This paper considers the finite-time stabilisation for a class of high-order nonlinear systems with both low-order and high-order nonlinearities. Based on the finite-time Lyapunov stability theorem together with the methods of dynamic gain control and adding one power integrator, a state feedback controller with gains being tuned online by two dynamic equations is proposed to guarantee the global finite-time stabilisation of the closed-loop system.

A cart-pendulum system is a typical underactuated mechanical system with two degrees of freedom and one control input. The fixed-time stabilization control problem for this system is studied in this paper. A fixed-time hierarchical sliding mode control method is developed to solve this problem. Firstly, the system is divided into two subsystems. And two first-level sliding mode surfaces are designed for these two subsystems respectively. Secondly, a second-level sliding mode surface is constructed by linearly combining two first-level sliding mode surfaces. After that, a hierarchical sliding mode controller is designed based on the designed sliding mode surfaces. It enables the state variables of closed-loop control system to be stabilized at the origin within a fixed-time. This means that the settling time can be limited within a range and does not depend on the initial state value of the system. Finally, a numerical example is given to show the effectiveness of the developed control method.

The wear fault is one of the gear failure modes which most frequently happen in gearboxes. Tracking the development of wear, especially estimating the remaining usage life for early wear is a challenge in gearbox fault diagnosis and prognosis. A method to extract the feature of gearbox's signal is proposed and the remaining usage life is evaluated in this paper. The total life vibration signal of experimental study is taken as the research basis. Extracting features from vibration signals is carried out by Time-Frequency analysis. The rule of gear wear progression is studied using the vibration signal feature. The remaining usage life estimate is implemented by Hidden semi-Markov model. Through the total life test of gearbox, the feasibility and effectiveness of this method is verified.

This paper considers the output feedback finite-time stabilization in probability for a class of large-scale high-order stochastic nonlinear feedforward systems. The output feedback finite-time stabilized controller in probability is firstly designed for the nominal systems by the adding one power integrator. Then with the homogeneous domination method, by introducing an appropriate coordination, an equivalent system of the original system with tunable gain is obtained. After that, by constructing a observer and determining the tunable gains, the output feedback stabilized controller in probability of the original systems is finally given and analysed.

Bearing failure is one of the most important causes of breakdown of rotating machinery. These failures can lead to catastrophic disasters or result in costly downtime. One of the key problems in bearing fault diagnosis is to detect the bearing fault as early as possible. This capability enables the operator to have enough time to do some preventive maintenance. Most papers investigate the bearing faults under rational assumption that bearings work individually. However, bearings are usually working as a part of complex systems like a gearbox. The fault signal of bearings can be easily masked by other vibration generated from gears and shafts. The proposed method separates bearing signals from other signals, and then the optimum frequency band which the bearing fault signal is prominent is determined by mean envelope Kurtosis. Subsequently, the envelope analysis is used to detect the bearing faults. Finally, two bearing fault experiments are used to validate the proposed method. Each experiment contains two bearing fault modes, inner race fault and outer race fault. The results demonstrate that the proposed method can detect the bearing fault easier than spectral Kurtosis and envelope Kurtosis.