[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Fractional-order State Observers for Integer-order Linear Systems

Journal of Applied Nonlinear Dynamics 6(2) (2017) 251--264 | DOI:10.5890/JAND.2017.06.010

Carolina Pacheco$^{1}$,$^{2}$ , Manuel A. Duarte-Mermoud$^{1}$,$^{2}$, Norelys Aguila-Camacho$^{1}$,$^{2}$ , Rafael Castro-Linares$^{3}$

$^{1}$ Electrical Engineering Department, University of Chile, Av. Tupper 2007, Santiago, Chile

$^{2}$ Advanced Mining Technology Center (AMTC), University of Chile, Av. Tupper 2007, Santiago, Chile

$^{3}$ Electrical Engineering Department, Mechatronics Section, CINVESTAV, Av. IPN 25018, México D.F., México

Download Full Text PDF

 

Abstract

To perform a robot-assisted surgery of a prosthesis implantation on a patient’s femur, we may need to get the femoral head-neck orientation for the application. We can extract that information from Computed Tomography scans, using image processing. In image processing, edge detection often makes use of integer-order differentiation operators (e.g. Canny and LoG operators). This paper shows that introducing non-integer (fractional) differentiation to edge detectors (Fractional Canny, Fractional LoG, Fractional Derivative operators) can improve automatic edge detection results

Acknowledgments

This work has been supported by CONICYT- Chile, under the grants FB0809 Advanced Mining Technology Center, FONDECYT Regular 1120453 Improvements of Adaptive Systems Performance by using Fractional Order Observers and Particle Swarm Optimization, FONDECYT Regular 1150488 Fractional Error Models in Adaptive Control and Applications and FONDECYT 3150007 Postdoctoral Program 2015.

References

  1. [1]  Kalman, R.E. (1960), A New Approach to Linear Filtering and Prediction Problems, Transactions of the ASME, Journal of basic Engineering, 82(1), 35–45.
  2. [2]  Luenberger, D. (1964), Observing the State of a Linear System,Military Electronics, IEEE Transactions on, 8(2), 74–80.
  3. [3]  Duarte-Mermoud, M. and La Rosa, P. (2003), Designing SISO observers with unknown inputs,IMA Journal of Mathematical Control and Information, 20(4), 387–391.
  4. [4]  Banks, S.P. (1981), A Note on Non-linear Observers,International Journal of Control, 34(1) 185-190.
  5. [5]  Braiek, E. and Rotella, F. (1994), State Observer Design for Analytical Non-linear Systems, Systems, Man, and Cybernetics, 1994. Humans, Information and Technology, 1994 IEEE International Conference on, Vol.3, 2045-2050.
  6. [6]  Luders, G. and Narendra, K.S. (1973), An Adaptive Observer and Identifier for a Linear System, Automatic Control, IEEE Transactions on , 18(5) 496-499.
  7. [7]  Carroll, R.L. and Lindorff, D. (1973), An Adaptive Observer for Single-Input Single-Output Linear Systems, Automatic Control, IEEE Transactions on, 18(5), 428-435.
  8. [8]  Dadras, S. andMomen, H. (2011), Fractional Sliding Mode Observer Design for a Class of Uncertain Fractional Order Nonlinear Systems, Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on, 6925-6930.
  9. [9]  Dadras, S. and Momeni, H. (2011), A New Fractional Order Observer Design for Fractional Order Non- linear Systems,International Design Engineering Technical Conferences and Computers and Information in Engineering, ASME 2011, 403-408.
  10. [10]  Martínez-Martínez, R., Mata-Machuca, J., Martínez-Guerra, R., León, J., and Fernández-Anaya, G. (2011), A New Observer for Nonlinear Fractional Order Systems, Decision and Control and European Control Con- ference (CDC-ECC), 2011 50th IEEE Conference on, 3319-3324.
  11. [11]  N′Doye, I., Voos, H., Darouach, M., Schneider, J., and Knauf, N. (2012), An Unknown Input Fractional- Order Observer Design for Fractional-Order Glucose-Insulin System, Biomedical Engineering and Sci- ences(IECBES), 2012 IEEE EMBS Conference on, 595-600.
  12. [12]  Matignon, D. (1996), Stability Results for Fractional Differential Equations with Applications to Control Processing, CESA 96 IMACS Multiconference: computational engineering in systems applications, 963-968.
  13. [13]  Matignon, D. and D′Andrea-Novel, B.(1996), Some Results on Controllability and Observability of Finite- Dimensional Fractional Differential Systems, CESA 96 IMACS Multiconference: computational engineering in systems applications, 952-956.
  14. [14]  Cruz-Victoria, J., Martínez-Guerra, R., Pérez-Pinacho, C., and Gómez-Cortés, G. (2015), Synchronization of nonlinear fractional order systems by means of PIra reduced order observer, Applied Mathematics and Computation, 262224-231.
  15. [15]  Martínez-Guerra, R., Pérez-Pinacho, C., Gómez-Cortés, G., and Cruz-Victoria, J. (2015), Synchronization of incommensurate fractional order system, Applied Mathematics and Computation, 262260-266.
  16. [16]  Aguila-Camacho, N. and Duarte-Mermoud, M.A. (2013), Fractional Adaptive Control for an Automatic Voltage Regulator, ISA Transactions, 52(6), 807–815.
  17. [17]  Duarte-Mermoud, M.A., Aguila-Camacho, N. and Castro-Linares, R.(2015), Fractional order control of the Thomson ring magnetic levitation system, Advances in Electrical and Computer Engineering. Proceedings of the 6th NAUN International Conference on Circuits, Systems, Control and Signals (CSCS 15), 340-48.
  18. [18]  Cafagna, D. (2007), Fractional Calculus: AMathematical Tool From the Past for Present Engineers, Industrial Electronics Magazine, IEEE, 1(2), 35-40.
  19. [19]  Kilbas, A., Srivastava, H., and Trujillo, J. (2006), Theory and Applications of Fractional Differential Equa- tions, Elsevier, .
  20. [20]  Podlubny, I. (1998), Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Mathematics in Science and Engineering, Elsevier Science.
  21. [21]  Chen, J., Lundberg, K., Davison D., and Bernstein, D. (2007) , The Final Value Theorem Revisited - Infinite Limits and Irrational Functions, Control Systems, IEEE, 27(3), 97-99.
  22. [22]  Luenberger, D. (1971), An Introduction to Observers, Automatic Control, IEEE Transactions on, 16(6), 596-602.
  23. [23]  Chen, C.T. (1995), Linear System Theory and Design, Oxford University Press, 2nd Edition.
  24. [24]  Pacheco, C. (2014), Análisis de observadores fraccionarios de estado en sistemas dinámicos lineales, Electrical Engineering Undergraduate Thesis, Universidad de Chile, Chile.
  25. [25]  Valério, D. (2005), Ninteger v.2.3: Fractional Control Toolbox for Matlab, Universidade Técnica de Lisboa.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates