scholarly journals Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Victor Kamdoum Tamba ◽  
Viet-Thanh Pham
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Phase Portraits ◽  
Adaptive Sliding Mode Control ◽  
Coexistence Of Attractors ◽  
Route To Chaos ◽  
Two Parameters

A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method.

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

2017 ◽  
Vol 27 (13) ◽  
pp. 1750198 ◽  
Author(s):  
Ahmad Hajipour ◽  
Hamidreza Tavakoli
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Financial System ◽  
Period Doubling ◽  
Largest Lyapunov Exponent ◽  
Sliding Mode Controller ◽  
Adaptive Sliding Mode Controller ◽  
Uncertain Dynamics ◽  
Route To Chaos ◽  
Doubling Sequence

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of [Formula: see text]. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

scholarly journals Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
P. K. Santra ◽  
G. S. Mahapatra ◽  
G. R. Phaijoo
Keyword(s):  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Phase Portraits ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
And Control

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

Robust adaptive tracking control for uncertain nonholonomic mobile manipulator

2021 ◽  
pp. 095965182110277
Author(s):  
Abdelkrim Brahmi ◽  
Maarouf Saad ◽  
Brahim Brahmi ◽  
Ibrahim El Bojairami ◽  
Guy Gauthier ◽  
...  
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Robust Adaptive Control ◽  
Convergence Time ◽  
Adaptive Sliding Mode Control ◽  
Mobile Manipulator ◽  
Control Law ◽  
Adaptive Tracking Control ◽  
Robust Adaptive ◽  
Manipulator Robot

In the research put forth, a robust adaptive control method for a nonholonomic mobile manipulator robot, with unknown inertia parameters and disturbances, was proposed. First, the description of the robot’s dynamics model was developed. Thereafter, a novel adaptive sliding mode control was designed, to which all parameters describing involved uncertainties and disturbances were estimated by the adaptive update technique. The proposed control ensures a relatively good system tracking, with all errors converging to zero. Unlike conventional sliding mode controls, the suggested is able to achieve superb performance, without resulting in any chattering problems, along with an extremely fast system trajectories convergence time to equilibrium. The aforementioned characteristics were attainable upon using an innovative reaching law based on potential functions. Furthermore, the Lyapunov approach was used to design the control law and to conduct a global stability analysis. Finally, experimental results and comparative study collected via a 05-DoF mobile manipulator robot, to track a given trajectory, showing the superior efficiency of the proposed control law.

Disturbance Adaptive Discrete-Time Sliding Control With Application to Engine Speed Control

1998 ◽  
Vol 123 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Mooncheol Won ◽  
J. K. Hedrick
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Control Method ◽  
Sliding Mode ◽  
Input Saturation ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
Sliding Surface ◽  
Sliding Control ◽  
Error Dynamics

This paper presents a discrete-time adaptive sliding control method for SISO nonlinear systems with a bounded disturbance or unmodeled dynamics. Control and adaptation laws considering input saturation are obtained from approximately discretized nonlinear systems. The developed disturbance adaptation or estimation law is in a discrete-time form, and differs from that of conventional adaptive sliding mode control. The closed-loop poles of the feedback linearized sliding surface and the adaptation error dynamics can easily be placed. It can be shown that the adaptation error dynamics can be decoupled from sliding surface dynamics using the proposed scheme. The proposed control law is applied to speed tracking control of an automatic engine subject to unknown external loads. Simulation and experimental results verify the advantages of the proposed control law.

scholarly journals Adaptive Sliding Mode Control Method for Z-Axis Vibrating Gyroscope Using Prescribed Performance Approach

2020 ◽  
Vol 10 (14) ◽  
pp. 4779 ◽  
Author(s):  
Cheng Lu ◽  
Liang Hua ◽  
Xinsong Zhang ◽  
Huiming Wang ◽  
Yunxiang Guo
Keyword(s):  
Sliding Mode Control ◽  
Error Bound ◽  
Control Method ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Sliding Mode Control ◽  
Performance Control ◽  
Prescribed Performance ◽  
Adaptive Sliding Mode ◽  
Mode Control

This paper investigates one kind of high performance control methods for Micro-Electro-Mechanical-System (MEMS) gyroscopes using adaptive sliding mode control (ASMC) scheme with prescribed performance. Prescribed performance control (PPC) method is combined with conventional ASMC method to provide quantitative analysis of gyroscope tracking error performances in terms of specified tracking error bound and specified error convergence rate. The new derived adaptive prescribed performance sliding mode control (APPSMC) can maintain a satisfactory control performance which guarantees system tracking error, at any time, to be within a predefined error bound and the error convergences faster than the error bound. Besides, adaptive control (AC) technique is integrated with PPC to online tune controller parameters, which will converge to their true values at last. The stability of the control system is proved in the Lyapunov stability framework and simulation results on a Z-axis MEMS gyroscope is conducted to validate the effectiveness of the proposed control approach.

Adaptive Integral Sliding Mode Control of Single Electromagnetic Guiding System Suspension Altitude in Linear Elevator

2013 ◽  
Vol 321-324 ◽  
pp. 1704-1707
Author(s):  
Qing Hu ◽  
Hong Bin Du ◽  
Dong Mei Yu
Keyword(s):  
Steady State ◽  
Sliding Mode Control ◽  
Control Method ◽  
Sliding Mode ◽  
Adaptive Sliding Mode Control ◽  
Mode Switching ◽  
Matlab Simulation ◽  
Mode Control ◽  
Perturbation Problem ◽  
Guiding System

For external disturbances and parameter perturbation problem of Electromagnetic guiding system, the adaptive sliding mode control method is used, take advantage of sliding mode switching surface eliminate the steady-state error and increase the precision at steady-state and robust performance of single electromagnetic guiding system. Matlab Simulation results show that the proposed control strategy shows good tracking performance and strong robustness

scholarly journals Control of Chaos in Rate-Dependent Friction-Induced Vibration Using Adaptive Sliding Mode Control and Impulse Damper

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ehsan Maani Miandoab ◽  
Aghil Yousefi-Koma ◽  
Saeed Hashemnia
Keyword(s):  
Sliding Mode Control ◽  
Control Method ◽  
Sliding Mode ◽  
Control Technique ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
Adaptive Sliding Mode ◽  
Chaotic Vibration ◽  
Mode Control ◽  
Rate Dependent

Two different control methods, namely, adaptive sliding mode control and impulse damper, are used to control the chaotic vibration of a block on a belt system due to the rate-dependent friction. In the first method, using the sliding mode control technique and based on the Lyapunov stability theory, a sliding surface is determined, and an adaptive control law is established which stabilizes the chaotic response of the system. In the second control method, the vibration of this system is controlled by an impulse damper. In this method, an impulsive force is applied to the system by expanding and contracting the PZT stack according to efficient control law. Numerical simulations demonstrate the effectiveness of both methods in controlling the chaotic vibration of the system. It is shown that the settling time of the controlled system using impulse damper is less than that one controlled by adaptive sliding mode control; however, it needs more control effort.

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