An underactuated two-dimensional translational oscillator with rotational actuator (2DTORA) consisting of an actuated rotational proof-mass and two unactuated translational carts is presented. Passivity-based control design is employed for 2DTORA based on its Euler–Lagrange structure and passivity property. Firstly, the dynamics of 2DTORA are derived based on Euler–Lagrange equations. Motivated by constructing a damped close-loop Euler–Lagrange system, the controller dynamics is designed to shape the potential energy and inject the required damping. As a result, the designed controller stabilizes the underactuated 2DTORA with the feedback of the rotational actuator’s position only. Moreover, by modifying controller dynamics with a saturation function, the control input can be constrained to certain bounds. Finally, simulation results demonstrate the feasibility and effectiveness of the proposed controllers.
Most of the disturbance in the power system is nonlinear and no-stationary. Hilbert-Huang transform (HHT) is an efficient time-frequency analysis method which can detect different kinds of power quality disturbance. HHT consists of empirical-mode decomposition (EMD) and Hilbert transform (HT). EMD can self-adjust according to the characteristics of the signal itself, and decompose the signal into IMFs, so that the disturbance can be separated and studied. Ensemble empirical mode decomposition (EEMD), which improved the performance of EMD, overcomes the mode mixing phenomena which restrain the usage of EMD. This paper did a contrast study on power quality detection using EMD and EEMD. It is concluded that EEMD has better effect on detecting some of power quality disturbances.
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