displacement and velocity of open-loop nominal system

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Fig. 3

State trajectories of displacement and velocity of closed-loop uncertain system

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Fig. 4

State trajectories of displacement and velocity of uncontrolled uncertain system

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