Hybrid Control of Self-Oscillating Resonant Converters

Abstract

We describe parallel and series resonant converters via a unified set of input-dependent coordinates whose dynamics is intrinsically hybrid. We then propose a hybrid feedback showing a self-oscillating behavior whose amplitude and frequency can be adjusted by a reference input ranging from zero to π. For any reference value in that range we give a Lyapunov function certifying the existence of a unique nontrivial hybrid limit cycle whose basin of attraction is global except for the origin. Our results are confirmed by experimental results on a series resonant converter prototype.

Hybrid Control of Self-Oscillating Resonant Converters With Three-Level Input

“…For our main stability result we require a mild underdamped assumption (see [12, Remark 1]) for the oscillating behavior, requiring that flowing solutions revolve in the phase-plane of Fig. 2, which ensures existence of a non trivial asymptotically stable hybrid limit cycle (as defined in [12] and recalled below) for any reference input φ ∈ [0, π /2).…”

“…In our new model ( 4), ξ := (z 1 , z 2 , σ, d) collects the four states: two physical and two logical ones. The logical state σ denotes the switch position, as in [11], [12]. The new logical state d ∈ {−1, 1} plays an important role when σ = 0 as it stores the past value of σ, so that the next value will be assigned as the opposite one (i.e.…”

“…Carlos Olalla and Luis Martínez-Salamero are with the Departament d'Enginyeria Electr ònica, El èctrica i Autom àtica, Escola T ècnica Superior d'Enginyeria, Universitat Rovira i Virgili, 43007 Tarragona, Spain. In our previous works [11], [12], we addressed the control of second-order parallel and series resonant converters (PRC and SRC, respectively) with the hybrid formulation of [13] in a unified way. To represent the switching input voltage v s of the resonant tank we used there a discrete variable σ ∈ {−1, 1}.…”

Hybrid Persistency of Excitation in Adaptive Estimation for Hybrid Systems

“…For this, we first note that 2V G pjq " ˇˇB 1 2 pt j`1 , jqζpt j`1 , jq ˇˇ2 . Then, using (32), we obtain…”

“…This is the case under the presence of impacts provoking instantaneous changes in the state, as in manufacturing systems [29], cyberphysical systems [30] or when combining continuous and discrete state variables, or in the presence of shocks and reflection-propagation [31]. It is also the case under constrained sensing and actuation, as in power [32] and network control systems [33]. In the aforementioned situations the solutions have a continuous evolution, governed by a continuous-time system, provided that they stay in a set called the flow set.…”