The effects of using frequency-domain approximation in numerical simulation fractional-order systems are analytically studied. main aim the study is to determine number, location and stability property equilibriums a system its frequency-based approximating counterpart. comparison shows that original may differ from each other some or all issues considered study. Unfortunately, these differences can lead wrong consequences special cases such as detecting chaos systems. It shown methods...

This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using fractional differentiator, and other constructed integrator. It has been shown that techniques can be used to suppress chaotic oscillations in 3-D systems. To show practical capability of methods, some experimental results control chaos circuits are presented.

This paper is devoted to the analysis of fractional order Van der Pol system studied in literature. Based on existing theorems stability incommensurate systems, we determine parametric range for which a with specific can perform as an undamped oscillator. Numerical simulations are presented support given analytical results. These results also illuminate main difference between oscillations oscillator and its integer counterpart. We show that contrary case, trajectories do not converge unique cycle.

This study deals with a generalised version of lead/lag compensators known as fractional‐order compensators. Exact and simple formulas are found for designing this introduced type in order to provide the required magnitude phase at given frequency. Also, region phase‐magnitude plane, which is accessible by these compensators, analytically found. Moreover, numerical examples experimental results presented show applicability achievements control system design.

Proportional-integral (PI) controllers are the most common form of feedback used in industrial applications today [1][3]. The use proportional and integral also has a long history practical [4]. For example, middle 18th century, centrifugal governors as were applied to regulate speed windmills [5]. By 19th it was known that using could remove offsets appearing working with [6]. At present, PI control, still very basic feedback, is one first solutions often considered control systems [7]. On...

Phase-locked loops (PLLs) are nonlinear automatic control circuits widely used in telecommunications, computer architecture, gyroscopes, and other applications. One of the key problems analysis PLL systems has been stated by Floyd M. Gardner as being "to define exactly any unique lock-in frequency." The range concept describes ability PLLs to reacquire a locked state without cycle slipping its calculation requires analysis. present work analyzes second-order type 2 phase-locked loop with...

In this paper, conditions for checking the realizability of fractional-order impedance functions by passive networks composed a fractional element (either capacitor or inductor) and some RLC components are derived. To end, at first newly obtained network extended to include case that polynomials involving in function can have roots on imaginary axis. Then, necessary sufficient found be realized components. Furthermore, procedure finding realization realizable cases is proposed. Finally,...

This paper deals with realization of fractional-order impedance functions by passive electrical networks composed a fractional capacitor and some RLC components. The necessary sufficient conditions for the existence such are found in general case. Also described class transfer functions, realizability stated as algebraic on parameters function. Moreover, procedure is proposed implementation Numerical examples presented to show usefulness results design circuits.