Closed-Form Critical Conditions of Saddle-Node Bifurcations for Buck Converters

Abstract

A general and exact critical condition of saddle-node bifurcation is derived in closed form for the buck converter. The critical condition is helpful for the converter designers to predict or prevent some jump instabilities or coexistence of multiple solutions associated with the saddle-node bifurcation. Some previously known critical conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme.

Submitted to IEEE Transactions on Automatic Control on Jan. 9, 2012. Seven of my arXiv manuscripts have a common reviewer

References in corpus (3)

• Analysis and Control of Period-Doubling Bifurcation in Buck Converters Using Harmonic Balance
• Comments on "Prediction of Subharmonic Oscillation in Switching Converters Under Different Control Strategies"
• Local Bifurcations in DC-DC Converters

Cited by in corpus (9)

• The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
• Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters
• Boundary Conditions of Subharmonic Oscillations in Fixed-Switching-Frequency DC-DC Converters
• Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control
• Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters
• Saddle-Node Bifurcation Associated with Parasitic Inductor Resistance in Boost Converters
• Unified model of voltage/current mode control to predict saddle-node bifurcation
• Unified Subharmonic Oscillation Conditions for Peak or Average Current Mode Control
• Sampled-Data and Harmonic Balance Analyses of Average Current-Mode Controlled Buck Converter