scholarly journals Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Bao Shi ◽  
Jian Yuan ◽  
Chao Dong
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Sliding Mode Control ◽  
Fractional Differential Equations ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Law ◽  
Mode Control ◽  
Fractional Differential ◽  
Control Methodology

This paper deals with the problem of pseudo-state sliding mode control of fractional SISO nonlinear systems with model inaccuracies. Firstly, a stable fractional sliding mode surface is constructed based on the Routh-Hurwitz conditions for fractional differential equations. Secondly, a sliding mode control law is designed using the theory of Mittag-Leffler stability. Further, we utilize the control methodology to synchronize two fractional chaotic systems, which serves as an example of verifying the viability and effectiveness of the proposed technique.

A New Result on Fractional Differential Inequality and Applications to Control of Dynamical Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Ngo Van Hoa ◽  
Tran Minh Duc ◽  
Ho Vu
Keyword(s):  
Dynamical Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Differential Inequality ◽  
Sliding Mode ◽  
Control Law ◽  
Asymptotically Stable ◽  
Mode Control ◽  
Fractional Differential

In this work, we establish a new estimate result for fractional differential inequality, and this inequality is used to derive a robust sliding mode control law for the fractional-order (FO) dynamic systems. The sliding mode control law is provided to make the states of the system asymptotically stable. Some examples are given to illustrate the results.

scholarly journals A continuous integral terminal sliding mode control approach for a class of uncertain nonlinear systems

2019 ◽  
Vol 52 (5-6) ◽  
pp. 720-728
Author(s):  
Huawei Niu ◽  
Qixun Lan ◽  
Yamei Liu ◽  
Huafeng Xu
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Control Law ◽  
Terminal Sliding Mode Control ◽  
Terminal Sliding Mode ◽  
Control Approach ◽  
Mode Control ◽  
Time Control

In this article, the continuous integral terminal sliding mode control problem for a class of uncertain nonlinear systems is investigated. First of all, based on homogeneous system theory, a global finite-time control law with simple structure is proposed for a chain of integrators. Then, inspired by the proposed finite-time control law, a novel integral terminal sliding mode surface is designed, based on which an integral terminal sliding mode control law is constructed for a class of higher order nonlinear systems subject disturbances. Furthermore, a finite-time disturbance observer-based integral terminal sliding mode control law is proposed, and strict theoretical analysis shows that the composite integral terminal sliding mode control approach can eliminate chattering completely without losing disturbance attenuation ability and performance robustness of integral terminal sliding mode control. Simulation examples are given to illustrate the simplicity of the new design approach and effectiveness.

scholarly journals Uncertain Unified Chaotic Systems Control with Input Nonlinearity via Sliding Mode Control

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Zhi-ping Shen ◽  
Jian-dong Xiong ◽  
Yi-lin Wu
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Controller Design ◽  
Sliding Mode ◽  
Control Law ◽  
Sliding Mode Controller ◽  
Stabilization Problem ◽  
Input Nonlinearity ◽  
Mode Control ◽  
Unified Chaotic Systems

This paper studies the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Based on the sliding mode control theory, we present a new method for the sliding mode controller design and the control law algorithm for such systems. In order to achieve the goal of stabilization unified chaotic systems, the presented controller can make the movement starting from any point in the state space reach the sliding mode in limited time and asymptotically reach the origin along the switching surface. Compared with the existing literature, the controller designed in this paper has many advantages, such as small chattering, good stability, and less conservative. The analysis of the motion equation and the simulation results all demonstrate that the method is effective.

Sliding Mode Based LMI Criterion for Robust Stabilization of Uncertain Fractional Order Nonlinear Systems

2013 ◽  
Author(s):  
Sara Dadras ◽  
YangQuan Chen
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Nonlinear Dynamical Systems ◽  
Sliding Mode ◽  
Control Technique ◽  
Control Law ◽  
Mode Control ◽  
Systems Model ◽  
Control Scheme

A robust sliding mode control (SMC) technique is introduced in this paper for a class of fractional order (FO) nonlinear dynamical systems. Using the sliding mode control technique, a sliding surface is determined and the control law is established. A new LMI criterion based on the sliding mode control law is derived to make the states of the FO nonlinear system asymptotically gravitate toward the origin which can work for any order of the system, 0<q<2. The designed control scheme can also control the uncertain FO nonlinear systems, i.e. the controller is robust against the system uncertainty and guarantees the property of asymptotical stability. The advantage of the method is that the control scheme does not depend on the order of systems model and it is fairly simple. So, there is no complexity in the application of our proposed method. An illustrative simulation result is given to demonstrate the effectiveness of the proposed robust sliding mode control design.

Fractional Dynamic Sliding Mode Control for uncertain chaotic systems Applied to a Chaotic Robot arm under dynamic load.

2020 ◽  
Vol 10 ◽  
Author(s):  
Sara Gholipour P ◽  
Sara Minagar ◽  
Javad Kazemitabar ◽  
Mobin Alizadeh
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Qualitative And Quantitative ◽  
Mode Control ◽  
Quantitative Characteristics ◽  
Dynamic Sliding Mode Control ◽  
Dynamic Sliding Mode ◽  
Qualitative And Quantitative Characteristics

Background: A novel type of control strategy is presented for control of chaotic systems particularly a chaotic robot in joint and workspace which is the result of applying fractional calculus to dynamic sliding mode control. Objectives: To guarantee the sliding mode condition, control law is introduced based on the Lyapunov stability theory. Methods: A control scheme is proposed for reducing the chattering problem in finite time tracking and robust in presence of system matched disturbances. Conclusion: Also, all of chaotic robot's qualitative and quantitative characteristics have been investigated. Numerical simulations indicate viability of our control method. Results: Qualitative and quantitative characteristics of the chaotic robot are all proven to be viable thru simulations.

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

Sign in / Sign up

Export Citation Format

Share Document