Complex Interaction Between Tori and Onset of Three-Frequency Quasi-Periodicity in a Current Mode Controlled Boost Converter

Research of the time irreversibility in voltage mode controlled DCM Buck converter

“…when circuit structure changes, the circuit structure complexity will change at the same time, and it cannot product multi-volume wave chaotic state, so we must study on chaos state according to the characteristics of the switching converter itself. Many scholars have adapt qualitative researches on the chaotic characteristics of switching converter by using state space average [2], Jacobian [3], and parameter perturbation [4]. But qualitative viewpoint to analyze switching converter chaotic system is not enough to fully understand the essential characteristics of chaos state.…”

“…ii) when converter is in unstable state, relative entropy is 0. In the period state, the relative entropy maintain in 3 …”

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.…”

“…Despite their engineering use, one of the main drawbacks of PWL and PWM systems is this nonlinearity making them prone to exhibit a large variety of complex dynamic and undesired behaviors [5], [12], [13]. Although each subsystem is linear and its describing differential equations can be solved in closed-form, the dynamics of the complete switched system is highly nonlinear and its analysis requires sophisticated computational tools [16].…”

Nonlinear stability analysis and a new design methodology for a PEM fuel cell fed DC–DC boost converter

“…In the past it was believed that the slow behaviour of the FC does not interact with the fast scale nonlinearities of the converter. However, it has been recently demonstrated [6,20] that it is possible for the voltage/current controlled boost converter to exhibit slow scale bifurcations [3] and these may interact with the slow scale dynamics of the FC.…”