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This paper pursues the construction of a valid strong Lyapunov function for second-order sliding mode algorithms, usually employed for control, observation, and differentiation purposes. The developed solution is based on combining convex representations of such algorithms with the direct Lyapunov method, which leads to stability conditions expressed in the form of linear matrix inequalities. The proposed methodology enlarges the set of gains for which the algorithms are guaranteed stable in prior literature.

Se realizó el diseño y análisis por el Método del Elemento Finito (MEF) en Ls -Dyna de un herramental didáctico para el engargolado por rodillo conducido de láminas metálicas, la propuesta de diseño para satisfacer la necesidad considera seis elementos: base de apoyo, celda de carga, resorte, soporte principal, porta rodillos y elementos rodantes, el análisis por elemento finito se enfoca en los porta rodillos tanto del pre - engargolado como del engargolado final, considerando dos configuraciones de material acero – acero, acero - aluminio, a fin de determinar la combinación con mayor eficiencia en el proceso de engargolado y la calidad de producto final.

This paper deals with the design of robust regulation for both angular speed stability enhancement and voltage in synchronous generator machines with an excitation control system. The designed controller is based on the block control technique combined with a sliding-mode (SM) control approach. The block control is used to design a nonlinear sliding manifold with the desired stability property. In order to attenuate the chattering effect which can appear in the presence of the exciter's unmodeled dynamics, a high-order SM algorithm and a robust exact differentiator are employed. The efficiency of the proposed controller, i.e., robustness and high accuracy, is verified via simulations.

In this paper, a control strategy is proposed for robust stabilization of nonlinear perturbed plants in the presence of actuator unmodeled dynamics. The block control technique is applied to design a nonlinear SM manifold for achieving the error tracking, and High Order Sliding Mode (HOSM) algorithm is implemented to ensure finite time convergence of the state vector to the designed SM manifold. A robust exact differentiator is designed to obtain the estimates of the sliding variable and its derivatives. The proposed method is applied to design robust controllers for a power electric system in the presence of the exciter system unmodeled dynamics.