Border collision bifurcations in a one-dimensional piecewise smooth map for a PWM current-programmed H-bridge inverter

Abstract

In this article, we are studying the non-linear e ects in a single-phase H-bridge inverter. The PWM control is related to a current feedback control. We are proposing an analytical model, which is a piecewise linear map. The distinctive feature of this study lies in the investigation of the map's properties. This investigation allows for the analytical determination of the ®xed points, their domains of stability, and of the bifurcation points. More precisely, we will show that some of these bifurcations are discontinuous. The analysis is performed while keeping in mind the current controller's tuning. In this particular setting, we will show that all the bifurcations are of a certain type: border collision bifurcations. Although we are treating the appearance of chaos in a converter, the work presented stays close to the preoccupations of the engineer, because the particularities of the digital control are shown as an advantage. Moreover, we have strived to comment on the di erent modes observed, periodic or not, by underlying their practical interest or disadvantages.

Slow-Scale and Fast-Scale Instabilities in Voltage-Mode Controlled Full-Bridge Inverter

“…In AC-DC PFC converters, the period-doubling bifurcation emerging from the line frequency is also reported and analyzed [10,15]. However, few studies have been done on the AC power supply system, apart from the border collision and its control in a current-mode controlled full-bridge inverter reported by Robert and Iu [5,11]. Due to the use of the current-mode control strategy, only the border collision bifurcation is observed in their work.…”

A Time-Domain Asymptotic Approach to Predict Saddle-Node and Period Doubling Bifurcations in Pulse Width Modulated Piecewise Linear Systems

“…Most of the PWL systems studied in the literature are characterized by switching among linear subsystems when certain time-varying and T − periodic boundaries in the state space are reached. This is the case of Pulse Width Modulation (PWM) systems like switching dc-dc power converters [3], [4], [5], [6], [9], [10], dc-ac inverters [11], temperature control systems [12], switched capacitor networks and chaos generators [13] and hydraulic and fluid valve drivers [14], [15]. In steady-state, during a switching period of length T , a trajectory of these systems starts at time instant nT and is described by the vector field f 1 (x) = A 1 x + B 1 u, intersects a switching boundary described by the equation σ(x(t), t) := Fx(t) − r(t) = 0 at switching instant t s = DT , and then goes to another linear system described by the vector field f 2 (x) = A 2 x + B 2 u, where r is a time-varying T −periodic external signal, x ∈ R n is the vector of the state variables, n is the order of the system A i ∈ R n×n and B i ∈ R n×m , i = 1, 2 are the system state matrices for phase i (i = 1, 2) and u ∈ R m is the vector of the system inputs in both the plant and controller, m being the number of the external inputs to the system which are supposed to be constant within a switching cycle.…”

Stabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller

“…Such problem has been observed particularly in power electrical systems such as power converters [1][2][3]. In most cases, designers try to avoid the chaotic behavior, considered as hazardous, by adjusting the system parameters securely far from the values that lead to chaos.…”