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Fault detection based on Lyapunov exponents estimation for stabilized mechanical systems

Puzyrov Volodymyr, Acho Leonardo, Pujol Gisela, Rodellar José

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 2

519--531

We study a stabilizable mechanical system in the vicinity of an equilibrium position. This position, as a rule, is unstable, and the system is underactuated. It is assumed that faults affect the technical process and its control. We suggest a fault diagnosis technique based on estimation of Lyapunov characteristic exponents of measured variables. A model of a linear switching system is involved for the system with faults description, and a common quadratic Lyapunov function is used to evaluate the deviation of the maximum exponent with respect to the default system. A scheme of fault magnitude estimation is suggested related to the degree of this deviation. An example of a 2-degree of freedom system is presented to illustrate the procedure.