Related papers: Fractional-Order Partial Cancellation of Integer-O…
As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that such non-minimum phase zeros cannot be cancelled by unstable…
The non-minimum phase (NMP) zero of a linear process located in the feedback connection cannot be cancelled by the same pole of controller according to the internal instability problem. However, such a zero can partly be cancelled by the…
We generalize notions of passivity and dissipativity to fractional order systems. Similar to integer order systems, we show that the proposed definitions generate analogous stability and compositionality properties for fractional order…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…
As a well understood classical fact, non- minimum phase zeros of the process located in a feedback connection cannot be cancelled by the corresponding poles of controller since such a cancellation leads to internal instability. This…
We consider the fractional oscillator being a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by stochastic…
A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are…
This paper proposes an original solution to input saturation and dead zone of fractional order system. To overcome these nonsmooth nonlinearities, the control input is decomposed into two independent parts by introducing an intermediate…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
We consider the robust control of a two-mass oscillator with a dominant input delay. Our aim is to compare a fractional-order tuning approach including the partial compensation of non-minimum phase zeros with a classical H-infinity…
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of…
To handle the control difficulties caused by high-order dynamics, a control structure based on fractional order [proportional integral] (PI) controller and fractional order Smith-like predictor for a class of high order systems in the type…
In this paper, a framework for the combination of robust fractional order CRONE control with non-linear reset is given for both first and second generation CRONE control. General design rules are derived and presented for these CRONE reset…
This article presents proposals for the design of reduced-order controllers for high-dimensional dynamical systems. The objective is to develop efficient control strategies that ensure stability and robustness with reduced computational…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…