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Research Papers

Global Finite Time Stabilization of a Class of Uncertain MIMO Nonlinear Systems

[+] Author and Article Information
Ali Abooee, Masoud Moravej-Khorasani

Advanced Control Systems Laboratory,
Sharif University of Technology,
Tehran 11155-4363, Iran

Mohammad Haeri

Advanced Control Systems Laboratory,
Sharif University of Technology,
Tehran 11155-4363, Iran
e-mail: haeri@sina.sharif.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 24, 2015; final manuscript received November 20, 2015; published online December 23, 2015. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 138(2), 021007 (Dec 23, 2015) (9 pages) Paper No: DS-15-1128; doi: 10.1115/1.4032065 History: Received March 24, 2015; Revised November 20, 2015

It is aimed to obtain global finite time stabilization of a class of uncertain multi-input–multi-output (MIMO) nonlinear systems in the presence of bounded disturbances by applying nonsingular terminal sliding mode controllers. The considered nonlinear systems consist of double integrator subsystems which interact with each other. In the proposed methods, new terminal sliding surfaces are introduced along with design of proper control inputs. The terminal sliding surfaces are defined such that the global finite time stability of sliding mode dynamic is attained. The control inputs are designed to steer the states into sliding motion within finite time and retain them on the terminal sliding surfaces. The presented approaches guarantee the finite time convergence of states with low sensitivity to their initial values. The convergence rate could be adjusted by proper choice of existing arbitrary parameters in the suggested control schemes. Three numerical simulation examples including van de Pol system and two robotic manipulators are provided to confirm the applicability and effectiveness of the proposed control schemes.

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Figures

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Fig. 3

A simple conceptual schematic of two-link rigid robot manipulator [35]

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Fig. 1

Time responses of x1 and x2 by applying control inputs (34) and (36)

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Fig. 4

Time responses of x1=q1 and x3=q2  using control inputs (42) and (43)

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Fig. 5

Time variations of torques applied to joints of robot: (a) using control input (42) and (b) using control input (43)

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Fig. 6

Time responses of x1=q1 and x3=q2 using control inputs (47) and (48)

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Fig. 7

Time variations of torques applied to the prismatic manipulator: (a) using control input (47) and (b) using control input (48)

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