Gain Calculation of 0-Degree Homogeneous Controllers

https://doi.org/10.58571/CNCA.AMCA.2023.013

Resumen: This paper presents sets of gains for the nested discontinuous controller family. The methodology for obtaining gains is based on a control Lyapunov function, this function determines the conditions for the value of each of the controller gains, the last gain being the one that is directly related to the boundaries of the disturbances and uncertainties. In this way the algorithm for obtaining gains can be summarized in three steps. The first step concerns about establishing the value of the weight vector, the degrees of homogeneity of the r-homogeneous functions that make up the proposed Lyapunov function. The second step consists of establishing the value of the first gain, which, for second and higher order controllers, is sufficient for it to be real positive. The third step is to determine the maximum value of an objective function. Moreover, it allows us to obtain the lower bound of the set of values for the gain that stabilize the system. The results show that the set of gains obtained stabilize the closed-loop system.

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Iglesias Rios, Matias; Fridman, Leonid M.; Moreno, Jaime A. Gain Calculation of 0-Degree Homogeneous Controllers. Memorias del Congreso Nacional de Control Automático, pp. 80-85, 2023. https://doi.org/10.58571/CNCA.AMCA.2023.013

Palabras clave

Control Discontinuo (modos deslizantes); Control de Sistemas No Lineales

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