Design of fractional order sliding mode controller via non-integer order backstepping by fractional order derivative of Lyapnov function

2014 ◽  
Author(s):  
Takahiro Takamatsu ◽  
Koushirou Kubo ◽  
Hiromitsu Ohmori
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Order Derivative ◽  
Sliding Mode Controller ◽  
Fractional Order Derivative ◽  
Integer Order

scholarly journals Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yan-Ping Wu ◽  
Guo-Dong Wang
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Chen System ◽  
Integer Order ◽  
Response Systems ◽  
Hyperchaotic Systems

The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.

scholarly journals CentrifugationSynchronization Control of Fractional Order Chaotic Systems Based on Memristor and Its Hardware Implementation

2021 ◽  
pp. 289-297
Author(s):  
Zhaohan zhang, Huiling Jin
Keyword(s):  
Fractional Order ◽  
Hardware Implementation ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Controlled System ◽  
Integer Order ◽  
The Stability ◽  
Dynamic Phenomena

This paper studies the synchronization control of fractional order chaotic systems based on memristor and its hardware implementation. This paper takes the complex dynamic phenomena of memristor turbidity system as the research background. Starting with the integer order memristor system, the fractional order form is derived based on the integer order turbid system, and its dynamics is deeply studied. At the same time, the turbidity phenomenon is applied to the watermark encryption algorithm, which effectively improves the confidentiality of the algorithm. Finally, in order to suppress the occurrence of turbidity, a fractional order sliding mode controller is proposed. In this paper, the sliding mode controller under the function switching control method is established, and the conditions for the parameters of the sliding mode controller are derived. Finally, the experimental results analyze the stability of the controlled system under different parameters, and give the corresponding time-domain waveform to verify the correctness of the theoretical analysis.

Geometric interpretation of fractional-order derivative

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Differential Geometry ◽  
Fractional Order ◽  
Infinite Series ◽  
Fractional Derivatives ◽  
Geometric Interpretation ◽  
Order Derivative ◽  
Jet Bundles ◽  
Fractional Order Derivative ◽  
Integer Order ◽  
Derivatives Of

AbstractA new geometric interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders is proposed. The suggested geometric interpretation of the fractional derivatives is based on modern differential geometry and the geometry of jet bundles. We formulate a geometric interpretation of the fractional-order derivatives by using the concept of the infinite jets of functions. For this interpretation, we use a representation of the fractional-order derivatives by infinite series with integer-order derivatives. We demonstrate that the derivatives of non-integer orders connected with infinite jets of special type. The suggested infinite jets are considered as a reconstruction from standard jets with respect to order.

scholarly journals Fast Fractional-Order Terminal Sliding Mode Control for Seven-Axis Robot Manipulator

2020 ◽  
Vol 10 (21) ◽  
pp. 7757
Author(s):  
Jie Wang ◽  
Min Cheol Lee ◽  
Jae Hyung Kim ◽  
Hyun Hee Kim
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Order Derivative ◽  
Terminal Sliding Mode Control ◽  
Sliding Surface ◽  
Terminal Sliding Mode ◽  
Surface Design ◽  
Fractional Order Derivative

This paper proposes a novel controller, fast fractional-order terminal sliding mode control (FFOTSMC), for a seven-degree-of-freedom (7-DOF) robot manipulator with tracking control. The new controller applies the fractional-order derivative on both the sliding surface design and the sliding control/reaching law. Compared to previous research, which only applies the fractional-order derivative on the sliding surface design, the proposed controller has a faster convergence for reaching the sliding surface and maintaining stay on it because of the new fractional-order control law, which helps the tracking accuracy. To implement the controller on the robot with less chattering, a sliding perturbation observer (SPO) is used to estimate the disturbance and uncertainties. Stability analysis is analyzed using Lyapunov functions for fractional-order systems. The controller performance is evaluated by a simulation of a single-input and single-output (SISO) system in MATLAB Simulink and experiments on the robot manipulator.

Edge enhancement of magnetic data using fractional-order-derivative filters

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. J7-J17 ◽  
Author(s):  
Muzaffer Özgü Arısoy ◽  
Ünal Dikmen
Keyword(s):  
Fractional Order ◽  
Order Derivative ◽  
Magnetic Data ◽  
Frequency Noise ◽  
Edge Enhancement ◽  
Traditional Use ◽  
Data Set ◽  
Fractional Order Derivative ◽  
Detection Techniques ◽  
Integer Order

Edge enhancement and detection techniques are fundamental operations in magnetic data interpretation. Many techniques for edge enhancement have been developed, some based on profile data and others designed for grid-based data sets. Methods that are traditionally applied to magnetic data, such as total horizontal derivative (THD) and analytic signal (AS), require the computation of integer-order horizontal and vertical derivatives of the magnetic data. However, if the data set contains features with a large variation in amplitude, then the features with small amplitudes may be difficult to outline. In addition, because most edge enhancement and detection filters are derivative-based filters, they also amplify high-frequency noise content in the data. As a result, the accuracy of derivative-based filters is restricted to data of high quality. We suggested the modification of the THD and AS filters by combining the amplitude spectra of fractional-order-derivative filters with ad hoc phase spectra, particularly designed for edge detection in magnetic data. We revealed the capability of the proposed algorithm on synthetic magnetic data and on aeromagnetic data from Turkey. Compared with the traditional use of THD and AS (with integer-order derivatives), we developed the method based on fractional-order derivatives that produced more effective results in terms of suppressing noise and delineating the edges of deep sources.

scholarly journals Numerical Solution of the Bagley-Torvik Equation Using the Integer-Order Derivatives Expansion

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Afrah Sadiq Hasan
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Fractional Order ◽  
Infinite Series ◽  
Exact Analytical Solution ◽  
Second Order ◽  
Order Derivative ◽  
Fractional Order Derivative ◽  
Integer Order

Numerical solution of the well-known Bagley-Torvik equation is considered. The fractional-order derivative in the equation is converted, approximately, to ordinary-order derivatives up to second order. Approximated Bagley-Torvik equation is obtained using finite number of terms from the infinite series of integer-order derivatives expansion for the Riemann–Liouville fractional derivative. The Bagley-Torvik equation is a second-order differential equation with constant coefficients. The derived equation, by considering only the first three terms from the infinite series to become a second-order ordinary differential equation with variable coefficients, is numerically solved after it is transformed into a system of first-order ordinary differential equations. The approximation of fractional-order derivative and the order of the truncated error are illustrated through some examples. Comparison between our result and exact analytical solution are made by considering an example with known analytical solution to show the preciseness of our proposed approach.

Fractional-order sliding mode control synthesis of supercavitating underwater vehicles

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1909-1919
Author(s):  
Bui Duc Hong Phuc ◽  
Viet-Duc Phung ◽  
Sam-Sang You ◽  
Ton Duc Do
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
High Speed ◽  
Sliding Mode ◽  
Underwater Vehicle ◽  
Sliding Mode Controller ◽  
Integer Order ◽  
Mode Control ◽  
Supercavitating Vehicle ◽  
Control Actions

A high-speed supercavitating vehicle is a future underwater vehicle which exploits the supercavitating propulsion technology providing a promising way to increase the vehicle speed. Robust control challenges include complex vehicle maneuvering dynamics caused by factors such as undesired switching, delayed state dependency, and nonlinearities. As effective and applicable controllers, a novel fractional-order sliding mode controller is proposed to robustly control the uncertain high-speed supercavitating vehicle system against external disturbances. The control scheme uses sliding mode control and can produce better control actions than conventional the integer-order counterpart. In this algorithm, the fractional calculus is applied to calculate the noninteger integral or derivative in the sliding mode control algorithm, providing new capabilities for uncertain high-speed supercavitating vehicle control in seeking to operate the underwater vehicle better. The performance of the proposed fractional-order sliding mode controller has been proven through analytic simulation results, which show fast responses with smooth control actions and the ability to deal with nonlinear planing force and external disturbance. One of the interesting features of the fractional-order control system is the time convergence rate of the sliding variable vector, which is greatly improved compared with the integer-order sliding mode control. Finally, the robust control system with a novel fractional-order sliding mode controller algorithm, using high flexibility of controlling undersea vehicles, can provide superior dynamical performance with stability compared with its integer-order counterpart against system uncertainties and disturbances.

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