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

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.

KEYWORDS:

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

Acknowledgments

The authors would like to thank the editors and anonymous reviewers for providing insightful suggestions and comments to improve the quality of research paper.

Additional information

Funding

This work was supported in part by the Consejo Nacional de Ciencia y Tecnología, CONACYT–Fondo Sectorial de Investigación para la Educación under project A1-S-24762, and in part by Secretaría de Investigación y Posgrado-Instituto Politécnico Nacional, México. Proyecto Apoyado por el Fondo Sectorial de Investigación para la Educación.