American Journal of Mechanical Engineering
ISSN (Print): 2328-4102 ISSN (Online): 2328-4110 Website: http://www.sciepub.com/journal/ajme Editor-in-chief: Kambiz Ebrahimi, Dr. SRINIVASA VENKATESHAPPA CHIKKOL
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American Journal of Mechanical Engineering. 2017, 5(6), 298-302
DOI: 10.12691/ajme-5-6-13
Open AccessArticle

Input-state Linearization of Mechanical System

Tomáš Lipták1, , Michal Kelemen1, Alexander Gmiterko1, Ivan Virgala1 and Darina Hroncová1

1Department of Mechatronics, Faculty of Mechanical Engineering, Technical University of Košice, Košice, Slovakia

Pub. Date: December 15, 2017

Cite this paper:
Tomáš Lipták, Michal Kelemen, Alexander Gmiterko, Ivan Virgala and Darina Hroncová. Input-state Linearization of Mechanical System. American Journal of Mechanical Engineering. 2017; 5(6):298-302. doi: 10.12691/ajme-5-6-13

Abstract

The article deals with the issue of input-state linearization of the mechanical systems. The introductory part of article contains theory about exact linearization that we used. Further we explained the basic principle and procedure of input-state linearization. Then it contains the determination of state space for mechanical systems, the computing of vector fields, the investigation of controllability and involutivity of the systems and the calculation of input and state transformation.

Keywords:
input-state linearization state space vector field Lie bracket mechanical system with one degree of freedom one-link manipulator

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References:

[1]  J. J. Slotine and L. Weiping, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, USA, 1991.
 
[2]  LAMBERT, J. D.: Numerical Methods for Ordinary Differential Systems, John Wiley & Sons, Chichester, 1991.
 
[3]  QUARTERONI, A.-SACCO, R.-SALERI, F.: Numerical Mathematics, Springer-Verlag, New York, 2000.
 
[4]  ATKINSON, K.-HAN, W.-STEWART, D.: Numerical Solution of Ordinary Differential Equations, John Wiley & Sons, Inc., Hoboken, New Jersey, 2009.
 
[5]  NAJM, F. N.: Circuit Simulation, John Wiley & Sons, Inc., Hoboken, 2010.
 
[6]  BROCKETT, R. W.: Nonlinear Systems and Differential Geometry, Proc. Of IEEE 64 No. 1 (1976), 61-71.
 
[7]  JAKUBCZYK, B.-RESPONDEK, W.: On Linearization of Control Systems, Bull. Acad. Polonaise, Sci., Ser. Sci. Math. 28 (1980), 517-522.
 
[8]  BYRNES, C. I.-ISIDORI, A.: Local Stabilization of Minimum Phase Nonlinear Systems, Syst. Control Lett. 11 (1988), 9-19.
 
[9]  J. Bronislaw, “Introduction to geometric nonlinear control; controllability and lie bracket,” in Mathematical Control Theory, Lectures Notes of a Minicourse, pp. 107-168, Abdus Salam International Center Theoret Physics, Trieste, Italy, 2002.
 
[10]  A. J. Krener, “Approximate linearization by state feedback and coordinate change,” Systems & Control Letters, vol. 5, no. 3, pp. 181-185, 1984.
 
[11]  S. Renou and S. Saydy, “Real time control of an inverted pendulum based on approximate linearization,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering (CCECE ’96), vol. 2, pp. 502-504, May 1996.
 
[12]  N. Bedrossian, Nonlinear control using linearizing transformations, Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass, USA, 1991.
 
[13]  N. S. Bedrossian, “Approximate feedback linearization: The cart-pole example,” in Proceedings of the IEEE International Conference on Robotics and Automation, vol. 3, pp. 1987-1992, 1992.
 
[14]  J. Deutscher and C. Schmid, “A state space embedding approach to approximate feedback linearization of single input nonlinear control systems,” International Journal of Robust and Nonlinear Control, vol. 16, no. 9, pp. 421-440, 2006.
 
[15]  L. Guzzella and A. Isidori, “On approximate linearization of nonlinear control systems,” International Journal of Robust & Nonlinear Control, vol. 3, no. 3, pp. 261-276, 1993.