Bifurcation Mechanism and Stabilization of V²C Controlled Buck Converter

Abstract

The V 2 C controlled buck converter by constant-frequency pulse-width modulation in continuous conduction mode gives rise to a great variety of instability behaviors, depending on the circuit parameter values. In this paper, the discrete-time model of the regulator is built by taking a current sampling resistor into consideration. The resulting Monodromy matrix is used to investigate the bifurcation phenomenon and stabilization property. The converter shows a series of period-doubling bifurcation phenomena accordingly as the feedback amplification coefficient increases. At the same time, a couple of Floquet multipliers pass through the unit circle along the negative real axis. Therefore, it reveals the mechanism of a series of perioddoubling bifurcations happened in the system from the perspective of stability. Based on Floquet theory, a sine voltage compensation method is proposed to stabilize the bifurcation and chaotic behaviors. The simulations and experimental results proved the theoretical analysis. INDEX TERMS V 2 C control, buck converter, period-doubling bifurcation, chaos.

Period-doubling bifurcation analysis and chaos control for load torque using FLC

“…Analysis of Chaos using Floquet theory was discussed in [25][26][27][28][29][30]. Floquet Theory (Filippov's method) is applied to analyze the stability based on Floquet multipliers ( [34,37,38] and [39]). Monodromy matrix is shown equally:…”

“…Stabilization of the system using Floquet theory was discussed in [26,30,[37][38][39]. This technique is used to handle the effects of bifurcation and chaos that occur as a result of changing the torque of the load by forcing the path to be in period -1 (steady-state).…”

“…Consequently, studying chaos behavior and suppressing it has been the major target of researchers for practical nonlinear systems. Consequently, there are numerous methods to control chaotic systems, such as the (Ott, Grebogi and Yorke) OGY method [31], feed-back linearization method [32][33][34], a realtime cycle to cycle variable slope compensation method [35], time-delay feedback control [36], developing Floquet theory [26,30,[37][38][39], fuzzy control [41,43,45,46].…”

“…This interpretation of the Poincaré map is seldom used as it requires developing information for a limited cycle location [24,25]. While, the Floquet theory depends on the State Transition Matrix (STM) for the full cycle [34,35,[37][38][39]. Both methods give the same results; however, the Floquet theory fits well with mechanical switching systems and simpler to be implemented as compared to the Lyapunov exponent method [25][26][27][28][29][30].…”

“…Most researchers deal with the impact of changing the input voltage of PMDC motors or the controller gains on the chaos behavior [20,30,35,41]. Another research gap is that most control techniques deal with eliminating chaos and bifurcation without taking into consideration the performance of the system [32,33,[37][38][39]. Therefore, the contribution of this work is to investigate another important factor in the PMDC motor which is the impact of changing the load torque on chaos behavior with taking into consideration the performance of the system.…”