Analysis, Control and FPGA Implementation of a Fractional-Order Modified Shinriki Circuit

In this paper, we introduce a novel integer-order memristor-modified Shinriki circuit (MMSC). We investigate the dynamic properties of the MMSC system and the existence of chaos is proved with positive largest Lyapunov exponent. Bifurcation plots are derived to analyze the parameter dependence of the MMSC system. The fractional-order model of the MMSC system (FOMMSC) is derived and the bifurcation analysis of the FOMMSC system with the fractional orders is carried out. Fractional-order adaptive sliding-mode controllers (FOASMCs) and genetically optimized PID controllers are designed to synchronize identical FOMMSC systems with unknown parameters. Numerical simulations are conducted to validate the theoretical results. FPGA implementation of the FOASMC controllers is presented to show that the proposed control algorithm is hardware realizable. MMSC has trigonometric functions which make the system more complex and the optimization and synchronization of such systems in the integer order itself are harder, so the paper does the same in fractional order. The proposed system is a memristive circuit which can show special features such as multistability, hyperchaos, and multiscroll attractor. Such a system with these features is very rare in the literature.

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Hyperchaotic Chameleon: Fractional Order FPGA Implementation

Complexity ◽

10.1155/2017/8979408 ◽

2017 ◽

Vol 2017 ◽

pp. 1-16 ◽

Cited By ~ 28

Author(s):

Karthikeyan Rajagopal ◽

Anitha Karthikeyan ◽

Prakash Duraisamy

Keyword(s):

Resource Utilization ◽

Fractional Order ◽

Field Programmable Gate Array ◽

Dynamic Properties ◽

Fpga Implementation ◽

Hyperchaotic System ◽

Hidden Attractor ◽

Hidden Attractors ◽

Field Programmable ◽

Fractional Orders

There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA) implementations of the systems with their power and resource utilization are presented.

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Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization

Complexity ◽

10.1155/2017/1892618 ◽

2017 ◽

Vol 2017 ◽

pp. 1-19 ◽

Cited By ~ 46

Author(s):

Karthikeyan Rajagopal ◽

Laarem Guessas ◽

Anitha Karthikeyan ◽

Ashokkumar Srinivasan ◽

Girma Adam

Keyword(s):

Fractional Order ◽

Chaotic System ◽

Sliding Mode ◽

Dynamic Properties ◽

Adaptive Sliding Mode Control ◽

Equilibrium System ◽

Integer Order ◽

Adaptive Sliding Mode ◽

Mode Synchronization ◽

Fractional Order Pid

This paper introduces a fractional order memristor no equilibrium (FOMNE) chaotic system and investigates its adaptive sliding mode synchronization. Firstly the dynamic properties of the integer order memristor no equilibrium system are analyzed. The fractional order memristor no equilibrium system is then derived from the integer order model. Lyapunov exponents and bifurcation with fractional order are investigated. An adaptive sliding mode control algorithm is derived to globally synchronize the identical fractional order memristor systems and genetically optimized fractional order PID controllers are designed and used to synchronize the FOMNE systems. Finally the fractional order memristor no equilibrium system is realized using FPGA.

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Dynamical Analysis and FPGA Implementation of a Novel Hyperchaotic System and Its Synchronization Using Adaptive Sliding Mode Control and Genetically Optimized PID Control

Mathematical Problems in Engineering ◽

10.1155/2017/7307452 ◽

2017 ◽

Vol 2017 ◽

pp. 1-14 ◽

Cited By ~ 35

Author(s):

Karthikeyan Rajagopal ◽

Laarem Guessas ◽

Sundarapandian Vaidyanathan ◽

Anitha Karthikeyan ◽

Ashokkumar Srinivasan

Keyword(s):

Sliding Mode ◽

Dynamic Properties ◽

Lyapunov Stability Theory ◽

Dynamical Analysis ◽

Adaptive Sliding Mode Control ◽

Pid Controllers ◽

Hyperchaotic System ◽

The Novel ◽

Unknown Parameters ◽

Theory Use

We announce a new 4D hyperchaotic system with four parameters. The dynamic properties of the proposed hyperchaotic system are studied in detail; the Lyapunov exponents, Kaplan-Yorke dimension, bifurcation, and bicoherence contours of the novel hyperchaotic system are derived. Furthermore, control algorithms are designed for the complete synchronization of the identical hyperchaotic systems with unknown parameters using sliding mode controllers and genetically optimized PID controllers. The stabilities of the controllers and parameter update laws are proved using Lyapunov stability theory. Use of the optimized PID controllers ensures less time of convergence and fast synchronization speed. Finally the proposed novel hyperchaotic system is realized in FPGA.

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Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

10.1063/1.3256242 ◽

2009 ◽

Author(s):

Bijoy K. Mukherjee ◽

Santanu Metia ◽

Sio-Iong Ao ◽

Alan Hoi-Shou Chan ◽

Hideki Katagiri ◽

...

Keyword(s):

Fractional Order ◽

Pid Controller ◽

Pid Controllers ◽

Integer Order ◽

Fractional Order Pid ◽

Fractional Order Pid Controller

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FPGA implementation of adaptive sliding mode control and genetically optimized PID control for fractional-order induction motor system with uncertain load

Advances in Difference Equations ◽

10.1186/s13662-017-1341-9 ◽

2017 ◽

Vol 2017 (1) ◽

Cited By ~ 7

Author(s):

Karthikeyan Rajagopal ◽

Guessas Laarem ◽

Anitha Karthikeyan ◽

Ashokkumar Srinivasan

Keyword(s):

Sliding Mode Control ◽

Induction Motor ◽

Fractional Order ◽

Pid Control ◽

Motor System ◽

Sliding Mode ◽

Fpga Implementation ◽

Adaptive Sliding Mode Control ◽

Adaptive Sliding Mode ◽

Mode Control

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Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Mathematical Problems in Engineering ◽

10.1155/2018/1603629 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 6

Author(s):

Bo Meng ◽

Xiaohong Wang

Keyword(s):

Neural Networks ◽

Fractional Order ◽

Sliding Mode ◽

Small Region ◽

Hopfield Neural Networks ◽

Adaptive Synchronization ◽

Unknown Parameters ◽

External Disturbances ◽

Lyapunov Stability Criterion ◽

Order Extension

Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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Angular control of differential shape-memory alloy spring actuator for underactuated dynamic system

Journal of Vibration and Control ◽

10.1177/10775463211021670 ◽

2021 ◽

pp. 107754632110216

Author(s):

M Banu Sundareswari ◽

G Then Mozhi ◽

K Dhanalakshmi

Keyword(s):

Shape Memory Alloy ◽

Shape Memory ◽

Fractional Order ◽

Position Control ◽

Sliding Mode ◽

Control Effort ◽

Control Laws ◽

Integer Order ◽

Two Degree Of Freedom ◽

Outer Primary

This article dwells on two technical aspects, the design and implementation of an upgraded version of the differential shape-memory alloy–based revolute actuator/rotary actuating mechanism for stabilization and position control of a two-degree-of-freedom centrally hinged ball on beam system. The actuator is configured with differential and inclined placement of shape-memory alloy springs to provide bidirectional angular shift. The shape-memory alloy spring actuator occupies a smaller space and provides more extensive reformation with justifiable actuation force than an equally able shape-memory alloy wire. The cross or diagonal architecture of shape-memory alloy springs provides force amplification and reduces the actuator’s control effort. The shape-memory alloy spring–embodied actuator’s function is exemplified by the highly dynamic underactuated custom-designed ball balancing system. The ball position control is experimentally demonstrated by cascade control using the control laws that have been unattempted for shape-memory alloy actuated systems; the ball is positioned with linear (integer-order and fractional-order) proportional–integral–derivative controllers optimized with genetic algorithm and particle swarm optimization at the outer/primary loop. Angular control of the shape-memory alloy actuated beam is obtained with nonlinear (integer-order and fractional-order sliding mode control) control algorithms in the inner/secondary loop.

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