Fault detection based on Lyapunov exponents estimation for stabilized mechanical systems

We study the stabilizable mechanical system in the vicinity of an equilibrium position. This position, as a rule, is unstable, and a 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 linear switching system is involved for system with faults description, and common quadratic Lyapunov function is used to evaluate the deviation of maximal exponent value with respect to default system. The scheme of the 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.