Modeling, Model Reduction, and Control of a Hands-Free Two-Wheeled Self-Balancing Scooter

Designing a two-wheeled self-balancing scooter involves in the synergistic approach of multidisciplinary engineering fields with mutual relationships of power transmission, mass transmission, and information transmission. The scooter consists of several subsystems and forms a large-scale system. The mathematical models are in the complex algebraic and differential equations in the form of high dimension. The complexity of its controller renders difficulties in its realization due to the limit of iteration period of real time control. Routh model reduction technique is employed to convert the original high-dimensional mathematical model into a simplified lower dimensional form. The modeling is derived using a unified variational method for both mechanical and electrical subsystems of the scooter, and for the electronic components equivalent circuit method is adopted. Simulations of the system response are based on the reduced model and its control design. A prototype is developed and realized with Matlab-Labview simulation and control environment.

Rolling element bearing weak feature extraction based on improved optimal frequency band determination

Conventional Kurtosis method represents the statistical property of signal in the time domain. Correlated Kurtosis is proposed that combines the correlation coefficient and Kurtosis in order to indicate the periodicity and impact of signal. In this study, correlated Kurtosis is introduced into frequency domain to improve the recognition accuracy of the optimal frequency band. It does not perform well under the lower signal-to-noise ratio. And then, maximum correlation Kurtosis de-convolution method is used for extracting the approximate impact signal before selecting the optimal frequency band. However, it is limited in diagnosing rolling element bearing fault in the case of the algorithm iteration period is unknown. In addition, filter length also affects the filtering results. To eliminate the confusion, correlated Kurtosis of the frequency domain is applied to iteration period calculation. In this research, a new index is also proposed based on entropy and correlated Kurtosis to optimize the filter length. Then, the full bandwidth of filtered signal is partitioned into several sub-bands according to the refined wavelet packet binary tree. The correlated Kurtosis for each sub-band is calculated. The optimal sub-band for which the correlated Kurtosis is maximal is extracted to analysis. In the end, the efficiency of the new index and the fault diagnosis method are verified by using simulation data and experimental data.