Essay with regards to a Nonlinear-System Way of Analysis and Design of Power-Electronic Converters with Saturation and Bilinear Terms

IEEE TRANSACTIONS UPON POWER CONSUMER ELECTRONICS, VOL. twenty six, NO . two, FEBRUARY 2011

399

A Nonlinear-System Approach to Analysis and

Design of Power-Electronic Converters With

Saturation and Bilinear Terms

Tingshu Hu, Senior Member, IEEE

Abstract—Power-electronic converters happen to be intrinsically non-linear. This paper proposes a Lyapunov way of analysis and design of a class of nonlinear systems as a result of power-electronic conversion. The system contains a bilinear term as the merchandise of the state and the input—the duty routine, which is controlled by strict limitation (or saturation). The non-linearities and the suggestions saturation are considered in this paper by using piecewise-quadratic Lyapunov functions and by talking about the system which has a piecewiselinear gear inclusion. The difficulties considered contain controller style for powerful stability, and estimation of stability place and monitoring domain. These kinds of analysis and design danger is converted into numerically efficient search engine optimization algorithms concerning linear-matrix inequalities (LMIs). A buck–boost dc–dc converter can be used to demonstrate the proposed methods. The optimization results demonstrate that a basic state-feedback legislation can be built to achieve pretty much global stabilization and checking, which is theoretically confirmed by Lyapunov strategy. An fresh buck–boost converter is made to verify the checking of a sq reference differing almost between the upper as well as the lower limit.

Index Terms—Bilinear system, linear-matrix inequality (LMI), power-electronic conversion, saturation, balance, tracking.

We. INTRODUCTION

IGH-EFFICIENCY power-electronic converters use

pulsewidth modulators (PWMs) to adjust the work cycle of switched-mode semiconductor devices. The duty cycle is used as the input to control the output ac electricity, current, or perhaps power. A crucial task in the converter design and style is to create a feedback law that adjusts the work cycle depending on available dimension so that the outcome voltage, current, or electricity, follows specific reference. The feedback control system is subject to input vividness due to the hard limit within the duty pattern, which is restricted within [0, 1], or a smaller sized range due to the constraint of the moving over devices and nonidealities with the circuit elements. Furthermore, the differential formula of the style obtained simply by averaging

H

Manuscript received January 18, 2010; modified April 13, 2010; acknowledged June 15, 2010. Day of current version Feb . 4, 2011. This work was reinforced in part by the National Technology Foundation (NSF) under Grant ECS-0621651 and Grant ECCS-0925269. Recommended intended for publication by simply Associate Publisher B. Choi.

The author is to use the Division of Electric and Pc Engineering, School of Massachusetts, Lowell, MOTHER 01854 USA (e-mail: [email protected] edu).

Color versions of 1 or more of the п¬Ѓgures with this paper can be found online by http://ieeexplore.ieee.org.

Digital Object Identifier 10. 1109/TPEL. 2010. 2054115

over one switching pattern (the state-space averaging unit developed by Middlebrook [22]) provides a bilinear term, which is the item of the responsibility cycle and the state. In traditional style, the saturation has generally been neglected and the bilinear term continues to be discarded because high-order terms to obtain a linearized model beneath the small-signal assumption (e. g., see [23, p. 351], or perhaps [7, p. 221]). Even though switched-mode electric power conversion can be

a well-established technology and lots of high-performance

power-electronic converters have been completely constructed by simply neglecting these types of non-linearities, there are still continuing analysis efforts committed toward better understanding the theory behind you see, the non-linear program (see [2], [3], [6], [8]–[11], [15], [18], [24], [26], [29], and [31] for any sample of recent literature. )

A single basic trouble of a power-electronic circuit is usually stability. If the linearized style is used intended for control design and style, the outlet will be locally stable when the variations...

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[21] 3rd there’s r. D. Middlebrook, " A general uniп¬Ѓed way of modeling switchingconverter power stages, ” Int. J. Electron., vol. 42, pp. 521–550, 1977.

[22] R. G. Middlebrook, " A general unified approach to building switchingconverter electricity stages, ” in Proc. IEEE Electrical power Electron. Specification. Conf., 1976,

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