A Filippov Method Based Analytical Treatise on Stability Analysis and Chaos Control of Converters

Abstract

Stability analysis of non-autonomous systems with dual forcing functions, such as dc-ac inverters, is a challenging task due to absence of inherently closed periodic switching cycles. To address this, quasi-static approximation is usually applied at the differential equation formulation stage. This assumption can be taken after deriving generalized saltation matrices also, which can assess stability of both switching and fundamental cycles. Expressions of saltation matrices have been derived from the generalized matrix at various phase angles of the fundamental waveform by Filippov method. Resistive parasitics usually avoided in modeling for simplicity, delay the onset of Hopf bifurcations, while slightly advance period-doubling bifurcations, and overall expand the stable parameter region. Inherent time delays in analog control circuits introduce distinct instability mechanisms, depending on topology, control scheme, modulation type, and operating conditions. It is modeled using first-order Padé approximation and comparative studies with higher-order Padé approximations and pure time delay show negligible error in predicting bifurcation points. Importantly, parasitics and time delays may counterbalance one another depending on parameter space location and instability type, offering insights into natural compensation mechanisms. Experimental realization of pure time delay through a first-order all-pass filter has been achieved. Filippov method based analysis also shows strong similarity between PI and PR controllers, with resonant gain inducing Hopf bifurcations much like integral gain. Notch filter-based compensators combined with PI or PR controllers are shown to suppress the period-doubling route to chaos and delay Hopf bifurcations. Building on internal model principles, a novel unified resonant-notch chaos controller has been conceptualized. Quantitative differences between first harmonic approximation based linearized model and switched model of inverter with nonlinear rectifier load have been demonstrated. newline