Using steady-state response for predicting stability boundaries in switched systems under PWM with linear and bilinear plants

A. El Aroudi, M. Al-Numay, K. Al Hosani, N. Al Sayari

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Switching systems under Pulse Width Modulation (PWM) are commonly utilized in many industrial applications. Due to their associated nonlinearities, such systems are prone to exhibit a large variety of complex dynamics and undesired behaviors. In general, slow dynamics in these systems can be predicted and analyzed by conventional averaging procedures. However, fast dynamics instabilities such as period doubling (PD) and saddle-node (SN) bifurcations cannot be detected by average models and analyzing them requires the use of additional sophisticated tools. In this chapter, closed-form conditions for predicting the boundary of these bifurcations in a class of PWM systems with linear and bilinear plants are obtained using a time-domain asymptotic approach. Previous studies have obtained similar boundaries by either solving the eigenvalue problem of the monodromy matrix of the Poincaré map or performing a Fourier series expansion of the feedback signal. While the former approach is general and can be applied to linear as well as bilinear plants, the later approach is applicable only to PWM systems with linear plants. The conditions for fast scale instability boundaries presented in this chapter are obtained from the steady-state analysis of the Poincaré map using an asymptotic approach without resorting to frequency-domain Fourier analysis and without using the monodromy matrix of the Poincaré map. The obtained expressions are simpler than the previously reported ones and allow to understand the effect of different system’s parameters on its stability. In PWM systems with linear plants, under certain practical conditions concerning these parameters, the matrix form expression can be approximated by standard polynomial functions expressed in terms of the operating duty cycle weighted by the Markov parameters of the linear part of the system.

Original languageBritish English
Title of host publicationStructural Nonlinear Dynamics and Diagnosis - Selected papers from CSNDD 2012 and CSNDD 2014
EditorsMohamed Belhaq, Mohamed Belhaq
Pages367-391
Number of pages25
DOIs
StatePublished - 2015
EventInternational Conferences on Structural Nonlinear Dynamics and Diagnosis, CSNDD 2012 and International Conferences on Structural Nonlinear Dynamics and Diagnosis, CSNDD 2014 - Agadir, Morocco
Duration: 21 May 201423 May 2014

Publication series

NameSpringer Proceedings in Physics
Volume168
ISSN (Print)0930-8989
ISSN (Electronic)1867-4941

Conference

ConferenceInternational Conferences on Structural Nonlinear Dynamics and Diagnosis, CSNDD 2012 and International Conferences on Structural Nonlinear Dynamics and Diagnosis, CSNDD 2014
Country/TerritoryMorocco
CityAgadir
Period21/05/1423/05/14

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