This paper proposes a controller-observer strategy for a class of second-order uncertain nonlinear systems with only available position measurement. The third-order sliding mode observer is first introduced to estimate both velocities and the lumped uncertain terms of system with high accuracy, less chattering, and finite time convergency of estimation errors. Then, the proposed controller-observer strategy is designed based on non-singular fast terminal sliding mode sliding control and proposed observer. Thanks to this combination, the proposed strategy has some superior properties such as high tracking accuracy, chattering phenomenon reduction, robustness against the effects of the lumped uncertain terms, velocity measurement elimination, finite time convergence, and faster reaching sliding motion. Especially, two period times, before and after the convergence of the velocity estimation takes place, are considered. The finite time stability of proposed controller-observer method is proved by using the Lyapunov stability theory. Final, the proposed strategy is applied to robot manipulator system and its effectiveness is verified by simulation results, in which a PUMA560 robot manipulator is employed. INDEX TERMS Uncertain nonlinear systems, non-singular fast terminal sliding mode control, third-order sliding mode observer, controller-observer strategy, uncertainty compensation, robot manipulators.

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Feature extraction from a signal is the most important step in signal-based fault diagnosis. Deep learning or deep neural network (DNN) is an effective method to extract features from signals. In this paper, a novel vibration signal-based bearing fault diagnosis method using DNN is proposed. First, the measured vibration signals are transformed into a new data form called multiple-domain image-representation. By this transformation, the task of signal-based fault diagnosis is transferred into the task of image classification. After that, a DNN with a multi-branch structure is proposed to handle the multiple-domain image representation data. The multi-branch structure of the proposed DNN helps to extract features in multiple domains simultaneously, and to lead to better feature extraction. Better feature extraction leads to a better performance of fault diagnosis. The effectiveness of the proposed method was verified via the experiments conducted with actual bearing fault signals and its comparisons with well-established published methods.

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