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.

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.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

Conditional integrator sliding mode control of an unmanned quadrotor helicopter

2021 ◽  
pp. 095965182110498
Author(s):  
Yohan Díaz-Méndez ◽  
Leandro Diniz de Jesus ◽  
Marcelo Santiago de Sousa ◽  
Sebastião Simões Cunha ◽  
Alexandre Brandão Ramos
Keyword(s):  
Sliding Mode Control ◽  
Transient Response ◽  
Tracking Control ◽  
Position Control ◽  
Sliding Mode ◽  
Control Technique ◽  
Control Law ◽  
Control Problems ◽  
Control Activity ◽  
Mode Control

Sliding mode control (SMC) is a widely used control law for quadrotor regulation and tracking control problems. The purpose of this article is to solve the tracking problem of quadrotors using a relatively novel nonlinear control law based on SMC that makes use of a conditional integrator. It is demonstrated by a motivation example that the proposed control law can improve the transient response and chattering shortcomings of the previous approaches of similar SMC based controllers. The adopted Newton–Euler model of quadrotor dynamics and controller design is treated separately in two subsystems: attitude and position control loops. The stability of the control technique is demonstrated by Lyapunov’s analysis and the effectiveness and performance of the proposed method are compared with a similar integral law, also based on SMC, and validated by tracking control problems using numerical simulations. Simulations were developed in the presence of external disturbances in order to evaluate the controller robustness. The effectiveness of the proposed controller was verified by performance indexes, demonstrating less accumulated tracking errors and control activity and improvement in the transient response and disturbance rejection when compared to a conventional integrator sliding mode controller.

scholarly journals Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems

2008 ◽  
Vol 3 (1) ◽  
pp. 6 ◽  
Author(s):  
Hafedh Abid ◽  
Mohamed Chtourou ◽  
Ahmed Toumi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Fuzzy Model ◽  
Uncertain System ◽  
Control Technique ◽  
Control Law ◽  
Mode Control ◽  
Equivalent Control ◽  
Fuzzy Sliding Mode ◽  
Discrete Nonlinear Systems

In this work we are interested to discrete robust fuzzy sliding mode control. The discrete SISO nonlinear uncertain system is presented by the Takgi- Sugeno type fuzzy model state. We recall the principle of the sliding mode control theory then we combine the fuzzy systems with the sliding mode control technique to compute at each sampling time the control law. The control law comports two terms: equivalent control law and switching control law which has a high frequency. The uncertainty is replaced by its upper bound. Inverted pendulum and mass spring dumper are used to check performance of the proposed fuzzy robust sliding mode control scheme.

Fractional sliding mode control of wind turbine for maximum power point tracking

2018 ◽  
Vol 41 (2) ◽  
pp. 447-457 ◽  
Author(s):  
Aghiles Ardjal ◽  
Rachid Mansouri ◽  
Maamar Bettayeb
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Maximum Power Point Tracking ◽  
Control Law ◽  
Maximum Power Point ◽  
Mode Control ◽  
Point Tracking ◽  
Power Point Tracking ◽  
Power Point

This paper deals with a nonlinear control algorithm based on a sliding mode theory to reach the maximum power point tracking of a variable-speed wind energy conversion system. The proposed method allows us to combine the sliding mode and fractional-order theory. The fractional-order component of the control law is introduced by a sliding surface. In order to validate this controller, fractional and integer sliding modes are developed. The proposed fractional-order sliding mode control law is tested in a Simulink/Matlab environment. The simulation results show the effectiveness of the proposed scheme, suppression of the chattering phenomenon and robustness of the proposed controller compared to the integer sliding mode control law.

scholarly journals A Novel Compound Nonlinear State Error Feedback Super-Twisting Fractional-Order Sliding Mode Control of PMSM Speed Regulation System Based on Extended State Observer

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Peng Gao ◽  
Guangming Zhang ◽  
Xiaodong Lv
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Regulation System ◽  
Control Law ◽  
Error Feedback ◽  
Mode Control ◽  
Speed Regulation ◽  
Nonlinear State ◽  
State Error

In this article, a novel compound nonlinear state error feedback super-twisting fractional-order sliding mode control (NLSEF-STFOSMC) is proposed for the control of the permanent magnet synchronous motor (PMSM) speed regulation system. Firstly, a novel fractional-order proportion integration differentiation (FOPID) switching manifold is designed. A modified sliding mode control (SMC) is constructed by a super-twisting reaching law and the novel FOPID sliding surface. Secondly, the nonlinear state error feedback control law (NLSEF) has been widely used because of high control accuracy, fast convergence, and flexible operation. Therefore, combining the modified SMC with the NLSEF, the compound NLSEF-STFOSMC is proposed, which has an excellent performance. At the same time, the external disturbance of the system is observed by a novel extended state observer. Finally, the performance of the corresponding control law to the speed operation of the PMSM is fully investigated compared with other related algorithms to demonstrate the effectiveness. The comparison results show that the proposed compound control strategy has excellent dynamic and static performance and strong robustness.

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