Search results

With the increasing demands of industrial applications, it is imperative for robots to accomplish good contact-interaction with dynamic environments. Hence, the purpose of this research is to propose an adaptive fractional-order admittance control scheme to realize a robot–environment contact with high accuracy, small overshoot and fast response.

Fractional calculus is introduced to reconstruct the classical admittance model in this control scheme, which can more accurately describe the complex physical relationship between position and force in the interaction process of the robot–environment. In this control scheme, the pre-PID controller and fuzzy controller are adopted to improve the system force tracking performance in highly dynamic unknown environments, and the fuzzy controller is used to improve the trajectory, transient and steady-state response by adjusting the pre-PID integration gain online. Furthermore, the stability and robustness of this control algorithm are theoretically and experimentally demonstrated.

The excellent force tracking performance of the proposed control algorithm is verified by constructing highly dynamic unstructured environments through simulations and experiments. In simulations and experiments, the proposed control algorithm shows satisfactory force tracking performance with the advantages of fast response speed, little overshoot and strong robustness.

The control scheme is practical and simple in the actual industrial and medical scenarios, which requires accurate force control by the robot.

A new fractional-order admittance controller is proposed and verified by experiments in this research, which achieves excellent force tracking performance in dynamic unknown environments.

As a powerful mathematical analysis tool, the local fractional calculus has attracted wide attention in the field of fractal circuits. The purpose of this paper is to derive a new ℑ-order non-differentiable (ND) R-C zero state-response circuit (ZSRC) by using the local fractional derivative on the Cantor set for the first time.

A new ℑ-order ND R-C ZSRC within the local fractional derivative on the Cantor set is derived for the first time in this work. By defining the ND lumped elements via the local fractional derivative, the ℑ-order Kirchhoff voltage laws equation is established, and the corresponding solutions in the form of the Mittag-Leffler decay defined on the Cantor sets are derived by applying the local fractional Laplace transform and inverse local fractional Laplace transform.

The characteristics of the ℑ-order R-C ZSRC on the Cantor sets are analyzed and presented through the 2-D curves. It is found that the ℑ-order R-C ZSRC becomes the classic one when ℑ = 1. The comparative results between the ℑ-order R-C ZSRC and the classic one show that the proposed method is correct and effective and is expected to shed light on the theory study of the fractal electrical systems.

To the best of the authors’ knowledge, this paper, for the first time ever, proposes the ℑ-order ND R-C ZSRC within the local fractional derivative on the Cantor sets. The results of this paper are expected to give some new enlightenment to the development of the fractal circuits.

The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.

The fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.

A fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.

The spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.

The fractional order HIV model has an important role in biological science. To study the HIV model in a better way, the model is presented with the help of Atangana- Baleanu operator which is in Caputo sense. Also, the characteristics of the solutions are described briefly with the help of the advance numerical techniques for the different values of fractional order derivatives. This paper aims to discuss the aforementioned objectives.

In this work, Adams-Bashforth method and Euler method are used to get the solution of the HIV model. These are the important numerical methods. The comparison results also are described with the physical meaning of the solutions of the model.

HIV model is analyzed under the view of fractional and AB derivative in Atangana-Baleanu-Caputo sense. The uniqueness of the solution is proved by using Banach Fixed point. The solution is derived with the help of Sumudu transform. Further, the authors employed fractional Adam-Bashforth method and Euler method to enumerate numerical results. The authors have used several values of fractional orders to present the outcomes graphically. The above calculations have been done with the help of MATLAB (R2016a). The numerical scheme used in the proposed study is valid and fruitful, and the same can be used to explore other real issues.

This investigation can be done for the real data sets.

This paper aims to express the solution of the HIV model in a better way with the effect of non-locality, this work is very useful.

In this work, HIV model is developed with the help of Atangana- Baleanu operator in Caputo sense. By using Banach Fixed point, the authors proved that the solution is unique. Also, the solution is presented with the help of Sumudu transform. The behaviors of the solutions are checked for different values of fractional order derivatives with the physical meaning with help of the Adam-Bashforth method and the Euler method.

The aim of this article is to draw attention to the importance of open discussion for the proper development of science.

In the phase of the developed market economy we are currently in, the evaluation of each human activity, including scientific work, which is based on an evaluation of the value of the profit it brings. Unfortunately, it does not always work correctly.

The problem will be analyzed using as an example the erroneous (according to the author) use of fractional derivatives in electrical engineering.

To the best of the author’s knowledge, this is the author's original point of view on the problem of improper use of fractional derivatives in electrical engineering.

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).

The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.

The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

The fractal and fractional calculus have obtained considerable attention in the electrical and electronic engineering since they can model many complex phenomena that the traditional integer-order calculus cannot. The purpose of this paper is to develop a new fractional pulse narrowing nonlinear transmission lines model within the local fractional calculus for the first time and derive a novel method, namely, the direct mapping method, to seek for the nondifferentiable (ND) exact solutions.

By defining some special functions via the Mittag–Leffler function on the Cantor sets, a novel approach, namely, the direct mapping method is derived via constructing a group of the nonlinear local fractional ordinary differential equations. With the aid of the direct mapping method, four groups of the ND exact solutions are obtained in just one step. The dynamic behaviors of the ND exact solutions on the Cantor sets are also described through the 3D graphical illustration.

It is found that the proposed method is simple but effective and can construct four sets of the ND exact solutions in just one step. In addition, one of the ND exact solutions becomes the exact solution of the classic pulse narrowing nonlinear transmission lines model for the special case 9 = 1, which strongly proves the correctness and effectiveness of the method. The ideas in the paper can be used to study the other fractal partial differential equations (PDEs) within the local fractional derivative (LFD) arising in electrical and electronic engineering.

The fractional pulse narrowing nonlinear transmission lines model within the LFD is proposed for the first time in this paper. The proposed method in the work can be used to study the other fractal PDEs arising in electrical and electronic engineering. The findings in this work are expected to shed a light on the study of the fractal PDEs arising in electrical and electronic engineering.

The purpose of this paper is to find a simpler model for the reactance components in the high-frequency range on the premise of ensuring the accuracy.

In this paper, based on the fractional calculus theory and the traditional integer-order model, a reactance model suitable for high frequency is constructed, and the mutation cross differential evolution algorithm is used to identify the parameters in the model.

By comparing the integer-order model, high-frequency fractional-order model and the actual impedance characteristic curve of inductance and capacitance, it is verified that the proposed model can more accurately reflect the high-frequency characteristics of inductance and capacitance. The simulation and experimental results show that the oscillator constructed based on the proposed model can analyze the frequency and output waveform of the oscillator more accurately.

The model proposed in this paper has a simple structure and contains only two parameters to be identified. At the same time, the model has high precision. The fitting errors of impedance curve and phase-frequency characteristic curve are less than 5%. Therefore, the proposed model is helpful to improve the simplicity and accuracy of circuit system analysis and design.

The purpose of this paper is to derive a new fractal active low-pass filter (LPF) within the local fractional derivative (LFD) calculus on the Cantor set (CS).

To the best of the author’s knowledge, a new fractal active LPF within the LFD on the CS is proposed for the first time in this work. By defining the nondifferentiable (ND) lumped elements on the fractal set, the author successfully extracted its ND transfer function by applying the local fractional Laplace transform. The properties of the ND transfer function on the CS are elaborated in detail.

The comparative results between the fractal active LPF (for γ = ln2/ln3) and the classic one (for γ = 1) on the amplitude–frequency and phase–frequency characteristics show that the proposed method is correct and effective, and is expected to shed light on the theory study of the fractal electrical systems.

To the best of the author’s knowledge, the fractal active LPF within the LFD calculus on the CS is proposed for the first time in this study. The proposed method can be used to study the other problems in the fractal electrical systems, and is expected to shed a light on the theory study of the fractal electrical systems.