Describing function

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

Nonlinear stability and post-critical analysis of an uncertain plant with describing functions and integral quadratic constraints

Abstract: Two approaches to tackle the nonlinear robust stability problem of a plant are considered. The first employs a combination of the Describing Function method and μ analysis, while the second makes use of Integral Quadratic Constraints (IQCs). The model analyzed consists of an open-loop wing's airfoil subject to freeplay and LTI parametric uncertainties. One of the main contributions of the work is to provide methodologies to quantitatively determine the post-critical behaviour of the system, known as Limit Cycle Oscillation (LCO). When the first approach is adopted, this is studied by means of a worst-case LCO curve, whose definition is given in the paper. The IQC framework, typically used to find asymptotic stability certificates, is applied to this scenario by introducing a restricted sector bound condition for the nonlinearity.

An Extended Describing Function Model for A Hybrid Frequency/Phase-shift Controlled SiC-Based High-Gain DC-DC Resonant Converter Module

Abstract: An improved hybrid variable-frequency and phase shift control scheme that is well-suited for extending the soft-switching operation and providing output voltage regulation simultaneously for a DC/DC step-up converter module with a simple passive auxiliary circuit is presented in this paper. The proposed converter incorporates transformer non-idealities (such as the leakage and magnetizing inductances) into a basic operation of the CLL resonant circuit. To eliminate the reverse recovery losses of the diodes, the resonant inductor in the presented converter module is integrated with the high-frequency voltage multiplier to form a current-driven structure. To analyze the presented control algorithm, the small-signal model and the control-to-output transfer functions are obtained using extended describing function (EDF); which can handle multistate variables. Simulation results on a modular 1kVDC/34.2kVDC, 1.2MW are first given to verify with the theoretical analysis of the proposed converter module. The accuracy and validity of the presented small-signal model and the performance of the proposed converter system are further verified using a 1.4kW (two-modules), 140V/1.6kV proof of concept prototype.

Enhancing Settling Performance of Precision Motion Systems by Phase-Based Variable Gain Feedback Control

Abstract: In this article, phase-based variable gain feedback control is utilized to improve settling performance of precision motion systems. Describing function analysis of the control strategy is presented, stability analysis is given by common quadratic Lyapunov function method and data-based tuning approach for variable gain parameter based on finite difference method is proposed. Simulation and experiment on a precision motion system both validate the phase-based variable gain feedback control algorithm and the proposed tuning approach.

Multiloop controller design for multivariable plants

Abstract: The extension of the SISO (single-input single-output) relay tuning method to a class of multivariable plans is demonstrated. These are diagonally dominant n-by-n plants which are gain stabilizable and with all elements having low-pass characteristics. Gain stabilizability is required in order to lend any purpose to the procedure while the others ensure some accuracy to the information obtained. The requirement of diagonal dominance is made clear. The extension of the theory of describing functions to MIMO (multiple-input multiple-output) systems is given. An example is used to illustrate the analysis. This is followed by preliminary results on controller design which show that Ziegler-Nichols rules can still be used to design multiloop PI (proportional plus integral) controllers for multivariable systems. >