Research Papers

Reliable Robust Control Design for Uncertain Mechanical Systems

[+] Author and Article Information
R. Sakthivel

Department of Mathematics,
Sungkyunkwan University,
Suwon 440-746, South Korea
e-mail: krsakthivel@yahoo.com

Srimanta Santra, A. Arunkumar

Department of Mathematics,
Anna University - Regional Centre,
Coimbatore 641 047, India

K. Mathiyalagan

Department of Mathematics,
Anna University - Regional Centre,
Coimbatore 641 047, India
e-mail: kmathimath@gmail.com

1Corresponding authors.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 23, 2013; final manuscript received May 4, 2014; published online September 10, 2014. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(2), 021003 (Sep 10, 2014) (11 pages) Paper No: DS-13-1527; doi: 10.1115/1.4027705 History: Received December 23, 2013; Revised May 04, 2014

In this article, we consider the problem of reliable H control for a class of uncertain mechanical systems with input time-varying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable H controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable while satisfying a prescribed H performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable H controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable H control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible H performance index over some existing works.

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Grahic Jump Location
Fig. 1

Trajectories of system in Example 4.1

Grahic Jump Location
Fig. 2

Trajectories of vehicle suspension system




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