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Flexible Manipulator State Reconstruction Using Luenberger and First Order Sliding Mode Observers Under Parametric Uncertainties

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This paper deals with the problem of state reconstruction fora one-link flexible manipulator using Luenberger Observer (LO) and First Order Sliding Mode Observer (FOSMO) under parametric uncertainties.The design techniques and the comparison of the state observers are presented.The mechanical equations of the system are derived using the Lagrangian approach, and the elastic movement is approximated by the assumed modes method for an Euler-Bernoulli beam. The sliding mode observer is derived based on the available outputs, and it is compared to the classical Luenberger one. The simulation results included in the paper evaluate the observers’ ability to reconstruct the state, to lower the error of estimation and to shorten the required time for the error to converge.
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State Reconstruction; Flexible Manipulator; Luenberger Observer; Sliding Mode Observer; Parametric Uncertainties

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S.K. Dwivedy, P. Eberhard, Dynamic analysis of flexible manipulators: a literature review, Mechanism and Machine Theory 41 (7) (2006) 749–777.

M. Mirshekaran, F. Piltan, Z. Esmaeili, T. Khajeaian, M. Kazeminasab, Design Sliding Mode Modified Fuzzy Linear Controller with Application to Flexible Robot Manipulator, International Journal of Modern Education and Computer Science 5 (10) (2013) 53–63.

Al-Khafaji, A., Shaharuddin, N., Mat Darus, I., Modelling of a Flexible Single-Link Manipulator Using Metaheuristic Algorithms, (2014) International Review of Mechanical Engineering (IREME), 8 (6), pp. 1075-1092.

Yatim, H., Mat Darus, I., Intelligent Parametric Identification of Flexible Manipulator System, (2014) International Review of Mechanical Engineering (IREME), 8 (1), pp. 11-21.

Hongjun Yang, Jinkun Liu, Xu Lan, Observer design for a flexible-link manipulator with PDE model, Journal of Sound and Vibration, Volume 341, 14 April 2015, 237-245

M. Mosayebi, M. Ghayour, M. Jafar Sadigh ,A nonlinear high gain observer based input–output control of flexible link manipulator, Mechanics Research Communications, Volume 45, October 2012, 34-41

Ali Tavasoli, Mohammad Eghtesad, Hamed Jafarian, Tw’o-time scale control and observer design for trajectory tracking of two cooperating robot manipulators moving a flexible beam, Robotics and Autonomous Systems, Volume 57, Issue 2, 28 February 2009, 212-221

N.G. Chalhoub, G.A. Kfoury, B.A. Bazzi, Design of robust controllers and a nonlinear observer for the control of a single-link flexible robotic manipulator, Journal of Sound and Vibration, Volume 291, Issues 1–2, 21 March 2006, 437-461

V.Kumar.E,J.Jerome, S.Ayyappan, Comparison of four state observer design algorithms for MIMO system, Archives of control Sciences, Volume 23(LIX), 2013, pp:131-144

Bravo R. Vibration control of flexible structure using smart materials, PhD dissertation. McMaster University, Canada,2000.

Vadim I. Utkin, Sliding Modes in Control and Optimization, Communications and Control Engineering Series (1992).

A. Mohammadi, M. Tavakoli, H.J. Marquez, F. Hashemzadeh , Nonlinear disturbance observer design for robotic manipulators, Control Engineering Practice, Volume 21, Issue 3, March 2013, 253-267

R. Morales, V. Feliu, V. Jaramillo, Position control of very lightweight single-link flexible arms with large payload variations by using disturbance observers, Robotics and Autonomous Systems, Volume 60, Issue 4, April 2012, 532-547

Bakhti, M., Idrissi, B., Highly Nonlinear Flexible Manipulator State Estimation Using the Extended and the Unscented Kalman Filters, (2016) International Review of Automatic Control (IREACO), 9 (3), pp. 151-160.

Nounou, M. N., Nounou, H. N., Mahmoud, M. S. (2007) Robust adaptive sliding-mode control for continuous time-delay systems, IMA J. Math. Control Inform. 24 (3), 299–313.

Chalhoub, Nabil G., and Giscard A. Kfoury.Development of a robust nonlinear observer for a single-link flexible manipulator. ASME 2004 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2004

Choi, S. B., Cheong, C. C., Thompson, B. S., & Gandhi, M. V. Vibration control robust to parameter variations in a very flexible manipulator fabricated from composite laminates. Journal of sound and vibration, 162(2), 195-207.1993.

Shouman, M., El Bayoumi, G., Adaptive Robust Control of Satellite Attitude System, (2015) International Review of Aerospace Engineering (IREASE), 8 (1), pp. 35-42.

Moujahed, M., Ben Azza, H., Jemli, M., Boussak, M., Speed Estimation by Using EKF Techniques for Sensor-Less DTC of PMSM with Load Torque Observer, (2014) International Review of Electrical Engineering (IREE), 9 (2), pp. 270-279.

Benbouzid, M., Beltran, B., Amirat, Y., Breton, S., Sensorless Control of Doubly-Fed Induction Generator-Based Wind Turbines Using a High-Order Sliding Mode Observer, (2014) International Review of Electrical Engineering (IREE), 9 (1), pp. 49-55.


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