Fixed Time Control and Synchronization for Perturbed Chaotic System Via Nonsingular Terminal Sliding Mode Method

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Haipeng Su ◽  
Runzi Luo ◽  
Jiaojiao Fu ◽  
Meichun Huang
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Fixed Time ◽  
Stability Theorem ◽  
Terminal Sliding Mode ◽  
Time Control ◽  
Definite Integration ◽  
Control And Synchronization

Abstract This paper investigates the fixed time control and synchronization of chaotic system in the presence of compound disturbances. By using the definite integration and variable substitution, we present a new fixed time stability theorem for continuous nonlinear systems. In order to offset the bad effects of the compound disturbance, some novel sliding modes are constructed to improve the robustness of the controlled system and error system. For obtaining the robust controllers, some sufficient conditions of fixed time control and synchronization of the chaotic system are proposed by means of the sliding mode control method and the given stability theorem. Numerical simulation results are presented to verify and demonstrate the effectiveness of the proposed schemes.

scholarly journals Formation Tracking Control for Multi-Agent Networks with Fixed Time Convergence via Terminal Sliding Mode Control Approach

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1416
Author(s):  
Guang-Hui Xu ◽  
Meng Li ◽  
Jie Chen ◽  
Qiang Lai ◽  
Xiao-Wen Zhao
Keyword(s):  
Tracking Control ◽  
Sliding Mode ◽  
Fixed Time ◽  
Stability Theorem ◽  
Control Task ◽  
Terminal Sliding Mode ◽  
Formation Tracking ◽  
Multi Agent ◽  
Error System ◽  
Agent Networks

This paper investigates formation tracking control for multi-agent networks with fixed time convergence. The control task is that the follower agents are required to form a prescribed formation within a fixed time and the geometric center of the formation moves in sync with the leader. First, an error system is designed by using the information of adjacent agents and a new control protocol is designed based on the error system and terminal sliding mode control (TSMC). Then, via employing the Lyapunov stability theorem and the fixed time stability theorem, the control task is proved to be possible within a fixed time and the convergence time can be calculated by parameters. Finally, numerical results illustrate the feasibility of the proposed control protocol.

Immersion and invariance adaptive finite-time control of air-breathing hypersonic vehicles

2018 ◽  
Vol 233 (7) ◽  
pp. 2626-2641 ◽  
Author(s):  
Chao Han ◽  
Zhen Liu ◽  
Jianqiang Yi
Keyword(s):  
Control System ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Second Order ◽  
Hypersonic Vehicles ◽  
Terminal Sliding Mode ◽  
Air Breathing ◽  
Immersion And Invariance ◽  
Time Control

In this paper, a novel adaptive finite-time control of air-breathing hypersonic vehicles is proposed. Based on the immersion and invariance theory, an adaptive finite-time control method for general second-order systems is first derived, using nonsingular terminal sliding mode scheme. Then the method is applied to the control system design of a flexible air-breathing vehicle model, whose dynamics can be decoupled into first-order and second-order subsystems by time-scale separation principle. The main features of this hypersonic vehicle control system lie in the design flexibility of the parameter adaptive laws and the rapid convergence to the equilibrium point. Finally, simulations are conducted, which demonstrate that the control system has the features of fast and accurate tracking to command trajectories and strong robustness to parametric and non-parametric uncertainties.

A New Finite Time Control Solution for Robotic Manipulators Based on Nonsingular Fast Terminal Sliding Variables and the Adaptive Super-Twisting Scheme

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Vo Anh Tuan ◽  
Hee-Jun Kang
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Robotic Manipulators ◽  
Control Law ◽  
Continuous Control ◽  
Terminal Sliding Mode ◽  
Finite Time Convergence ◽  
Position Errors ◽  
Time Control

In this study, a new finite time control method is suggested for robotic manipulators based on nonsingular fast terminal sliding variables and the adaptive super-twisting method. First, to avoid the singularity drawback and achieve the finite time convergence of positional errors with a fast transient response rate, nonsingular fast terminal sliding variables are constructed in the position errors' state space. Next, adaptive tuning laws based on the super-twisting scheme are presented for the switching control law of terminal sliding mode control (TSMC) so that a continuous control law is extended to reject the effects of chattering behavior. Finally, a new finite time control method ensures that sliding motion will take place, regardless of the effects of the perturbations and uncertainties on the robot system. Accordingly, the stabilization and robustness of the suggested control system can be guaranteed with high-precision performance. The robustness issue and the finite time convergence of the suggested system are totally confirmed by the Lyapunov stability principle. In simulation studies, the experimental results exhibit the effectiveness and viability of our proposed scheme for joint position tracking control of a 3DOF PUMA560 robot.

Fixed-time fractional-order sliding mode control for nonlinear power systems

2020 ◽  
Vol 26 (17-18) ◽  
pp. 1425-1434 ◽  
Author(s):  
Sunhua Huang ◽  
Jie Wang
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Fixed Time ◽  
Sliding Mode Controller ◽  
Mode Control ◽  
Time Control

In this study, a fractional-order sliding mode controller is effectively proposed to stabilize a nonlinear power system in a fixed time. State trajectories of a nonlinear power system show nonlinear behaviors on the angle and frequency of the generator, phase angle, and magnitude of the load voltage, which would seriously affect the safe and stable operation of the power grid. Therefore, fractional calculus is applied to design a fractional-order sliding mode controller which can effectively suppress the inherent chattering phenomenon in sliding mode control to make the nonlinear power system converge to the equilibrium point in a fixed time based on the fixed-time stability theory. Compared with the finite-time control method, the convergence time of the proposed fixed-time fractional-order sliding mode controller is not dependent on the initial conditions and can be exactly evaluated, thus overcoming the shortcomings of the finite-time control method. Finally, superior performances of the fractional-order sliding mode controller are effectively verified by comparing with the existing finite-time control methods and integral order sliding mode control through numerical simulations.

Duffing Chaotic System Stability Control Based on Sliding Mode Control

2012 ◽  
Vol 605-607 ◽  
pp. 1639-1642
Author(s):  
Ding Ma
Keyword(s):  
Chaotic System ◽  
Control Method ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability Control ◽  
System Stability ◽  
Terminal Sliding Mode ◽  
Sliding Mode Variable Structure ◽  
The Stability ◽  
And Control

Considering the Duffing chaotic system, the problem of stability control based on the terminal sliding mode variable structure is studied. A new terminal sliding mode surface and control law are designed. On this basis, the stability of closed-loop system is analyzed. Simulation results show the effectiveness of the control method.

scholarly journals Adaptive Fixed-Time Nonsingular Terminal Sliding Mode Attitude Tracking Control for Spacecraft with Actuator Saturations and Faults

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhiguo Han ◽  
Minghao Wang ◽  
Xunliang Yan ◽  
Hang Qian
Keyword(s):  
Control Method ◽  
Actuator Saturation ◽  
Fault Tolerant ◽  
Sliding Mode ◽  
Fixed Time ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Nonsingular Terminal Sliding Mode ◽  
Attitude Tracking ◽  
Attitude Tracking Control

This paper focuses on the potential actuator failures of spacecraft in practical engineering applications. Aiming at the shortcomings and deficiencies in the existing attitude fault-tolerant control system design, combined with the current research status of attitude fault-tolerant control technology, we carry out high-precision, fast-convergent attitude tracking algorithms. Based on the adaptive nonsingular terminal sliding mode control theory, we design a kind of fixed-time convergence control method. This method solves the problems of actuator faults, actuator saturation, external disturbances, and inertia uncertainties. The control method includes control law design and controller design. The designed fixed-time adaptive nonsingular terminal sliding mode control law is applicable to the development of fixed-time fault-tolerant attitude tracking controller with multiple constraints. The designed controller considers the saturation of the actuator output torque so that the spacecraft can operate within the saturation magnitude without on-line fault estimation. Lyapunov stability analysis shows that under multiple constraints such as actuator saturation, external disturbances, and inertia uncertainties, the controller has fast convergence and has good fault tolerance to actuator fault. The numerical simulation shows that the controller has good performance and low-energy consumption in attitude tracking control.

Robust active finite-time control of gas compressor system surge in the presence of unmatched disturbance and uncertainty

2021 ◽  
pp. 095965182110574
Author(s):  
Jianhua Sun ◽  
Hai Gu ◽  
Jie Zhang ◽  
Hashem Imani Marrani
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Sliding Mode ◽  
Characteristic Curve ◽  
Parametric Uncertainty ◽  
Terminal Sliding Mode ◽  
Finite Time Stability ◽  
Time Control ◽  
Unmatched Uncertainties ◽  
Fuzzy Approximator

Active and robust control of surge instability is a special necessity for optimal and safe operation of centrifugal compressors, and for the purpose, this article presents a new hybrid scheme based on fuzzy and terminal sliding mode methods. The Greitzer model is used to design a novel controller when the disturbance instability in the flow and pressure alike the uncertainity in the compressor characteristic curve and throttle valve are embedded in it. The fuzzy approximator is used to estimate the effects of parametric uncertainty and the nonlinear terms, and the robustness of the proposed method is guaranteed using the terminal sliding mode control method. The Lyapunov criterion is utilized to verify the finite-time stability of the closed-loop system. The performance of the presented method is compared with other methods in the literature through simulations in MATLAB software. The results suggest that our designed controller outperforms the existing ones in terms of surge prevention and robustness against unmatched uncertainties and disturbances.

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