Design of self‐oscillating resonant converters based on a variable structure systems approach

Abstract

A mathematical model is derived for the parallel resonant converter (PRC) in which a simple comparator circuit applied to the inductor current is used to establish stable oscillations at the resonant frequency in cases of high Q. Second order differential equations are solved to construct a piecewise phase-plane trajectory explaining the generation of a stable limit cycle and predicting its amplitude and period. The self-oscillating mechanism is explored in other resonant converters and verified by simulation. In all cases, switching between the two circuit configurations of the converter is produced by the change of the input inductor current sign. Measurements in a 100 W PRC prototype oscillating around 500 kHz are in good agreement with the theoretical predictions.

Delay effects on the limit cycling behavior in resonant inverters with state feedback

“…Many approaches used by scientists and engineers to study the dynamics of switched systems such as averaging [10], the time-domain Hamel locus [11] describing function (DF) or First Harmonic Approximation (FHA) method [12][13][14] fail to give accurate results whenever the repulsive sliding dynamics plays a relevant role [15,17]. Mostly, the sliding region, a subset of the switching manifold i.e., the region of the state-space where the field is discontinuous, is attractive and then techniques of sliding control can be applied [18].…”

Limit cycle bifurcations in resonant LC power inverters under zero current switching strategy

“…On the contrary, when such normal components are in opposition, we adopt the Filippov convex method. In the sequel, we will closely follow reference [16] to describe the Filippov method regarding system (11).…”

“…In particular, constant sliding solutions are called pseudo-equilibria of the system. When β = 0, equation (12) reduces toẋ 1 = 0, and so every point in the sliding set is a pseudo-equilibrium point of system (11). When β > 0, the origin is the only pseudo-equilibrium point.…”

“…Now, we can state the following fact. For β > 0, system (11) can have at most two crossing limit cycles because the map P is concave down and so, its graph meets the secondary diagonal at most in two points. The existence and stability of these crossing limit cycles are studied in Subsection 3.4 after analyzing the closed curves containing the full sliding set or a part of it.…”

“…Different types of resonant inverters exist and these are classified according to the type of switching network, the configuration of the resonant tank circuit, and the number of the energy storage components. The parallel resonant converter (PRC) and the series resonant converter (SRC) are examples of topologies with two energy-storage elements [10,11], corresponding to the simplest possible configurations.…”