On the robustness of the Slotine-Li and the FPT/SVD-based adaptive controllers

J. Tar, I. Rudas, G. Hermann, J. F. Bitó, J. A. Tenreiro Machado

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes.

Original languageEnglish
Pages (from-to)686-700
Number of pages15
JournalWSEAS Transactions on Systems and Control
Volume3
Issue number8
Publication statusPublished - Aug 2008

Fingerprint

Singular value decomposition
Fixed point
Robustness
Controller
Controllers
Rough
Friction
Disturbance
Unknown
Simulation
Approximate Model
Imprecision
Internal friction
Axles
Dynamical Model
Pendulum
Pendulums
Robustness (control systems)
Mechanical Systems
Analytical Model

Keywords

  • Adaptive control
  • Complete stability
  • Fixed point transformation
  • Lyapunov function
  • Robustness analysis
  • Singular value decomposition
  • Sliding mode/variable Structure Controllers
  • Slotine-Li robot control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Artificial Intelligence
  • Mathematics(all)

Cite this

On the robustness of the Slotine-Li and the FPT/SVD-based adaptive controllers. / Tar, J.; Rudas, I.; Hermann, G.; Bitó, J. F.; Tenreiro Machado, J. A.

In: WSEAS Transactions on Systems and Control, Vol. 3, No. 8, 08.2008, p. 686-700.

Research output: Contribution to journalArticle

Tar, J. ; Rudas, I. ; Hermann, G. ; Bitó, J. F. ; Tenreiro Machado, J. A. / On the robustness of the Slotine-Li and the FPT/SVD-based adaptive controllers. In: WSEAS Transactions on Systems and Control. 2008 ; Vol. 3, No. 8. pp. 686-700.
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