Global asymptotic stability of input-saturated one degree-of-freedom Euler–Lagrange systems with Rayleigh dissipation under nonlinear control

Javier Moreno-Valenzuela, Jerónimo Moyrón, Mizraim Martinez-Lopez, Marco Jiménez-Quiroz

Research output: Contribution to journalArticlepeer-review

Abstract

In this manuscript, the regulation of one degree-of-freedom Euler–Lagrange systems subject to input saturation is addressed. In particular, the design and analysis of a nonlinear static state feedback controller is presented. As a result, it is proven via Lyapunov's direct method that, in the presence of Rayleigh dissipation, the closed-loop equilibrium point is globally asymptotically stable with a strict Lyapunov function. Since saturation occurs in the system which contains the actuator model, the proposed control law is unconstrained and can be simplified to a proportional-derivative with desired gravity compensation algorithm. As a by-product global asymptotic stability is also proven for the case where Rayleigh dissipation is null. Numerical simulations on a crank-slider mechanism are presented. Moreover, experimental results on a DC-DC buck power converter are also shown and confirm the viability of our approach.

Original languageEnglish
Pages (from-to)2100-2112
Number of pages13
JournalInternational Journal of Control
Volume96
Issue number8
DOIs
StatePublished - 2023
Externally publishedYes

Keywords

  • DC-DC power converters
  • Euler–Lagrange systems
  • global asymptotic stability
  • input saturation
  • real-time experiments
  • strict Lyapunov function

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