Control of a PWM Inverter Using Proportional Plus Extended Time-Delayed Feedback

Abstract

Pulse width modulation (PWM) current-mode single phase inverters are known to exhibit bifurcations and chaos when parameters vary or if the gain of the proportional controller is arbitrarily increased. Our aim in this paper is to show, using control theory and numerical simulations, how to apply a method to stabilize the interesting periodic orbit for larger values of the proportional gain. To accomplish this aim, a time-delayed feedback controller (TDFC) is used in conjunction with the proportional controller in its simple form as well as in its extended form (ETDFC). The main advantages of those methods are the robustness and ease of construction because they do not require the knowledge of an accurate model but only the period of the target unstable periodic orbit (UPO). Moreover, to improve the dynamical performances, an optimal criterion and an adaptive law are defined to determine the control parameters.

Application of Time-Delayed Feedback Control Techniques in Digital Phase-Locked Loop

“…By controlling chaos and bifurcation one can suppress the chaotic behavior where it is unwanted (e.g., in power electronics [14,24] and mechanical systems [9]), and on the other hand in electronic systems one can exploit chaos in chaos-based electronic communication systems [15]. The methodology of controlling chaos in dynamical systems was first introduced in [21] and is well known as the OGY method.…”

“…It has been shown in Refs. [8,24] that to achieve the optimum condition we have to find out the parameter values for which the spectral radius of J of Eq. (14) is minimum, which is equivalent to make the discriminant of J equal to zero, i.e.,…”

“…i.e., the input to the LDF can be written as (24) Now, let us define ψ k = ω 0 G 0 ζ k . Thus, finally we get the following phase error equations that describe the system:…”

Control and Synchronization Chaotic Satellite using Active Control

“…In recent years, there has been increasing interest in the study of synchronizing chaotic systems. Chaos synchronization has many potential applications in laser physics [1,2], secure communication [3,4], power electrical systems [5], aerospace [6,7] and gyro [8] and so on. Various control approaches were reported to realize the chaotic synchronization, such as Adaptive Control [9], Impulsive Control [10], Back Stepping [11], Fuzzy Control [12,13], Sliding Mode Control [14,15], Nonlinear Control [16], Active control [17,18].…”

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

“…The second, uses the control strategy to achieve synchronization between two identical or different chaotic systems [9][10][11][12][13]. The third, is the most important when it comes to the control of chaotic systems, and concerns the stabilization of unstable periodic orbits embedded in the chaotic attractor [14][15][16][17][18][19].…”