Controlling Chaos by Hybrid System Based on FREN and Sliding Mode Control

2005 ◽  
Vol 128 (2) ◽  
pp. 352-358 ◽  
Author(s):  
C. Treesatayapun ◽  
S. Uatrongjit
Keyword(s):  
Sliding Mode ◽  
Adaptive Controller ◽  
Descent Method ◽  
Fuzzy Rules ◽  
System Stability ◽  
Steepest Descent Method ◽  
Upper And Lower Bounds ◽  
Adaptation Algorithm ◽  
Control Effort ◽  
Fine Tune

This paper presents a direct adaptive controller for chaotic systems. The proposed adaptive controller is constructed using the network called fuzzy rules emulated network (FREN). FREN’s structure is based on human knowledge in the form of fuzzy rules. Parameter adaptation algorithm based on the steepest descent method is presented to fine tune the controller’s performance. To improve the system stability, the modified sliding mode algorithm is applied to estimate the upper and lower bounds of the control effort. The suitable control effort is generated by FREN and kept within these bounds. Some computer simulations of using the controller to control the Hénon map have been performed to demonstrate the performance of the proposed controller.

scholarly journals ADAPTIVE WAVELETS SLIDING MODE CONTROL FOR A CLASS OF SECOND ORDER UNDERACTUATED MECHANICAL SYSTEMS

2021 ◽  
Vol 61 (2) ◽  
pp. 350-363
Author(s):  
Fares Nafa ◽  
Aimad Boudouda ◽  
Billel Smaani
Keyword(s):  
Sliding Mode Control ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Adaptive Controller ◽  
Descent Method ◽  
Second Order ◽  
Gradient Descent Method ◽  
Underactuated Mechanical Systems ◽  
Mode Control

The control of underactuated mechanical systems (UMS) remains an attracting field where researchers can develop their control algorithms. To this date, various linear and nonlinear control techniques using classical and intelligent methods have been published in literature. In this work, an adaptive controller using sliding mode control (SMC) and wavelets network (WN) is proposed for a class of second-order UMS with two degrees of freedom (DOF).This adaptive control strategy takes advantage of both sliding mode control and wavelet properties. In the main result, we consider the case of un-modeled dynamics of the above-mentioned UMS, and we introduce a wavelets network to design an adaptive controller based on the SMC. The update algorithms are directly extracted by using the gradient descent method and conditions are then settled to achieve the required convergence performance.The efficacy of the proposed adaptive approach is demonstrated through an application to the pendubot.

FEA-based tracking control of flexible body switching dynamic structure

Robotica ◽  
2021 ◽  
pp. 1-20
Author(s):  
M. R. Homaeinezhad ◽  
F. FotoohiNia
Keyword(s):  
Continuum Mechanics ◽  
Tracking Control ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Operating Conditions ◽  
System Stability ◽  
Control Input ◽  
Element Analysis ◽  
Control Effort ◽  
Modeling Uncertainties

Abstract In dynamically switched systems with unknown switching signal, the control system is conventionally designed based on the worst switching scenario to ensure system stability. Such conservative design demands excessive control effort in less critical switching configurations. In the case of continuum mechanics systems, such excessive control inputs result in increased structural deformations and resultant modeling uncertainties. These deformations alter differential equations of motion which cripple the task of control. In this paper, a new approach for tracking control of uncertain continuum mechanics multivariable systems undergoing switching dynamics and unknown time delay has been proposed. Control algorithm is constructed based on the mathematical rigid model of the plant and a Common Lyapunov Function (CLF) is proposed upon sliding hyperplane regarding all switching configurations. Considering the model-based nature of sliding mode control (SMC) and inevitable uncertainties induced from modeling simplifications of continuum system or parameter evaluation errors, Finite Element Analysis (FEA) is utilized to approximate total model uncertainties. To obtain robust stability, instead of conventional switching functions in the construction of control law, the control inputs are selected such that system dynamics reside within stability bounds which are calculated based on the Lyapunov asymptotic stability criterion. Therefore, the unwanted chattering issue caused by continuous switching is not observed in control input signals. Eventually, the accuracy of the proposed method has been verified through the student version of ANSYS® mechanical APDL-based simulations and its effectiveness has been demonstrated in multiple operating conditions.

scholarly journals L2-Gain-Based Practical Stabilization of an Underactuated Surface Vessel

2021 ◽  
Vol 9 (3) ◽  
pp. 341
Author(s):  
Weilin Luo ◽  
Xin Qi
Keyword(s):  
Controller Design ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
System Stability ◽  
Surface Ship ◽  
Continuous Feedback ◽  
Robust Adaptive ◽  
Feedback Laws ◽  
Surface Vessel ◽  
L2 Gain

To obtain a stabilizer for an underactuated surface vessel with disturbances, an L2-gain design is proposed. Surge, sway, and yaw motions are considered in the dynamics of a surface ship. To ob-tain a robust adaptive controller, a diffeomorphism transformation and the Lyapunov function are employed in controller design. Two auxiliary controllers are introduced for an equivalent sys-tem after the diffeomorphism transformation. Different from the commonly used disturbance ob-server-based approach, the L2-gain design is used to suppress random uncertain disturbances in ship dynamics. To evaluate the controller performance in suppressing disturbances, two error sig-nals are defined in which the variables to be stabilized are incorporated. Both time-invariant dis-continuous and continuous feedback laws are proposed to obtain the control system. Stability analysis and simulation results demonstrate the validity of the controllers proposed. A comparison with a sliding mode controller is performed, and the results prove the advantage of the proposed controller in terms of faster convergence rate and chattering avoidance.

Solution of inverse coefficient problem for fractional anomalous diffusion equation

2012 ◽  
Vol 9 (2) ◽  
pp. 65-70
Author(s):  
E.V. Karachurina ◽  
S.Yu. Lukashchuk
Keyword(s):  
Anomalous Diffusion ◽  
Fractional Derivatives ◽  
Descent Method ◽  
Extremum Problem ◽  
Steepest Descent Method ◽  
Coefficient Problem ◽  
Caputo Fractional Derivatives ◽  
Inverse Coefficient Problem ◽  
Residual Functional ◽  
Inverse Coefficient

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

scholarly journals Complex dynamical behaviors of a novel exponential hyper–chaotic system and its application in fast synchronization and color image encryption

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042110033
Author(s):  
Javad Mostafaee ◽  
Saleh Mobayen ◽  
Behrouz Vaseghi ◽  
Mohammad Vahedi ◽  
Afef Fekih
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Sliding Mode ◽  
Color Image ◽  
Equilibrium Points ◽  
Lyapunov Stability Theory ◽  
System Stability ◽  
Color Image Encryption ◽  
Terminal Sliding Mode ◽  
Finite Time Stability

This paper proposes a novel exponential hyper–chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan–Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper–chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high–order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper–chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper–chaotic system to increase the security of image encryption.

scholarly journals Improved Immune Algorithm Combined with Steepest Descent Method for Optimal Design of IPMSM for FCEV Traction Motor

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3904
Author(s):  
Ji-Chang Son ◽  
Myung-Ki Baek ◽  
Sang-Hun Park ◽  
Dong-Kuk Lim
Keyword(s):  
Optimal Design ◽  
Permanent Magnet Synchronous Motor ◽  
Torque Ripple ◽  
Descent Method ◽  
Immune Algorithm ◽  
Electric Machines ◽  
Steepest Descent Method ◽  
Superior Performance ◽  
Element Analysis ◽  
Traction Motor

In this paper, an improved immune algorithm (IIA) was proposed for the torque ripple reduction optimal design of an interior permanent magnet synchronous motor (IPMSM) for a fuel cell electric vehicle (FCEV) traction motor. When designing electric machines, both global and local solutions of optimal designs are required as design result should be compared in various aspects, including torque, torque ripple, and cogging torque. To lessen the computational burden of optimization using finite element analysis, the IIA proposes a method to efficiently adjust the generation of additional samples. The superior performance of the IIA was verified through the comparison of optimization results with conventional optimization methods in three mathematical test functions. The optimal design of an IPMSM using the IIA was conducted to verify the applicability in the design of practical electric machines.

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