Describing function

About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.

A Describing Function based method for predicting the stability of higher-order high-pass Σ-Δ modulators

Abstract: This paper presents the stability analysis for higher-order single-loop high-pass Σ-Δ modulators based on a combination of the Describing Function (DF) method and the quasi-linear modeling of the quantizer. Closed form mathematical expressions are derived for the stability curves for different quantizer gain values. The stability prediction for the maximum stable input limits for third-, fourth-, and fifth-order Type-II-Chebyshev-based high-pass Σ-Δ modulators are established. The theoretical results are shown to be in good agreement with the simulation results for different sinusoidal input amplitudes. The proposed mathematical models of the quantizer will immensely help in speeding up the design of higher order high-pass Σ-Δ modulators.

Tuning of CgLp based reset controllers: Application in precision positioning systems

Abstract: This paper presents the tuning of a reset-based element called "Constant in gain and Lead in phase" (CgLp) in order to achieve desired precision performance in tracking and steady state. CgLp has been recently introduced to overcome the inherent linear control limitation - the waterbed effect. The analysis of reset controllers including ones based on CgLp is mainly carried out in the frequency domain using describing function with the assumption that the relatively large magnitude of the first harmonic provides a good approximation. While this is true for several cases, the existence of higher-order harmonics in the output of these elements complicates their analysis and tuning in the control design process for high precision motion applications, where they cannot be neglected. While some numerical observation-based approaches have been considered in literature for the tuning of CgLp elements, a systematic approach based on the analysis of higher-order harmonics is found to be lacking. This paper analyzes the CgLp behaviour from the perspective of first as well as higher-order harmonics and presents simple relations between the tuning parameters and the gain-phase behaviour of all the harmonics, which can be used for better tuning of these elements. The presented relations are used for tuning a controller for a high-precision positioning stage and results used for validation.

Direct Design Approach for Virtual Oscillator Control Synchronisation Condition & Parameter Selection using Describing Functions

Abstract: Virtual Oscillator Controls (VOCs) allow inverters to self-synchronise and form robust and stable microgrids. The existing design methodology requires an iterative tuning of key design parameters with time domain simulations required at each step. This paper presents an improved design methodology based on a per unit approach, Describing Functions (DFs) and control systems stability concepts. Direct calculation of key VOC parameters are derived, and this methodology is confirmed by simulation studies.

Accurate Open-Loop Impedance Model of Single-Phase Voltage Source Inverter (VSI) Considering the Dead-Time Effects

Abstract: The impedance-based approach has been widely adopted to analyze converter-grid interactions. The dead-time have a significant impact on the output impedance of the voltage source inverter (VSI), which will further affect the stability of the grid-connected VSI. The dead-time can be elaborated as a nonlinear block, which highly depends on the output current. Moreover, the current ripple also has an impact on the dead-time effect especially in light load condition, which is usually overlooked in previous work. This paper presents an accurate analytical model to characterize the dead-time effect considering current ripple, which is established based on the double input describing function (DIDF). Both the simulation and experimental results confirm the accuracy of the proposed impedance model considering the dead-time effects.