scholarly journals Realization of a fractional-order RLC circuit via constant phase element

2021 ◽  
Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano
Keyword(s):  
Experimental Data ◽  
Carbon Black ◽  
Fractional Order ◽  
Constant Phase Element ◽  
Polymeric Matrix ◽  
Fractional Order Systems ◽  
New Device ◽  
Rlc Circuit ◽  
Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

Functional interval observer design for singular fractional-order systems with disturbances

2020 ◽  
pp. 014233122094489
Author(s):  
Dinh Cong Huong ◽  
Dao Thi Hai Yen
Keyword(s):  
Fractional Order ◽  
Design Method ◽  
Observer Design ◽  
Effective Algorithm ◽  
Fractional Order Systems ◽  
Full State ◽  
Simulation Results ◽  
Interval Observer ◽  
Interval Observers ◽  
State Functions

In this study, we consider the problem of designing functional interval observers for a class of singular fractional-order systems. The goal of this work is to design not a full state interval observer for singular fractional-order systems, but to design an observer for state functions of this kind of systems. Conditions for the existence of such functional interval observers are given and an effective algorithm for computing unknown observer matrices is provided in this study. Two numerical examples and simulation results are provided to illustrate the effectiveness of the proposed design method.

scholarly journals Fractional-Order Models for Biochemical Processes

2020 ◽  
Vol 4 (2) ◽  
pp. 12 ◽  
Author(s):  
Eva-H. Dulf ◽  
Dan C. Vodnar ◽  
Alex Danku ◽  
Cristina-I. Muresan ◽  
Ovidiu Crisan
Keyword(s):  
Experimental Data ◽  
Fractional Order ◽  
Computational Models ◽  
Complex Behavior ◽  
Time Constants ◽  
Fractional Order Calculus ◽  
Biochemical Processes ◽  
Present Complex ◽  
Simulation Results ◽  
Erythritol And Mannitol

Biochemical processes present complex mechanisms and can be described by various computational models. Complex systems present a variety of problems, especially the loss of intuitive understanding. The present work uses fractional-order calculus to obtain mathematical models for erythritol and mannitol synthesis. The obtained models are useful for both prediction and process optimization. The models present the complex behavior of the process due to the fractional order, without losing the physical meaning of gain and time constants. To validate each obtained model, the simulation results were compared with experimental data. In order to highlight the advantages of fractional-order models, comparisons with the corresponding integer-order models are presented.

Synchronization of Chaotic Fractional-Order Systems via Fractional-Order Adaptive Controller

2011 ◽  
Vol 109 ◽  
pp. 333-339 ◽  
Author(s):  
Ali Fayazi
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Adaptive Controller ◽  
Control Signal ◽  
Fractional Order Systems ◽  
Sliding Surface ◽  
Adaptation Mechanism ◽  
Simulation Results ◽  
And Performance ◽  
Fractional Order Controller

In this paper, an adaptive fractional-order controller has been designed for synchronization of chaotic fractional-order systems. This controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. PID coefficients are updated using the gradient method when a proper sliding surface is chosen. To illustrate the effectiveness and performance of the controller, the proposed controller implements on a pair of topologically inequivalent chaotic fractional-order systems. The Genesio-Tessi and Coullet systems. Performance of fractional-order adaptive PID controller (PαIλDμ) on the basis of speed of synchronization, error of synchronization, and level of control signal, is compared with the conventional ones (adaptive PID controller) and sliding mod controller (SMC). The simulation results reducing the level of control signal indicate the significance of the proposed controller.

CHAOS SYNCHRONIZATION OF FRACTIONAL ORDER UNIFIED CHAOTIC SYSTEM VIA NONLINEAR CONTROL

2011 ◽  
Vol 25 (03) ◽  
pp. 407-415 ◽  
Author(s):  
XIANG RONG CHEN ◽  
CHONG XIN LIU
Keyword(s):  
Nonlinear Control ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Fractional Order Systems ◽  
Unified Chaotic System ◽  
Simulation Results ◽  
Nonlinear Control Method ◽  
The Stability

Based on the stability theory of fractional order systems, an effective but theoretically rigorous nonlinear control method is proposed to synchronize the fractional order chaotic systems. Using this method, chaos synchronization between two identical fractional order unified systems is studied. Simulation results are shown to illustrate the effectiveness of this method.

A New Fractional Order Observer Design for Fractional Order Nonlinear Systems

2011 ◽  
Author(s):  
Sara Dadras ◽  
Hamid Reza Momeni
Keyword(s):  
Fractional Order ◽  
Original System ◽  
Observer Design ◽  
Fractional Order Systems ◽  
State Variables ◽  
Lyapunov Approach ◽  
Error System ◽  
Simulation Results ◽  
System States ◽  
The Stability

In this paper, a class of fractional order systems is considered and simple fractional order observers have been proposed to estimate the system’s state variables. By introducing a fractional calculus into the observer design, the developed fractional order observers guarantee the estimated states reach the original system states. Using the fractional order Lyapunov approach, the stability (zero convergence) of the error system is investigated. Finally, the simulation results demonstrate validity and effectiveness of the proposed scheme.

scholarly journals Fractal Control and Synchronization of the Discrete Fractional SIRS Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Miao Ouyang ◽  
Yongping Zhang ◽  
Jian Liu
Keyword(s):  
Infectious Disease ◽  
Fixed Point ◽  
Fractional Order ◽  
Fractal Theory ◽  
Julia Sets ◽  
Order System ◽  
Fractional Order Systems ◽  
Sirs Model ◽  
Simulation Results ◽  
Control And Synchronization

SIRS model is one of the most basic models in the dynamic warehouse model of infectious diseases, which describes the temporary immunity after cure. The discrete SIRS models with the Caputo deltas sense and the theories of fractional calculus and fractal theory provide a reasonable and sensible perspective of studying infectious disease phenomenon. After discussing the fixed point of the fractional order system, controllers of Julia sets are designed by utilizing fixed point, which are introduced as a whole and a part in the models. Then, two totally different coupled controllers are introduced to achieve the synchronization of Julia sets of the discrete fractional order systems with different parameters but with the same structure. And new proofs about the synchronization of Julia sets are given. The complexity and irregularity of Julia sets can be seen from the figures, and the correctness of the theoretical analysis is exhibited by the simulation results.

State estimation in fractional-order systems with coloured measurement noise

2017 ◽  
Vol 40 (6) ◽  
pp. 1819-1835 ◽  
Author(s):  
Behrouz Safarinejadian ◽  
Nasrin Kianpour ◽  
Mojtaba Asad
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Fractional Order ◽  
Estimation Error ◽  
Measurement Noise ◽  
Space Systems ◽  
Fractional Order Systems ◽  
State Space Systems ◽  
Simulation Results ◽  
Order State

This paper presents new estimation methods for discrete fractional-order state-space systems with coloured measurement noise. A novel approach is proposed to convert a fractional system with coloured measurement noise to a system with white measurement noise in which the process and measurement noises are correlated with each other. In this paper, two new Kalman filter algorithms for fractional-order linear state-space systems with coloured measurement noise, as well as a new extended Kalman filter algorithm for state estimation in nonlinear fractional-order state-space systems with coloured measurement noise, are proposed. The accuracy of the equations and relations is confirmed in several theorems. The validity and effectiveness of the proposed algorithms are verified by simulation results and compared with previous work. Results show that for linear and nonlinear fractional-order systems with coloured noise, the proposed methods are more accurate than conventional methods regarding estimation error and estimation error covariance. Simulation results demonstrate that the proposed algorithms can accurately perform estimation in fractional-order systems with coloured measurement noise.

scholarly journals Adaptive Neural Backstepping Control of Nonlinear Fractional-Order Systems with Input Quantization

2021 ◽  
Author(s):  
Chao Cheng ◽  
Huanqing Wang ◽  
Haikuo Shen ◽  
Peter Xiaoping Liu
Keyword(s):  
Fractional Order ◽  
Tracking Control ◽  
Disturbance Observer ◽  
External Disturbance ◽  
Rbf Neural Networks ◽  
Fractional Order Systems ◽  
Backstepping Method ◽  
Input Quantization ◽  
Lyapunov Stability Analysis ◽  
Simulation Results

Abstract This article addresses the tracking control problem of uncertain fractional-order nonlinear systems in the presence of input quantization and external disturbance by combining with radial basis function(RBF) neural networks(NNs), fractional-order disturbance observer(FODO) and backstepping method. The unknown nonlinearities of fractional-order systems is approximated by RBF NNs. The design of hysteretic quantizer achieves quantification of input signal and avoids chattering. The FODO is utilized to evaluate the external disturbance exist in fractional-order systems. According to fractioanlorder Lyapunov stability analysis, the bounds of all the signals in the closedloop system is proved. The effectiveness of the proposed method is confirmed by the simulation results.

BEHAVIORAL MODEL OF A LINEAR VOLTAGE STABILIZER IN THE SPICE LANGUAGE

2019 ◽  
Author(s):  
Aleksey Malahanov
Keyword(s):  
Experimental Data ◽  
Behavioral Model ◽  
Voltage Stabilizer ◽  
Static Mode ◽  
Technical Description ◽  
Simulation Results ◽  
Chip Manufacturer ◽  
Linear Voltage

A variant of the implementation of the behavioral model of a linear voltage stabilizer in the Spice language is presented. The results of modeling in static mode are presented. The simulation results are compared with experimental data and technical description of the chip manufacturer.

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