Nonlinear state observer for estimating and controlling of friction-induced vibrations

Abstract This paper focuses on the nonlinear estimating of friction-induced vibrations (FIV) related to the mode-coupling mechanism. This task is a key step for implementing control laws when FIV are required to be mitigated. Then, this study proposes nonlinear state observers based on the gradient descent method. Two types are investigated: the first one is the gradient descent nonlinear observer (GDNLO) which gives estimations of vibrations by minimizing the gradient of the error between the system and observer outputs, while the second, called the modified GDNLO, gives estimations by minimizing the gradient of the errors between the high order derivatives of the system and observer outputs. Performances of both observers are analysed by considering the properties of their convergences when used for the estimation of the mode-coupling based vibrations and when used for controlling the vibrations via linearizing and stabilizing feedbacks. Based on numerical simulations, the modified GDNLO has shown better and more suitable convergence properties than the GDNLO. High accuracy levels are obtained for the estimated vibrations. Moreover, this accuracy is kept when the modified GDNLO is inserted in a control loop for the mitigating of the FIV.

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