scholarly journals Chaos Synchronization of a Finance Chaotic System with an Integral Sliding Mode Controller

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jingjing Wang ◽  
Chunzhi Yang
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Small Neighborhood ◽  
Sliding Mode Controller ◽  
Fuzzy Logic Systems ◽  
Integral Sliding Mode ◽  
Integral Sliding Surface ◽  
Better Than

In this paper, an integral sliding mode controller is proposed to realize the synchroniza-tion of a class of finance chaotic systems. First, an integral sliding surface with tanh function is designed. Then, fuzzy logic systems are used to estimate unknown functions, and then based on the Lyapunov stability theorem, the proposed control method can quickly drive the synchroniza-tion error into a small neighborhood of zero, and the range of this neighborhood can be estimated. The simulation results verify that the proposed method in this paper is better than the traditional method.

scholarly journals Design of Adaptive Sliding Mode Controller for Uncertain Pendulum System

2021 ◽  
Vol 39 (3A) ◽  
pp. 355-369
Author(s):  
Dina H. Tohma ◽  
Ahmed K. Hamoudi
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
External Disturbances ◽  
Control Effort ◽  
Pendulum System ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller ◽  
Parameters Uncertainty ◽  
Better Than

This work aims to study and apply the adaptive sliding mode controller (ASMC) for the pendulum system with the existence of the parameters uncertainty, external disturbances, and coulomb friction. The adaptive sliding mode controller has several features over the conventional sliding mode control method. Firstly, the magnitude of the control signal is reduced to the minimally acceptable level defined by special conditions concerned with ASMC algorithm. Secondly, the upper bounds of uncertainties are not necessary to be defined before starting the work. For this reason, the ASMC can be used successfully to control the pendulum system with minimum control effort. These properties of the ASMC are confirming graphically by the simulation results using MATLAB 2019. The ASMC achieves an asymptotically stable system better than the Classical Sliding Mode Controller (CSMC). The unwanted phenomenon is called “chattering", which is appearing in the control action signal. These drawback properties are suppressed by employing a saturation function. Finally, the comparison between the results of the ASMC and CSMC showed that ASMC is the better one.

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.

scholarly journals A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ahmadreza Haghighi ◽  
Roveida Ziaratban
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Control Method ◽  
Controller Design ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Slip Surface ◽  
Direct Method ◽  
Distributed Model ◽  
Sliding Mode Controller

Abstract In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering and undesirable vibration effects. The advantages of the proposed control method are rapid convergence to the equilibrium point, the absence of chattering and unwanted oscillations, high resistance to uncertainties, and the possibility of applying this method to most fractional order chaotic systems. We applied the direct method of Lyapunov stability theory and the frequency distributed model to prove the stability of the slip surface and closed loop system. Finally, we simulated this method on two commonly used and practical chaotic systems and presented the results.

A Nonlinear Integral Sliding Surface to Improve the Transient Response of a Force-Controlled Pneumatic Actuator With Long Transmission Lines

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Khurram Butt ◽  
Nariman Sepehri
Keyword(s):  
Transient Response ◽  
Sliding Mode ◽  
Nonlinear Function ◽  
Pneumatic Actuator ◽  
System Response ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
Integral Sliding Mode ◽  
Initial Errors ◽  
Integral Sliding Surface

AbstractA force-controlled pneumatic actuator with long connecting tubes is a well-accepted solution to develop magnetic resonance imaging (MRI)-compatible force control applications. Such an actuator represents an uncertain, second-order, nonlinear system with input delay. The integral sliding mode control, because of guaranteed robustness against matched uncertainties throughout the system response, provides a favorable option to design a robust controller for the actuator. However, if the controller is based on a linear integral sliding surface (LISS), the response of the actuator overshoots, especially when there are large initial errors. Minimizing overshoot results in a smaller controller bandwidth and a slower system response. This paper presents a novel nonlinear integral sliding surface (NLISS) for a sliding mode controller to improve the transient response of the actuator. The proposed surface is a LISS augmented by a nonlinear function of tracking error and does not have a reaching phase when there are initial errors and even multiple steps in the desired trajectory. The surface enables the integral sliding mode controller to offer variable damping, which changes from low to high as the transient error approaches small values and vice versa. Simulation studies and experimental results show that the controller based on the proposed sliding surface successfully eliminates the overshoot without compromising the controller bandwidth, rise, and settling times. For performance evaluation, the controller parameters are tuned using the globalized and bounded Nelder–Mead (GBNM) algorithm with deterministic restarts. The study also establishes the asymptotic stability of the controller based on the proposed sliding surface using Lyapunov's stability criterion.

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