Local Bifurcations in PWM DC-DC Converters

Abstract

ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract A general sampled-data model of PWM DC-DC converters [1, 2] is employed to study types of loss of stability of the nominal (periodic) operating condition and their connection with local bifurcations. In this work, the nominal solution's periodic nature is accounted for via the sampled-data model. This results in more accurate predictions of instability and bifurcation than can be obtained using the averaging approach. The local bifurcations of the nominal operating condition studied here are period-doubling bifurcation, saddle-node bifurcation, and Neimark bifurcation. Examples of bifurcations associated with instabilities in PWM DC-DC converters are given. In particular, input filter instability is shown to be closely related to the Neimark bifurcation.

Comments on "Bifurcations in DC-DC Switching Converters: Review of Methods and Applications"

“…The stability conditions such as (42) and ( 45) are important because they lead to many other important critical conditions of DC-DC converters [2,3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The condition (42) was first known in [5,6] in 1997-1998, and the condition (45) was first known in [3,5] in 1997-1999.…”

Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters

“…Instability occurs when there exists a sampled-data pole outside the unit circle in the complex plane. There are three ways that the sampled-data pole leaves the unit circle, thus causing three typical instabilities in DC-DC converters [1], [2], [3]. When the sampled-data pole leaves the unit circle through 1 in the complex plane, the instability is generally a saddle-node bifurcation (SNB) [2] (or pitchfork and transcritical bifurcations [4] which are less seen in DC-DC converters).…”

“…When the pole leaves the unit circle through -1, the instability is a period-doubling bifurcation (PDB) [6], which generally involves fast-scale subharmonic oscillation. When the pole leaves through a point other than 1 or -1 on the unit circle, the instability is a Neimark-Sacker bifurcation (NSB), which generally involves a slow-scale quasi-periodic oscillation [1], [2], [3]. Many instability examples of DC-DC converters are shown in [7], [8], [9], [10], [11].…”

Saddle-Node Bifurcation Associated with Parasitic Inductor Resistance in Boost Converters

“…A saddle-node bifurcation (SNB) associated with the parasitic inductor resistance in a boost converter under current mode control (CMC) has been reported in [2] by simulation without deriving the bifurcation critical condition. Analysis of SNB may explain some sudden disappearances or jumps of steady-state solutions observed in switching converters [3,4,5,6,7,8].…”

“…Similar analysis as in VMC (see(4)) can be applied. For a large k p , I peak /k p can be ignored, and SNB occurs when v * For a small k p , based on (19), the bifurcation point D S is larger than 1 − √ η because I peak has a large value at high duty cycle.…”