Describing function

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

Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances

Abstract: In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.

Precision motion control with disturbance observer for pulsewidth-modulated-driven permanent-magnet linear motors

Abstract: In this paper, we address the problem of precision motion control of permanent-magnet linear motors (PMLMs) under the influence of significant disturbances. We establish a mathematical model of a PMLM driven by a sinusoidal pulsewidth-modulated (PWM) amplifier, obtaining it from a describing function analysis of the essentially nonlinear characteristics. The overall model (PWM+PMLM) inevitably inherits uncertainties in the face of load changes, system parameter perturbation, noise, and inherent system nonlinearities, etc., all of which constitute disturbances to the control system that will adversely affect the precision and accuracy. We propose a robust control scheme employing a disturbance observer to address the sensitivity of the control performance to the disturbances. Real-time experimental results are provided to verify and confirm the practical effectiveness of the proposed approach.

Multiband Hysteresis Modulation and Switching Characterization for Sliding-Mode-Controlled Cascaded Multilevel Inverter

Abstract: In this paper, a generalized multiband hysteresis modulation and its characterization have been proposed for the sliding-mode control of cascaded H-bridge multilevel-inverter (CHBMLI)-controlled systems A frequency-domain method is proposed for the determination of net hysteresis bandwidth for a given desired maximum switching frequency of the inverter The switching transition concept of Tsypkin's method and the describing function of nonlinear relay have been used for the derivation of results A hierarchical switching algorithm has been suggested for the modular cells of the cascaded multilevel inverter The hierarchy of each cell is swapped sequentially to provide the self-balancing capability in case the dc-link voltage is supported by the capacitors The simulation and experimental verification of the derived results are provided through a single-phase distribution static compensator (DSTATCOM) model The application in the three-phase system has been shown through simulation studies on a 33-kV distribution-system compensation using DSTATCOM Verification on both single- and three-phase systems is obtained using a five-level cascaded-multilevel-inverter topology

Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method

Abstract: Active disturbance rejection control (ADRC) is a new design concept that shows promising power in dealing with the uncertainties of control systems. However, most of the previous work has been numerical time-domain development and frequency-domain analysis for the linear framework. This paper focuses on the frequency-domain analysis of the nonlinear ADRC behavior using the describing function method and characterizes the effect of the ${\rm fal}$ nonlinearity parameter on the performance of the closed-loop system. Both the describing function of the nonlinearity and the transfer function description of the system's linear portion are derived. The stability, dynamic stiffness, and tracking performance are analyzed for a second-order single-input single-output plant. The analysis results show that the nonlinearity parameter plays a crucial role in the system performance. The nonlinear ADRC has higher control efficiency than the linear ADRC but reduces the stability margin of the system. Using the fast tool servo case, simulations and hardware experiments are conducted, and the results further support the analysis.