Parameter Selection for the Virtual Oscillator Control Applied to Microgrids

Virtual Oscillator Control (VOC) is a promising technique that allows several inverters connected to a microgrid to naturally synchronize, without communication. However, the selection of the VOC parameters often require iterative or optimization procedures that render its practical use not straightforward. In this paper, this problem is overcome with the proposition of a novel methodology for determining the dead-zone type VOC parameters based on the describing function method. The methodology consists of a set of analytical equations that use as input data few basic electrical system parameters from the converter and from the microgrid, namely, the operating voltage and frequency ranges, besides rated power. The proposed set of equations is used to calculate the parameters required to control an inverter in voltage mode. The validity of the proposed approach is demonstrated in experiments that encompass different situations such as pre-synchronization, connection, and disconnection of a second inverter from a microgrid.

The estimation of aircraft control system stability boundaries by the describing function method

In this paper, the conditions for periodic modes formation in the closed-loop pilot-vehicle system in the compensatory control mode are established. The case of high gain pilot task is considered under the conditions of a sudden disturbance, as well as under the influence of the system nonlinearities, such as actuator position and rate limit. Sinusoidal input describing function method and parametric resonance equation were used to determine the onset conditions for self-oscillations and forced oscillations. The case when this methods lead to erroneous results is established. The numerical limits of permissible pilot gain, time delay and reference signal at which unstable periodic modes do not arise are calculated.

Dynamics Analysis on Planar Articulated Trusses Considering Cubic Nonlinearity of Joints

A large number of joints that make possible the smooth deployment of an articulated truss may lead to the unexpected variation of the whole dynamic characteristics of the truss. In this paper, attention is focused on exploring the joint characteristics and their effects not strictly following the conventional linear assumption. Particularly, the effects of cubic nonlinear characteristics of joints on the dynamic behavior of articulated trusses are investigated. First, the equivalent dynamic model of the truss cell in the frequency domain is developed for enhancing the computational efficiency. With the employment of the describing function method (DFM), the frequency responses of the planar articulated truss considering the cubic nonlinearity of joints are obtained analytically. Moreover, the transient responses of the articulated truss under external shock loads are obtained numerically. Subsequently, the variations in frequency obtained by the fast Fourier transformation (FFT) of the numerical results show consistent tendency compared with those obtained by the equivalent dynamic model of the planar articulated truss. Finally, several conclusions are presented at the end.

Chattering of proxy-based sliding mode control in the presence of parasitic dynamics

This paper reports an analysis on proxy-based sliding mode control (PSMC), which is a controller proposed by Kikuuwe & Fujimoto (2006, Proceedings of the 2006 IEEE International Conference on Robotics and Automation, pp. 25–30) originally for position control of robot manipulators. The describing function method is employed to investigate the chattering behavior of PSMC combined with a simple second-order plant with parasitic dynamics. The results show that PSMC is capable of achieving a lower tendency to chattering than the boundary-layer implementation of sliding mode control with the same sliding surface, without affecting the insensitivity to disturbance.